[{"data":1,"prerenderedAt":4},["ShallowReactive",2],{"Ao0QcL63tz":3},"# PhysicsLogic\n\nPhysicsLogic is a Lean 4 project for parsing the formal logic of theoretical\nphysics papers.\n\nThe present objective is faithful logical reconstruction, not technical proof\ncompletion. A paper formalization must expose:\n\n- typed physical vocabulary;\n- proposition-valued definitions of the paper's claims and principles;\n- explicit hypotheses for imported mathematics, physical principles,\n  approximations, and calculations;\n- Lean theorems deriving the paper's conclusions from those hypotheses;\n- primary-source anchors for claims and transitions;\n- unresolved assumptions, approximations, deformations, and interpretations.\n\nA citation graph or an enumeration of opaque claim names is not the\nformalization. Source maps are auxiliary provenance. The formal content lives\nin Lean data, predicates, definitions, and checked deductions.\n\nA source statement does not become true by being cited. Unproved physics and\nmathematics enter theorem signatures as explicit propositions. Lean then checks\nthe logical consequences without pretending to prove those inputs.\n\n## Development Strategy\n\nThe [light-cone review](docs/review/LightConePropagation.html) separates the\nMinkowski interval, future orientation, and an explicit signal-speed bound.\nIt repairs the selected Minkowski boost readout so both time readings describe\nthe same event under an admissible boost. Three duplicate signalling predicates\nnow delegate to the existing signalling context with unchanged meanings.\nThe independent coordinate test does not replace the paper's explicit\ngeometric hypotheses or constitute human semantic approval.\n\nThe paper's signal route now requires an actual global time/Euclidean-three-space\nchart, tied to its own first-frame coordinate values for every worldpoint.\nStrictly timelike interior points and null light-signal endpoints have separate\nroles. Signal exclusion and the distance/time value c follow from this explicit\ninterpretation, not from an arbitrarily named causal relation. The same review\nexposes every calibration clause and concrete stationary-signal and transverse-\nseparation counterexamples. This realizes the flat causal-coordinate sector,\nnot all worldline derivatives, force laws, or frame transformations in the paper.\n\nHuman semantic review is a separate requirement from compilation and automated\naudits. The repository is currently a research corpus with substantial automated\nverification, not a human-validated, production-mature physics specification.\nThe review obligation covers all meaning-bearing declarations, including\nstructure constraints, inductive alternatives, implicit instances, and theorem\nhypotheses, not only declarations introduced with `def`. Calling a concept\ncentral or peripheral does not change that obligation. Development now\nprioritizes complete reviewable argument slices and demonstrated semantic\nconsolidation over further breadth. New papers and frameworks are frozen during\nthe semantic-consolidation stage. No reviewed production subset is claimed\nuntil actual human approvals cover its meaning-bearing dependencies; the wider\ncorpus remains experimental. The first reviewability pilot exposes\nGuth's eight causal definitions in\n[`RadiationHorizon/Definitions.lean`](PhysicsLogic/Papers/Guth1981/RadiationHorizon/Definitions.lean).\nIts implementation proves both the fixed-emission distance characterization\nand the particle-horizon characterization; neither is an assigned access flag.\nThermal and flatness obligations remain separate paper-local modules.\nThis is a candidate for human review, not a completed semantic approval.\n\nThe same core now distinguishes a signal between comoving worldlines from\none shared past event for a whole nonempty region. A closed radial interval\nhas a regular common past exactly when its physical width is below four times\nthe age; the particle-horizon radius remains twice the age. An explicit interval\nshares one past event while its extreme worldlines cannot have signalled each\nother by that epoch. Guth's entropy-rescaled closed region also has one shared\nevent under the existing subhorizon inequality. None of these geometric results\nestablishes thermal equilibration or an inflationary history.\n\nThe radiation review also derives the expansion rate from the scale factor,\nand shows why its inverse equals the particle horizon specifically in this\nmodel. An explicit incoming null ray has local radial speed -1 but proper\ndistance rate H D - 1. A constructed ray starts at distance 6 at time 1,\noutside the Hubble radius 2, with proper-distance rate +2, yet arrives at the\norigin at time 16. The same trajectory obeys the causal speed bound throughout.\nThis tests the distinction between local light speed, recession, and future\nreception without adding a physical definition or assuming an event horizon.\nThe radiation approximation is retained throughout the example, not asserted\nacross a full inflationary history; the numbers are not observations.\n\nThe [interactive semantic-review pilot](docs/review/GuthRadiationHorizon.html)\nstarts at the radiation-horizon characterization and exposes its actual\nmeaning dependencies separately from proof references. Nodes show elaborated\ntypes, predicate bodies, parameters, joint hypotheses, and external mathematical\nboundaries. Review records are scoped to content versions; no human review has\nyet been recorded. This is one complete causal argument, not validation of the\nwhole Guth paper or the full library. Regeneration and review rules are in\n[CONTRIBUTING.md](CONTRIBUTING.md#semantic-review).\n\nA second [prediction review slice](docs/review/UniformForecast.html) connects\nthe dynamics paradigm to a metric forecast obstruction and an explicit linear\nflow. Its checked examples distinguish failure of the nominal forecast from\nfailure of every forecast compatible with the same initial information, retain\nthe strict factor-two error bound, and reject vacuous success on empty input.\nThis is information-limited accuracy feasibility, not a claim of computational\npredictability. It now also separates existence and uniqueness from continuous\ndependence, and fixed-time continuity from one error bound for every future\ntime. The paradigm contract is named `TotalDeterministicEvolution`; its earlier\n`WellPosedForwardEvolution` name is deprecated because it did not assert\nstability. Existing consumers remain compatible. Human review remains pending.\n\nThe [density-functional review slice](docs/review/DensityVariational.html)\nadds a checked expansion into explicit quantum-state constraints. Its\nthree-site counterexamples separate fixed-number minima, density-dependent\nconstrained energies, and local-potential eigenstate representability. All\nmodel fields remain inspectable; this finite diagnostic does not settle the\ncontinuum representability problem or constitute human semantic approval.\nIt now distinguishes nondegeneracy from literal wavefunction uniqueness:\nthe ground eigenspace is one complex line, and its normalized vectors form\nexactly one global-phase orbit. A sign-change control preserves density and\nenergy but changes the vector. The [HK quotient review](docs/review/HKGroundStateQuotient.html)\nnow exposes a conditional construction of the complete framework on classes,\npreserving its readouts and representable-density domain. The original\ndetermination and variational arguments are reused there; global phase is\nan explicit unit-modulus relation, not an arbitrary label. Concrete continuum\ndomain and invariance inputs, and human semantic approval, remain open.\n\nThe [chemical-force review](docs/review/ConstrainedChemicalForces.html)\nconnects Onsager's ideal-solution free-energy formula to its actual derivative.\nThe variation contract now explicitly conserves total amount, as do the\nselected and reference populations. This removes the common RT term from the\nderivative; the resulting variations determine only force differences, not\nthree absolute forces. A positive reference state separates this derivative\nfrom an amount-adding direction and separates the logarithmic force convention\nfrom its common-shift freedom. The former arbitrary approximation-comparison\nfield is replaced by the actual first-order derivative at the reference state.\nThe linearized forces and a stationary reference reproduce mass-action rates.\nA positive nearby-state family retains detailed balance at the reference and\nfirst-order agreement, but substituting exact logarithmic forces into the same\ncoefficient map gives a nonzero rate error at arbitrarily small positive\ndisplacement. A separate quantitative scalar-force estimate gives, on\n|x/n|\u003C=1/2, an error of at\nmost 2 RT (x/n)^2. The positive cutoff min(1/2,tolerance/2) controls the error\nrelative to the linearized force for every positive reference amount. Absolute\nsmallness alone fails uniformly as that reference varies: x=n can be arbitrarily\nsmall while the RT=1 force error stays 1-log(2)>0. These are consequences of the\nideal logarithm, not error bars stated by Onsager or bounds on kinetic-rate error.\nFifteen literal definition contracts and twenty-eight statement contracts\nexpose these distinctions. The bounds required no additional physics definitions.\nThis is the paper's chemical analogy, not a general transport theorem or a\nhuman semantic approval.\n\nThe [self-consistent energy review](docs/review/SelfConsistentEnergy.html)\ndistinguishes a stationary state, a total-energy minimum and convergence of\nfrozen-Hamiltonian ground-state updates. In the existing two-site Hartree\nmodel, the premature eigenvalue subtraction misses exactly the quadratic\nenergy of the output-minus-input density. At fixed particle number this is\nfive times the squared site-density residual. The actual alternating ground\nupdates have identical successive energies but a nonzero density jump and\nno density limit. These are finite diagnostics of the self-consistency\ncondition before Kohn-Sham equation (2.10), not a general XC error bound or\nan algorithmic failure attributed to the paper. Human review remains pending.\n\nThe [exact HK determination review](docs/review/HKExactDetermination.html)\nnow starts from ten physical fields, instead of requiring the full 51-field\npaper record. The existing paper proofs invoke this core, with the original\nenergy, fixed-number domain and source premises preserved by checked\nequalities and equivalences. The full-model bridge remains inspectable;\nresponse expansions and atomic predictions have not been erased or filled\nwith defaults. This reduces review scope, not the need for physical judgment.\n\nThe [Bell common-probability review](docs/review/BellCommonProbability.html)\nexposes one probability measure and two local dichotomic responses. It derives\nalmost-everywhere opposition, the single-response integral, and Bell's original\nthree-setting bound, then excludes agreement with the actual singlet density\nmatrix on unit directions. Explicit controls separate a null set for each\nsetting from one null set for all settings, and a common law from separately\nnormalized setting-dependent laws. EPR predetermination and angular-averaged\nnonapproximability are separate routes; human semantic review remains pending.\nThe real spin values are defined directly as `+1` and `-1`. A checked equality\npreserves the original generic encoding, which remains inspectable through\nits own review statement. The complete exclusion specification no longer\ndepends on that generic arithmetic-record interface; no dependency is\nhidden by the viewer. The real-valued bound is also stated directly, with a\nchecked equivalence and consumer compatibility readback for the old interface.\n\nThe [locality and averaging review](docs/review/LocalityAndAveraging.html)\ncharacterizes deterministic locality directly by remote-setting independence.\nThree checked equivalences remove the need to mentally unpack auxiliary\npossibility relations; they add no physical definitions. A finite diagnostic\nthen averages actual response pairs with one fair hidden law. Both observed\nmarginals are uniform despite remote-setting dependence at every hidden value.\nA different local realization gives the same complete joint distributions.\nThe distinction is locality of a specified response model versus existence of\nsome local model of its statistics, not a Bell-inequality violation or a singlet\nreconstruction. All four diagnostic definitions and both response structures\nremain inspectable; human review is pending.\n\nThe [nuclear-expansion review](docs/review/NuclearExpansionControl.html)\nseparates the source's leading-contact resummation from one derivative insertion,\nexact elastic unitarity, and numerical remainder control. In the declared\nreference-scale window, checked amplitude bounds give a relative insertion of\nat most `1/32` and a range-resummation difference of at most `1/1024`.\nA bound on unknown higher terms of `k cot(delta)` is still a separate input.\nAn explicit polynomial has the same first two low-energy coefficients and\nexact elastic unitarity, yet differs substantially from the truncated amplitude.\nIt does not realize a finite-range nuclear potential or refute controlled EFT\npower counting. Seven original source fields and all diagnostic data remain\nvisible; no new physical definitions were introduced. Human review is pending.\n\nThe nuclear review also distinguishes forward stability from inverse recovery.\nThe exact amplitude-to-phase distance identity divides by both amplitude\nmagnitudes. A uniform positive amplitude floor therefore gives a checked\nreconstruction bound on the actual selected predictions. On 1\u003C=p\u003C=2, bounding\nboth real phase functions by one gives phase error at most nine times the\namplitude error in the fixed normalization. By contrast, K=L and K=2L have\nexactly unitary amplitudes with arbitrarily small difference on that same\nband while retaining a phase difference at least one. This changes scattering\nlength across models, outside the large-length regime; it is not a potential\nrealization, an experimental fit, or a regulator change. No definitions are\nadded, and human review remains pending.\n\nThe nuclear review's finite-chart exercise separates a choice from its\nconsequences. `NonvacuousElasticSWaveAt` now contains only positive momentum\nand the real-K formula f=(K-ip)^(-1). A checked equivalence preserves the\nprevious contract, which also listed elastic unitarity. Both scalar S-matrix\nunitarity and the optical theorem follow from the formula. The zero-contact\namplitude satisfies both laws but is outside the finite-K chart. One redundant\nclause was removed; no physical definition was added or removed. Reality,\ndomain, normalization and interpretation still require human validation. This\nis not a reduction of the whole nuclear framework to two physical choices.\n\nThe default nuclear review statement now exposes one complete conditional\nargument: the source bubble formula with real contact implies unit norm of\n`1 + i p M A/(2 pi)`. Its five quantities and five premises are written with\nordinary real and complex arithmetic, without project-defined predicates.\nThe existing seven-field source API calls this theorem and retains its stronger\nglobal assumptions. The PDS integration and resummation are an explicit formula\ninput; this does not prove their correctness or the model's physical accuracy.\nPositive mass and nonnegative momentum delimit the physical interpretation,\neven though they are not required by the algebra. The nonpole restriction is\nretained to exclude a totalized quotient at a physical pole. An independent\nconsumer keeps the amplitude fixed and changes the normalization denominator\nfrom `2 pi` to `4 pi`, changing the S-matrix norm square from one to one half.\nNo physics definitions have been deleted or added, and neither the source\ninterpretation nor practical human manageability has yet been approved.\n\nThe [ordered-limit review](docs/review/OrderedMagneticLimits.html) exposes\nboth iterated limits as checked epsilon/delta equivalences. These show exactly\nwhich size cutoff may depend on a fixed field and which field cutoff may\ndepend on a fixed size. One normalized two-orientation diagnostic realizes\ndifferent limiting magnetizations and rejects a cutoff uniform near zero\nfield. Other controls distinguish the value at zero from its positive-field\nlimit, exclude empty approaches, and separate source certification from\nmathematical existence. This is not a short-range Heisenberg model or a\ncounterexample to Mermin-Wagner; human semantic review remains pending.\n\nThe same review now exposes a repaired Mermin-Wagner spectral assumption.\nThe earlier Gibbs contract required every field-dependent Hamiltonian to be\ndiagonal in one fixed basis, unintentionally forcing them to commute. The\noriginal p. 1134 instead uses a complete energy basis of the selected\nHamiltonian. An explicit channel- and field-dependent matrix now supplies\nthose coordinates, with completeness and diagonalization stated as conditions.\nThermal averages and the spectral inner product use the same transformed\noperator entries. Two checked readbacks reconstruct the Hamiltonian and the\nfixed-coordinate thermal trace. A finite two-field diagnostic has noncommuting\nHamiltonians, valid Gibbs states, and an expectation changed by ignoring the\neigenvectors. It is not a Heisenberg lattice or a new no-order calculation.\n\nThe spin-observable audit makes Cartesian Hermiticity explicit in the same\nfixed Hilbert inner product. Commutators and the Casimir alone did not imply\nit. Three checked consequences give mutual adjoints for the ladder operators,\nreal Gibbs averages for Hermitian observables, and real Cartesian spin averages.\nOrdinary spin-half matrices satisfy the repaired contract. A nonunitary\nrescaling retains the algebra and a selected zero-Hamiltonian Gibbs state but\nfails that contract; the normalized vector (3/5,4i/5) gives its x matrix the\nnonreal expectation 9i/25. The graph exposes the full condition, explicit\nmatrices and local state. These are finite diagnostics, not a Fourier-lattice\nrealization or a complete no-order proof. Human review is pending.\n\nThe [measurement review](docs/review/CalibratedMeasurementRecords.html)\nseparates basis calibration, linearity, record agreement, and a definite\noutcome. Checked equivalences expose transport of every complex amplitude\nand exactly when a pointer or match-only record determines a value. A\nnormalized two-component input retains both sectors after communication.\nA deliberately nonlinear rule calibrates the unit basis and preserves\nnormalization while selecting a sector, but fails superposition. This is a\ndiagnostic outside linear quantum mechanics, not a model attributed to Everett\nor a resolution of the measurement problem. Human semantic review is pending.\n\nThe [typicality review](docs/review/TypicalityAndJointClaims.html) exposes the\nsingle selected state before the quantifier over all licensed properties.\nA finite canonical diagnostic has 100 tests, each passing with probability\n99/100, but no common passing state. Dropping one test leaves a sound,\nnonempty common set of probability only 1/100. Individual high probability,\nnonempty selection, sound selection, and high joint probability are distinct.\nThe existing two-level Gibbs example also separates typical agreement from\nuniversal truth and exact finite-frequency equality. These are diagnostics,\nnot a derivation of Bohmian typicality or completed human semantic review.\n\nThe [DGZ finite-time review](docs/review/DGZFiniteTimeAgreement.html) exposes\nthe paper's common-law inference as explicit empirical sums and reference-law\nintegrals. Agreement at every selected time uses a summed failure budget;\nagreement at most times uses an average divided by the tolerated bad-time\nfraction. Controls distinguish a strict joint budget, the closed tail,\ntime-dependent measures, rare conditioning environments, and empty selections.\nA separate complete scope retains the actual paper's Born-law specialization.\nConditioned bounds and disintegration remain inputs, not proved physics or\nclaims about every configuration. Human semantic review remains pending.\n\nThe [Witten spectral-index review](docs/review/WittenSpectralIndex.html) follows\na convergent graded trace to an actual normalized charge-kernel state. Two\nchecked equivalences expose the complete basis/operator representation and the\nvacuum predicate's positive normalization, symmetric charges, and normalized\ncommon kernel. Controls separate pair cancellation from trace convergence,\nthe index from a normalized thermal expectation, and zero infimum from an\nattained ground state. The larger four-charge physical specialization retains\nall of the paper model's fields and its momentum, rotation, and trace bridges.\nThis does not compute the SU(N) index or establish its infinite-volume limit;\nthe diagnostic spectra are not Yang-Mills spectra. Human review remains pending.\n\nThe [Bethe triplet-range review](docs/review/BetheTripletRange.html) separates\nsquared parahydrogen data from a signed coherent amplitude, making the selected\nsign explicit before a scattering-length decoder can be calibrated. Equal-record\nalternatives test the lost information. The paper join retains equation (19)'s\nbound-energy range and the separate replacement-error budget. A further check\npreserves the printed plus sign in (25) while exposing its conditional conflict\nwith the fixed-mass binding-energy response. These are central-value and\nconditional inference checks, not exact empirical knowledge or an approved\nerratum. Human semantic review remains pending.\n\nThe actual Bethe intensity context now uses the shared `mapRecords` operation\non the signed-record context, removing duplicate domain and value assignments.\nA checked equality retains the original squared formula and full physical\ndescription. All squared-record value constraints already follow from signed\nrecords. With the additional coherent-sign restriction on both domains, their\nconstraints are equivalent for every property, not just for one chosen decoder.\nThe existing opposite-sign ambiguity remains. No physical definition or\ndiagnostic model is added by this consolidation; human review is still pending.\n\nThe [physical-observer review](docs/review/PhysicalObserverRoles.html) separates\nan occupied physical role from an interaction that produces an accessible\nrecord. The physical-role predicates share one definition family and are\nunchanged by arbitrary consciousness reclassification. Everett's model no\nlonger requires an unused consciousness relation; its operational specialization\nstill exposes calibration, branch correlation, and record-interpretation inputs.\nAn explicit realization premise now connects that role to the same calibrated\ncoefficient model and supported first-record amplitude. Every operational\nrecord determines a value in a nonempty pointer fiber; zero-output measurement\ndynamics cannot realize a role, even when the primitive role and correlation\nlabels are retained. Both the direct route and shared-framework bridge require\nthis realization; neither derives it from a label or assumes a global outcome.\nFinite role assignments are interface diagnostics, not physical machine models\nor a theory of consciousness. Human semantic review remains pending.\n\nThe same review now checks Rovelli's observer adapter against the actual\ncoefficient model in P's description. Three separate premises require calibrated\ndynamics, equality with the stored post-measurement coefficients, and nonzero\nfirst-record support. Every operational record determines its correlated value\nin that description; zero dynamics or zero input cannot supply it. Changes to\nother coefficient descriptions leave the selected role unchanged. This does not\nidentify P's coherent description with O's conditioned account or a later\ncomparison reference. The repair adds no physical definition; independent\nreadbacks and mutations check the existing adapter's reference and record data.\n\nThe [cosmological-inference review](docs/review/CosmicInferenceQuantifiers.html)\nseparates the variance of a chosen estimator from impossibility for every\nalternative decoder. It connects the explicit Gaussian moment calculation to\nthe full-sky estimator law and noise-free sampling result. A finite diagnostic\nhas unbiased readings with variance one yet allows exact decoding of either\nunknown target. The shared paradigm states the different, cross-model\nobstruction from a common accessible realization with unequal targets. A scalar\nGaussian contrast excludes a common almost-surely exact decoder by transferring\nnull sets, not by projecting an estimator-variance assumption. This is not a\nfull-sky optimality theorem. The degenerate zero-power boundary demonstrates\nwhy both Gaussian variances must be positive. All eleven statements and their definitions remain\npending human semantic review.\n\nThe [impermeable-layer review](docs/review/ImpermeableLayerLimit.html) tests the\nthin-layer operators with an actual periodic viscous flow. Unlike the separate\nsuction diagnostic, it keeps normal wall velocity zero and the same oscillating\nwall forcing for every parameter. Its full and retained balances are exact,\nand the far-field condition is a checked limit of the profile. Nevertheless,\npointwise outer recovery and uniform recovery away from the wall do not give\nuniform convergence on the whole open half-line. Wall shear vanishes while\ninterior viscous acceleration remains nonzero; deleting the time acceleration\nbreaks the equation. This is neither Prandtl's steady flat plate nor a\nfixed-initial-data limit theorem. All thirteen statements remain pending review.\n\nThe [Onsager variational review](docs/review/OnsagerFixedTemperatureVariation.html)\nexposes the fixed-temperature argument through actual linear entropy supply,\nquadratic dissipation, spatial integral representations, and boundary fluxes.\nA checked characterization retains the source's force normalization\n`X = -grad(T)/T`, distinct from `grad(1/T)` and from an unnormalized\ntemperature gradient. The constitutive entropy identity cannot be substituted\nbefore varying the flow. Explicit matrix controls distinguish nonnegative\ndissipation from uniqueness and strict dissipation from reciprocity. Isolation,\nthe stationary power constraint, and prescribed normal-flux profiles restrict\nthe trial as well as the physical flow. This is not a universal\nmaximum-entropy-production principle or a derivation of microscopic\nreversibility. All sixteen selected statements remain pending human review.\n\nThe [coarse-graining review](docs/review/CoarseGrainingAndClosure.html) exposes\nan independent finite Ising test of prediction preservation, generated\ninteractions, and model closure. Its exact marginal retains an outer-spin\npair mean but is not any pairwise Gibbs law, even allowing additive energy\nconstants. Two positive-mass states with the same retained configuration\nalso obstruct almost-sure recovery of the hidden spin. A separate null-state\ncontrol distinguishes that obstruction from merely pointwise disagreement.\nThe readable normalization equivalence adds no new physical assumptions.\nRescaling requires reexpressing observables; successive decimation requires\nthe transformed domain. The chain's Boltzmann weights and probability bounds\nare shown separately from its algebraic composition identities. These eighteen\nstatements are diagnostics of RG distinctions, not Kadanoff's critical lattice\nor an interacting fluid, and remain pending human semantic review.\n\nThe [Hubble calibration review](docs/review/HubbleDistanceCalibration.html)\njoins the finite radial-fit argument without replacing the solar correction\nby a label. Positive distance rescaling preserves every radial readout and\nfixed-weight loss while changing the coefficient. An exact distance anchor\nremoves this scale freedom; a sufficiently small anchor error only bounds it.\nAn independent positive-distance diagnostic shows unbounded coefficients when\nthe error budget reaches the anchor distance, despite unchanged residuals.\nThe full paper adapter and its tentative cosmological interpretation remain\nseparate inspectable scopes. These are conditional calibration statements, not\na historical refit, quoted probable errors, or proof of cosmic expansion.\nThe joint-fit extension now varies the solar solution at fixed distances.\nOpposite sky directions cancel its projection in a sum; a common direction\nat different distances uses a difference. Both decoders retain peculiar\nresiduals. The bounded-residual result supplies an interval, with an explicit\nnonzero-error control attaining the bound and a second compatible coefficient\nwith zero residuals for the same observations. A separate two-direction sample\nkeeps its distinct, exact distances and every residual while K changes from\n500 to 600. Thus removing the distance-scale freedom need not resolve the\njoint fit. These nine additional theorems use the existing physical vocabulary;\nall local example data remain visible in their statements.\nAll twenty-five selected statements remain pending human semantic review.\n\nThe [local-invariance review](docs/review/LocalInvarianceClauses.html) repairs\nan actual quantifier error in the equivalence-principle paradigm: position\ninvariance previously compared arbitrary frames and therefore implied Lorentz\ninvariance by definition. It now holds a repeatable laboratory configuration\nfixed across places; the Lorentz clause independently changes configuration\nat one place. A checked transfer theorem exposes the intermediate frame's\navailability. Numeric diagnostics separate both clauses and show why inhabited\nbut disconnected comparison scopes do not imply global agreement. The five\ncontext fields remain unchanged. Matching conventions and local calibration\nremain interpretation obligations, not a canonical identification of tangent\nframes. This is not a complete dynamical theory or a proof of EEP; all eleven\nstatements remain pending human semantic review.\n\nThe [frequency-reference review](docs/review/FrequencyReferenceControl.html)\nrepairs a missing Atomichron input in Hughes's nuclear scan, independently of\nthe atomic route. Positive numerical configurations show that even an exact\nnull ratio can hide unbounded common frequency variation. Independent reference\naccess recovers the frequency; finite ratio and reference allowances instead\ngive the bound `d + e + d*e`, attained by a checked example. These use the philosophy layer's actual\nrecord-determination and record-constraint definitions. The expanded fifteen\nstatements also expose the diagonal rank-two spin spectrum: an unchanged\nspin-half gap, three spin-three-halves gaps, their positivity domain, and the\nseparate need for field stabilization. Two arbitrary reference predicates\nhave been replaced by one frequency-response map and an explicit zero-response\ncondition. The proton control follows only after identifying that physical\nresponse with the model calculation. Cesium dynamics, nuclear matrix elements,\nline-width conversion, and human semantic review remain open.\n\nThe [work-sampling review](docs/review/WorkSamplingTail.html) tests a tempting\nconverse of Jarzynski's practical warning. An independent canonical two-state\nquench has work variance below `1/1000` in thermal units and satisfies the exact\nwork identity. Nevertheless, at every positive sample count up to 1000, the\nspecified estimator has probability at least `999/1000` of both exceeding its\n25-percent relative exponential error and misestimating free energy by more\nthan `log(2)`. The actual rare-event probability, product sampling law, and\nlogarithmic readout are exposed. Ten statements also retain the source\ninterface's independent-repetition and exponential-moment premises. This is\nnot an obstruction to every estimator or every finite count. No production\ndefinition is added; human semantic review remains pending.\n\nThe [state-positivity review](docs/review/StatePositivity.html) repairs an\ninsufficient shared state predicate. A normalized complex-linear functional\ncan have a nonnegative real part on every `a* a` while assigning `1/2+i` to a\nyes/no projection. The repaired predicate requires reality as well as\nnonnegativity, yields real projection probabilities in `[0,1]`, and is retained\nby vector states, finite ground averages, and nontrivial-filter weak limits.\nAn independent two-outcome algebra checks both rejection and an ordinary\nequal-mixture control. Ground-sector realization and human review remain\nseparate obligations.\n\nThe [local-operation review](docs/review/UnitaryInfluence.html) connects a\ncommutator estimate to the actual expectation change under a unitary\npreparation. A normalized vector supplies both full positivity and the\ncontracting-functional bound. An independent two-qubit Hamiltonian changes a\nremote Y expectation from zero to `-sin(t)` after a first-site bit flip, while\nretaining exact equal-time exclusion. For every tolerance and candidate finite\nfront velocity, a positive earlier time has a nonzero but smaller-than-tolerance\nreadout change and commutator norm. Unit separation and interaction-energy time\nunits are explicit. This is a finite diagnostic, not an infinite-lattice\nLieb-Robinson proof or a relativistic signalling claim; human review is pending.\n\nThe [phase-mixing review](docs/review/PhaseMixingRecovery.html) connects\nvanishing number-density contrast to retained velocity information. An ideal\nvelocity reversal of the existing positive, neutral two-species solution\npreserves the instantaneous density; subsequent forward streaming recovers\nthe complete initial modulation. For every tolerance, the initial contrast\ncan be uniformly smaller while later contrast is exactly `1/2`. Actual kinetic\nequations and Poisson closure remain checked. This is an externally controlled\nrecovery, not autonomous recurrence, entropy production, a nonlinear plasma\necho, or Landau's fixed-ion field damping. The separate source argument exposes\nits contour asymptotics and nonzero residue. Human review remains pending.\n\nThe [thermal-calibration review](docs/review/ThermalProbeCalibration.html)\ndistinguishes common from relative gain uncertainty. Actual matrix traces\ngive detector-squared noise and detector-times-drive response. Matched nonzero\ngains cancel in a ratio that identifies the four-level Gibbs state under explicit\nnormalization and commutation assumptions. Independently uncertain positive\ngains instead allow two different stationary states to give identical complete\nrecords in all three nonzero channels. The measurement layer consequently\nexcludes exact recovery and certification at the declared temperature. These\nare finite inverse-inference diagnostics, not additional Callen-Welton source\nclaims, empirical estimates, or human semantic approval.\n\nThe [thermal-probe review](docs/review/ThermalProbeCompleteness.html) tests the\nconverse of fluctuation-dissipation inference. Two strictly positive stationary\nstates of the same four-level Hamiltonian have identical full correlations,\nnoise, and response for one Hermitian probe. The alternative is not Gibbs at\nany real inverse temperature, yet its selected spectral line obeys the same\nFDT. The measurement layer excludes thermal certification from that record.\nThree separately resolved adjacent-transition balances and normalization\ninstead determine the Gibbs populations within the diagonal family. These\nprobes still miss a positive state's off-diagonal coherence even when all\ntheir individual noise and response records agree with Gibbs. A cross\ncorrelation detects that coherence, and actual free evolution changes the\nstate. Commutation with this nondegenerate Hamiltonian removes the ambiguity;\nnormalization and the adjacent balances then identify the full density matrix.\nThe direct record route now decodes each pair from its noise at zero and response\nat `pi/(2 log 2)`. Probes 0 and 2 suffice to recover all four diagonal entries;\nthese four calibrated entries and commutation identify Gibbs without assumed\npopulation balances. The measurement layer certifies this conditional claim,\nnot the commutation premise. A stationary positive non-Gibbs state still matches\nall three equal-time records. No new physical definitions were needed.\nThese ideal records are not finite measured samples or full state tomography.\nThe test is independent of the original Callen-Welton forward derivation;\nhuman review remains pending.\n\nStructure inspection now displays every field type in an ordered table under\nthe shared constructor parameters and earlier fields. Local field names link\nto their exact qualified declarations; dependencies and full projection\nsignatures remain available beside each row. All field types stay visible,\nincluding proposition-valued restrictions and instance bindings, without\nshrinking the text. These are Lean-derived types, with explicit links\nto parameter, field, instance, and declaration dependencies. Full structure\nand projection types remain available. Constructor-signature checks retain\nparameter order, dependent fields, and proposition-valued restrictions;\ndiamond inheritance is not flattened away. Earlier schema-4 exports remain\ncomparable, with the schema change distinguished from a change in physics.\nThis improves readability without changing production physics definitions.\n\nStatements with local definitions now have a separate scoped inspection view.\nIt exposes each assigned value and its type, retains later hypotheses and\nshadowed or unused bindings, and links references to their actual earlier\npositions. Defined proofs are not labeled independent assumptions. Hubble's\ncompeting datasets are a concrete use: their values can be inspected before\nreading the conclusion. Reconstruction is checked against the original Lean\ntype, which remains visible. Schema-4 and schema-5 exports remain comparable;\nthis tooling check does not certify physical meaning or human approval.\n\nEach review page can compare two selected statements' complete meaning scopes.\nShared, current-only, and comparison-only declarations are listed separately\nfrom external mathematical boundaries, with both exact statement types and\nlinks into the correct argument context. Shared names do not mean identical\ninstantiated premises, independent assumptions, or prior human approval. This\nhelps avoid repeated navigation without shrinking the semantic review scope.\nStatement selection order no longer labels every secondary result a diagnostic;\nsource attribution remains in the review scope and exercises.\n\nThe [representation review](docs/review/RepresentationAndPhysicalValues.html)\nexposes nonempty assignment soundness through all seven primitive relations.\nAn independent bounded-bias thermometer makes the obligation concrete: every\nadmitted temperature and bias must satisfy the decoder equation. An exact\nreference correction satisfies it inside that model. One correct reading\ndoes not establish global soundness, and a sound partial representation need\nnot cover other physical states. Recorded estimates and informative bounds\nremain distinct from exact values. Neither the model's truth in nature nor\nhuman semantic approval follows from these checked results.\n\nThe same review exposes deterministic record processing through one shared\noperation that leaves admitted configurations and physical values unchanged.\nFifteen exact results distinguish lossless relabeling, reflection of a selected\nrecord fiber, and lossy processing. A finite quantum pointer retains its outcome\nunder injective relabeling. Squaring a thermometer reading above one preserves\nits constraints because the other preimage is outside the admitted domain.\nIn the existing Pound-Rebka mean-response diagnostic, dropping thermometry\nretains signal and calibration but loses gravity identification. A constant\nprocessing function also shows why an attained output cannot certify an\nimpossible original record. Everett's original p. 458 and Pound-Rebka's\ntemperature companion p. 275 ground the distinctions; these constructed\nmodels do not assert collapse, experimental precision, or human approval.\nAn exact shared criterion now characterizes preservation of every proposition\nabout a selected value: each processed-compatible alternative must have a value\nalready realized in the original record fiber. Full records need not survive.\nThe quantum example merges outcomes 0 and 2 but retains whether the outcome\nwas 1. Reversal signal, calibration, and thermal differences retain gravity\nin the specified mean-response model while discarding common-offset information,\nfollowing the distinction in Pound-Rebka's original pp. 339-340. Both use the\nsame theorem. Their local value selection and encodings are exposed in Lean\nand the review graph; this is not a claim about statistical sufficiency.\n\nThe [residual-inference review slice](docs/review/ResidualInference.html)\nuses Penzias-Wilson's bounded-error record model to distinguish a positive\nresidual, an exact temperature, and an origin claim. A checked interval\ncharacterization exposes what is constrained and what remains unspecified.\nIts controls retain actual-model compatibility and the strict sum of an\nadditional other-contribution bound and the error budget. Neither a\nconfidence level nor a cosmological identification is inferred from the\nscalar record alone; human semantic review remains pending.\n\nThe same review now connects bounded component errors to the actual subtraction\nused by the record model. The sharp uniform budget includes both the component\nerror sum and any shift of the center. The numerical control's backlobe and\nrecentered radius are diagnostic choices, not revised historical measurements.\nThe resulting compatible record transfers positivity to that same subtraction.\nThe separate spectral route now derives exclusion instead of importing it:\na strictly steeper candidate cannot supply the whole high-frequency residual\nwithout exceeding the low-frequency sky budget. Diagnostic controls preserve\nthe equality boundary and possible partial contributions. The observed bound,\nknown-source classification, and source spectra remain explicit inputs.\n\nEach review page also offers a **Complete project specification** view: every\nmeaning-bearing declaration for the selected statement, with exact Lean types,\ndata and predicate bodies, fields, binders, and direct dependency links. Groups\nput dependencies first and keep mutual references together; external types\nremain explicitly unexpanded boundaries. This removes the neighborhood limit\nfrom inspection, not the need to review the meaning of every declaration.\nThe **Connection to selected statement** disclosure gives one shortest path\nthrough actual specification references to the declaration being inspected.\nEvery step is navigable, including inherited fields and selected instances;\nexternal boundaries terminate the path. Declarations reached only through\nproof exploration are explicitly outside that statement's meaning closure.\nThis is neither a chain of logical implications nor a smaller review scope.\nEach statement also exposes which declarations and earlier binders occur in\neach parameter, hypothesis, and conclusion. These Lean-derived links separate\nthe meaning of a premise from that of the result; they do not say whether a\npremise is necessary or used by the proof. Local references retain their\ntelescope positions even when names are shadowed.\nFor a project predicate at the head of a statement part, **One-step predicate\nexpansions** substitutes its actual arguments into its definition. The extractor\nkernel-checks definitional equality and preserves implicit instances, proof\narguments and assigned local values. Original applications and remaining\nreferences stay visible. This is one substitution, not recursive simplification,\nan independently written characterization or physical validation. External\ndefinitions and predicates hidden inside larger expressions are not unfolded.\nStructure fields retain Lean's elaborated declaration order and distinguish\nexplicit, implicit, and instance fields. Every direct parent is separately\nlisted in `extends` order, including parents reconstructed from shared fields\nin diamond inheritance. Parent structures and projection bodies are inspectable\nwithout misrepresenting reconstructed parents as additional stored fields.\n\nThe same pages can export their inspection as compact JSON and compare a prior\nexport locally. The comparison covers the selected statement's complete meaning\nclosure, shows exact before/after values, and distinguishes changed declarations\nfrom declarations entering or leaving scope. Owning-source and configuration\nfingerprints are compared separately. It never imports review approvals or\nequates unchanged displayed specifications with physical correctness; source\nchanges can still invalidate a review. No build copies are needed.\n\nThe **Inspection notebook** keeps reader-authored observations, open questions,\nand suspected mismatches separate from the human-review ledger. Entries attach\nto exact declaration-meaning fingerprints; external-type notes conservatively\ntrack the entire extraction snapshot. Older notes remain visible when a version\nchanges. Browser storage retains entries where available; compact JSON export\nand merge provide portable backups without replacing existing notes. A matching\nattachment is not an authenticated author, a semantic approval, or a completed\nreview of any dependency. Unsubmitted text survives in-page navigation only.\n\nGuth's radiation horizon now has actual causal semantics. From\n`a(t) = A sqrt(t)`, `A > 0`, Lean computes the integrable conformal-time\nintegral and derives the physical particle-horizon radius `2t`.\nRadial causal curves from strictly positive emission times reach exactly\nits open interior. Entropy rescaling can place a selected region inside\nthat horizon without making all space accessible. Continuing this radiation\nmodel into the future gives no future event horizon, despite a finite\nparticle horizon at each age. Independent examples test a nonunit scale\nnormalization and reject treating a divergent integral's default Lean\nvalue as a physical radius. This remains paper-local flat-radiation\nkinematics, not a complete inflationary history or measurement theory.\n\nCanonical preparation now has an explicit approximation regime. For each\nfixed finite ensemble, coupling, observable, and positive error-per-field\ntolerance, Lean derives a positive field radius controlling the remainder.\nThe same bound realizes the existing paradigm's `ControlledApproximation`\nwith absolute error `tolerance * radius`. Kubo uses the actual isothermal\ncoefficient; Mori's orthogonality gives a small force mean on that window.\nRescaling the coupling by `s` transports the window to `radius/|s|`\nand its error-per-field tolerance to `tolerance*|s|`. The positive three-state\ndiagnostic retains zero derivative and local control at every coupling scale,\nyet refutes any common field cutoff giving absolute error at most `1/14`.\nThis separates model-dependent local validity from an unsupported uniform\nclaim. It provides no numerical radius, quadratic remainder constant,\ntime-uniform control, or thermodynamic-limit estimate.\n\nThe Mori-Kubo preparation refinement now derives response from a normalized\nfinite ensemble with energy `E-h*A`, rather than assigning its linear\ncoefficient. Differentiating the partition sum gives the connected covariance.\nMori's finite sampling bridge uses the existing projected-force geometry and\nequilibrium moments to derive a zero linear response; Kubo's finite diagonal\nbridge identifies the existing isothermal admittance with the actual derivative\nwhile retaining a different isolated response. A positive three-state model\nrejects exact finite-field cancellation from orthogonality alone. An independent\nnonuniform four-state consumer checks both zero and nonzero susceptibilities,\nobservable-offset invariance, and a nonzero nonlinear residual mean. These are\nfinite classical/commuting specializations, not quantum, continuum, bath, or\nmost-probable-path proofs. The existing source-route inventories are unchanged.\n\nThe bounded-record parity inference now feeds the complete selected Wu and\nGLW parity routes. The paper adapters construct the earlier observation\ncalculations from calibrated records rather than assuming a physical rate\ninequality. Wu still requires gamma calibration, time/directional reports,\nthree artifact controls, and physical prediction/interpretation. GLW still\nrequires the precession apparatus, polarization interpretation and scoped\nstopped-pion control. Its formerly arbitrary count-rate-distinction predicate\nnow means actual inequality. A separated record for an unrelated system does\nnot calibrate a symmetric angular law. Independent consumer tests quantify\nover every compatible analyzer coefficient: they reject all symmetric\ncandidates while retaining two different asymmetric coefficients for the same\nrecord. Generic integration clients additionally check the full paper-route\ncontracts and actual proof dependencies; they are not inhabited reconstructions\nof the historical experiments.\n\n\nThe parity-experiment refinement now separates finite rate records from\nphysical mean rates. Explicit bounds on both measurement errors give an\ninterval for the actual mean contrast. An inhabited record separated by\nmore than the combined budget rules out equal means; Wu and GLW adapters\nuse the selected angular observables and physical reflection to reject\nangular invariance without assuming the rate inequality. A reflection-\nsymmetric finite sampling law still permits an asymmetric record, and GLW's\nreported null band admits both equal and unequal normalized means. The\nindependent consumer combines these APIs with its own angular law to derive\nphysical symmetry breaking. Error coverage, detector corrections and the\npaper's interpretation remain explicit inputs, not automatic consequences\nof a finite sample or printed error bar.\n\nRiess and Perlmutter now share explicit population-selection semantics:\ndetection efficiencies reweight a population, light-curve correction removes\nthe modeled shape term, and the remaining distance bias is a residual mean\nshift. The relative comparison retains the difference of the two shifts.\nPerlmutter's main systematic assessment now bounds that numerical difference\nby [-0.01, 0.03] mag under the stated source estimates, replacing an opaque\nbound predicate. Inhabited controls distinguish brightness selection from\ndistance bias and matching shape distributions from bias cancellation. A\nseparate consumer reconstructs different populations through the public API.\nThese finite realizations do not reproduce survey simulations, jointly refit\nthe width correction, or establish the empirical error-budget assumptions.\n\nBlatt-Jackson's empirical range route now reduces actual spin-weighted\nthreshold equations instead of accepting an opaque extraction flag. The\ncoherent amplitude and epithermal rate select a central triplet length only\non the declared physical sign branch; the shared measurement API checks\nthat identification. The same calibrated length and binding momentum give\nthe central range with explicit rounding control. Under the stated central\ncalibration, rounding and bound-state truncation errors add; this is not an\nexperimental confidence interval. Two-method comparison bounds a\nmethod-specific error only under explicit error controls. Actual scattering\nmodels with equal measured records but different positive ranges show why\nagreement cannot remove an uncontrolled common offset. Independent numerical\nclients test the branch, calibration, information, and combined-error\ndistinctions without importing the production countermodels.\n\nThe finite-accuracy route now propagates bounded errors in all three inputs\nthrough the nonlinear triplet decoder and inverse bound-state formula.\nExplicit sign and positive-denominator conditions give a conservative range\ninterval; the separately controlled model error widens it further. This\nroute does not require exact central calibration. Its physical error bounds\nremain assumptions, not consequences of recording error bars, and no\nstatistical confidence or reproduction of the historical fit is claimed.\n\nObserved-state determinism now connects the paradigm and stochastic prediction\nlayers. Both endpoints must come from the same admitted history; exact\nfuture-state closure is equivalent to uniqueness of the induced observed\ntransition. The existing Mori and cosmological-history closure tests\nnow use this shared logic. An independent free-particle consumer checks actual\nderivatives, position-only branching despite unique phase evolution, closure\non a fixed-velocity sector, and closed velocity evolution without full-state\nrecovery. No statistical Markov property, objective randomness, or existence\nof an unrepresented state follows from this pointwise relation.\n\nChoptuik and Evans-Coleman now share actual threshold-mass logic in\n`Framework/CriticalCollapseScaling`. A positive exponent and one common\nnear-threshold relative-error bound derive a one-sided zero limit. Separate\nphysical-family realization supplies evolutions, positive masses, and\nmatching ideal horizons, giving arbitrarily small black holes in the selected\nfamily. Both primary adapters consume the same nonvacuous result. Finite\nnumerical fits do not certify these continuum hypotheses or an exact threshold.\n\nEvans-Coleman's printed fit labels and grid spacings are no longer combined\nwith invented exact residuals or a stipulated out-of-range failure. Physical\nparameter calibration and approximation budgets are explicit; a finite polar\nslice is strictly outside its apparent horizon and estimates final mass only\nwithin a supplied budget. Actual two-point mass curves, not residual flags,\ntest finite-fit overclaims. The separate Lake consumer has twelve new source\ntheorems and five audited framework API uses, with its own nonexact mass curve\nand Schwarzschild mass/horizon data. It imports no paper or production\ndiagnostic. These are algebraic readout tests, not Einstein-matter evolution\nproofs or held-out-paper validation.\n\nThe original onset paragraph uses both mass scaling and echoing, and the\nsource graph now requires both routes. The finite formula package is recovered\ndirectly from the numerical calculation without requiring extrapolation.\nSix new inhabited boundaries include a continuous positive-mass curve fitting\nevery point of any finite positive sample exactly while approaching nonzero\nmass, fixed absolute tolerance, a varying coefficient, zero exponent,\nthreshold-location error, and zero curves without positive objects. An\nindependent eleven-theorem paper-API client also retains its own nonexact curve\nand horizon readouts. The shared extraction adds no new primary paper or\nframework module and claims no collapse simulation or genericity theorem.\n\nMermin-Wagner's zero-field limit is now derived from its dimension-specific\nsmall-field estimates, rather than supplied by the infrared-calculation\npremise. Each estimate has a positive neighborhood and one common coefficient\nat the selected positive temperature. The original 1966 erratum is archived\nand cited for equations (2), (8), (9), and (14) and the real-space omega sum.\nThe finite selected readouts now tie magnetization to the thermal spin mean,\nthe mode denominator to the double commutator, and the corrected squared\nnumerator to the same magnetization. Their scalar Bogoliubov conversion is\nproved. The denominator bound retains its nonstrict zero-mode boundary;\nthe ratio formulas retain positive-omega and nonzero-field domains.\n\nSusceptibility is an actual eventually defined field derivative with a\nspecified limit, not an assigned predicate. A bounded odd response satisfies\nboth corrected estimates, has zero spontaneous limit, and has divergent\nsusceptibility. Controls distinguish zero temperature, field-dependent\ncoefficients, the uncorrected field factor, and the zero-exchange domain.\nThe reported exchange moment must equal the actual sum even in the finite-\nrange branch. A fresh bounded response at temperature three independently\nuses both limit theorems and has finite susceptibility one-third. These are\nresponse-level diagnostics, not microscopic Heisenberg constructions. The\nfinite spin sums, infrared integrals, physical Gibbs realization, and\nuniformity across a temperature family remain distinct obligations.\n\nThe FPU numerical-validation route now requires a Hamiltonian computed from\nthe same bond forces and sampled particle states. Separate linear/nonlinear\ncomponent errors bound the discrepancy with the reported energy; a small\nreadout drift gives a physical-energy drift bound only after including the\nevaluation errors at both endpoints. Seven additional constructed controls\nseparate modal energies, nonlinear energy, equations of motion, weak forces,\nand finite-time scope. An independent fifteen-theorem cubic-chain client\nchecks the energy components and unequal readouts without reusing production\ncountermodels. The original LA-1940 typescript is archived alongside the\nreprint: its energy equations are (5a)/(5b), while the reprint repeats (5a).\nThe coordinate dictionary, evaluation bounds, numerical trajectory accuracy,\nand reconstruction of the original computation log remain distinct obligations.\n\nRabi's detector route now uses a full magnetic-sublevel transition matrix\nand an incoherent initial population at every speed. The auxiliary spin-half\nprobability, selected higher-spin pair, any reorientation, aperture rejection,\nmean signal loss, and finite observed decrease are different formal objects.\nActual projections, normalized rows, populated resolved channels, and controlled\ngain/background derive the detector inference. It concludes some populated\nreorientation, not a unique pair or an independently identified isotope.\n\nThe higher-spin reconstruction is checked against original Majorana 1932,\nRabi 1937, and Rabi 1939 scans. Separate literal-expression diagnostics retain\ntwo factorial-printing discrepancies and distinguish a continuous polynomial\nendpoint from totalized tangent division. All matrix entries and row sums for\nJ=1/2, 1, and 3/2 are proved; general-spin normalization, physical realization\nof the effective pulse, and exact laboratory evolution are not silently supplied.\nAn independent mixed-population beam computes its unequal-speed detector\nmeans and explicit finite-reading bounds through the new APIs. The retained\nbinary client remains a selected-channel diagnostic. Rabi has 47 inhabited\nfidelity boundaries; no new shared framework or paper benchmark is claimed.\n\nRabi's precision route now also requires a physically interpreted molecular\nspectrum, a nonempty electronic sector whose restricted first-order moment\noperator vanishes, and an explicit interaction-energy bound. Lean derives\nrelative moment accuracy from adjacent multiplet gaps and the same h, spin,\nfield, and signed moment used by the Li-7 readout. Arbitrary precision needs\nuniform control across a valid field family and access to sufficiently large\nvalid fields. It is not inferred from one high-field result. A solved\nrotating-frame countermodel makes the moment error arbitrarily small while\nthe unshifted and shifted pulses retain probabilities 1 and 9/25. A separate\nspin-3/2 client checks all nine gaps of two nonzero interactions and keeps\nits finite validity range. Pulse approximation, line-minimum location, and\nempirical calibration remain distinct obligations.\n\nThe detector route now also requires a molecular-force reduction. The same\nenergy spectrum supplies actual spectator and interaction derivatives;\nadiabatic force identification, secular approximation, and spectator\ntransport remain explicit inputs. Joint outgoing PMFs and possibly infinite\ndiscrete spectator populations retain spectator-dependent slit transmission.\nThe nuclear-only mean signals are derived only after calculating their nuclear\nmarginals and effective preparation weights. A separate force-slope error\nbudget preserves aperture decisions only with an adequate margin.\nAn actual spectator-only joint unitary produces a detector loss without\nnuclear reorientation, and a source-direction filter changes transmitted\nflux despite endpoint cancellation. A fresh spin-3/2, three-spectator client\nderives joint-model signals 6 and 59/16 and error-resolved nuclear reorientation.\nThese conditional model results neither identify a microscopic molecular\nHamiltonian nor establish full laboratory evolution or apparatus error bounds.\n\nThe shared nebular calibration diagnostic now distinguishes changes of\nreduction from changes of cosmic realization. Its weighted/unweighted and\nindividual/grouped comparisons retain the same assigned catalogs but distinct\nprinted coefficients; they supply neither an ensemble target nor cosmic\nsampling variation. The original 43-object Stromberg catalog replaces the\nOCR-derived 48, and Hubble's fitting method is not labeled as a precise\nleast-squares algorithm. Relabeling without changing the numerical report,\nor substituting a different catalog, fails the corrected comparison.\n\nBoth nebular papers now use `NebularRadialData` in the existing calibration\nframework for actual observer-corrected radial residuals and fixed-weight\ndistance-scale identities. The adapters retain Hubble's selected angular\nsolar-reflex projection and Lemaitre's separate first-order correction. A\nprescribed coefficient is distinct from recomputing an estimator. A separate\nconsumer constructs three new objects with residuals `(2,-1,3)` and weighted\nloss `42`; seven audited public-API uses certify the positive scale comparison,\nretain the loss while changing `K=7` to `7/2`, and check paired numerical\nreference offsets. Counterexamples reject one-sided data changes, zero-scale\nresidual invariance, negative distances, and empty-sample nonvacuity. These are\nkinematic diagnostics, not historical catalog reconstructions or new cosmic\nexpansion measurements.\n\nLemaitre's calibration now computes positive photometric distances from\napparent magnitudes and the assumed common absolute magnitude, applies the\nselected first-order solar correction, and forms weighted and unweighted\nmeans on the same finite sample. The 43-to-42 catalog exclusion acts on actual\nidentifier sets. Explicit data-to-report controls derive coefficient bounds\nthat retain the separate 6.25 and 3 km/s rounded-mean residuals; the printed\n625 and 575 reports are not silently replaced by ratios of rounded means.\nA two-object diagnostic has zero weighted mean residual yet a strictly larger\nsquared-residual sum than another positive coefficient. It distinguishes the\nmean estimator from least squares without recalculating historical data or\ncertifying that the proposed weighting removes systematic error.\n\nThe same actual data now expose calibration sensitivity. Shifting the assumed\ncommon absolute magnitude rescales all assigned distances by `10^(-shift/5)`;\nthe selected identifiers and corrected velocities are unchanged. The\nunweighted coefficient scales inversely. For the weighted coefficient,\ncommon weight transport is sufficient, not necessary. One finite control\npreserves every radial residual and the fixed-weight loss while its recomputed\nweighted mean changes differently; an exactly proportional control preserves\ninverse scaling despite nonuniform reweighting. Neither control changes the\nhistorical calibration or certifies new uncertainty or regime assessments.\n\nHubble's calibration refinement now preserves the distinction between a\nradial-velocity fit and its independently supplied distance scale. A common\npositive distance rescaling and reciprocal coefficient change preserve each\nselected solar-corrected readout and weighted residual sum. The individual,\ngrouped, and adopted solutions keep separate calibrated families. An exact\nnonzero distance anchor removes this particular freedom; a controlled anchor\nand positive scale floor give a conditional coefficient-error bound. An\ninhabited two-object counterexample retains positive distances and nonzero\nresiduals. It is not a historical recalibration or a claim that shared-data\nfits are independent validation.\n\nBethe's empirical branch now computes the dimensionless Coulomb function from\nmeasured phases and separates finite calibration and validation samples.\nThe laboratory-energy convention derives the slope-to-range conversion and\npropagation of slope and reporting errors. Wilson's error-compatible\ncomparison is distinct from Dearnley's unexplained upward departure. The\ncharge readout uses the same fitted intercept, with independent zero-energy\nextrapolation control rather than an assumed exact threshold value.\n\nFive empirical fidelity cases now use actual phase curves, unitary relative\namplitudes, and derivatives instead of assigned curvature and energy-error\nflags. They distinguish finite sampling from continuum control, a fitted\nline from a resolved curvature sign or higher-energy agreement, and the\nlaboratory-energy conversion from the relative-energy conversion. These\nare inhabited logical diagnostics, not historical measurements or claimed\nfixed-potential reconstructions; no new framework is extracted from one paper.\n\nThe localization limit audit now uses actual complex kernels in place of an\nassigned infinite-volume proof flag. Decay at every fixed width can coexist\nwith a nonzero limit at the exact aspect ratio N/M = 100. A second, bounded\nkernel family has the same asymptotic decay rate at every width but a\nwidth-dependent onset. A separate uniform-tail condition suffices for\nfixed-aspect attenuation; these diagnostics do not construct Anderson\nHamiltonians or refute the paper's qualified numerical conclusions.\n\nThe MacKinnon-Kramer resolvent normalization now separates the literal\npositive rate printed in equation (1) from the negative rate for actual\nattenuation. The former finite-bar contract implied kernel growth; it is no\nlonger used as a physical decay premise. A separately sourced reconstruction\npremise, exact recursion, and full selected-kernel calibration now produce\nactual attenuation at fixed width. The source route also proves the literal\nsign discrepancy. Complex-amplitude controls distinguish decay from inverse-\nkernel growth and reject an independently assigned localization length.\nThe selected length denotes a defining rate parameter, not an exact finite\nnoisy estimate; no author-approved erratum or microscopic Anderson proof is\nclaimed.\n\nThe localization-scaling refinement connects AALR 1979 and MacKinnon-Kramer\n1981 to an actual positive logarithmic-scale trajectory. AALR's derivative\nreadout is no longer independently assignable. Its zero-conductance limit\nand exclusion of a persistent conducting response are checked consequences\nof negative monotone beta and a separately recorded global-continuation\npremise. The numerical paper's two-length differential and fixed-aspect beta\nproduct are actual chain rules for calibrated scaling and transport functions.\nFive new fidelity boundaries test fictitious derivatives, finite continuation,\nfinite-data ambiguity, and aspect-ratio changes. An independent consumer uses\nfour public API deductions on conductance curves with or without a small\npositive floor. These are conditional flow diagnostics, not microscopic\nAnderson-model or universal localization proofs.\n\nThe DGZ typicality refinement now derives conditioned agreement-set bounds\nbefore applying them to a selected configuration. Actual finite empirical\nmeans, normalized probability laws, bounded probes, and the sum of per-test\nfailure budgets replace the former direct weak-law-to-selected-state step.\nConditional-to-global disintegration remains explicit, and Born-reference\nidentification derives the property bridge. Six new fidelity boundaries\ninclude positive-probability exceptions and a rare environment with certain\nfailure despite a small averaged error. An independent Gibbs consumer uses\nthe shared typicality API with computed excitation probabilities and a\nnonzero exceptional sample. These finite diagnostics do not construct a\ncomplete Bohmian universe or prove the general large-sample limit.\n\nThe symmetry foundation now distinguishes arbitrary admissible states from\nlaw-specific selected vacuum or equilibrium families. Physical spontaneous\nbreaking requires a functional transformation preserving that family;\nmissing images and conflicting images no longer qualify. The chiral-vacuum\nadapters prove these action properties for their actual modular phase maps.\nNeutral vacuum-orbit statements now use `UnclassifiedSymmetryContext`,\nwhich has no physical, descriptive, observable, or variational classification\nfields. Unspecified interpretation is not encoded as a false proposition.\n`SymmetryActionContext` supplies the common law and state action.\n`PhysicalSymmetryContext` adds physical classification and readouts without\nrequiring vacuum selection; `SelectedPhysicalSymmetryContext` adds the\nselected family. `VariationalSymmetryContext` independently records\nvariational invariance and conservation, while the full `SymmetryContext`\ncombines explicitly supplied roles. Noether's adapter needs only the\nvariational interface. Microscopic reversal and parity tests need only the\nphysical interface; omitted conservation claims are not encoded as false.\nAn independent\nquantum consumer realizes the same neutral orbit both by global phase and by\nexchange of orthogonal states; their actual density matrices distinguish\nthe two interpretations. A separate continuous free-energy consumer\ndistinguishes an excited asymmetric configuration from asymmetric selected\nminima. An independent mechanics consumer computes translation-covariant\ndamped motion whose mechanical momentum decreases while the canonical\nmomentum of a time-weighted variational description is conserved. Its actual\nderivatives distinguish equation covariance, variational realization, and\nthe identity of the conserved quantity. See\n`docs/paradigm/symmetry-breaking-and-anomaly.md` for scope and API changes.\n\nThe current Blasius refinement derives the original similarity ODE and its\nboundary conditions from selected physical velocity fields. The stream-function\nidentities, continuity, and exact residual are checked deductions, while\nselection of the ansatz, reduced momentum balance, and numerical profile\nmatching keep distinct logical roles. Actual trial profiles reject replacing\nmomentum balance by wall matching and incompressibility; a local shear control\nseparates equation covariance from invariance of a selected solution. The\nindependent fluid consumer adds a dynamically valid suction layer that fails\nimpermeability. See `docs/targets/blasius-1908.md` for the precise scope.\n\nDevelopment is paper-first:\n\n1. reconstruct one paper locally;\n2. reconstruct a second paper with different logical structure;\n3. extract only the infrastructure independently required by both.\n\nThe emerging semantic architecture is layered: interpretive foundations and\nparadigm commitments constrain a technical physical framework, which in turn\nstates its mathematical realization obligations. Paper provenance and route\norder remain orthogonal to these layers. See\n`docs/architecture/semantic-layers.md` and the comprehensive\n`docs/architecture/philosophy-paradigm-roadmap.md`.\n\nThe active foundation contains 17 philosophy modules, 24 domain-neutral\nparadigms, and 12 explicitly scoped specialist paradigms. Every philosophy\nmodule and every domain-neutral paradigm has formalized original-paper clients\nfrom at least three registered physics families, with\nboth source-import and elaborated-declaration reuse audited. The 135 active\ntechnical frameworks each have a nonvacuous physical result consumed by at\nleast two independent original papers. All 191 active primary-paper formalizations now\ndirectly use at least one shared technical framework, with 302 independently\nchecked paper-to-framework integrations. Their 32 source-audited composition\nedges preserve actual physical child results and paper-specific dependency\norders. These are registration and checked-reuse counts, not completed human\nreviews of the physical interpretations.\n\nThe Hawking-Penrose geometry refinement now derives cosmological past trapping\nfrom actual metric-normal area variations and the expanding Friedmann branch.\nThe exact threshold is `mu*(R*r)^2 > 3`; the printed convergence scalar is\nkept separate from the normalized screen calculation, which gives half its\nvalue. Whole-surface, both-family error bounds derive the reduced positive\nmargin `delta-epsilon`. Hawking's 24 fidelity cases include actual area models\nrejecting saturated bounds, one-point or one-family control, and mixed\nnormalizations. A point-dependent positive example stays trapped.\nPenrose's future and Hawking's past geometries independently use one shared\noriented normal-area component. A separate framework-only consumer computes\nflat-space Jacobi area densities and rejects trapping despite actual ingoing\nfocusing. Ambient representation, physical perturbation estimates, and global\nincompleteness remain explicit obligations; local readouts are not global\nEinstein solutions. No new framework module, foundation, or paper is added.\n\nThe Kubo section-2 refinement derives classical and quantum first-order\nmean responses from retarded density solutions, actual integral domains,\nphase-volume conservation, and admitted trace operations. Probability\nnormalization and real response are checked. The time-domain result has\nits own route, independent of finite periodic calibration; two real probe\nquadratures then derive a finite Abel gain and fixed-time harmonic readout.\nNine added boundaries tested preparation, resonance, finite-amplitude\nerror, positivity, and measurement disturbance using actual matrix dynamics.\nThe subsequent operator-spectrum refinement added four independent\nfidelity cases. One faithful energy-coefficient representation now ties the\nselected Hamiltonian, Gibbs density, propagator, and observable pair to the\nsame spectral response. Density tests and separating evolution probes have\ndistinct trace domains. The canonical time-derivative identity follows from\nan explicit interchange input, which is proved for finite matrix systems.\nAn infinite diagonal control shows why density normalization does not make\nthe propagator trace class. The independent thermal consumer computes its\nown three-level matrix correlation and exercises three public spectral APIs,\nin addition to its earlier two causality results. General unbounded-operator\nand continuum-basis realizations and empirical observation remain separate\nobligations. No new shared framework, foundation, or paper is added.\n\nThe section-3 force-removal refinement replaces five schematic predicates\nwith actual force profiles, density readouts, and analytic conditions. The\nmain route derives `Phi(t)=C_full(t)-beta*I_AB`, both regulated admittance\nidentities, and the isolated static gain. A finite transform of `Phi` is\nderived at nonzero frequency and is not required at zero frequency. Generic\nfinite matrix systems prove the cutoff density integral, remote-past\npreparation, post-cutoff weak equation, and fixed-time readout limit.\nFive additional controls bring Kubo to 44 fidelity cases: finite nonzero-\nfrequency gain need not give an Abel tail; Abel relaxation need not settle;\na derivative does not fix invariant normalization; isolated preparation is\nnot perturbed-Gibbs equilibration; and a zero removal probe cannot identify\na relaxation curve. These are paper-local deductions, not a new shared\nresponse API or a proof of macroscopic irreversible relaxation.\n\nThe subsequent Kubo-Nakano source test earns a narrower shared canonical\noperator-correlation core. Actual Hamiltonian exponentials, Gibbs traces,\ncurrent matrix elements, and integral domains now derive Nakano's equations\n(2)-(4); the equal-energy coefficient follows from the same imaginary-time\nintegral. Kubo uses that core for his full canonical time correlation and its\nnegative response derivative, without equating it to the invariant-subtracted\nrelaxation. Five additional Nakano boundaries bring its fidelity matrix to\n26 cases. A current computed as a polarization's Heisenberg derivative has a\nnonzero canonical kernel but neither an ordinary DC integral nor late-time\nsettling. A separate degenerate observable exposes lost zero-gap weight and\nis proved not to be such a finite polarization current. The independent\nthree-level consumer computes its own thermal trace through eight additional\naudited public calls. The common correlation is one new reviewed component;\nno new framework module, foundation, paper, or client file is added.\n\nThe Callen-Welton refinement now derives the quantum force-noise relation\nfrom canonical absorption and the independently represented velocity\nfluctuations. Actual sinusoidal cycle averaging fixes the peak-amplitude\nfactor; the Heisenberg derivative and energy-gap Jacobian fix the noise\nnormalization. The comparison input no longer contains the final formula.\nThe pointwise theorem needs no finite-frequency-integral premise; the\nseparate finite readout retains its physical domain and angular measure.\nClassical behavior is a quantitative approximation, with whole-response-band\ncontrol required for an integrated error estimate. Seven new boundaries and\ntwo strengthened controls bring the paper to 45 cases, including actual\nfinite spectra and a nonintegrable continuum. A separate three-level thermal\nconsumer uses the public canonical-response API with non-unit hbar and a\ncomplex impedance. Dense-spectrum power correspondence, canonical spectral\nreconstruction, and measured readout identification remain explicit inputs.\nNo new framework, foundation, or paper is added.\n\nThe Nyquist refinement now derives the classical thermal-noise coefficient\nfrom actual finite standing-mode counts, quadratic energy moments, a\ncontrolled long-line limit, source correspondence, and Joule heating. The\nfilter argument distinguishes equal total power from equal band power;\nlocal spectral representation is explicit before using a pointwise density.\nComplex impedance and modulus-squared transfer derive the network and\nfinite current-noise equations with their frequency Jacobian. Twelve new\nfidelity boundaries include a computed family with noncommuting length and\nbandwidth limits, which genuinely uses the shared `OrderedLimits` paradigm.\nLiteral printed equation (8) is kept separate from its equation-(7) energy\nsubstitution. Thermalization, physical representation, the Planck-energy\nevaluation, and experimental qualifications remain explicit inputs.\nThis adds no new shared circuit framework or independent consumer fixture.\n\nThe Pound-Rebka refinement now computes the measured contrast from actual\ncounts and live exposures, calibrates it against opposite Doppler records,\nand retains line, gain-transfer, counting, and thermal residuals. Reversal\nderives twice the gravitational shift plus offset drift and those residuals;\ninversion stability removes only the drift. The reported uncertainty is an\nactual sampling RMS, not a deterministic error bound. Fourteen new fidelity\nboundaries test these distinctions, covariance, inverse-gain bias, partial\nabsorber sampling, and the separately printed table and ratio. The original\ntemperature paper and Josephson's separate mass-change explanation are\narchived and distinctly attributed. An independent affine mean-response\nconsumer uses two public measurement API results to recover gravity with\nthermometry and reject determination from the same counts without it.\nNo unpublished raw counts, microscopic lattice solution, or confidence\ncoverage has been manufactured.\n\nThe Kohn-Sham ground-state refinement now uses actual complex spin orbitals,\nCoulomb integrals, weak kinetic domains, and fixed-number density variations.\nLower analytic and noninteracting-reference inputs derive the potential\ngauge, local orbital equations, normalization, and energy double-counting\nidentities. Exact functional differentiation remains distinct from a known\nexplicit formula, and the nonlocal Fock alternative retains approximate\ncorrelation and its selected-orbital identification. Actual local energy\nintegrals must exist at the selected density and along admitted variations;\nscalar differentiability and the Fock integral domain are explicit, so\ntotalized Lean values cannot replace these physical domain requirements.\nTwenty-seven fidelity cases\ninclude an actual repulsive Hartree iteration with no density limit despite\na self-consistent global minimum. An independent three-site quantum consumer\nproves its constrained density minimum and exercises four shared API results.\nThe thermal extension now computes fermionic Gibbs occupations, mean-number\nfluctuations, complex weighted orbital densities, and grand-potential\nvariations. It separates the exact Mermin minimum from local stationarity,\ninternal free energy from grand potential, and fixed-number entropy from a\npath derivative with chemical work. The literal signs in (3.13) and (3.15)\nare tested separately from thermodynamic reconstruction; no author-approved\ncorrection is asserted. Actual entropy and heat derivatives retain controlled\ncomponent remainders and their slope bounds. An independent three-mode\nconsumer computes its own Gibbs probabilities, fluctuations, conditioning,\nand unequal ensemble entropies through seven audited public API uses.\nThis deepens paper logic, not continuum existence, universal SCF convergence,\nan unconditional bulk Sommerfeld limit, or full spin-response realization.\n\nThe BCS finite-temperature refinement now derives branch minima, actual gap\nclosure, normal Fermi occupations, and the finite heat-jump transition from\nexplicit integral and derivative inputs. The original variational free energy\nretains the pair-amplitude derivative and a controlled finite-cutoff correction.\nPhysical state and temperature representations, a complete variational\nreduction, and independent error budgets for the printed numerical estimates\nremain visible. Fifty-nine new source theorems replace two obsolete\nassigned-readout controls; six additional fidelity boundaries and fourteen\nindependent internal client theorems test actual functions and admissible\nstates. This thermal core remains paper-local, not a newly claimed shared\nframework or a microscopic BCS solution.\n\nThe shared effective-range error component now connects Bethe's actual\nradial comparison and Blatt-Jackson's stationary functional to the same\nuniform fourth-order remainder and actual low-energy coefficient limits.\nThe derivations stay paper-local: Bethe fixes one potential and zero-energy\nreference across momenta; Blatt-Jackson uses normalized trial-wave error.\nThe shared API proves coefficient uniqueness and composes independent errors.\nThirteen new independent consumer theorems retain a nonzero shape remainder,\ndistinguish equal coefficients from equal amplitudes, and reject unchanged\nphase-to-amplitude error tolerances. These are dimensionless diagnostics,\nnot empirical fits or fixed-potential reconstructions. No new framework or\nphilosophy module is added.\n\nThe Bethe radial-comparison refinement derives the infinite comparison from\nactual one-sided radial dynamics, finite Wronskian identities, and an explicit\nboundary limit. Actual overlap integrals and an interior error integral derive\na quantitative phase-error bound; the two-parameter prediction is no longer\nequated to the physical phase shift. Uniform quadratic range control, not\nmere continuity, gives quartic phase accuracy. Three new fidelity boundaries\nand nine independent client theorems test boundary matching, nonzero\nremainders, elastic unitarity, and composition of a separate readout error.\nThese are paper-local semantics, not a fixed-potential scattering solution or\nan added shared framework.\n\nThe charged Bethe refinement binds the phase shift to actual regular and\nirregular Coulomb waves. The dimensionless source function, common origin\nlogarithm, and two-proton normalization remain explicit. Separate routes\nderive the exact comparison, charged range error, same-potential neutralization\nerror, and a conditional nuclear threshold. Six new fidelity boundaries\nreject omitted Coulomb terms, normalization changes, exactness upgrades, and\nsuppression inferred from penetration alone. An independent consumer uses\nthe public scattering API to transfer a plotted-function error through the\nCoulomb conversion scale and amplitude denominators. Special-function\nrealization, boundary integration, empirical fits, and threshold regularity\nremain explicit inputs; no new shared framework or fixed-potential solution\nis claimed.\n\nThe weighted Bethe charge comparison now derives the neutral reciprocal\nlength from actual weighted Wronskian identities and a positive-cutoff\nboundary argument. Its estimate keeps radius, fit, wave, and truncation\nerrors separate. A strict calibrated gap implies unequal potentials only\nwith normalized-scattering uniqueness; pointwise closeness additionally\nrequires the cited depth calculation and common range and shape. The\nuncorrected exponential/Gaussian bracket remains an author expectation.\nActual potential profiles and eight new quantitative boundaries replace\ntwo scalar mismatch controls. A public-API consumer transfers parameter\nerrors to amplitude errors and demonstrates distinct amplitudes with equal\ncross sections. No new shared framework or original paper is claimed.\n\nThe HTML source-name audit now separates plain Lean references from notation\nand checks actual code tokens and qualified declarations. Stale API labels\nand non-theorem ledger entries have been corrected, and long inline source\nidentifiers wrap within the shared edition layout.\n\nThe Penrose surface refinement replaces independent expansion and convergence\nscalars with the printed reference metric, its computed sphere area, and\nactual normal-area derivatives on a compact two-surface. The reference\ncondition `r\u003C2m` no longer constrains a general nonspherical target.\nA strict relative bound on both expansions derives target trapping;\nmatching the same local optical area curve derives initial convergence,\nand the optical equalities derive concavity. The 23 fidelity boundaries\ninclude actual marginal spheres, one-point versus whole-surface contraction,\nreversed area-curve parameters, and equal initial areas with different\nderivatives. Every point and both normal families now have their own optical\nprofile. Transverse continuity on the compact surface derives a positive\nuniform convergence margin, and the all-normal optical calculation derives\narea zeros within one common affine bound. Discontinuous pointwise trapping,\nunbounded inverse-convergence estimates, and a positive-tail companion\nprofile reject shortcuts from pointwise or selected-generator results.\nAn independent internal metric client computes both convergence margins and\nboth area zeros. Ambient geometry, source estimates, every-normal\ncontinuation, caustic interpretation, and global causal topology remain\nexplicit obligations; no new shared framework or global collapse solution\nis claimed.\n\nThe Landau operational-transform refinement uses actual time and velocity\nintegrals, explicit coordinate coverage and integrability, and positive-time\nlimits of finite inverse contours. Integration by parts and the integrated\nkinetic/Poisson equations now derive the distribution and potential\nquotients. Four additional boundaries distinguish future support, genuine\nintegration, analytic continuation, endpoint reconstruction, and absolute\nintegrability. A six-theorem independent damped-signal client tests a larger\nconvergence domain, changed prehistory, and clock calibration. These are\npaper-local refinements, not a full plasma solution or a new framework.\n\nThe initial-value refinement now derives uniqueness of an actual selected\nFourier-mode state from the same initial datum, equilibrium, physical\nconstants, and common zero-free inverse contour. Its velocity distribution,\nPoisson potential, and electric field are computed from the readout;\nexistence uses an admissible readout with defined initial and evolved\ncharge-density moments. No independent global-determinism premise remains.\nThree new boundaries bring Landau to 35 cases: one Laplace sample does not\ndetermine a history, one Fourier mode does not determine the whole field,\nand zero-wave Poisson data leave a constant-potential gauge freedom. The\nindependent signal client also tests rationalized contour data with a\nremovable exceptional point. Inversion and analytic domains remain explicit;\nneither arbitrary-data PDE well-posedness nor nonlinear evolution is claimed.\n\nThe Anderson dynamics refinement binds equation (1) to actual future-time\namplitude derivatives and a defined summable hopping action. Explicit\nHermitian compatibility derives opposite bond currents and finite-site\nprobability conservation from the single-site initial state. Constructed\ncontrols reject fabricated derivatives, non-Hermitian conservation, and\naccidental diagonal hopping; an actual unbounded coherent lattice realizes\nthe new evolution interface. A separate complex-hopping client tests current\nsigns and conservation. Infinite-site operator domains and probability-sum\ninterchange remain separate obligations, not consequences of finite algebra.\n\nThe Anderson spectral-return refinement replaces a false all-late-times\nreturn-amplitude requirement with an actual energy-resolved pole calculation.\nFinite normalized locator limits derive positive pole weights; an explicit\nuniform bound and tracked-weight limit derive infinite-volume persistence.\nThe transport endpoint applies a separate conditional dynamical bridge.\nNormalized coherent evolution on an unbounded lattice has positive pole\nweights and positive mean return but arbitrarily late return zeros. Further\ncontrols distinguish finite positivity from positive limits, energy-grouped\nweights from degenerate mode squares, and the printed Laplace sign from the\nresolvent energy convention. An independent spectral client uses its own\nthree-mode data and isolated level. These are paper-local fidelity checks,\nnot a general spectral-to-dynamical localization theorem or a new framework.\n\nThe Hubble observer refinement distinguishes measured velocity, the actual\nangular solar reflex, corrected velocity, and peculiar residual. The main\nvalidation route derives a conditional relative-motion bound after solar\nsubtraction, replacing an incorrect raw-velocity inference. The individual,\ngrouped, and adopted solutions retain distinct solar parameters; their\nprinted Cartesian and polar reports are not asserted jointly exact.\nSeven new countermodel boundaries and a thirteen-theorem independent client\ntest correction signs, fit ownership, chosen-distance dependence, and\nconsistent observer changes. Group construction, numerical fitting, and\nthe quantitative interpretation of relative smallness remain explicit\ninputs. This is paper-local refinement, not an expansion theorem or a new\nshared framework.\n\nThe scalar zero-mode refinement replaces Witten's assigned deformation flags\nwith an actual one-dimensional differential family, square-integrable complex\nsolution spaces, and dimensions computed from those spaces. The printed\npotential `(m*x-g*x^2)^2` has minima escaping every fixed field bound as\n`g` approaches zero. Its diagnostic graded kernel index changes from one\nto zero despite pointwise continuity and formal charge grading. Witten 1981\nnow uses the same shared first-order/L2 interface: actual primitive-tail\nbounds exclude nonzero normalizable solutions, rather than defining\nnormalizability by two assigned signs. Thirteen independent consumer theorems\nuse different wells and `hbar=2`. Self-adjoint closure, trace identification,\nand four-dimensional physics remain separate realization obligations.\n\nThe molecular-beam refinement replaces Rabi's opaque refocusing and\ndetector predicates with actual ray maps, geometry-weighted gradients,\nfinite-aperture acceptance, and one common beam measure. Lean derives\nthe mean signal loss from populated, resolved transitions with explicit gain\nand background control. Observed readings have separate accuracy bounds: a\ndecrease must exceed the combined errors to establish a mean loss and infer\ntransitions. Ideal point refocusing, normalized baseline velocity\nstatistics, approximate experimental recovery, and field-scan resonance\nlocation remain distinct. A twenty-theorem client joins actual coherent\npulses at two flight times to different beam weights and a calibrated\ndetector and a resolved observed decrease. Paraxial validity, physical\npreparation, and readout accuracy remain scoped inputs;\nthe work is paper-local and adds no unearned shared framework.\n\nThe latest Landau refinement replaces bare microscopic commutation and\nconservation predicates with actual particle operators, a zero-curl joint\nkernel, Hamiltonian limits, and Schrodinger evolution. Sector ground states\nhave normalized eigenvectors and energy lower bounds; their existence, the\nstate domain of vorticity separation, the additional energy-gap inference,\nand physical level ordering remain explicit. A separate three-state client\nchecks actual reuse. The liquid's joint microscopic representation remains\nopen, and this paper-local work does not add an unearned shared framework.\n\nThe weighted-reversal refinement computes probabilities from actual finite\nsegment or tile weights. ECM's paired-weight aggregation is distinguished\nfrom its additional printed mean-exponential claim. GC's transverse-volume\ncorrection and its finite-weight/SRB-probability comparison remain separate;\ntheir bounds derive the actual event ratio. Uniform bounds across a whole\nobservation family, not merely positive bounds at each time, give the\ntime-normalized logarithmic limit. An independent driven-ring consumer tests\nnormalization, reversal from the actual endpoint, unequal preparations, and\nlong-time bias. These finite models do not establish a chaotic fluid, an SRB\nconstruction, or a universal arrow of time.\n\nFinite-resolution inference now keeps actual observation intervals distinct\nfrom exact-value representatives. The same weights derive a nonvacuous\nlog-ratio error bound and realize the approximation paradigm with the\ncomputed log ratio as target. ECM uses the maximum actual contraction spread;\nGC retains both reflected interval endpoints and both correction sources.\nGrowing observation durations, shrinking bin resolution, and sublinear\nlogarithmic errors are explicit conditions, not consequences of finite-time\ncontrol. Inhabited probability models and the independent walk consumer\nreject both fixed-width-to-central-rate inference and the converse claim\nthat every leading rate requires uniformly bounded multiplicative correction.\n\nThe shared decay-time refinement computes survival and conditional escape\nfrom actual measurable lifetime events under one probability law. Gamow's\nfinite interior probability admits an exponential record-law representation;\nidentifying measured lifetimes with that curve remains a separate bridge.\nGurney-Condon's observed exponential law supplies the selected record inputs,\nfrom which Lean derives residual-life memorylessness. Independent consumers\nreject memorylessness for an equal two-rate mixture and a lifetime reading\nof recurrent quantum occupation. These are statistical and interpretation\nchecks, not new nuclear tunneling calculations or quantum monitoring rules.\n\nThe Gamow refinement uses actual analytic wave branches, derivative matching,\nprobability current, and finite-region probability. The complex time phase\nderives damping and normalized survival; outgoing flux and an imported\nleading normalization derive the equation-(5) rate. The radial equation\ncontains the actual centrifugal term, and actual Coulomb-action derivatives\nyield the log-base-corrected slope, its decrease with energy, and a finite\ncomparison bound assembled from separate model and Taylor errors. Concrete\nwave and barrier controls distinguish standing amplitude from transmitted\ncurrent, leading exponentials from exact transmission, finite probability\nfrom global normalization, and suppression from zero escape. Printed\nderivative and radial-exponent discrepancies remain explicit diagnostics.\nUnknown-potential calculations and the approximation regimes remain inputs.\n\nThe Kennard refinement uses actual complex amplitudes, positive-sign Fourier\ntransformation, mean and variance integrals, and the paper's precision-squared\nequals twice variance convention. The reference Gaussian is matched to the\nsame selected width and means. Fourier moment identities and integrated\nfactorization identities remain analytic inputs; Lean derives the phase-current\ncancellation, the nonnegative derivative-remainder balance, and the uncertainty\nbound. Normalized continuum Gaussian tests distinguish density from phase,\nderivative energy, and the effect of a mismatched reference mean. Gaussian\nsaturation requires zero quadratic phase. The apparent inconsistency between\nthe original printed nonzero-phase parameter formulas is recorded, not silently\ncorrected or assumed. This remains a finite-moment, explicit-calculus-domain\nreconstruction, not a general unbounded-operator proof.\n\nThe Robertson refinement retains the original doubled Schwarz construction,\nits twice-variance norms, and its antisymmetric commutator overlap. Lean now\nderives the half-absolute-commutator uncertainty bound from those inputs;\nthe remaining calculation contract only calibrates commutator readouts.\nFinite Pauli-state tests distinguish the doubled overlap from covariance,\nthe doubled norm from a single variance, and source-pair saturation from\nsingle-vector Schwarz saturation. Operator domains, surface terms, and\nanalytic integration remain explicit obligations.\n\nThe BCS-Nambu response refinement uses complex spatial amplitudes and actual\ncurrent-response matrices. Tensor contraction derives pure-gauge cancellation;\nfinite-wavevector opposition is distinct from a positive London limit.\nBCS uses the finite-temperature gap and its actual inverse-temperature\nderivative. Nambu retains the contact-plus-vertex contraction, separate\nc-number and static-polarization conditions, and qualified transverse\ncorrections rather than exact equality. An independent anisotropic consumer\ndistinguishes selected-probe response from isotropy and a limit from the\nassigned zero-momentum value. Regulated calculation outputs, approximation\nestimates, and bulk-field interpretation remain explicit inputs; the controls\nare not microscopic superconductors.\n\nThe cosmological-history refinement ties radius, velocity, acceleration,\ndensity, and pressure to actual functions. Both Friedmann and Lemaitre use\nthe shared differential compatibility result. Constraint and conservation\nalone do not determine the pressure equation at a zero-rate point; actual\nhistory controls retain this limitation. Friedmann's nonstationarity\nand selected growth now require actual motion and numerical ordering.\nLemaitre's matter mass and radiation energy have different scaling, and his\nasymptotic past radius is distinct from finite-time emission. Radius growth\nand energy conservation are derived from the selected history obligations.\nAn independent coasting-fluid client checks pressure work and distinguishes\nexpansion from acceleration. Metric reduction, integration, and the chosen\nasymptotic dust solution remain explicit inputs.\n\nThe nuclear-spectrum refinement derives both partner energies from one\neffective central-field spin-orbit coefficient. Its sign, the level gap,\ndegeneracy-weighted centroid, and chemical-potential filling are checked;\nan s orbital has no fictitious lower partner. Actual finite spectra separate\nsplitting from shell isolation. Mayer's measured spins, moment-derived orbital\nassignments, and doubtful molybdenum report are distinct data. Haxel-Jensen-Suess's\ndeferred detailed account is not an asserted exact many-body result. The\neffective angular model and numerical controls are reconstructions, not\nmicroscopic nuclear-force calculations attributed to either original.\n\nThe Mayer source-boundary correction removes six predicates and their\nconclusions that had been attributed to Mayer from a neighboring letter on\nthe same scanned journal page. Her own isotope exceptions, limited data,\nwithin-shell ordering, pair-filling caveat, and isomerism interpretation\nremain. The adjacent original is archived for attribution only. This is a\nsource-fidelity repair, not new physics coverage, and illustrates why a\nsuccessful Lean build does not by itself establish faithful source parsing.\n\nThe Prandtl-Blasius refinement computes wall traction from the same velocity\nfields and integrates it over a finite plate face. It keeps dynamic viscosity,\none-sided wall derivatives, leading-edge integrability, and identical-face\ndoubling explicit. Blasius's coefficient is calibrated to the actual second\nprofile derivative; its printed bracket remains an unproved numerical input,\nnot a certified exact constant. Prandtl's incomplete `1,1...` report is not\nassigned an invented precision. Actual controls distinguish velocity accuracy\nfrom force accuracy and wall matching from solving the profile equation.\nAn independent exact channel flow computes unequal wall forces and pressure\nbalance through the public interface. General profile existence, the original\nnumerical accuracy, and a boundary-layer solution limit are not claimed.\n\nThe Bohm-Durr-Goldstein-Zanghi refinement uses actual squared-wave Born\nmeasures and a common configuration pushforward. Later agreement and\nprobability normalization are derived; wave measurability and construction\nof the transport from the differential equations remain explicit inputs.\nComputed oscillator controls distinguish equivariance from stationarity,\nphase information from Born density, and nontrivial coarse records from full\nconfiguration laws. Bohm's stationary balance no longer requires a positive\nenergy origin. An independently constructed translating-trap consumer checks\nthe public transport and detector-statistics interface. Neither a global\nflow through nodes nor a general relaxation theorem is claimed.\n\nThe Onsager-Casimir refinement defines correlations as integrals over an\nactual normalized stationary ensemble. Microscopic evolution, time reversal,\nfield reversal, and observable parity derive the correlation relation; a\nseparate finite-lag moment obligation then yields coefficient reciprocity.\nControlled moment errors instead bound the reciprocity defect. Both papers\nretain an explicit relative lag window, and an independent three-coordinate\nthermal consumer uses the same public interface. Actual Gaussian oscillator\ncontrols distinguish zero initial slope, finite-time change, mixed parity,\nfield-paired symmetry, and global exponential relaxation. These do not prove\nregression applicability or construct a microscopic heat or Hall conductor.\nOnsager's dissipation route also uses actual linear entropy and quadratic\nresistance functionals. Reciprocity and the constitutive equation derive the\nvariation gap; nonnegativity yields a maximum and strict positivity yields\nuniqueness. Isolation derives zero boundary exchange, and stationary\ncomparisons retain power and full normal-flux constraints at fixed temperature.\nConcrete matrices and an independently constructed client test the physical\nversus trial-flow distinction. Continuum integral/Green identities remain\nexplicit inputs; this variational interface stays paper-local pending reuse.\n\nOrdered-limit realization now uses one observable family, two nontrivial\napproach filters, and actual inner and outer limits. Mermin-Wagner retains\nfinite-volume convergence before the small-field limit; source certification\nof that order is distinct from mathematical commutation. Wetterich's original\nexponential profiles have checked limits for the full positive shape-parameter\nranges, with explicit wavefunction conditions before transferring inverse-\npropagator results to the regulator. Normalized magnetic controls and an\nindependent relaxation-model consumer test the distinctions. These controls\ndo not construct a complete Heisenberg model or interacting quantum field theory.\n\nWetterich's exact-flow formula now uses actual kernel-ring operations and\n`Ring.inverse`, not an independently supplied operation named inverse.\nThe connected-propagator trace and two-sided inverse identities are separate\ninputs; Lean derives their inverse-Hessian flow and retains it in the\npaper's shared result. Coherent quadratic and independent two-mode matrix\ncontrols test derivatives, Hessians, and trace substitution. False connected\npropagators and totalized singular inverses do not certify an exact flow.\nFunctional integration and analytic realization remain explicit obligations.\n\nFeynman's two-fluid audit now separates the original equation (42)'s literal\n`n^2` integral from the `n(1+n)` weight obtained by differentiating the moving\nBose occupation. The same spectrum, measure, and momentum data underlie both\nquantities. Integrability, differentiation under the integral, and full tensor\nisotropy are explicit inputs; the checked difference is a positive occupied\nmomentum moment when that sector is populated. Six-direction controls and an\nindependent finite-gas client test both directions of the distinction. This\ndoes not assert an author-approved erratum or construct microscopic helium.\n\nLandau's two-motion transport now computes mass, entropy, and reversible\nthermal currents from the same state, retaining the temperature factor and\nthe distinction between aperture-frame thermal transport and heat relative\nto mass flow. Rotation supplies calculated angular momentum and inertia, not\na separate capillary experiment. Source-observable correspondences retain\nthe selected density/current families and distinct endpoint normalizations.\nAn actual finite phonon response tests every exact atom partition; a\ncontrasting integer response admits an arithmetic partition without proving\na microscopic interpretation. Small constitutive counterflows are derived\nwithout claiming a solution of the hydrodynamic boundary-value problem.\n\nLandau and Feynman now independently use the shared equilibrium-excitation\nresponse component. It differentiates the actual moving occupation, retains\nthe statistics-dependent weight and full tensor isotropy, and keeps mass\nand number normalizations distinct. Landau's original zero-momentum roton\nhas a three-dimensional thermal population with its prefactor; heat is\nderived from the same energy functions. Radial moment inputs derive the\nper-unit-mass normal-fraction formula, and a gap-dependent bound controls\nthe quantum-statistics correction. The printed quartic heat statement is\nkept separate from the cubic derivative of quartic phonon energy. An\nindependent different-energy finite gas consumes the public response API.\nThese results do not establish microscopic helium, moving-wall equilibration,\nor dilute-gas validity at the lambda point. See\n`docs/framework/equilibrium-excitation-response.md`.\n\nStanley's critical-index appendix now uses the same represented free-energy\nfunctions as the noncritical calculation. Applying a response functional to\nthe limiting free energy is separated from taking the limit of finite-model\nresponses. A specific transport premise is needed to identify those operations.\nActual stable free-energy controls have uniform convergence but unequal\ncritical indices; another has uniform free-energy and entropy convergence\nwithout specific-heat convergence. These replace two scalar-only controls.\nThe constructed exponents are not attributed to Stanley's spin models, whose\ncritical-index comparison remains open in the original argument.\n\nBlatt-Jackson's variational route now constructs Schwinger's actual integral\nquotient. The standing-wave equation derives directional stationarity and\nthe quadratic trial-error identity. The zero-energy radial equation uses a\nregular integral form, avoiding an overly strong smoothness requirement at\npotential steps and rejecting discontinuous origin assignments. A fixed\nzero-energy trial is compared\nwith a consistently normalized exact wave, and uniform interaction/overlap\nbounds transfer its expansion to actual physical phase limits. This uses the\nshared approximation-composition paradigm. Computed operator controls retain\nboth error signs, the possibility of bounds with extra positivity, and a\nnonzero phase error despite vanishing unnormalized wave error. The original\ntrial-integral calculation remains an explicit input; the controls are not\nmicroscopic nuclear fits, and no new one-paper framework is extracted.\n\nIts bound-state route now derives the two corrections in equation (5.5)\nfrom the continued quartic phase remainder and a quantitative small-range\nbranch, instead of receiving the expansion as an input. Relative binding\naccuracy, a common uniform remainder bound, and inverse range-extraction\nerror remain distinct. Two entire phase families have the same first two\neffective-range coefficients and unitary on-shell S matrices with genuine\ncontinued zeros, yet different next binding coefficients. An independent\ndimensional client computes nonzero forward and inverse errors through the\npaper and shared APIs. These are controlled scattering-function diagnostics,\nnot microscopic nuclear Hamiltonians or new experimental fits.\n\nThe shared stochastic-prediction framework now applies those semantics to\nactual cosmological Gaussian histories. Arbitrary finite sharp-k bands\nderive Markov prediction from whole-history independence. A two-band\nGaussian-window control has exact Gaussian one-point laws but is not Markov.\nIndependent thermal consumers test conditional Gaussian kernels and separate\nexact static coarse-grained predictions from temporal predictive sufficiency.\nThe first-passage refinement now connects actual crossing events, killed\nsurvival measures, law-preserving first-hit reflection, and derivative-bound\ndensity families to the selected source formulas. Two actual Gaussian Markov\nhistories with identical one-point laws have different absorbed probabilities.\nContinuous field construction, reflection, and halo identification remain\nexplicit inputs; corpus size is not a completeness claim.\n\nThe sharp-k density now has actual field and variance derivatives, a checked\nheat equation, its Gaussian survival integral, and a one-sided boundary flux.\nActual mass calibration separates the negative cumulative derivative from\npositive differential abundance. The literal printed boundary and Gaussian\nexpressions are retained separately. Nonunit controls use a genuinely varying\nvariance curve, and four scalar-only tests no longer certify physical fidelity.\nThe Gaussian-tail derivative and path-to-halo identification remain explicit\ninputs; no cosmological Fourier process or halo catalog is thereby constructed.\n\nCrossing counts now come from actual sampled transitions, while smooth\ncontinuous crossings are separate root-and-derivative counting measures.\nTheir ensemble intensities give the first-crossing rate bound almost\neverywhere and, with continuity, at the selected variance. A normalized\nshifted-cubic control computes repeated crossings and their three rates.\nSeven new boundaries retain sampling, point-mass, endpoint, density-version,\nand singular-limit distinctions. These are paper-local semantics, not a\nconstruction of the cosmological Gaussian field or a new shared framework.\n\nThe Gaussian-rate refinement binds continuous finite counts, field-gradient\nlaws, and source formulas to the same ensemble. It retains explicit\ncrossing-window and Gaussian-integration inputs, the printed coherence-sign\nconvention, and the distinction between conditioning on the past and on the\ncurrent field. Actual Gaussian controls reject invalid density-version and\nregulator identifications. A separate law-preserving reflection route derives\nthe first-passage normalization without equating it to a sampled net-rate limit.\n\nActual survivor-history laws now retain every preceding barrier test in\nequation (3.10), distinguish propagation from killing at the new endpoint,\nand require an actual joint-density realization for the integral form.\nIn the two-band Gaussian-window control, two positive-probability cohorts\nsurvive the entire earlier interval and have identical current-field laws,\nbut opposite endpoint and first-passage outcomes. Their selection is\nmeasurable from the observed past. A bounded current-averaged forecast still\nexists and has the same ensemble mean as the full-history forecast; it does\nnot reproduce that forecast almost surely. Earlier assigned-number history\ntests are now explicitly scalar tests, not conditional-law guarantees.\nThe cosmological Fourier path construction and general-filter classification\nremain separate work.\n\nThe state-sufficiency refinement defines Markov prediction using conditional\nexpectations of all integrable observable queries given the entire observed\npast. It separates this property from deterministic closure, microscopic\nreconstruction, local-looking equations, and independent noise samples.\nMori and Zwanzig supply actual Gaussian oscillator realizations and\ncounterexamples; an independent consumer additionally retains an unobserved\ncoordinate and tests a genuinely stochastic three-time random walk.\nNo continuum, white-noise, or universal reduced-particle Markov limit is\ninferred from these finite examples.\n\nThe initial-ensemble refinement connects deterministic force evolution to\nactual probability laws of all finite collections of observation times.\nMori retains complementary observable evolution and its classical scalar\nproduct; Zwanzig retains a fixed initial system state and the shifted bath\npreparation. Counterexamples separate zero mean from absent fluctuations,\northogonality from independence, and stationary covariance from stationary\njoint laws. Gaussian integration is an explicit mathematical input, not an\naxiom or an automatically proved consequence of a named canonical ensemble.\n\nThe memory-kernel refinement computes actual finite-history errors rather\nthan encoding locality as a name. Mori retains the rotating carrier and\npositive Abel regulator; Zwanzig retains both coupling gradients, the printed\nDebye normalization, and separate continuum-replacement and localization\nbudgets. Primitive bounds preserve oscillatory cancellation. An independent\npublic-API consumer checks a changing history, a quantitative nonzero readout,\nrectangular cancellation, and matrix order. These are equation-residual\nresults, not global trajectory approximation or a derivation of white noise.\n\nThe response interface now computes past-time convolution, real-amplitude\nprobe derivatives, measure-valued impulses, and positive-time Fourier\nreadouts. Nakano's current and static-conductivity formulas and the FNS bare\nvelocity response independently use these operations. FNS does not thereby\nacquire the full equilibrium-to-conductivity transport contract. A Gaussian\nfluid witness derives spectral scaling from both force and velocity maps;\nModel-A fluctuation-dissipation normalization stays paper-local.\n\nThe two-dimensional viscosity refinement retains the higher-order term in\nthe source's differential equation. Only an explicit zero-remainder\ntruncation, positive viscosity, and the cutoff boundary give the leading-log\nsquare root. A supplied uniform weighted-remainder budget instead controls\nthe squared-viscosity error. An isolated regular-response consumer computes\ncontinuous-force, impulse, static, and finite-frequency readouts, with no\npaper or production-countermodel imports.\n\nThe response refinement computes the complex viscosity denominator and its\nreal spectral coefficient. Full-response scaling identifies viscosity only\nwith explicit nonzero-wave-number and finite-response hypotheses;\nequal real spectra do not supply that reconstruction. A source-qualified\ntwo-dimensional, zero-frequency one-loop ansatz now couples the actual running\nbare-coupling coordinate, viscosity, time exponent, and nonzero spectrum.\nThis is not a finite-frequency or all-order fluid solution. A separate\npublic-API consumer composes readouts with viscosities `4`, `2`, and `2/3`\nand detects an incorrect reset of the intermediate viscosity.\n\nFor the optional finite exponential correlation-length convention,\nsubexponential multiplicative corrections preserve the decay rate. Uniform\nrelative error strictly below one is sufficient on the connected channel;\nalgebraic prefactors are also allowed. Even one-percent relative agreement\nof raw correlations can conceal different connected lengths. None of these\nconditional results supplies the original paper's missing numerical error\nbounds or extends the above-critical formula to the critical isotherm.\n\nThe observable-scale refinement composes actual argument maps and scalar\nprefactors only on an inhabited transformed-domain intersection. Kadanoff's\ncell correlations and Forster-Nelson-Stephen's velocity spectra independently\nuse this interface. Supplied absolute residuals compose as\n`e1 + |a1| e2`; no numerical truncation estimate is inferred from scale matching.\nIndependent Gaussian-spectrum and normalized Ising-transition consumers test\nerror amplification, successive decimation, and loss of microscopic information.\n\nKadanoff's correlations retain both critical parameter windows. A separately\ndeclared finite exponential-length convention now connects the length readout\nto actual connected-correlation decay and derives length covariance from\nexact tail and mean-square reexpression. Critical-isotherm continuation remains\nan additional input; the literal printed equation (30) is not silently repaired.\nThe fluid client composes two shell steps at the updated coupling. Its\ntwo-dimensional one-loop flow demonstrates why resetting the bare coupling\nchanges the accumulated time exponent, without asserting an exact interacting\nfluid solution or quantitative control of generated couplings.\n\nControlled approximation now composes through explicit accuracy rules and\nactual observable readouts, retaining a common regime and an active target\nsector. Blasius's reported separation coefficients remain comparisons of\ntruncations, not certified error bounds against the exact flow. KSW and BHvK\nuse quantitative phase-to-amplitude bounds only with supplied remainders and\na positive lower momentum. A sixteenth independent consumer computes\neffective-range and shape-term budgets and proves that no uniform\nphase-to-amplitude error factor follows from positive momentum and unitarity\nalone. This strengthens error propagation without asserting EFT convergence.\n\nThe statistical coarse-graining refinement computes reduced probability laws\nfrom actual measurable projections. Kadanoff's two-valued cell configurations\nand Forster-Nelson-Stephen's regulated, transverse Fourier fields independently\nuse this interface. It separates retained observable laws, invertible\nreexpression, and exact closure in an effective-model family. A fifteenth\nindependent consumer computes a five-spin Ising marginal: the pair mean is\n1/9, but a nonzero generated four-spin coupling rules out every pairwise Gibbs\ndescription of the exact reduced law. This finite diagnostic neither supplies\ncritical scaling nor refutes controlled neglect of generated interactions.\n\nThe supersymmetry refinement computes Hamiltonians and energy expectations\nfrom actual supercharges. Witten 1981 retains normalized states, four-charge\nnormalization, and ground-state attainment; Witten 1982 connects a complete\nspectral basis to actual positive-energy pairs and convergent, unnormalized\nindex traces. Constructed counterexamples distinguish zero infimum from\nan attained vacuum and finite spectral sublevels from heat-trace convergence.\nA separate finite-operator consumer tests pairing, energy shifts, and two\nsystems with the same zero index but different supersymmetry-breaking status.\nWitten 1982 now also derives the actual zero-momentum restriction from a\njoint spectral bound and identifies physical fermion grading with four\nfinite quarter turns. A proper-sector operator witness preserves zero\nmodes and their parity while changing the full thermal trace.\nThe four-charge rest algebra now has an explicit Clifford multiplet,\ncommon vacuum kernels, and a checked normalization comparison. The\nnonzero-index existence theorem needs no rotation-covariance premise;\nthe separate vacuum-orbit theorem uses Hamiltonian-rotation invariance\nwithout asserting that each degenerate vacuum vector is fixed.\nPhysical domains, trace convergence in Yang-Mills theory, admissible\ndeformation, and infinite-volume transport remain explicit obligations.\n\nThe Majorana refinement now computes adjoints, canonical anticommutators,\noccupation parity, and effective energy blocks from actual finite fermionic\noperators. Kitaev, Fu-Kane, and Oreg-Refael-von Oppen retain their distinct\nnormalizations, phase conventions, and physical representation assumptions.\nAn independent two-site wire checks finite end splitting and distinguishes\ntotal parity from subsystem parity and electron-number conservation. This\nalgebra does not supply localization, a bulk phase, or a Josephson current.\n\nThe shared ordered-limit paradigm distinguishes a candidate iterated value,\nan actually established source order, a separately established reverse\norder, and a justified commutation principle. Stanley's unresolved critical\nlimit, Mermin-Wagner's thermodynamic-then-zero-field magnetization, and\nWitten's circle-decompactification-then-strong-coupling argument realize that\ncontract without inventing a reversed calculation. Wetterich supplies a\nfourth independent source: its actual regulator profile has commuting limits\nat the preferred exponent one and a divergent versus finite noncommuting\npair at exponent two. Physical observerhood and nuclear-outcome possibility\nlikewise remain separate from consciousness or ontic completeness when an\noriginal source supplies no such classification.\n\nThe finite driven-work refinement now composes computed canonical weights,\nactual stochastic updates, trajectory work and heat, and normalized path\nexpectations. Jarzynski and Crooks consume this common construction while\nretaining their different source routes. Physical reversal, actual final\nequilibration, and canonical reference entropy are separate checked claims.\nAn independent three-event process has a nontrivial heat update, an exact\nexponential work average of 9/8, and a final distribution that is not canonical.\n\nThe constrained-dynamics refinement now uses evaluated canonical functions\nand actual coordinate derivatives. Local first-order constraint completeness\nand the Poisson identity derive Dirac's first-class bracket closure;\nAnderson-Bergmann's invariant action commutator yields generator closure and\nquadratic-primary ambiguity on the same surface. Computed examples separate\nweak value, first-order action, global equality, and physical identification.\nAn independent p=2 system derives its completeness condition, nonzero\ngenerator commutator, and Hamiltonian translation.\n\nThe boundary-layer refinement now computes the full and retained momentum\noperators from actual time and space derivatives. Prandtl's steady equations\nhold on a selected inhabited physical patch; Blasius's general reduction\nretains the time derivative, continuity, and separate outer Euler input.\nDiscarded streamwise diffusion and pressure-gradient mismatch give a finite\nresidual budget, not an exact equation or convergence of solutions. Separate\nmixed-derivative control is needed to pass from small transverse pressure\nvariation to streamwise pressure matching. Curvature can leave first-order\npressure variation where the planar estimate is second order. An independent\ndecaying shear flow checks the shared operators, calibration error, and\nnonzero viscous acceleration without importing paper witnesses.\n\nThe entanglement framework now also has a finite complex density-matrix\nrealization. Separability is an actual convex product decomposition, partial\ntraces and spectral entropy are computed operations, and a calibrated\npartial-transpose witness proves nonseparability. CKW's singlet and GHZ\nreductions, AMPS's distinct Page-purification and pure-interior-pair controls,\nand Bell's original isotropic product-mixture comparison independently test\nthis infrastructure. The source-specific tangle, entropy, Bell-locality, and\nblack-hole assumptions are not identified with one another.\n\nThe Brownian refinement now uses actual probability measures and displacement\nobservables. Einstein's Gaussian route binds the printed densities and\nscalar readouts to normalized integrated moments. Smoluchowski's route\nconstructs fixed-angle three-dimensional paths from independent uniform\nazimuths and derives the finite-path moment from an explicit angular-average\ninput. Raw moments, central variance, collision independence, persistence,\nand the distinct large-count and small-angle approximations remain separate.\nAn independent Gaussian consumer has identical first observations but\ndifferent accumulated spreading, testing the need for joint-law information.\nEinstein's finite-step density, reduced continuum density, and displacement\ncount density are now distinct. Actual derivatives and exact residuals\nseparate the finite-step balance from the retained diffusion equation;\nextra bounds give a nonempty rate comparison, not an exact PDE. Individual\norigins give zero initial displacements without physical co-location. The\nGaussian count density is tied to a selected finite population and actual\nexpected bin counts, not an exact finite observed histogram. The independent\nconsumer also checks origin-invariant displacement statistics.\n\nThe predictive Brownian route now uses disjoint nonempty displacement\nintervals and actual trajectory-event probabilities. Their positivity is\nderived from the Gaussian law; it is no longer a supplied density label.\nFinite arithmetic mean-square readouts are distinguished from their ensemble\nexpectation. The molecular-count proposal derives an inverse-moment interval\nunder separate instrument-calibration and sampling-accuracy conditions, and\ndoes not assert that a finite observation exactly recovers the ensemble value.\nAn independent two-particle consumer represents the empirical record through\nthe public observation API and proves positive-probability sampling error\neven with noiseless readouts.\n\nEinstein's mesoscopic clock now binds selected time roles to actual readings.\nJointly independent stationary increments of the same histories derive the\ndisplacement-law convolution. Finite-step and retained continuum histories\nuse the same selected population and aligned initial laboratory positions,\nbut their later laws need not agree. Integrable density-error bounds transfer\nto actual expected bin counts; Gaussian bin positivity transfers only under\na sufficiently small actual probability error. The exact finite-step second\nmoment at mesh times separately supports the molecular-count readout method\nwithout an exact Gaussian finite-step law. The independent consumer has a\nprocess with Gaussian laws and diffusive moments at every prefix time but\ndependent increments, testing why marginal fits do not identify dynamics.\n\nGuth's converted-volume and percolation predicates now come from one actual\nthree-dimensional region history. Spatial density is a normalized Lebesgue\nvolume limit over expanding finite windows; percolation requires an unbounded\nconnected component. A growing geometric control has arbitrarily large\nconverted fraction but only bounded components, even though the whole region\nis unbounded. Additional controls distinguish infinite point cardinality from\nspatial extent and percolation from connectedness of the entire phase. These\npaper-local controls do not prove the unknown critical threshold, collision\nmechanism, or qualified exit assessment.\n\nGuth's nucleation refinement now uses actual Euclidean light fronts, birth\nconfigurations, and normalized Poisson laws. The same geometry derives the\nconformal spherical volume and keeps interior fictitious births inside real\nbubbles. Survival is the actual zero-engulfing-count event, with the physical\nvolume factor retained. The late constant-rate approximation computes its time\nconstant and a convergent exponent correction, not an exact finite-time pure\nexponential. Imported tunneling gives double-exponential parameter dependence,\nbut enormous expansion remains a qualified plausibility assessment.\n\nActual and retained ensembles remain distinct. Convergent integrated error\ntransfers the late decay law; separate spatial averaging relates it to the\nselected realized universe. A countable-time theorem also gives an almost-sure\nversion without selecting an arbitrary history as typical. Large converted\nfraction is now derived on this route, not supplied by the percolation input.\nSeven inhabited controls test local finiteness, fictitious containment, the\nvolume factor, expansion plausibility, the late correction, spatial averaging,\nand null-exception histories. Exact integration, approximation control, and\nspatial correspondence remain explicit inputs, not calculations claimed solved.\n\nKolmogorov's moving coordinates, velocity differences, and conditional\nfinite-point laws now come from an actual random field and its joint measure.\nThe retained increment ensemble is distinct from the absolute-velocity field;\nits exact local isotropy does not assert exact conditional independence for\nthe actual field. Probability accuracy and squared-moment accuracy are\nseparate inputs. Computed moment profiles, spatial partial derivatives, and\nstrain dissipation feed the radial source calculation and the shared fluid\nadapter. A selected coordinate match and the separate moment bound give an\nactual conditional longitudinal-moment prediction interval.\n\nThe named increments use the same sample-dependent moving points as the\nconditional joint law. A fixed source-point identity requires the selected\nbase-velocity condition. An incompressible rigid-rotation control agrees at\nthe selected conditioning sample but has positive-probability disagreement\nwhen that condition is dropped.\n\nThe turbulence fidelity matrix now has 25 boundaries. Actual drift and shear\nfields distinguish local increment laws from whole-velocity isotropy and\nunconditioned homogeneity from conditional homogeneity. Further controls\nreject exact two-endpoint independence at nonzero variance, transfer of\nunbounded squared moments from probability error alone, and independently\nassigned derivative values. The archived equation (18) has no visible equality\nsign between `1/a` and its square root. Literal-product and possible\nequality-chain readings are separate Lean propositions; the unit-normalization\nequations independently determine the positive time scale used by the main\nroute. The printed outer ratio `U/L` remains distinct from the crossing\ntime `L/U`. Local and Taylor isotropy also differ in both temporal\nstationarity and velocity scope, not by a blanket stronger/weaker ordering.\n\nThis refinement does not complete the fluid interfaces. Numerical Reynolds\nand geometric scale-window bindings, similarity-law transformations,\nasymptotic paths, and independent fluid-consumer reuse remain depth work.\n\nThe nonequilibrium-work framework now uses actual realization measures.\nJarzynski's switching ensemble and Crooks's path ensemble expose normalization\nand the exponential work moment separately from existence of the ordinary\nmean. Mathlib's integral Jensen theorem derives the work bound. An empty\nrealization space is rejected, and an inhabited mass-two counterexample shows\nwhy matching scalar equations cannot replace a probability ensemble. The\ntwo original Hamiltonian and forward/reverse derivations remain distinct.\nCrooks's joint path weights, reversed preparations, entropy pushforwards, and\nscaled-work pushforwards are now tied to those same measures. The measure route\nderives the integrated identity without a density-version assumption; source\ndensity formulas and the original v1 work-coefficient discrepancy remain\nseparately visible.\n\nThe cosmological sampling-variance framework now also has an actual-measure\nrealization. Normalized first and second estimator moments determine its\nvariance; positive variance and physical support derive distinct possible\nsky estimates. Scott-Srednicki-White's finite-patch integral and Knox's\nnoise-free harmonic calculation use this bridge without identifying their\nGaussian, survey, or likelihood assumptions. A separate consumer derives the\nfull-sky estimator formula from explicit Gaussian moment inputs and keeps its\nfull probability law distinct from matching moments.\n\nThe geodesic-focusing framework now derives finite collapse from actual\npositive-region evolution and explicit continuous extension. Penrose's area\ntransport fixes the first derivative, so positive convergence yields actual\ncontraction; his optical route no longer supplies this as an independent\nlabel implication. Raychaudhuri uses the same calculus for the past-directed\nG-profile while retaining G^3 as volume. An independent Minkowski null-ray\nclient computes the transverse Jacobi area and exhibits a caustic with\ncomplete geodesic continuations and an expanding outgoing family.\n\nThe quantum-locality framework now has an actual C*-algebra realization.\nLocal observables belong to star subalgebras, disjoint supports commute,\nfinite-volume Hamiltonians sum local self-adjoint interaction terms, and\nHeisenberg evolution is exponential conjugation. Lieb-Robinson's original\nasymptotic estimate and Nachtergaele-Sims's metric estimate now constrain\nactual operator norms. The latter's extended weighted interaction norm is\ncomputed from the metric, full one-site matrix dimensions, and interaction\noperators, with finiteness stated separately. A two-spin Ising model realizes\nthe printed separated-support bound but has a nonzero commutator at arbitrarily\nearly positive times. It therefore tests approximate locality without\npretending to realize the 1972 infinite-lattice asymptotic theorem.\nThe 1972 source now also uses actual integer lattice coordinates, Euclidean\ndisplacement lengths, full finite-region matrix algebras, and a faithful\nsupport-covariant translation action. Translation invariance transports the\nfinite interaction neighborhood at the origin to every site and derives\nspacetime covariance from the finite-volume limit. Explicit infinite-lattice\ninteraction controls distinguish exponential decay from finite range and\norigin-local finiteness from uniform finiteness. Both spin papers require\ndisjoint local algebras to generate their joint algebra.\n\nThe collisionless-plasma framework also retains actual phase-space\ndistributions, derivatives, signed charges, and velocity integrals. Landau's\nlinear equation is checked as the first variation of Vlasov dynamics, while\nBGK's stationary energy profiles are checked locally on their own orbit\nbranches. Both certified paper routes retain the resulting kinetic and\nPoisson equations. Positive integrable controls distinguish a first-order\nsolution from a nonlinear solution, and stationary species populations from\nself-consistent charge balance.\n\nLandau's late-time route now uses the actual transverse marginal, its\nhalf-line Laplace transform, and the residue of its printed resolvent.\nAn explicit contour estimate derives field decay; a vanishing marginal\nremainder and nonzero residue derive microscopic nondecay. A canceled\ncandidate pole establishes neither a genuine residue nor persistence, and\nzero frequency gives a constant leading term, not an oscillation. The\nnonsmooth-data assertion remains a separate unproved source calculation.\n\nThe entire-data premise now requires an everywhere analytic extension of the\nactual initial marginal. Plasma frequency and Debye length are computed from\nthe same Maxwellian density, charge, mass, and thermal energy, including in\nthe independent half-space branch. The wavelength formulas determine an\nestimated damped mode; an exact bound for the target field requires separate\nerror control. Smooth mode counterexamples show that arbitrarily close decay\nrates need not give an eventual bound at the estimated rate. The source's\nsmall-parameter qualifications are not replaced by a numerical accuracy\nclaim for every `ka \u003C 1` or `ka > 1`.\n\nThe wavelength routes now use actual real-wave-number families at fixed\nMaxwellian parameters. Explicit auxiliary mathematical limits yield the\nobservable long- and short-wave limits; decrement dominance is eventual as\n`k` tends to infinity, not an unconditional finite-`ka` inequality. The phase\nequation admits higher odd branches, so the principal-root selection remains\nseparate. Equation (20) is derived from that selection and equation (19).\nA nonempty comparison of leading and corrected frequency estimates uses the\nshared controlled-approximation paradigm, without claiming accuracy for the\nexact plasma solution. Physical controls reject the converse from small\nextrapolated relative damping to long-wave validity.\n\nA tenth independent consumer constructs a positive Gaussian cosine\ndisturbance in a neutral two-species Vlasov-Poisson plasma. Its actual\nnumber-density integral approaches equilibrium while each Fourier velocity\nmode keeps nonzero amplitude, and reversing the streaming recovers the\ninitial mode. A single-species zero-potential probe instead fails Poisson.\nThe test establishes phase mixing, not Landau's fixed-ion damping decrement,\na BGK trapped wave, collisional relaxation, or microscopic irreversibility.\n\nThe low-energy nuclear-resummation framework now also has an actual complex\nelastic S-matrix. KSW's real-contact bubble amplitude implies unit norm and\nthe optical theorem. BHvK's regulated square-root propagator has a checked\nlower-side on-shell limit; attaching external lines removes the auxiliary\nfield normalization and recovers the leading scattering-length amplitude.\nThe certified paper routes retain these formulas, while concrete controls\nreject a complex absorptive contact, the wrong square-root boundary value,\nand an unnormalized auxiliary propagator.\n\nKSW's mixed expansion now retains the actual resummed C0 amplitude and a\nsingle C2 insertion with its squared bubble denominator. The shared complex\namplitude API derives the first-order optical theorem and the quadratic\nunitarity defect of a finite truncation. An independent nuclear client\nreconstructs scale-independent leading and correction terms from running\ncontacts, then distinguishes that truncation from an exactly unitary\nresummation that adds higher-order terms. Neither scale hierarchy nor exact\nunitarity alone is treated as proof of EFT accuracy. Two resummations can be\nexactly unitary yet disagree between subtraction scales even while their\nretained leading and correction terms agree.\n\nThe band-Hall framework now also has actual differential response semantics.\nHaldane's signed weak-field density slope and separate fixed-chemical-potential\nStreda principle derive both Hall signs, rather than silently excluding the\nnegative-index phase. TKNN's Kubo coefficient is an actual electric-field\ncurrent derivative; its within-level gap invariant is distinct from the total\noccupied-sector index including filled lower Landau levels. A seventh\nindependent consumer connects honeycomb corner masses and cone spectra to\nsigned density response, and tests why zero-field quantization does not\ndetermine a finite-field current ratio.\n\nTKNN and Niu-Thouless-Wu now also share actual spectral Kubo data: domain-aware\nHamiltonians and operators, complete orthonormal eigenstates, occupied and\nempty sectors, energies, and convergent transition sums. Unitary basis\nidentification and hbar rescaling derive the transformed response. NTW's\ncurvature bracket uses actual ground-state derivatives; its torus average\nuses actual integrals and retains the reversal of derivative order in the\noriginal equation (2.9). The independent two-level client tests real response,\nrephasing invariance, and opposite Hall signs at the same gap, while rejecting\ninteger quantization from local spectral data alone.\n\nThe resonance-spectroscopy framework now also has actual complex two-state\nvectors and unitary pulse matrices. Ramsey's three source amplitude relations\nderive the interference probability, with the energy-valued laboratory\nHamiltonian and solved rotating-frame generator retained. Rabi's printed\nweak-field probability has a separate coherent realization; concrete controls\nprevent it from becoming an exact laboratory solution or silently changing\nthe historical frequency-ratio convention. Both certified paper routes use\nthis shared dynamics.\n\nRamsey's drive-free region now retains a spatial list of actual energy-valued\nHamiltonians in a common basis. Chronological phase multiplication and\nconstant positive molecular speed derive the source's time-to-space mean\nreduction. Equal mean splittings preserve the complete coherent response and\nits positive-speed beam average, even when both energies shift together.\nConcrete controls reject variable-speed weighting, an unaligned static energy\nbasis, and unconditional transverse\nmean-field averaging; the precision route derives these qualifications\ninstead of receiving them as an assumed conclusion.\n\nAn eighth independent consumer now tests this spectroscopy API without\nimporting either paper. It derives the resonant pulse response, uses the\noriginal normalized continuous beam weight, and proves a strict distinction:\nthe selected-speed molecule can invert completely while the coherent beam's\naverage transition probability remains between zero and one. A drive-free\ninterval preserves populations but changes the recombined fringe. Separate\ntests reject amplitude averaging across independent trials and automatic\ndephasing from a large single-molecule phase. The chosen pulse strength is\nnot claimed to optimize the beam or determine its linewidth.\n\nQuantum error recovery now also has actual complex code amplitudes, local\nrecovery matrices, binary supported-noise components, and reduced densities.\nCalderbank-Shor's final result uses the two preceding correction equations;\nSteane's uses the printed Cij identity through an explicit normalization\nbridge. Both derive restoration of every coherent superposition and a\nlogical-state-independent residual environment instead of receiving those\noutcomes as final calculation inputs. Source coding identities and physical\nmodel identifications remain explicit obligations.\n\nA ninth independent client constructs a three-qubit known-support code and\nan actual dephasing dilation. The first correction preserves normalization\nbut fails to restore a codeword's off-diagonal coherence; the complete\noperation restores it. Separate shared controls show that successful basis\ndensity recovery and state-independent apparatus probabilities do not by\nthemselves establish quantum recovery. No unknown-error-location or noisy\nfault-tolerance claim is made for this three-qubit example.\n\nThe same independent code now carries an entangled reference qubit through\nthe complete recovery. Actual joint density restoration preserves every\njoint observable and a calibrated nonseparability witness. A separate\nisometric logical-basis recorder restores all basis densities and both local\nmarginals but destroys their entanglement. The shared recovery framework\ntherefore composes with actual bipartite entanglement, while noise-environment\ndecoupling remains distinct from reference-code separability.\n\nFor example, Bethe's and Blatt-Jackson's original 1949 nuclear-scattering\narguments share effective-range reduction and a qualified deuteron-range\nextraction without being collapsed into the same derivation. Their composed\nLean results require independent reduction and extraction source proofs plus\na third historical handoff: Bethe retains radial comparison, ground-state\nspecialization, and binding/free-proton/parahydrogen evidence, while\nBlatt-Jackson retains the stationary variational functional, analytic\ncontinuation, its printed scattering-matrix pole formulas, and\nbinding/epithermal/coherent evidence. A physical countermodel keeps distinct\nscattering and bound-state energies, both component source explanations, and\nthe extracted result while rejecting a missing paper-specific handoff.\n\nWilson's original 1974 confinement argument and Creutz's original 1980 SU(2)\nMonte Carlo study likewise share finite-regulator gauge invariance and\nregulated loop-area confinement without conflating their physics. Wilson's\njoined proof retains compact angular-link equations, analytic minimal-surface\ntiling, normalized-loop formulas, and the small-hopping vacuum-loop\nrestriction; Creutz's retains pure SU(2), detailed-balance equilibration,\nindependent-start and finite-size checks, statistical uncertainty, and the\nprinted constant/perimeter/area square-loop fit. The shared result does not\nclaim continuum confinement, and its physical countermodel distinguishes the\ngauge groups and mechanisms while rejecting a missing joining derivation.\n\nTwo modern rigorous condensed-matter arguments, Hastings-Koma 2006 and\nNachtergaele-Sims 2006, share finite-propagation and spectral-gap clustering\nframeworks while retaining different physical logic. Hastings-Koma's joined\nproof requires an independently selected exponential support-chain branch,\nGaussian ground-sector subtraction, finite-volume uniform transfer, and its\ncorrected bosonic correlation formula. Nachtergaele-Sims instead retains\nweighted arbitrary-metric commutator bounds, target ground-projection\nconditions, analytic-contour optimization, and its explicitly restricted\nimaginary-time estimate. The shared composition neither accepts power-law\npropagation as exponential nor identifies corrected decay with unsubtracted\ncorrelation decay.\n\nFive historically broad shared frameworks additionally retain independently\ngoverned, source-valued physics without widening their neutral contracts.\nHeisenberg/Ozawa distinguish corrected microscope recoil, prepared-state\ndispersion, the full noise-disturbance commutator, and conditional product\nbounds. Everett/Zeh/Rovelli distinguish squared branch weights, memory trees,\nreduced versus global coherence, and physical observer comparison.\nGuth/Albrecht-Steinhardt distinguish subcritical percolation, wall\nthermalization, a radiative finite-temperature potential, and fluctuation\nreplacement. KSW/BHvK distinguish complex PDS loops, running contact beta\nfunctions, bound-state poles, pion counterterms, and a one-datum three-body\nlimit cycle, with both derivative-contact and sine-ratio running enforced at\ntwo distinct scales. TKNN/NTW distinguish magnetic Diophantine gaps, twist-torus\naveraging, and a degree-three fractional ground-space response that explicitly\ndoes not satisfy the integer-only shared endpoint. Each family has checked\nformula mutations, explicit unproved-claim boundaries, independent-client\nreuse, and a trusted-axiom audit.\n\nThe dimensional-analysis paradigm distinguishes a nonempty selection of\nrelevant physical inputs from the stronger assumption that this selection\ncovers every relevant input. Its finite countermodel selects length and time\nwhile leaving a genuinely relevant mass scale unselected, so dimensional\nadmissibility and a scoped result cannot silently establish exhaustive\nphysical input coverage.\n\nThe thermodynamic-limit paradigm distinguishes small and large finite systems,\ncritical versus off-critical control parameters and neighborhoods,\nlarge-volume exceptional points, and bounded-correlation versus spontaneous-\nmagnetization properties. Its countermodels keep actual finite-volume data\nwhile separating singular limiting behavior, empty accumulation scopes,\nuniform finite control, and the additional property-preservation bridge.\n\nThe renormalization-group paradigm distinguishes infrared and ultraviolet\neffective descriptions and running couplings while retaining a protected\nphysical amplitude with a definite scale-independent prediction. Separate\nfinite models distinguish an out-of-regime prediction from a selected\nprediction and a genuine one-scale prediction from a two-scale comparison;\nrunning parameters and formal agreement cannot substitute for physical\nnonvacuity.\n\nThe mathematics-and-nature philosophy keeps mathematical models, physical\nstates, coordinate quantities, physical observables, and mathematical versus\nphysical values distinct. Its finite witnesses separate charge from\ntemperature, selected from control states, and an actual physical value from\na mathematically assigned but spuriously represented one; representation\nfaithfulness therefore cannot be inferred from matching labels.\n\nThe observability philosophy likewise keeps weak system-scoped observable\navailability, operational access, performed measurement, and physical\nexistence separate using distinct spectroscopy and radiometry procedures,\nresonance-frequency and background-temperature quantities, matching\napparatuses, and observer-dependent availability. A nonvacuous availability\nsector must contain an actual available quantity; bare availability supplies\nneither a procedure nor an ontology. Its independence results therefore remain\nphysically discriminating after names or labels are changed.\n\nThe observer philosophy separately distinguishes physical targets,\nnonconscious instruments, conscious persons, actual versus unproduced\ninformation records, and reference frames. Its frame countermodels retain\ndifferent entities, position versus energy, invariant versus alternative\nphysical values, and frame-dependent coordinates without identifying a frame\nrepresentation with an observer's physical agency.\n\nThe probability philosophy distinguishes numerical predictions, objective\nphysical chances, population assignments, observed sample frequencies, and\nmeasure-relative typicality. Explicit bridges are required before one role\ncan justify another, while typicality becomes nonvacuous only when an actual\nselected state exists. Finite models retain different events, models,\nphysical states, populations, samples, measures, and exceptional properties.\n\nThe measurement philosophy separately models selected and control systems,\nreference preparations, active versus idle interventions, calibrated and\ncontrol detectors, actual versus reported values, recorded outcomes, and\nphysical state changes. A real control run cannot silently stand in for the\nmissing selected measurement or reference calibration.\n\nThe active benchmarks include:\n\n- Witten's 1981 analysis of dynamical supersymmetry breaking, including the\n  global vacuum-energy criterion, Goldstino consequence, perturbative\n  protection, lower-dimensional nonperturbative mechanisms, four-dimensional\n  zero-mode obstruction, qualified proposals, and unresolved conclusion;\n- Witten's supersymmetric-index argument for four-dimensional `N = 1`\n  supersymmetric Yang-Mills theory;\n- Einstein, Podolsky, and Rosen's original 1935 completeness argument,\n  separating the sufficient reality criterion, the single-system\n  noncommuting joint-representation obstruction, the Lean-derived\n  completeness-or-no-simultaneous-reality alternative, separated\n  conditional-state assignments, the concrete position-momentum route, the\n  incompleteness reductio, the distant-choice objection, and the open status\n  of a complete alternative theory;\n- Heisenberg 1927, Kennard 1927, Robertson 1929, and Ozawa 2003 as a\n  deliberately nonflattened uncertainty benchmark. Heisenberg now retains the\n  complete article's operational kinematics, microscope and energy-time\n  procedures, independent selected-Gaussian calculation, experiment-relative\n  value partitions, coherent versus measured transitions, high-excitation and\n  repeated-observation classical-limit routes, free-packet and grating cases,\n  jump timing, causality, resonance, weak quantization, coupled-system energy,\n  and proof-stage corrections. Kennard\n  retains transformation probabilities with pointwise square-modulus density\n  formulas, doubled-variance precision,\n  Gaussian saturation, the general positivity inequality, measurement\n  interpretations, and simple-motion scope. Robertson retains normalized\n  complex wavefunctions, centered rms deviations and doubled Schwarz overlaps,\n  actual noncommuting observable matrices with state-dependent positive and\n  zero bounds, integer-spin angular generators with their zero-magnetic and\n  extremal branches, and the stated but unproved operator extension. Ozawa\n  separates all three uncertainty formulations, derives the correlation-term\n  and generalized error-disturbance relations, recovers the product law under\n  independent intervention, and supplies a dependent-intervention violation\n  plus a qualified optical proposal. Kennard and Robertson alone earn the\n  prepared-state dispersion framework; Heisenberg and Ozawa independently\n  earn the operational error-disturbance framework without identifying their\n  epistemically different calculations;\n- Born's full 1926 collision paper, separating periodic-state frequencies,\n  the continuum limit, one-dimensional flux balance, directional scattering,\n  elastic and inelastic channel calculations, thresholds, the qualified\n  dipole approximation, limited diffraction evidence, practical rather than\n  ontic indeterminism, and the unresolved radiation extension. Born and\n  Kennard independently earn only the neutral shared amplitude-to-outcome-\n  probability route; Born's selected collision state and scattering amplitude\n  are not promoted to Kennard-style preparation and representation, and their\n  scattering and exact-observation meanings remain local. Both paper adapters\n  now retain their own `Complex.normSq` value formulas, but Born's discrete\n  coefficient weight and Kennard's continuous probability density are not\n  collapsed into one shared mathematical carrier;\n- Wu et al. 1957 and Garwin-Lederman-Weinrich 1957 as independent controlled\n  parity-falsification benchmarks. Their shared technical framework imports\n  the mature experimental-symmetry paradigm and retains an admissible\n  experiment, physical reflection between two admissible configurations,\n  controlled detection, invariant-law equality prediction, measured count-\n  rate distinction, and explicit breaking. Its finite countermodels retain\n  positive forward/reflected count rates `3` and `5`, calibration signal `1`,\n  and field-reversal residual `0`; those numbers are logical witnesses, not\n  historical measurements. They separately reject detection without the\n  invariant prediction, a physical test without detection, and distinctions\n  under nonphysical maps, while an independently considered detector-drift\n  hypothesis remains open after the selected remanence control. No\n  `Unit`-alternative truth table replaces the physical experimental data.\n  The shared route now\n  gives an ordinary structural explanation without paper provenance. A stricter\n  source-sensitive wrapper keeps the two granular derivations distinct: Wu\n  starts from gamma calibration, beta asymmetry, and three control families;\n  Garwin-Lederman-Weinrich starts from delayed stopped-muon detection,\n  precession, and the scoped stopped-pion null control. Each source theorem\n  exposes its derivation and entails the ordinary explanation without\n  consuming a terminal parity result. A converse model retains the full\n  falsification and ordinary explanation but has no source-sensitive\n  explanation when its source derivation is false. Cobalt orientation,\n  pion-muon transport, artifact-control mechanisms, decay dynamics, charge\n  conjugation, and time reversal remain paper-local. Wu's original Fig. 2\n  gamma-count quotient, opposite cold beta-count branches, common warm-rate\n  baseline, and two independent zero-asymmetry control specimens are actual\n  real-valued propositions with separate source-route dependencies and\n  inhabited counterexamples. Separate source-valued controls additionally\n  retain the reflection-odd `spin * momentum` pseudoscalar, approximate\n  cobalt coefficients, the unperformed time-reversal test, Garwin's\n  `0.75-2.0 microsecond` delayed gate, partial-polarization angular curve,\n  `0.989 +/- 0.028` stopped-pion null control, finite `g = 2.00 +/- 0.10`,\n  and distinct `1.92 +/- 0.19` versus `2.5` high-energy model comparison.\n  Twenty inhabited mutations prevent these source facts from being promoted\n  to exact asymmetry, exact magnetic moment, a completed future experiment,\n  or a uniquely established neutrino theory;\n- Wilson's original 1974 lattice-gauge confinement argument, separating\n  exact finite-spacing gauge invariance, transfer-matrix qualifications,\n  strong-coupling surface expansion, area-law binding, string-like\n  loop-surface structure, weak-coupling expectations, and the unresolved\n  continuum limit;\n- Witten's original 1979 large-rank baryon argument, separating reviewed\n  planar meson counting and the independent confinement premise from\n  N-quark combinatorics, Hartree control, scattering, exponentially\n  suppressed production, distinct transfer limits, and the final monopole\n  analogy. Its eleven directional paper-local countermodels are now\n  value-bearing: the rank-four witness retains `g^2 N=1`, relative\n  corrections `(1/16,1/4)`, six exact pairs with pair force `1/4` and total\n  interaction `3/2`, order-rank mass eight with a nonzero Hartree residual,\n  and pair-production weight `(1/2)^3=1/8`. Fixed momentum gives velocity\n  change `1/8`, whereas fixed velocity gives momentum transfer eight;\n  inverse-coupling baryon and monopole mass scalings do not imply identity,\n  and qualitative success does not bound finite-rank error `1/3` by `1/10`.\n  No proposition-pair or named-calculation truth table replaces these Witten\n  baryon distinctions;\n- Bell's original 1964 EPR no-go argument, including its exact inequality,\n  robustness argument, scope examples, and conditional physical conclusion.\n- Bell's original 1966 hidden-variable analysis, separating the explicit\n  spin-one-half dispersion-free construction with its value-level Pauli\n  observable, two eigenvalues, hidden-sign rule, and uniform average, the\n  rejected von Neumann and Jauch-Piron premises, the dimension-scoped Gleason\n  obstruction, context-dependent projector values, and Bohm's qualified\n  nonlocality lesson with its two-particle density, Schrödinger equation, and\n  guidance-velocity formulas. Its proof-free apparatus readout retains a\n  nonfactorizable two-by-two spin amplitude, positive density, distinct\n  remote analyzing fields, local currents, and density-divided velocities;\n  nonfactorability without remote current coupling has no trajectory effect,\n  while the explicit current bridge proves distant apparatus dependence.\n- Kochen and Specker's original 1967 hidden-variable analysis, separating\n  statistical reproduction from functional preservation, the finite\n  117-direction coloring obstruction, its spin-one and rhombic-field\n  realization, the homomorphic-relation objection, the positive\n  two-dimensional sphere-and-disk model, the von Neumann critique, and the\n  quantum-logic consequence. The source readout retains 117 distinct\n  normalized real rays, actual complex spin-one matrices and commutators,\n  complementary zero/nonzero squared-spin projectors, the metastable\n  orthohelium sector `n = 2, l = 0, s = 1`, the distinct-coefficient\n  rhombic Hamiltonian, all three equation-(8) reconstruction polynomials,\n  and the three measured energy branches. The paper's printed nonzero-spin\n  proposition is explicitly complemented into the shared exactly-one\n  zero-spin coloring convention; its inconsistent printed `J_z` prefactor is\n  isolated rather than assumed. The proposed adjustable external field is\n  not confused with fixed nickel-crystal evidence or a performed direct test.\n- Berry's original 1984 geometrical-phase argument, separating slow closed\n  eigenstate transport, dynamical and geometrical phases, interference\n  observability, gauge-dependent connection from gauge-invariant spectral\n  curvature, the two-level monopole and real sign rule, arbitrary-spin\n  predictions, the transported-box Aharonov-Bohm construction, and the\n  paper's isospectral and wider wave-physics qualifications.\n- Hannay's original 1985 classical angle-holonomy argument, separating the\n  physically assumed adiabatic angle-averaging principle from exact Liouville\n  conservation, action invariance from angle anholonomy, connection\n  convention dependence from invariant curvature, three independent physical\n  illustrations, the integrable many-freedom extension, and the explicit\n  failure of a generic mixed-system generalization.\n- Maldacena's original 1997 D3-brane route to AdS/CFT, separating the\n  large-`N` supergravity sector, the full quantum duality conjecture, evidence,\n  calculational regimes, and interpretive consequences. The original\n  equation-(2.2) full D3 metric now remains a proposition-valued source\n  formula before the fixed-`U` harmonic limit is used.\n- Townsend's original 1995 compactified-supermembrane argument and Witten's\n  original 1995 string-dynamics paper as an independent Kaluza-Klein tower\n  benchmark. Their common extraction separates the tower and charge/mass\n  matching calculations from a paper-local state-identification bridge and a\n  further compactified-origin interpretation. It stops at qualified evidence\n  for a higher-dimensional origin. The output-led established result is the\n  selected compactification setup together with a model-native nonvacuous\n  endpoint requiring the actual setup data, calculations, identified tower,\n  and origin support at one model. It does not store the implication-valued\n  bridges; a checked theorem reconstructs the complete route from the direct\n  outputs. Theory/world grounding requires the selected setup while remaining\n  independent of the tower calculations and conclusions.\n  The full raw route now also realizes an ordinary structural explanation of\n  supported compactified origin. Its source-sensitive form retains distinct\n  origin tokens that extend Townsend's black-hole/KK identification and\n  Witten's RR-BPS/sparse-spectrum/KK identification by their respective\n  origin-interpretation bridges. These explanation tokens are intentionally\n  stronger than the reduction tokens below, and Witten's separate\n  radius/decompactification calculation remains excluded.\n  A second checked projection maps the actual compactified higher-dimensional\n  description, calculated and matched KK tower, protected lower-dimensional\n  tower, and physical state identity into a nonvacuous\n  `ReductionAndEmergence.RealizationContext`. It stops at the selected tower\n  reduction: the stronger compactified-origin interpretation is deliberately\n  absent. Countermodels show that compactification without higher-tower\n  support and matched tower data without state identity are both insufficient.\n  Both papers now also realize that reduction directly from source inputs,\n  before any terminal origin result or shared endpoint exists. Townsend\n  executes the charged black-hole tower and KK matching calculations before\n  applying his conjectural state-identification bridge. Witten executes RR\n  charge provenance, protected-tower, sparse-spectrum, and KK matching stages\n  before state identification. Neither source reduction consumes the further\n  origin-interpretation bridge. A stronger source-sensitive projection now\n  retains typed, noninterchangeable paper-local derivations: Townsend's\n  charged-black-hole/KK identification and Witten's RR-BPS/sparse-spectrum/KK\n  identification. The realization relations contain the corresponding raw\n  paper inputs, not established shared outputs. A checked countermodel shows\n  that a completed tower-origin result, complete technical route, and ordinary\n  reduction still do not determine which source derivation obtained them;\n  a parallel countermodel keeps ordinary structural explanation but still has\n  no source-sensitive origin explanation when the source relation is false.\n  Witten's separate radius/decompactification calculation is excluded from\n  his tower token. Their compatibility adapters still consume\n  only the terminal origin result and reconstruct the complete stronger route.\n  Staged paper countermodels show that implication-shaped contracts can all\n  hold vacuously while direct origin evidence fails.\n  Townsend's membrane and p-brane\n  claims remain local, while Witten's `r = lambda^(2/3)` calculation,\n  strong-coupling decompactification, lower-dimensional U-duality,\n  heterotic/Type II consequences, enhanced-symmetry assessment, and\n  speculative Type I proposal remain separate paper-local routes.\n- Strominger-Vafa 1996, Callan-Maldacena 1996, and Horowitz-Strominger 1996\n  as a three-paper black-hole microstate-entropy benchmark. Their extremal,\n  near-extremal, protected-index, same-sector, weak/strong comparison,\n  radiation, and information-scope routes remain distinct.\n  Horowitz-Strominger's author-TeX formulas\n  `P = 2 pi n/L`,\n  `n_R = L(delta E + P)/(4 pi)`, and\n  `n_L = L(delta E - P)/(4 pi)` are now literal proposition-valued\n  inputs tied to total energy, momentum, and density readouts; checked\n  arithmetic recovers `n_L + n = n_R`, and a countermodel prevents a\n  named chiral-momentum definition from supplying the printed formulas.\n  Strominger-Vafa's microscopic branch now retains the displayed Cardy\n  2 pi sqrt(n c / 6) logarithmic-growth formula and selected c/n charge\n  substitution before the protected indexed-growth endpoint. They jointly earn\n  only the narrow shared inference from two valid same-sector entropy\n  calculations plus an explicit paper-local comparison bridge to a scoped\n  entropy agreement. The same raw route now directly realizes an ordinary\n  structural explanation of that scoped agreement, and a stricter explanation\n  retains four noninterchangeable typed microscopic derivations without\n  consuming an established match or reduction wrapper. That complete route\n  also realizes a direct scoped\n  derivational reduction: a typed microscopic state-counting description\n  supports the selected entropy behavior, a typed macroscopic black-hole\n  description exhibits the independently calculated entropy and agreement,\n  and the same-sector comparison supplies realization. This is entropy-level\n  reduction only, not reduction of the complete theories or dynamics. Invalid\n  descriptions with matching outputs and a microstate count without a\n  macroscopic entropy calculation are checked countermodels. A stronger\n  source-sensitive reduction now preserves four distinct microscopic\n  derivations: Strominger-Vafa's BPS bound-state/index-growth route,\n  Callan-Maldacena's extremal one-five-string count, their separate balanced\n  near-extremal excitation and T-duality count, and Horowitz-Strominger's\n  left/right-moving effective-string thermodynamic count. Each adapter starts\n  from raw paper-local setup and calculation predicates before invoking the\n  generic source theorem. A completed entropy match and ordinary reduction\n  with an unrealized derivation token has no source-sensitive reduction, so a\n  common entropy output cannot manufacture derivational provenance. A parallel\n  countermodel keeps the completed match, route, and ordinary structural\n  explanation but still has no source-sensitive explanation. The shared\n  proof-free model retains the two\n  descriptions, conserved sector, two regimes, two entropy values, and all\n  nine route-used physical relation families. Each paper constructs a named\n  exact model, proves a semantic-retention certificate, consumes it before\n  route applicability, and exposes a source-native physical setup with a\n  checked bridge to the shared grounding boundary. Grounding requires that\n  setup but consumes no entropy or comparison output. Every established paper\n  match is now output-led: exact selected semantics plus the direct\n  same-sector setup and four realized outputs, with all implication-valued\n  contracts reconstructed. An independent finite model realizes that proposition,\n  and exhaustive proofs show that changing any one of its seven indices or\n  nine relation families destroys the completed comparison.\n  Its six shared and eighteen paper-local directional countermodels are now\n  value-bearing. The shared witnesses retain area `4`, Newton constant `1`,\n  nonempty degeneracy/log-count data, charge and excitation sectors, validity,\n  comparison, leading-coefficient, finite-correction, and information\n  residuals. Strominger-Vafa retain `Q_H=1`, `Q_F^2/2=100`, `c=606`,\n  `n=1`, statistical and black-hole squared entropies `101,100`, distinct\n  actual degeneracies at fixed weighted index, and nonoverlapping weak/strong\n  bounds. Callan-Maldacena retain the `Q_1 Q_5 N` extremal value, three\n  balanced ratios `1/4`, contributions `1/2+1/2+1/2=3/2`, temperature\n  agreement with unequal radiation coefficients, and selected horizon-state\n  scope. Horowitz-Strominger retain `Q_-=1`, four bosonic species, low-density\n  `n_L=2,n_R=8` contributions `2,4`, matched leading entropy `6`, separate\n  transition/evidence residuals, comparison charge two, perturbative versus\n  nonperturbative unitarity, and unequal decay rates. Checked positive\n  witnesses realize every source boundary. No proposition-pair or status-enum\n  truth table replaces these entropy distinctions.\n- Gubser, Klebanov, and Polyakov's original 1998 correlator prescription,\n  separating the proposed boundary generating-functional dictionary,\n  controlled supergravity regime, asymptotic conformal symmetry, massless and\n  massive wave calculations, stress-tensor normalization, protected\n  partial-wave dimensions, and explicit higher-point and leg-factor\n  obligations.\n- Ryu and Takayanagi's original 2006 boundary-region entropy proposal,\n  separating the selected anchored minimal surface, exact `AdS3/CFT2` check,\n  thermal and massive checks, higher-dimensional structure, qualitative\n  strong/free comparison, horizon interpretation, and open covariant\n  extension.\n- Lewkowycz and Maldacena's original 2013 generalized-gravitational-entropy\n  argument, separating Euclidean density-matrix preparation, integer\n  replicas, continuation assumptions, the scalar check, replica-fixed-surface\n  Einstein calculation, cone area term, AdS/CFT subregion translation,\n  reflection entanglement, and open extensions.\n- Knox's original 1995 CMB forecast, separating ensemble spectra from one\n  realized sky, retaining equations (4)-(5)'s estimator-variance and\n  relative-uncertainty formulas with their positive noise-free limit,\n  fixed-weight beam comparison,\n  conditional likelihood precision, the signed inflationary consistency\n  relation and cosmological-constant correction, foreground scope, and\n  nuisance-parameter confusion.\n- Scott, Srednicki, and White's original 1993 small-scale CMB sample-variance\n  calculation, separating one-sky realization logic, Gaussian moment\n  calculation, beam-convolved equation (7), the exact circular-cap Bessel\n  integral and distinct equation-(9) limits, both lines of the linear-scan\n  equation (10), actual MAX/SP91 angular inputs, their linearized 25/30\n  percent amplitude uncertainties, the COBE galactic cut, idealized patch\n  counting, and qualified phenomenological interpretation.\n- the original 2012 AMPS firewall argument, separating the\n  strong-subadditivity and explicit Bogoliubov number-defect contradictions\n  from the mining-dependent and scrambling-time extensions. Its entropy route\n  now uses only `S_B >= 0`, treats strict thermality as a strengthening, and\n  makes pure-pair identification depend jointly on semiclassical exterior\n  physics and no drama. Its mode route separately represents the appendix-A\n  early projection, the observer's prediction, number-state selection, and\n  the fact that the early measurement need not actually be performed.\n- Gaiotto, Kapustin, Seiberg, and Willett's original 2014 generalized-global-\n  symmetry paper, including higher-form defect kinematics, the checked\n  Abelianity argument from explicit continuous defect-exchange witnesses at\n  positive form degree, the compact-spacetime\n  selection rule, Maxwell electric and magnetic one-form currents, their\n  mixed anomaly, Coulomb-phase symmetry breaking, and the photon Goldstone\n  interpretation.\n  A second typed entropy source now reconstructs semiclassical validity,\n  collapse mode mixing, horizon ray tracing, late-packet thermality, the\n  surface-gravity temperature, quarter-area entropy, and compensation before\n  realizing a source-sensitive structural explanation of generalized\n  nondecrease. The heuristic pair picture is not a premise of that source.\n- Jarzynski's original 1997 nonequilibrium work identity, separating the\n  isolated Hamiltonian calculation, weakly coupled physical reservoir,\n  equilibrium limits, ensemble consequences, numerical thermostat\n  extensions, and finite-sampling limitation.\n- Crooks's original 1999 fluctuation theorem, separating protocol-indexed\n  directed paths, microscopic reversal, the exact entropy-production\n  relation, the integrated exponential identity from its later Jensen\n  mean-second-law consequence, ensemble mean nonnegativity from pathwise\n  nonnegativity, equilibrium-work and steady-state specializations, and\n  qualified long-time heat and Gaussian approximations. Its distinction\n  between reversed-protocol microscopic path probabilities and\n  same-protocol state detailed balance now uses a genuinely stochastic\n  three-state model: all forward and reverse transition probabilities\n  are positive, both kernels are normalized, uniform stationary state\n  populations are normalized, and clockwise/counterclockwise probabilities\n  1/2 and 1/6 give a nonzero probability current 1/9. A separate\n  balanced model proves that microscopic reversibility permits detailed\n  balance as well; it neither requires nor forbids that stronger condition.\n- Metropolis et al.'s original 1953 modified Monte Carlo method, separating\n  the canonical target, symmetric proposal and acceptance rule, pairwise\n  balance, accessibility, asymptotic equilibration, rigid-sphere\n  specialization, virial pressure calculation, finite numerical evidence,\n  and unresolved convergence-rate and finite-size limitations.\n- Onsager's original 1931 reciprocal-relations analysis, separating\n  thermodynamic positivity from coefficient reciprocity, equilibrium from\n  detailed balance, the chemical triangle analogy from the fluctuation proof,\n  ensemble-average regression from pathwise dynamics, and now retaining the\n  printed simple-crystal equations (4.3)-(4.10): energy-displacement moments,\n  transverse fluctuation moments, force and flux laws, regression drifts, opposite-sign delayed\n  correlations, and reversal symmetry. Their checked comparison forces\n  equation (4.11), `omega_3 = 0`, before the abstract reciprocal-coefficient\n  result is used. The module also keeps the macroscopic time-and-length\n  regime, dissipation and stationary-flow variational principles, magnetic\n  and Coriolis exceptions, and the general transport theorem deferred beyond\n  Part I.\n- Nyquist's original 1928 thermal-noise argument, separating total\n  equilibrium exchange from frequency-local balance, the nondissipative\n  filter argument, matched transmission-line mode counting, the classical\n  voltage-noise law, general impedance and current-noise propagation,\n  microscopic-carrier scope, and the qualified Planck-energy replacement.\n  Its equation-(7) thermal factor `h*nu/(exp(h*nu/(k*T))-1)` and\n  equation-(8) one-sided voltage spectrum are represented as an alternative\n  to the classical `4*R*k*T` law, with an explicit zero-point-free energy;\n  countermodels separate a named quantum replacement from the printed\n  formula and exclude Callen-Welton's later positive half-quantum term.\n- Callen and Welton's original 1951 generalized-noise argument, separating\n  quantum transition dissipation, zero-force equilibrium fluctuations, the\n  generalized quantum noise-dissipation relation and classical limit,\n  Brownian, vacuum-radiation, and acoustic applications, and the concluding\n  coherence interpretation from the broader theory left for future work.\n- Kubo's original 1957 linear-response argument, separating weak\n  Hamiltonian response, the value-level phase-space response, after-effect\n  function, and past-time pulse convolution of equations (2.8)-(2.10), the\n  ensemble-to-observation qualification, canonical relaxation and static\n  limits, equilibrium correlations, exact magnetic and conduction formulas,\n  field-reversed reciprocity, fluctuation-dissipation, sum rules, Einstein\n  relations, and the paper's deferred applications.\n- Nakano's original 1956 conductivity argument, separating arbitrary-time\n  causal current response, the equilibrium thermal current-correlation\n  kernel, value-level equations (1)-(4) for the convolution, thermal\n  integral, normalized trace, and spectral kernel, equation (5)'s explicit\n  positive-time integral and Boltzmann-weighted energy-delta sum, present\n  non-evaluability, and the distinct perturbative one-relaxation-time\n  approximation for a typical subsystem model.\n- Ramsey's original 1950 separated-oscillating-fields argument as the first\n  dedicated atomic, molecular, and optical benchmark. It separates matched\n  pulse interactions from fixed-field phase evolution, single-velocity\n  probability from beam averaging, near and far approximations from the\n  interpolated middle interval, calculated line shape from Kusch's reported\n  potassium comparison, and general method advantages from proposed or\n  experiment-specific applications.\n- Noether's original 1918 invariant-variational-problem analysis, separating\n  finite-parameter divergence relations from arbitrary-function\n  Euler-Lagrange identities, retaining equation (13)'s finite-generator\n  `sum_i psi_i delta u_i^(lambda) = Div B^(lambda)` relation and both\n  converses, retaining equations (15)-(16)'s arbitrary-function-weighted\n  alternating derivative sum and vanishing identities, and separating\n  on-shell `Div B = 0`, multidimensional conservation, one-dimensional\n  first integrals, and Hilbert-energy consequences.\n- Hohenberg and Kohn's original 1964 inhomogeneous-electron-gas argument,\n  separating exact nondegenerate density determination and the\n  representable-density variational principle, including exact attainment of\n  the physical ground energy and a quantified minimum, from nearly uniform\n  response, the strictly nonconvergent but author-expected asymptotic status\n  of the slowly varying gradient series, and untested partial-summation routes.\n- Kaplan, Savage, and Wise's original 1998 nucleon-nucleon expansion,\n  separating pionless PDS and RG matching, large-scattering-length mixed\n  power counting, explicit-pion subleading completion, scale accounting,\n  numerical fit evidence from its validity interpretation, empirical fit\n  limitations formalized as an empirically adequate but uncontrolled\n  truncation, and mixed-order coupled-channel predictions.\n- Blatt and Jackson's original 1949 neutron-proton analysis, separating\n  Schwinger's stationary functional, controlled zero-energy reduction,\n  a shared controlled order-`k^2` truncation with explicit remainder,\n  intrinsic-range underdetermination, deuteron continuation, triplet and\n  singlet data status, higher-order shape sensitivity, and the conditional\n  Section VIII extraction of well parameters and interpolation formulas from\n  any assumed conventional well shape, with formula-validity and\n  exact-solvability qualifications retained. The distinct square and Yukawa\n  realizers also establish, in the selected low-energy context only,\n  derivational reduction together with autonomous multiple realization.\n- Einstein's original 1905 special-relativity paper and Minkowski's original\n  1908 space-time lecture, retaining their operational, kinematic, causal,\n  dynamical, electromagnetic, and qualified interpretive routes separately.\n  They jointly earn only the narrow inertial-frame inference from a finite\n  invariant light structure, two explicitly distinct selected frames,\n  admissible frame reexpression, law covariance, and an explicit physical\n  no-preferred-frame bridge; synchronization,\n  coordinate calculations, rods and clocks, causal cones, proper time,\n  force laws, point-charge fields, and Minkowski's gravity proposal remain\n  paper-local. Minkowski's local section-I route now retains the printed\n  positive-`c` upper hyperboloid\n  `c^2 t^2 - x^2 - y^2 - z^2 = 1`, the selected\n  `(x,y,z,t) -> (x',y,z,t')` preservation relation, and a checked\n  derivation of the transformed upper-sheet equation; this coordinate formula\n  is deliberately not promoted into the neutral shared inference. Their paper-local\n  countermodels are now value-bearing. Einstein's original pp. 892-893 clock\n  readings retain emission, reflection, and return times: equal outbound and\n  return durations fix the reflection reading to the midpoint, while the same\n  two local endpoint readings admit an asymmetric distant assignment.\n  Section 3 retains a finite-light rescaling counterexample; Section 4 keeps\n  squared length contraction distinct from intrinsic deformation; Sections\n  5 and 10 retain parallel velocity composition, the stated longitudinal and\n  transverse mass conventions, and an independently falsifiable force law.\n  Minkowski's separate-print pp. 3-14 countermodels retain a preserved\n  quadratic value off the unit hyperboloid, a null orientation signal with a\n  superluminal material counterexample, covariant law residuals on distinct\n  situations, a timelike worldline without the point-mass force equation,\n  distinct electric/magnetic transverse components with the same field\n  invariant, and bounded Kepler/tested-observation residuals with an\n  uncontrolled untested residual. No enum truth table substitutes for these\n  physical distinctions. Typed shared countermodels\n  keep light preservation, law covariance,\n  and physical no-preference independent, while a collapsed one-frame model\n  shows why mere reflexive covariance is insufficient. A nonvacuous\n  source-shaped model realizes the complete two-frame route. The established\n  result is output-led: exact selected semantics and\n  `NonvacuousInertialFrameKinematicsAt` are retained, while the derivation\n  route is reconstructible rather than stored. In that direct result,\n  distinct inertial frames, common-situation representation, finite light,\n  one actual preserving reexpression, law covariance, and no-preference all\n  hold together. Both papers derive that direct proposition. Semantic\n  grounding requires the paper's inhabited two-frame and finite-light setup\n  but no transformation, covariance, no-preference bridge, route, or terminal\n  result. An empty-setup countermodel blocks vacuous implication-shaped\n  bridges from faking it, and\n  direct mutation theorems make every selected object and relation family\n  falsify it when changed. Independent source-valued framework witnesses now\n  also retain Einstein's `0,2,4` synchronization, `c=5`, `v=3`, and\n  `gamma=5/4` Lorentz boost, relative simultaneity, undeformed intrinsic rod,\n  oriented clock dilation, and `25/7` velocity composition. Minkowski's\n  separate witness retains the upper hyperboloid, distinct null/timelike\n  quadratic values, an independently supplied world postulate, and qualified\n  gravity/universality boundaries. These are concrete historical\n  countermodels, not additional assumptions of the neutral shared route;\n- Einstein's original 1916 general-relativity synthesis, separating the\n  physical motivation for extended relativity, operational covariance,\n  metric meaning, geodesic extension, vacuum and sourced field equations,\n  the independent limitation on source selection from relativity alone,\n  conservation, the Newtonian limit, and static-field predictions.\n- Schwarzschild's original 1916 exact exterior point-mass solution,\n  separating the determinant-preserving coordinate construction, reduced\n  vacuum equations, exact integration and uniqueness, finite-approximation\n  limitation, orbital and Mercury calculation, practical radial comparison,\n  circular-orbit law, and conditional molecular analogy.\n- Kerr's original 1963 algebraically special spinning-mass solution,\n  separating the imported Goldberg-Sachs characterization, diverging\n  nonorthogonal null-congruence ansatz, massless and massive integrability\n  branches, degenerate stationary specialization, exact Type-D vacuum\n  metric with its displayed stationary line element, asymptotic coordinates\n  with the Euclidean-radius quartic relation and ring-exception scope,\n  third-order EIH identification of mass and angular momentum, and unresolved\n  exact multipoles and interior solution.\n- Penrose's original 1965 gravitational-collapse theorem, separating the\n  symmetry limitation of earlier exact models, nonspherical trapped-surface\n  construction, null-energy focusing, compact causal boundary, noncompact\n  Cauchy topology obstruction, future null incompleteness, physical\n  alternatives, and the absence of a curvature-divergence or black-hole\n  theorem.\n- Hawking's original 1965 open-universe argument, separating the expanding\n  flat/open cosmological model, large-sphere past-null convergence,\n  past-trapped-surface construction, imported global incompleteness route,\n  finite-margin perturbation robustness, weaker matter-flow conditions, and\n  the open closed-universe extension.\n- Guth's original 1981 inflationary-universe proposal, separating the\n  horizon and flatness diagnosis, entropy criterion, false-vacuum mechanism,\n  local-patch argument, conserved-charge and monopole consequences, the\n  graceful-exit failure, including near-complete converted volume without\n  percolation, and the unresolved modification outlook.\n- Goldstone, Salam, and Weinberg's original 1962 broken-symmetry analysis,\n  separating the perturbative inverse-propagator argument, the general\n  conserved-current spectral proof, the charge-and-Lorentz argument,\n  approximate composite-order-parameter extension, and unresolved\n  alternatives.\n- Anderson's original 1963 plasmon analysis, separating the uncoupled\n  superconducting matter spectrum from the interacting physical spectrum,\n  gauge-invariant finite-frequency plasma response, Coulomb conversion of the\n  Goldstone mode, the nonrelativistic massive-vector analogy, and unresolved\n  non-Abelian extension.\n- Bardeen, Cooper, and Schrieffer's original 1957 superconductivity theory,\n  separating effective attraction, the coherent variational ground state, the\n  qualified common-pair-momentum persistent-current argument, zero- and\n  finite-temperature gap calculations, thermodynamics, case-I/case-II\n  coherence factors, Meissner/Pippard response, empirical comparisons, and\n  the explicitly unfinished model, transport, and strong-coupling extensions.\n  Its zero-temperature route now retains the paper-local equation-(2.40) gap\n  value, equation-(2.50) quasiparticle dispersion, and equation-(2.49)\n  pair-breaking threshold value rather than only named gap predicates.\n- Feynman 1954, Feynman-Cohen 1956, and Girvin-MacDonald-Platzman 1986 as a\n  cross-system variational-excitation benchmark. The helium and fractional\n  Hall vocabularies remain paper-local; only the density-mode trial-state\n  construction, energy calculation, and fixed-momentum upper-bound inference\n  are shared. Feynman 1954 and GMP 1986 independently earn the component,\n  while Feynman-Cohen is retained as a dependent refinement. Feynman's seven\n  calculation-dependent stages are output-led, its shared adapter consumes\n  only the terminal established spectrum, and a staged countermodel separates\n  all seven vacuous calculation contracts from the paper's physics. Its\n  paper-local later chain now also retains Eq. (25)'s free-energy integral,\n  Eq. (26)'s Bose occupation, and Eqs. (39)-(43)'s moving-energy,\n  distribution, normal-density, and current formulas, including Eq. (41)'s\n  selected position, local `v_s(r)`, and checked substitution into the\n  same constrained occupation as Eq. (40), without widening the shared\n  variational component. GMP's\n  nine stages are likewise output-led, including explicit certified\n  unprojected-diagnosis and projected-trial intermediates. Its paper-local\n  source model now evaluates actual noncommuting complex density matrices,\n  equation (4.18)'s Gaussian cyclotron subtraction, a three-state positive\n  density-response measure, its exact zeroth and first moments, and the\n  unsaturated 98% oscillator-strength fraction. A quartic visible response\n  with a density-dark excitation below every proposed gap demonstrates why\n  the source's finite first moment cannot prove an exact many-body gap. Its\n  shared adapter consumes only the terminal projected bound, while 20\n  inhabited countermodels retain both the nine vacuous-contract distinction\n  and these physical nonimplications. Both independent terminal\n  routes now also realize a typed structural explanation of the selected\n  sector-energy upper bound, without asserting exactness, saturation, or\n  accuracy. The later Feynman-Cohen paper now follows the complete article\n  through eighteen routes: inherited spectrum,\n  packet continuity, return flow, exact symmetrization and linearization,\n  diffraction data, zero-temperature identities, corrected Kirkwood input,\n  separate norm and numerator calculations, optimization, momentum scope,\n  error budget, thermodynamic qualifications, and vortex interpretation. Its\n  paper-local scalar spine now retains Eq. (9)'s\n  `E_1(k) = hbar^2 k^2 / (2 m S(k))`, Eq. (61)'s printed backflow quotient\n  with the source coefficients and denominator condition, and Eq. (63)'s\n  `1.85 inverse Angstrom` optimized momentum and `11.5 K` gap. These packages\n  remain staged in the simple benchmark, improved spectrum, and optimized\n  gap rather than widening the shared variational component.\n- Anderson 1958 as the locator-expansion, probabilistic-localization,\n  isolated-system no-diffusion, and inverse-cube-boundary benchmark. Its\n  Green-function-decay route now supplies one independent realization of the\n  shared resolvent-decay-localization component while the locator expansion\n  and transport conclusions remain paper-local. The first-order lane now also\n  retains pp. 1495 and 1498 equations (9), (11), and (28) as a typed\n  paper-local readout:\n  the off-diagonal squared-coupling locator sum and\n  `Im V_0(s) = -s X(s)`. Lean checks denominator positivity and the\n  nonpositive imaginary-self-energy consequence at positive Laplace scale;\n  a countermodel prevents a named locator-distribution calculation from\n  supplying those equations by itself. The same lane now retains pp. 1498-1499\n  equations (29)-(33): the Fourier representation of `P(X)`, the\n  characteristic-function exponent, the radial-energy integral with explicit\n  integrability hypotheses, equation (32)'s small-`x` approximation,\n  and equation (33)'s large-`X` heavy-tail density. Lean checks positivity\n  and the inverse-three-halves envelope of that density; a second countermodel\n  prevents a named heavy-tail output from supplying equation (33).\n- Abrahams et al. 1979 as the analytic one-parameter localization-scaling\n  hypothesis benchmark.\n- MacKinnon-Kramer 1981 as the finite numerical localization-length collapse\n  and reconstructed-conductance scaling benchmark.\n\nThe active expansion is deliberately balanced across classical mechanics,\nstatistical mechanics, plasma physics, atomic, molecular, and optical physics,\nquantum mechanics, quantum field theory, general relativity, cosmology,\ncondensed matter, nuclear physics, and string theory. All eleven listed\ninitial rows are now active. See\n`docs/architecture/balanced-paper-benchmarks.md`. The cross-paper extraction\ndecision is recorded in\n`docs/architecture/technical-framework-reuse-audit.md`.\n\nThese reconstructions independently require named argument routes for\nprovenance, so route grouping and route-dependency validation are shared\nsource-mapping infrastructure. Their semantic vocabularies and theorem\nhypotheses remain paper-local.\n\nRoute dependencies are declared as immediate edges. The shared validator\ncomputes their transitive closure, makes every ancestor route's declared\noutputs available to descendants, and separately checks topological order.\nInternal intermediate claims do not leak across route boundaries. A later\nroute that needs one must require the producing route to export it explicitly.\nPaper source maps therefore record both the actual argument graph and honest\nroute interfaces rather than flattening every ancestor into each `dependsOn`\nlist.\n\nJustification statuses also propagate through the actual claim-premise graph.\nThe basis retains both each status and the exact source-mapped step that\nintroduced it. This keeps distinctions that matter to the papers: a\nconclusion may remain conjectural, approximate, deferred, expected,\ninterpretive, or unresolved, while an independent calculation in the same\nroute does not inherit those statuses merely by route membership. Exact\nstep origins lead back to primary-source anchors; logical conditionality\nencoded inside a claim's formula remains separate from this provenance\nanalysis.\n\nAuditable source maps give every claim node exactly one producing step. When\ntwo routes establish the same physical proposition, they use distinct claim\nidentifiers whose formulas may coincide. This preserves each route's exact\npremises and epistemic history instead of merging alternative derivations.\n\nPaper-local structures represent quantitative physical outputs as data,\nconstrained by proposition-valued definitions and checked equalities rather\nthan used as proof registries.\n\nTemporary reductio assumptions have explicit discharge steps. Their\nepistemic origin propagates through internal intermediate claims, is removed\nonly by the named discharge, and is excluded from route outputs and inherited\ndependency claims. The route validator also rejects a discharge placed in a\ndifferent route from its temporary assumption.\n\nOrdinary routes are semantically executable. Certified predecessor routes\nsupply their declared outputs, and sound local steps propagate truth in route\norder to derive the descendant route's outputs from the graph itself.\nCoverage proofs therefore need not establish the same outputs independently.\nRoutes containing temporary reductio introductions remain explicit paper-local\nproofs because those assumptions are valid only inside their discharged\nsubarguments.\n\nThe previous broad-library, global-assumption, and metadata-heavy experiments\nare preserved under `deprecated/`. They remain available as historical source\nmaterial but sit outside the Lean package tree and cannot be imported by the\nactive root. Reuse requires a fresh primary-source comparison and must satisfy\nthe current paper-first rules.\n\nFramework-to-framework imports are also exact audited interfaces. Every child\ndependency must enter a declared semantic context, model, or compatibility\nbridge and must be used by a checked parent deduction or refinement theorem.\nThe policy derives all such edges from the Lean imports and rejects missing,\nstale, or merely decorative dependencies. The current 31-edge audit is\nrecorded in `docs/architecture/technical-framework-reuse-audit.md`.\n\n## Active Layout\n\n- `PhysicsLogic/Framework/ActionPhaseComposition.lean`: the narrow\n  action-phase, intermediate-composition, and stationary-action route\n  independently realized by Dirac 1933 and Feynman 1948. Their transformation\n  function and path contribution remain distinct paper-local amplitude data;\n  Dirac's adapter now retains value-level equations (7)-(9), the selected\n  binary intermediate-coordinate integral from equation (11), and the\n  derivative-zero stationary-action condition as explicit propositions rather\n  than only named phase, composition, and stationarity predicates.\n  no duplicate route-mode enum is retained. The context owns ten selected\n  indices and exposes their unique exact model; changing any selected index or\n  any of fifteen relation families fails the original context's exact\n  semantics. The established result is output-led: exact selected semantics\n  is conjoined directly with `NonvacuousActionPhaseCompositionAt`, where the\n  complete setup, phase,\n  composition, zero-parameter-limit, cancellation, and stationary-action chain\n  holds at one model. It stores no implication-valued calculation or route\n  proof; those contracts are reconstructed from the direct relations. A\n  false-setup countermodel blocks both vacuous contracts and grounding,\n  and exhaustive direct mutations make every selected index and relation\n  family destroy that proposition. Both paper adapters derive the direct\n  result from their source-anchored routes. The ordinary structural\n  explanation executes the shared route without requiring paper provenance.\n  A stricter source-sensitive explanation begins from ten granular Dirac\n  premises or fifteen granular Feynman premises, retains a typed paper-local\n  derivation, exposes it, and entails the ordinary explanation when provenance\n  is forgotten. Neither explanation accepts a terminal paper or framework\n  result. The ordinary constraint, source wrapper, stationary-action\n  phenomenon, and paper-local derivation types remain distinct. A converse\n  model retains the complete endpoint, route, and ordinary explanation but has\n  no source-sensitive explanation when its source derivation is false. The same endpoint realizes\n  the mature controlled-classical-recovery contract at the explicit zero\n  limit: phase/composition supplies the valid quantum description,\n  cancellation and stationary selection supply the recovery calculation, and\n  stationary action supplies the classical behavior. A finite-small/no-zero-\n  limit countermodel blocks conflation with approximate recovery, and no\n  exact-replacement judgment is inferred. Theory/model/world grounding\n  separately requires exact selection, the real endpoint/history/partition\n  setup, and the explicit zero-parameter limit, but no phase, composition,\n  cancellation, or stationary-action output. A setup-complete model can be\n  grounded while composition still fails. It defines no path measure, probability\n  rule, wave function, Schroedinger equation, operator algebra, or\n  field-boundary functional.\n  A checked limit boundary now retains all ten selected phase/composition\n  indices together with positive finite Planck and action scales,\n  nonstationary action variation, cancellation residual, finite stationarity\n  residual and tolerance, and the separate limiting Planck and stationarity\n  residuals. Its exact model bridge retains the inhabited setup, phase,\n  composition, endpoint, and cancellation facts. Dirac and Feynman each\n  realize finite-small stationary-phase dominance while the zero-limit and\n  exact stationary-action endpoint fail; a positive shared witness supplies\n  both zero residuals. No constant small-parameter predicate substitutes for\n  these scales, residuals, or the limiting condition.\n  A second checked boundary now makes the earlier logical separation\n  value-level as well: `ActionPhaseCompositionBoundaryReadout` retains a\n  positive Planck scale, action, nonzero complex normalization, local\n  amplitude, endpoint amplitude, and independently calculated intermediate\n  composition. Its local-phase predicate is the explicit normalized\n  `exp(i S / hbar)` equality, while its composition predicate is a separate\n  endpoint equality. The shared, Dirac, and Feynman countermodels all realize\n  the former and fail the latter. The remaining paper-local countermodels no\n  longer use enum truth tables: Dirac retains ordered momentum derivatives,\n  endpoint/time-step phase, boundary geometry, and probability/grounding\n  residuals; Feynman retains measured and coherent sums, short-time errors,\n  temporal-memory/additivity defects, Gaussian and two-history values,\n  final-state sums, formal-equation residuals, and measurement/prediction\n  scope. These are checked physical non-implications, not renamed status\n  labels.\n  Feynman's paper-local path endpoint now nevertheless retains the original\n  finite-time formulas before any shared extraction: equation (9)'s\n  time-slicing limit of the regional path integral, the explicit\n  `exp(i S[path] / hbar)` contribution with partition-dependent common\n  normalization, equation\n  (10)'s segmented action sum, and equation (11)'s minimum classical segment\n  action. Equation (12)'s normalized exponential regional path integral is\n  now a separate value-level endpoint supplied by an explicit calculation\n  contract that combines equation (9), the action-phase formula, and equation\n  (10), while equation (11) remains the separate definition of segment\n  action. The limit, integral, minimization, and normalization remain imported\n  mathematics. The same paper-local adapter now also retains journal equation\n  (18)'s first-order one-step recursion and equations (22)-(30)'s selected\n  one-dimensional scalar-potential derivation. The readout owns represented\n  mass, Planck constant, time step, potential, wave function, derivatives,\n  action, normalization, and real-line integral data. Equation (18) carries\n  its bounded second-order residual, equations (22) and (23) use a\n  positive-side little-o-of-epsilon witness for the source's\n  smaller-than-first-order error, and equation (24) records its exact change\n  of variables while reusing equation (23)'s residual. Equations (25), (27),\n  and (29) keep controlled Taylor residuals, while equations (26), (28), and\n  (30) retain the Gaussian moments, normalization square, and resulting\n  Schroedinger equation. A countermodel prevents a named wave-equation output\n  from replacing these source formulas.\n- `PhysicsLogic/Framework/CompleteIntegralDynamics.lean`: the narrow\n  complete-integral trajectory-reconstruction route independently realized\n  by Hamilton 1834 and Jacobi 1837. Its exact model retains twelve selected\n  physical indices and nine relation families: a represented evolution, one\n  selected first-order equation, a separately complete parameter family,\n  separate momentum and parameter derivative calculations, motion recovery,\n  and a separate completeness calculation. `CompleteIntegralAt` is the\n  conjunction of first-order equation satisfaction and parameter-family\n  completeness; finite countermodels show that neither conjunct supplies the\n  other. Jacobi's adapter now keeps the endpoint-defined principal function\n  separate from the arbitrary complete integral used for reconstruction, and\n  selects the latter for the shared model; a countermodel blocks promotion of\n  endpoint-principal data into arbitrary-complete-integral data. Jacobi's\n  paper-local route now also retains p. 104's value-level Hamilton-Jacobi\n  equation and pp. 107-109's parameter, velocity, momentum, and Newton\n  recovery formulas at a selected configuration and time; those one-paper\n  formulas are not exported into the shared component. The selected\n  evolution is exposed through `Paradigm.Dynamics.Dynamics`, and each completed paper route now\n  supplies an inhabited `HasForwardEvolutionAt` witness. A route-complete\n  finite model nevertheless has two distinct continuations from the same\n  initial configuration and time, blocking promotion of reconstruction to\n  `ForwardDeterministicAt` or `UniqueForwardEvolutionAt`. This is a limit of\n  the shared contract, not a claim that either source theory branches.\n  The complete route also realizes a typed structural explanation of the\n  selected solved motion and complete family of motion integrals. Its\n  constraint contains the complete-integral setup and four implication-valued\n  calculations but no reconstruction output. A finite model declares both\n  outputs while invalidating the setup and therefore has no explanation; a\n  separate branching model has the explanation without determinism or\n  uniqueness. Hamilton and Jacobi rebuild the explanatory route from their\n  original granular calculations rather than established recovery bundles.\n  A separate proof-free source constraint now retains their derivational\n  difference. Hamilton's typed token requires varying action, opposite-signed\n  endpoint derivatives, parameter recovery, and characteristic-equation\n  verification; Jacobi's requires the endpoint-derived PDE and the theorem for\n  a separately selected arbitrary complete integral. A converse model keeps\n  the complete route and reconstructed outputs while making the source\n  relation false, so common output cannot manufacture paper provenance.\n  Technical completion and theory/model/world grounding remain independent.\n  It defines no action,\n  Hamiltonian, energy law, canonical geometry, Kepler problem, general\n  characteristic system, or Pfaff theory.\n- `PhysicsLogic/Framework/ParentActionDualReduction.lean`: the narrow local\n  parent-action route independently realized by Rocek-Verlinde 1991 and de la\n  Ossa-Quevedo 1992. An exactly selected symmetry is gauged with an auxiliary\n  field and flatness constraint; separate paper-local eliminations recover\n  the original action and produce a dual action. The established result\n  projects the complete setup, both elimination calculations, and both action\n  outputs. Typed countermodels keep the eliminations independent, prevent the\n  two outputs from reconstructing a missing setup, and exhibit a completed\n  local reduction whose actions are not physically equivalent. Technical\n  completion and theory/model/world grounding are independent in both\n  directions. Its nine selected indices, eight route-used relation families,\n  exact model retention, exhaustive transfer, and seventeen-component\n  mutation audit are checked. The established result projects to\n  `NonvacuousParentActionDualReductionAt`, where validity, description,\n  symmetry action, gauging, flatness, gauge fixing, and both elimination\n  outputs hold directly at one model instead of only behind implication-valued\n  calculations. It also projects to two separately typed\n  `DerivationBridge` results: constraint-field elimination realizes recovery\n  of the original action, while auxiliary-field elimination realizes\n  production of the dual action. Their combined result is only a conjunction\n  of those two derivations, not an equivalence relation between the actions.\n  A proof-free source description now retains the exact selected model and a\n  typed paper-local derivation. Rocek-Verlinde realize it from the raw\n  first-order bosonic setup and calculation; de la Ossa-Quevedo realize it\n  from the nonabelian setup, parent path-integral construction, and elimination\n  calculation. The generic source theorem executes both branches without an\n  established or nonvacuous endpoint. A converse model retains both completed\n  outputs and output-led reductions while falsifying the independent source\n  relation, so the source-sensitive reductions do not follow.\n  One-sided countermodels show that either derivation can hold without the\n  other. A false-setup model shows why the implication-shaped\n  calculations alone are insufficient. The retained sensitivity model\n  realizes that direct proposition, and changing any of its nine selected\n  indices or eight relation families destroys it. Both paper adapters expose\n  both derivational results while scoping every relation to their exact\n  selected actions, fields, symmetries, and regimes. It deliberately asserts no global equivalence,\n  conformality, determinant correction, transformation rule, or surviving\n  dual symmetry.\n- `PhysicsLogic/Framework/AmplitudeOutcomeProbability.lean`: the narrow route\n  independently realized by Born 1926 and Kennard 1927 from an exactly\n  selected valid state and an admissible amplitude associated with that state\n  in a selected representation, through a paper-local outcome-weight\n  calculation, to a separate paper-local probability interpretation. Its\n  proof-free model retains eight selected\n  indices and eight route-used relation families. Its output-led established\n  result contains exact selected semantics and\n  `NonvacuousAmplitudeOutcomeProbabilityAt`, where all eight route-used\n  physical relations hold together at one selected situation rather than\n  behind implication-valued calculation wrappers. Complete setup, calculation\n  contracts, the interpretation bridge, and the route are reconstructed from\n  those direct facts. Grounding requires the complete selected setup but no\n  calculated weight or assigned probability. Typed countermodels separate\n  setup from calculation, calculation from interpretation, the assigned\n  probability from its derivation, and technical completion from\n  theory/model/world grounding in both directions; a false setup can keep the\n  implication contracts true without satisfying the direct proposition. Exact\n  selected setup and raw route now give an ordinary structural explanation of\n  the calculated-and-interpreted probability phenomenon. A stronger\n  source-sensitive explanation adds a typed paper-local derivation: Born's\n  token requires elastic scattering asymptotics; Kennard's distinct token\n  requires transformation and alternative exact-observation inputs. Neither\n  source theorem consumes the completed endpoint or ordinary explanation, and\n  a countermodel proves that completed outputs plus ordinary explanation cannot\n  reconstruct missing source provenance. Exact model retention,\n  exhaustive claim transfer, and a sixteen-component mutation\n  audit are checked. The retained finite model realizes the direct complete\n  route, and exhaustive direct mutations make every selected index and\n  relation family destroy that proposition itself. The neutral shared route\n  stops at the paper-local calculation relation, while governed source-valued\n  witnesses separately retain Born's normalized squared channel frequencies,\n  directional solid-angle weight, inelastic energy jump and `pi^2 k^2`\n  factor, plus Kennard's density-versus-interval distinction, Gaussian\n  `hbar/2` saturation, and regulated transformation kernel. Deterministic\n  wave evolution does not establish deterministic outcomes or ontic\n  indeterminism.\n- `PhysicsLogic/Framework/Entanglement.lean`: the bipartite\n  nonseparability route independently realized by Coffman-Kundu-Wootters 2000\n  and AMPS 2012, with a further finite-density-matrix client in Bell 1964.\n  `FiniteQuantumState` supplies positive unit-trace operators, actual partial\n  traces, convex product-mixture separability, spectral entropy, and a proved\n  partial-transpose witness bound. Its model retains a prepared parent state, selected reduced\n  joint state, two distinct subsystem roles, separability, classical\n  correlation, purity, an independent witness calibration, witness value, and\n  marginal entropy. A positive witness is insufficient: the checked route\n  also requires calibration plus the selected separable-state upper bound\n  before deriving nonseparability. The output-led established result retains\n  exact selected semantics, the direct nonvacuous prepared-pair endpoint, and\n  calibration without storing a route object. CKW supply squared-concurrence\n  tangle plus a zero-tangle bridge; AMPS supply thermal late-mode entropy plus\n  pure-pair separable-entropy bridge. The shared layer identifies neither\n  tangle with entropy nor entanglement with correlation, Bell violation,\n  signalling, or a sharing inequality. It projects only inhabited\n  nonseparability to `Paradigm/QuantumNonseparability.lean` and composes with\n  tripartite sharing through an explicit pair-to-demand handoff. A finite\n  countermodel keeps a positive nonseparable state while deleting witness\n  calibration, so endpoint truth cannot reconstruct the source route. Its\n  ordinary structural explanation retains only the common calibrated-witness\n  route; source-sensitive explanations keep distinct CKW tangle and AMPS\n  pure-pair entropy derivation tokens, with a false-provenance countermodel\n  blocking reconstruction from ordinary explanation. Source-sensitive\n  tripartite composition additionally requires independent bipartite,\n  sharing-exclusion, and pair-to-demand derivations; CKW's dominant `AB`\n  channel yields the constructive endpoint, while AMPS's competing `BC`\n  channel yields the checked contradiction. A finite countermodel retains\n  both sourced child explanations and ordinary composition while withholding\n  the source derivation for their handoff. CKW's paper-local residual keeps\n  all eight complex state amplitudes and the original four diagonal, six\n  planar, and two tetrahedral monomials. Lean derives\n  `tau_ABC = 4 * abs(d1 - 2*d2 + 4*d3)` from the explicitly imported\n  determinant calculation on the two-dimensional range, not the vanishing\n  full four-dimensional determinant. The individual polynomials are invariant\n  under generating qubit swaps; the normalized GHZ state has unit residual,\n  every single-excitation state has zero residual and saturates its pairwise\n  bound, and actual planar and phase-reversed tetrahedral states require the\n  printed `-2`, `4`, and absolute-value factors. Residual permutation\n  invariance is itself a derived equality of the same physical tangle with\n  the original and both permuted polynomial values, not an independently\n  asserted proposition or paper-framework field.\n- `PhysicsLogic/Framework/StateDispersionUncertainty.lean`: the narrow\n  prepared-state dispersion route independently realized by Kennard 1927 and\n  Robertson 1929. A valid selected state and two observables receive\n  paper-local dispersion readouts, a paper-local lower-bound value, and an\n  explicit product-bound calculation. Its proof-free model retains all nine\n  selected indices and exactly the six relation families used by the route.\n  Each paper-local context owns those nine values and constructs one exact\n  `selectedModel`; all nine index mutations and all six relation mutations\n  fail selected semantics. Kennard and Robertson supply that certificate\n  before applicability can be established. The retained finite model itself\n  realizes the complete route with distinct observables and role-matched\n  distinct dispersions. The output-led established result is exact selected\n  semantics together with `NonvacuousStateDispersionUncertaintyAt`, where\n  validity, preparation, both\n  observable selections, both represented dispersions, the selected lower\n  bound, and the product relation hold together at one model instead of\n  hiding behind implication-valued calculation contracts. A false-setup\n  countermodel cannot exhibit that proposition, and exhaustive direct\n  mutations make every selected index and retained relation destroy it.\n  The older direct activity theorems independently show that every selected\n  index and retained relation changes a route-used proposition.\n  The complete route now also realizes a typed structural explanation of the\n  selected state-dispersion lower-bound phenomenon. Its constraint contains\n  the nine selected values but no dispersion representation, bound\n  identification, or product inequality. Kennard and Robertson derive the\n  explanation from their direct route adapters without consuming the\n  established or nonvacuous endpoint. A false-validity model has all terminal\n  outputs but no explanation, while a route-complete zero-bound model shows\n  that structural explanation does not imply strict positivity.\n  A stronger source-sensitive constraint retains one typed paper-local\n  derivation and an independent proposition that it obtains. Kennard's token\n  is realized by his general amplitude factorization and nonnegative\n  remainder on pp. 338-339; Robertson's distinct token is realized by his\n  one-particle Hermitian-rms, integration-by-parts, Schwarz, and commutator\n  route on pp. 163-164. Both adapters construct this explanation directly\n  from raw source contracts. A countermodel preserves the complete route,\n  established shared result, and ordinary explanation while falsifying the\n  derivation relation, so common outputs cannot reconstruct source\n  provenance.\n  It stores no implication-valued calculation contracts; a checked theorem\n  reconstructs the complete route from the inhabited outputs. Separate\n  interpretations ground the exact named model and its valid prepared-state\n  and observable setup in each paper's theory and represented system. They do\n  not consume dispersion readouts, lower-bound calculations, product\n  inequalities, route applicability, or established results. Converse models\n  separate technical completion from grounding and grounding from technical\n  completion. A false prepared-state setup cannot be grounded even when every\n  declared theory and world claim is made true.\n  Both adapters expose named exhaustive certificates transferring every\n  retained claim through the explicit theory/model/world bridges. The\n  framework defines no measurement disturbance,\n  Gaussian packet, Fourier transform, commutator, operator domain, or\n  universally positive bound. Strict positivity remains outside the exact\n  model because Robertson's state-dependent bound may vanish. Heisenberg's\n  operational microscope argument therefore remains outside this component;\n  the new structural result is not an apparatus error-disturbance explanation.\n  Separate source-valued witnesses retain Kennard's pointwise amplitude\n  probabilities, doubled-variance precision and `h/(2*pi)` product bound,\n  Gaussian saturation, distinct arbitrary-amplitude factorization and\n  nonnegative remainder, mutually exclusive exact observations, and\n  classical packet-center motion with unavoidable initial spread. Robertson's\n  independent witnesses retain rms normalization and `h/(4*pi)`, Hermitian\n  observables, vanishing boundary terms, the Schwarz/commutator route, its\n  printed linear-momentum restriction, a valid zero-commutator state, and\n  extremal angular-momentum saturation. Thirty-four controlled mutations\n  reject swapped source formulas, missing proof hypotheses, false universal\n  positivity, an invented polynomial-operator proof, and identification with\n  apparatus error or disturbance.\n- `PhysicsLogic/Framework/OperationalErrorDisturbance.lean`: the narrow\n  apparatus-level inference independently realized by Heisenberg 1927,\n  Bohr 1935, and Ozawa 2003. Its exact model retains sixteen selected indices,\n  including\n  separate prepared-object and composite interaction-input states, and eleven\n  route-used relation families, including an explicit proposition-valued\n  bridge from preparation to interaction input. The context owns that\n  complete measurement instance and constructs one `selectedModel`; changing\n  any index therefore fails exact semantics instead of selecting a new model\n  from the candidate's own fields. The heuristic microscope, fixed-slit\n  diffraction/recoil, and operator-measurement universal routes remain\n  definitionally distinct. The\n  established result retains the selected preparation-to-input bridge,\n  measurement run, operational error and disturbance representations,\n  quantitative tradeoff, qualified scope, and explicit non-identification\n  with prepared-state dispersion. Operator\n  commutators, correlation terms, corrected inequalities, optical recoil,\n  quadrature transducers, and experimental proposals remain paper-local.\n  Countermodels separate preparation and performance from an interaction-input\n  bridge, performance from quantitative representation, representation from\n  tradeoff, and technical completion from theory/model/world grounding. The\n  complete applicable route now also realizes a typed structural explanation:\n  its constraint retains all sixteen apparatus data, while its distinct\n  phenomenon retains only the observable- and apparatus-indexed quantitative\n  tradeoff. All three papers realize it directly from their own route inputs.\n  A second, source-sensitive projection retains a typed derivation token and\n  its proposition-valued realization in addition to the complete ordinary\n  route. Heisenberg supplies the microscope setup, corrected recoil,\n  selected-Gaussian calculation, role distinction, and addendum scope as raw\n  premises; Bohr supplies his p. 697 fixed-support slit, prepared incident\n  plane wave, photographic record, de Broglie wavelength, local diaphragm\n  recoil, qualitative `Delta p Delta q ~ h`, and apparatus/state role\n  distinction; Ozawa supplies the system-probe setup, rms definitions,\n  commutator/correlation calculation, generalized relation, and formulation\n  separation. Their source theorems reach the same apparatus phenomenon\n  without identifying those derivations or accepting a shared terminal result.\n  Bohr's distinct p. 699 EPR preparation retains two narrowly separated slits,\n  two short incident wavelengths, and the shared preparation diaphragm's\n  measured before/after momentum balance. It fixes `q1 - q2` and `p1 + p2`\n  while leaving `q1 + q2` and `p1 - p2` undetermined. His actual local slit\n  state change independently realizes\n  `Philosophy.Measurement.StateChangeMeasurementContext.DisturbsAt`; a joint\n  theorem proves that this genuine local disturbance, the double-slit source\n  preparation, and the nonvacuous technical route all coexist with mechanical\n  nondisturbance of the remote particle for either later EPR arrangement.\n  Countermodels show\n  that a declared tradeoff without the preparation-to-input bridge and a\n  calculated tradeoff misidentified as prepared-state dispersion realize no\n  such explanation. A completed tradeoff and full ordinary route with a false\n  source relation also fail the source-sensitive explanation.\n  Sixteen index mutations and eleven relation mutations fail exact semantics,\n  while a direct audit proves that every selected physical value affects a\n  route-used predicate.\n- `PhysicsLogic/Framework/OneParameterLocalizationScaling.lean`: the narrow\n  localization-flow structure independently realized by Abrahams et al. 1979\n  and MacKinnon-Kramer 1981. Its proof-free context owns eight selected\n  physical indices and all fourteen route-used relation families, including\n  the three predicates negated by the qualified scope assessment. The\n  analytic block-composition and finite-size numerical-reconstruction methods\n  remain in distinct paper-local calculation and scope predicates rather than\n  a duplicate shared route tag. Each context constructs one named exact model,\n  supplies a retention certificate before applicability, and requires that\n  model in its theory/world interpretation. Shared projection and exhaustive\n  claim theorems preserve the complete route, while direct data-sensitivity\n  and mutation countermodels show that changing any retained index or relation\n  changes the formal semantics. Both clients now also project to a direct\n  output-led endpoint requiring the finite-scale setup, direct closure, flow,\n  regularity, asymptotic and dimensional outputs, and the complete qualified\n  scope, but no implication-valued calculation contract. Grounding separately\n  requires exact selected semantics and the finite-system setup while supplying\n  no scaling output or route. The ordinary structural explanation executes the\n  shared qualified scaling route without treating provenance as physics. A\n  source-sensitive refinement keeps the two derivations distinct: the 1979\n  client supplies analytic finite-hypercube block composition, while the 1981\n  client supplies recursive finite-bar collapse and reconstructed conductance\n  flow. Each source-facing adapter constructs applicability directly from its\n  component results rather than consuming the terminal paper result, and the\n  generic necessity theorem executes the scaling route rather than consuming\n  an established endpoint. A converse model retains the endpoint,\n  reconstructed route, ordinary explanation, and dimensional-flow phenomenon\n  but has no source derivation, so it has no source-sensitive explanation.\n  Countermodels enforce both directions\n  of the grounding separation, and direct mutations of all eight indices and\n  fourteen relation families destroy the endpoint. Thouless-number definitions, transfer\n  matrices, numerical error control, Landauer assumptions, crossover\n  calculations, critical data, and other mechanisms remain paper-local.\n- `PhysicsLogic/Framework/ResolventDecayLocalization.lean`: the narrower\n  propagation-kernel-decay route independently realized by Anderson 1958 and\n  MacKinnon-Kramer 1981. Its exact model retains five selected physical\n  indices and eight relation families. The clients select different concrete\n  kernels and descriptors, while analytic probabilistic convergence and\n  controlled finite-bar numerical status remain in paper-local calculations\n  and scope predicates rather than a duplicate route tag. Both clients supply\n  a decay calculation, a separate localization interpretation, and an\n  explicit exclusion of unqualified all-state localization. Anderson's\n  locator resummation, no-diffusion result, bath scope, and inverse-cube\n  transport remain outside the common route; source-valued audit readouts\n  nevertheless retain the positive-Laplace locator, rare-resonance heavy\n  tail, exact `Gamma(1/2) = sqrt(pi)` coefficient, physically correct\n  exponential suppression, and equation (19)'s normalized finite-width\n  disorder box `P(E) = 1/W` for `|E| \u003C W/2` and zero outside. The actual\n  paper's high-order path calculation owns that full value-level density;\n  shared source controls independently reject its wrong height, missing\n  support, incorrect Gamma factor, and altered suppression coefficient.\n  Coherent versus nonrepeating paths, isolated-system qualification,\n  finite-bar recursion, two- and three-dimensional sampled ranges,\n  `W_c = 16 +/- 0.5`, `nu = s = 1.2 +/- 0.3`, and explicit Landauer and\n  dominant-channel assumptions. Countermodels\n  separate setup, decay, interpretation, universality, and theory/model/world\n  grounding. The established route also projects to a direct nonvacuous\n  proposition requiring the selected setup, calculation, decay outputs,\n  interpretation, scoped localization, and denied all-state overclaim. A\n  false-setup model fails that endpoint, and direct mutations of all five\n  indices and eight relation families destroy it.\n- `PhysicsLogic/Framework/SpinOrbitShellClosure.lean`: the narrow\n  nuclear-shell inference independently realized by Mayer 1949 and\n  Haxel-Jensen-Suess 1949. Its proof-free context owns six selected indices\n  and the twelve proposition-valued relation families that make those\n  selections physically meaningful, and constructs one exact `selectedModel`.\n  Both papers use named exact models and named exact selected-setup adapters\n  in their applicability theorems, exhaustively realize all seventeen shared\n  claims, and transfer them through explicit theory/model/world grounding.\n  Grounding independently\n  requires `SelectedSpinOrbitShellClosureSetupAt`: the exact selected model\n  and its valid independent-particle\n  central-field setup; it is not indexed by an established closure result and\n  does not consume the spin-orbit, filling, comparison, or interpretation\n  routes. Converse models separate technical completion from grounding and\n  grounding from technical completion. Mayer's square-well route and\n  Haxel-Jensen-Suess's oscillator, anharmonicity, and Yukawa construction\n  remain paper-local. Mayer's close-within-shell/nonfixed-table-order\n  qualification, thallium near-degenerate crossing, and pair-only\n  `h11/2` caveat are not promoted into the shared route. The\n  Haxel-Jensen-Suess letter also retains its seven printed oscillator-group\n  labels, six complete multiplicities and cumulative totals, five explicit\n  closure sums from `8 + 6 = 14` through `112 + 14 = 126`, and the\n  opposite-parity rule between oscillator quantum number and orbital angular\n  momentum as a quantified modulo-two relation with concrete marked-orbital\n  occurrences. Its literal printed source-coordinate equation\n  `r = r1 + r2 + r3` remains distinct from physical zero-based Cartesian\n  occupations `N = nx + ny + nz`, which instead obey\n  `r = nx + ny + nz + 1`. The `r = 1` ground shell has the unique physical\n  `(0,0,0)` state; `(1,0,0)`, `(0,1,0)`, and `(0,0,1)` belong to `r = 2`.\n  The `r = 4`, `N = 3` shell retains all ten actual occupation triples,\n  their complete membership characterization, and their spatial cardinality.\n  Five independent value-bearing countermodels prevent conflating source and\n  physical coordinates, incomplete enumeration, or incorrect degeneracy.\n  The marked `d` through `i` terms additionally retain\n  `l = 2,...,6` and doubled `2j = 5,7,9,11,13` values, with a checked\n  deduction of their `j = l + 1/2` instances. The five closed-shell counts\n  now require an explicit assembly bridge before yielding the displayed\n  `{14, 28, 50, 82, 126}` pattern; the Mayer-compatible higher subset is\n  a checked erase-`14` projection rather than a second paper-local\n  calculation.\n  Mayer now likewise retains the full displayed\n  `{2, 8, 20, 28, 50, 82, 126}` sequence, an explicit ordered-filling\n  assembly bridge, and a checked erase-`2`/erase-`8`/erase-`20`\n  projection to the shared higher pattern. Her selected `f`, `g`,\n  `h`, and `i` partner pairs retain common orbital values and doubled\n  total-angular-momentum values, and both paper adapters make the shared\n  partner-splitting relation consume their checked `j = l +/- 1/2`\n  instances rather than trusting spectroscopic names. The repeated doubled-j\n  arithmetic itself is now the narrow shared proposition\n  `SpinHalfOrbitalPartnerRule`: it exposes both `j = l - 1/2` and\n  `j = l + 1/2` branches, proves their natural-number realizations, and has a\n  countermodel showing that a named partner does not supply the rule. The two\n  paper-local `JEqualsLPlusOrMinusHalf` predicates delegate to this shared\n  definition instead of carrying disconnected duplicate formulas.\n  A proof-free `ReducedNuclearInteraction` now retains positive potential\n  depth, radius, radial-profile exponent, spin-orbit strength, a checked\n  `f7/2` state count, and the calculated higher-closure list. Two physically\n  different potential readouts match `{28, 50, 82, 126}`, so closure\n  agreement does not determine the interaction. Their unit-scale depths,\n  radii, and profile exponents are logical witnesses, not historical nuclear\n  measurements. Mayer's source boundary `83`, qualified `h11/2`-`3s1/2`\n  parity adjacency, and incomplete tail remain paper-local; the HJS\n  `r = 4` to `r = 3` regrouping, `20 + 8 = 28`, and extra closure `14`\n  also remain paper-local.\n  The common\n  route now requires the higher-`j` partners\n  to be lowered and regrouped into the preceding shell relative to the two\n  selected schemes; a wrong-sign or merely nonzero splitting cannot satisfy\n  it. A finite source-shaped witness realizes the complete route with\n  distinct central/spin-orbit schemes and calculated/observed pattern values;\n  the established route projects to\n  `NonvacuousSpinOrbitShellClosureAt`, and direct activity theorems make all\n  six indices and twelve relations destroy that direct proposition when\n  changed. The direct endpoint also projects to a typed mechanistic\n  explanation of the observed closure pattern, keeping empirical prediction\n  separate from the physical-account bridge; a finite countermodel satisfies\n  the former while denying the latter. Here prediction means model-level\n  calculated-pattern agreement, not historical novelty. A second shared\n  projection separates ordinary `SpinOrbitShellClosureConstraint`, its\n  source-sensitive wrapper, and the distinct\n  `ObservedSpinOrbitShellClosurePhenomenon`. The ordinary theorem executes the\n  complete shared route without paper provenance; the stricter source theorem\n  adds an independently realized derivation token, exposes it, and entails the\n  ordinary explanation when provenance is forgotten. Haxel-Jensen-Suess supply\n  their oscillator-table, anharmonic-classification, marked-high-`j` filling,\n  and assessment route; Mayer supplies her square-well, strong-spin-orbit,\n  ordered-filling, bounded isotope-assessment, and qualified-interpretation\n  route. Neither theorem consumes the established or nonvacuous shared\n  endpoint. A finite converse model retains the complete shared result and\n  ordinary explanation while denying source derivation, so reusable route\n  logic does not manufacture provenance. A vacuity\n  countermodel prevents implication-valued shell calculations without setup\n  from counting as an inhabited closure route.\n- `PhysicsLogic/Framework/Charge.lean`: the first shared technical-framework\n  component, extracted from the independently realized chiral-charge sectors\n  of Witten 1982 and the Seiberg-Witten 1994 electromagnetic BPS\n  sectors, and now also realized by Maldacena's quantized D3 five-form charge,\n  Polchinski's D-brane Ramond-Ramond charge, Laughlin, Haldane, and\n  Arovas-Schrieffer-Wilczek fractional excitations, and charged Maxwell lines.\n  Seiberg-Witten's seventeen independently audited paper-local boundaries\n  retain projective singularity support, the printed monodromy matrices and\n  their fixed `(1,0)` and `(1,-1)` charges, the exact monopole-point values\n  `a_D(1) = 0` and `a(1) = 4 / pi`, period and BPS mass values, candidate\n  counts, asymptotic Higgs winding, quantized magnetic flux, distinct\n  F-term and D-flat vacuum equations, nonzero deformation and modulus\n  derivative, separate magnetic Higgs and electric-confinement outcomes,\n  distinct electric/magnetic patches with nonzero Dirac pairing, and the\n  exterior real-axis period ratio. Lean checks that real nonzero `a` and\n  purely imaginary nonzero `a_D` force `Im(a_D/a) != 0`; path connection,\n  matrices, and labels alone cannot supply the missing physics. No\n  `Unit`-carrier or empty-state truth table replaces those distinctions.\n  It formalizes charge existence, uniqueness, applicability of functional\n  assignment to an admissible carrier, unique sector occupancy, shared\n  sectors, sector distinction, and the equivalence relation on well-defined\n  charged carriers. For uniquely occupied charges it proves\n  exact equality/same-sector and inequality/distinct-sector criteria without\n  depending on a functional implementation. Countermodels show that\n  admissibility alone, bare assignment without admissibility, or equal charge\n  labels do not identify physical carriers, and that unequal assigned charges\n  do not establish distinct sectors without uniqueness. The policy audit\n  discovers every shared\n  framework module and requires at least two inspectable independent\n  paper-local realizations before admitting it. Shared framework imports are\n  also exact-manifested: a philosophy, paradigm, or lower-framework\n  dependency is retained only when the module actually uses it.\n  Its base semantics remains relational, while an optional `ofFunction`\n  realization captures the independently repeated pattern in which a paper\n  supplies admissibility and paper-local charge data. The context owns the\n  paper-selected charge map, carrier, and regime together with both relation\n  families; `SelectedChargeSemanticsAt` is equality with the resulting unique\n  proof-free model, while `SelectedChargeAssignmentSetupAt` additionally\n  requires selected-carrier admissibility before grounding.\n  `FunctionallyRealizedBy`\n  validates that exact paper-local map against the retained relation, and\n  the output-led `EstablishedFunctionalChargeAssignmentAt` retains exact\n  selected semantics together with direct functional realization, occupancy\n  of the selected sector, and charge existence and uniqueness. The route is\n  reconstructed from those outputs rather than stored in the endpoint.\n  `ChargeAssignmentClaim` gives this result an exhaustive\n  proposition-valued semantics: selected semantics, functional realization,\n  carrier admissibility, route applicability, selected-sector occupancy,\n  well-definedness, and the established assignment itself. A shared theorem\n  proves that every established assignment realizes all seven claims. The\n  module imports `Philosophy/TheoryModel.lean` and\n  `Philosophy/MathematicsAndNature.lean`, and separates a value-producing\n  `ChargeModel`, a `ChargeTheory`, and a\n  represented `ChargeWorld`.\n  Each paper supplies a `ChargeInterpretation` specifying how its mathematical\n  map is used by the selected theory, which physical carrier it represents,\n  and what the theory-level and world-level charge claims mean.\n  `TheoryModelGroundingAt` combines grounding of the selected numerical charge\n  with grounding of every technical assignment claim. Numerical model\n  entailment itself now requires carrier admissibility as well as equality to\n  the paper-local map, so a total map does not assert a physical charge outside\n  its declared domain. The generic\n  `theory_model_inputs_establish_grounding` constructor consumes exact\n  selected semantics, selected-carrier admissibility, model-use,\n  representation, and conditional transfer bridges; it mentions no\n  functional-realization, applicability, occupancy, uniqueness, or\n  established-assignment result.\n  `TheoryModelGroundedFunctionalChargeAssignmentAt` retains the output-led\n  result plus explicit theory-transfer and world-soundness bridges; all eight\n  active paper clients delegate their output-independent grounding to the\n  generic constructor, transfer every shared claim, and only then combine it\n  with their established exact-map assignments. Polchinski's adapter exposes\n  the physical RR-source statement as a separate bridge rather than embedding\n  the boundary-state route in model representation. Countermodels show both\n  that a completed assignment need not be grounded and that admissible setup\n  plus grounding need not supply either a functional assignment route or the\n  direct output; they also reject a wrong map, an\n  inadmissible model conclusion, bare physical charge truth, and declarations\n  of all theory/world assignment claims as route substitutes. The grounded\n  endpoint also projects to a quantity-representation context with distinct\n  mathematical and physical charge-quantity types. Faithfulness and an\n  established physical charge value follow only through the paper-local\n  world-transfer bridge. Laughlin 1983, Witten 1982, and Polchinski 1995 expose\n  named cross-domain adapters, while a countermodel retains the exact\n  mathematical assignment and represented value but denies physical charge\n  possession. Thus a successful charge calculation is not definitionally a\n  physical charge fact. The\n  older existential `FunctionallyRealized` interface is\n  preserved as a weaker abstraction, but it cannot validate an arbitrary\n  externally supplied map; a checked countermodel separates the two\n  strengths. Shared theorems also derive unique occupancy and\n  same/distinct-sector tests from\n  the relational interface. Distinct\n  sectors require admissibility of both carriers, and another countermodel\n  shows why transitivity requires uniqueness of the intermediate carrier's\n  charge. The direct `NonvacuousFunctionalChargeAssignmentAt` proposition\n  requires exact graph realization, actual occupancy of the selected sector,\n  and a charge that exists uniquely. Its\n  index-sensitive finite model is inhabited, and direct mutation theorems make\n  the selected map, carrier, regime, admissibility predicate, and assignment\n  relation all route-active. Every one of the eight paper clients derives\n  this proposition from its established paper-local assignment without\n  importing its numerical charge calculation into the shared layer. Each\n  adapter constructs the output directly from its own admissibility premise;\n  policy forbids using the generic route-to-result theorem as the endpoint\n  proof.\n  The same context now exposes proof-free selected constraint, typed\n  derivation-constraint, and situated phenomenon records. The ordinary\n  structural theorem starts from the raw exact-map route and explains the\n  direct selected assignment without consuming the output-led endpoint. The\n  stricter source theorem additionally requires an independently realized\n  typed paper derivation, exposes that provenance, forgets to the ordinary\n  explanation, and only then entails the established assignment. Witten,\n  Laughlin, Arovas-Schrieffer-Wilczek, Maldacena, and Polchinski supply\n  distinct source-sensitive adapters: Cartan-pair charge sequencing,\n  screening or orbital counting, density/Berry/electromagnetic matching,\n  charged-D3 five-form quantization, and boundary-state/annulus/Dirac\n  pairing. Polchinski's pairing branch now retains author equations\n  (14)-(15) as a typed flux readout: source-normalized linking-sphere flux,\n  equality with the dual-field integral and small-sphere potential holonomy,\n  the separate Dirac-string invisibility equation, and the derived\n  electric-magnetic charge product. Lean checks the elimination of the flux\n  variable and the `n = 1` specialization; a countermodel prevents a\n  named pairing calculation from manufacturing those source formulas. A\n  value-bearing D-brane countermodel now retains a `p=3` mixed-boundary\n  split `(4,6)`, one of two bulk supercharges, six transverse modes,\n  inverse-coupling disk tension, a nonzero direct boundary source, a\n  vanishing three-term oscillator sum, nonzero `(1,-1)` NSNS/RR exchange,\n  the printed annulus normalization and one Dirac unit, and the factor-of-two\n  two-brane normalization conflict. The constant positive top-form witness\n  records quantization as an open question, not as a claim of nonquantization.\n  No proposition-pair truth table replaces these D-brane distinctions. A\n  finite false-source model keeps the route, established\n  assignment, and ordinary explanation while denying the derivation relation,\n  so common charge semantics cannot manufacture paper provenance.\n- `PhysicsLogic/Framework/FractionalHallQuasiholeCharge.lean`: the narrower\n  Hall-quasihole inference independently realized by Laughlin 1983, Haldane\n  1983, and Arovas-Schrieffer-Wilczek 1984. Its exact proof-free model retains five\n  selected values and five complete relation or function families: charge\n  admissibility, relational charge assignment, the selected charge map,\n  Hall-fluid status, and quasihole localization. Each paper constructs a named\n  model and proves exact semantic retention before route applicability. The\n  route adds proper filling, positive reference charge, and a paper-local\n  calculation of `q = nu e`; the established result derives the selected\n  charge sector and strict bounds `0 \u003C q \u003C e`. The output-led established\n  result directly retains selected physical setup, functional assignment,\n  exact value, sector, and bounds, and reconstructs the implication-valued\n  calculation and complete route. It projects to a direct nonvacuous endpoint\n  with the same physical outputs. Grounding requires the selected Hall setup,\n  proper filling, and positive reference charge but remains independent of the\n  charge assignment and calculation. All thirteen claims transfer exhaustively, and a direct\n  ten-way audit makes the five realized outer indices and five realized\n  relation families endpoint-active. The three nested assignment-selection\n  fields remain exact route-binding data rather than extra physical facts.\n  Directional countermodels separate grounded setup from charge outputs in\n  both directions.\n  Laughlin supplies independent screening and orbital state-counting\n  calculations; Haldane supplies spherical-parent filling identification and\n  fixed-field excitation counting without consuming its assumed parent gap;\n  Arovas-Schrieffer-Wilczek supplies adiabatic density-phase matching.\n  All four routes independently realize a typed structural explanation of\n  the localized occupied `q = nu e` sector with `0 \u003C q \u003C e`. A finite model\n  retains every charge output but removes the selected Hall fluid, proving\n  that occurrence of fractional charge alone does not reconstruct this\n  explanation.\n  Wavefunctions, plasma screening, Berry phases, electromagnetic phase\n  matching, statistics, Hall conductance, and topological order remain outside\n  the neutral charge inference. Separate source-valued controls retain the\n  odd `m = 3` planar Jastrow trial state, independent screened and flux-counted\n  `e/3` charges, Haldane's `2S = m(N - 1)` monopole shift and distinct `4/9`\n  finite versus `1/3` thermodynamic filling, fixed-field creation of three\n  `e/3` holes, and Arovas's `2 pi nu` winding versus `pi nu` exchange phase.\n  They also retain the nontrivial statistical potential, unproven daughter\n  Coulomb gap, variational-state qualification, and the distinction between\n  symmetric hole coordinates and adiabatic Berry holonomy. The same Haldane\n  coordinate symmetry is explicitly compatible with both zero and nonzero\n  geometric phase; only Arovas's independent transport calculation selects\n  the nonzero exchange result.\n  The stronger\n  `SourceSensitiveFunctionalChargeSupportedFractionalHallChargeAt`\n  additionally retains the exact nested charge model, inhabited fractional\n  endpoint, independent source-sensitive functional-charge and Hall-charge\n  explanations, and a third source-local joining derivation. Laughlin's\n  plasma handoff preserves his literal equations-(7)-(8), phantom insertion,\n  complete screening, and `m q = e`; his distinct one-flux/one-orbital\n  counting handoff is explicitly forbidden from assuming plasma screening.\n  Arovas's handoff preserves normalization, the nondynamical\n  state-inner-product phase, the inhabited density decomposition and\n  large-loop correction, electromagnetic matching, and `q = nu e`, while\n  governance excludes the later two-hole exchange argument. A physical\n  missing-handoff model retains the distinct `e/3` and `e/5` charges, unit\n  phantom, opposite quasiparticle sign, finite-hole correction, and\n  variational scope while rejecting composition without its joining proof.\n- `PhysicsLogic/Framework/ParityResolvedFractionalJosephsonResponse.lean`:\n  the fixed-parity phase-response inference independently realized by\n  Kitaev 2001 and Fu-Kane 2009. It retains two opposite-parity sectors, a\n  paper-local branch-retention condition, local `2pi` return with sector\n  exchange, `4pi` sector return, and a separate calculation of a fixed-sector\n  current that is `4pi` rather than `2pi` periodic. Its exact model retains\n  all six selected indices and eleven route-used relations. Establishment is\n  output-led: it stores the exact inhabited junction setup and seven direct\n  response outputs, while checked theorems reconstruct the three implication-\n  shaped contracts and complete route. Grounding requires that selected setup\n  but no return, exchange, current-periodicity, fractional-effect,\n  calculation, or route output. Directional countermodels separate setup\n  grounding from response outputs in both directions. Its direct nonvacuous\n  endpoint is witnessed by a\n  route-shaped model and fails under each of six selected-index and eleven\n  relation-family mutations. The completed route additionally realizes a\n  typed structural explanation whose constraint contains the exact junction,\n  parity sectors, advances, regime, branch evolution, current calculation,\n  and fractional-effect interpretation. Branch-only and current-without-\n  interpretation countermodels block weaker explanations. Majorana chains,\n  QSHI edges, protected crossings, parity anomalies, avoided crossings,\n  switching noise, materials, and experimental realization remain\n  paper-local.\n- `PhysicsLogic/Framework/FiniteBarrierMetastableDecay.lean`: the\n  finite-barrier metastable-decay inference independently realized by Gamow\n  1928 and Gurney-Condon 1928. It retains a classically forbidden finite\n  barrier, attenuated but nonzero wave coupling, a separate positive-rate\n  calculation, spontaneous decay, and a cross-system energy-rate trend only\n  under an explicit comparable-barrier condition. A separately earned\n  `ExponentialMetastableSurvivalReadout` distinguishes a positive rate,\n  normalized exponential survival, correctly conditioned future survival,\n  and elapsed-time escape probability. Gamow derives the full-exponent\n  survival curve from the actual complex-energy phase and identifies it\n  with the finite interior probability divided by its initial value;\n  Gurney and Condon retain their explicitly recalled observed exponential\n  law and require a positive observation duration. Rate comparisons through\n  escape probabilities require one common duration, and concrete models\n  separate positive rates from survival laws and exponential survival from\n  correct future conditioning. Both source routes construct the stronger\n  `NonvacuousMemorylessFiniteBarrierDecayAt` endpoint without identifying a\n  rate with an objective chance. Its proof-free exact model\n  retains all sixteen selected data values and all sixteen route-used relation\n  families. Both papers certify a named context-derived model before the\n  technical route and prove a named selected-comparison setup bridge from\n  their two local barrier setups, comparable profiles, and energy ordering.\n  They independently ground that same setup without any attenuation, overlap,\n  rate, penetration, or trend output. Both established endpoints are\n  output-led and reconstruct their calculation contracts from realized\n  outputs. The reusable one-decay endpoint\n  has its own false-setup countermodel and a nineteen-component direct audit\n  over eight selected values and eleven route relations. A separate\n  thirty-two-component comparison audit prevents either selected physical\n  value or relation family from becoming decorative. The complete one-decay\n  route now directly realizes a typed mechanistic explanation before either\n  an established one-decay endpoint or the two-system comparison exists: a metastable interior,\n  outgoing channel, and finite barrier form the component; the attenuated\n  nonzero wave and rate form the activity; and the organized system produces\n  the selected spontaneous decay. Both papers expose this endpoint for both\n  selected systems directly from source-stage inputs. Gamow executes the\n  rectangular-barrier, damped-outgoing, and two radial-transfer calculations;\n  Gurney and Condon execute the two wave-overlap calculations independently.\n  Neither source theorem consumes the Geiger-Nuttall comparison or the\n  objective-chance bridge; terminal comparison adapters remain compatibility\n  paths. A stronger source-sensitive projection now retains a typed local\n  derivation inside the mechanism's under-barrier activity. Gamow distinguishes\n  lower and higher damped-outgoing radial transfers; Gurney and Condon\n  distinguish the lower and higher interior/exterior wave overlaps. The\n  derivation relation is proposition-valued rather than proof-carrying. A\n  checked forgetful theorem strips only source provenance and recovers the\n  ordinary barrier mechanism from the same physical witnesses. A countermodel\n  completes the shared decay route and ordinary mechanism while making that\n  relation false, so shared outputs cannot reconstruct which original\n  calculation obtained. A second countermodel retains positive-rate production\n  and the spontaneous-decay prediction while deleting the barrier-wave\n  activity, so output labels do not manufacture a mechanism. An explicit\n  `ObjectiveChanceContext` bridge now classifies the two selected rates as\n  objective chances only from paper-local probability-role semantics:\n  Gamow uses transition probability, decay constant, and spontaneous\n  emission, while Gurney and Condon additionally require their\n  history-independent chance premise. A complete technical decay with no\n  objective-chance role is a checked countermodel. The mechanism does not\n  determine an individual decay time or classify the rate as chance. Nuclear\n  potentials, complex energies, barrier integrals, Geiger-Nuttall formulas,\n  scattering checks, and analogies remain paper-local.\n  Separate source-valued witnesses remain reduced scalar and source-flag\n  diagnostics, not actual wavefunction realizations or certification that\n  conflicting printed formulas agree. They additionally retain Gamow's doubled\n  amplitude-to-rate tunneling exponent, complex-energy damping, radial\n  barrier integral, higher-angular-momentum suppression, required s-wave\n  preparation, approximate curved Geiger-Nuttall relation, and explicitly\n  unproved gamma-ray mechanism. The earlier rectangular/radial route and\n  later Coulomb/logarithmic comparison are separately inhabited source\n  branches with distinct typed derivations; the comparison branch retains\n  the complete prior radial calculation. Gurney and Condon instead retain small\n  finite overlap, history-independent chance, conditional similar-potential\n  ordering, an independent incoming-scattering turning point, and a\n  field-emission analogy that does not derive nuclear decay. Forty-three\n  mutation controls prevent these source arguments, formulas, probability\n  roles, and scope qualifications from collapsing into one another or\n  broadening the generic decay contract.\n- `PhysicsLogic/Framework/SubthresholdExcitationStability.lean`: the narrow\n  selected-excitation stability inference independently realized by Landau\n  1941 and Bogoliubov 1947. Its proof-free model retains seven selected\n  physical indices and all fifteen route-used relation families: a valid\n  elementary spectrum, paper-local excitation content and positive\n  energy-per-momentum threshold, selected subthreshold motion, positive\n  moving-frame energy, exclusion of the selected momentum-transfer and\n  dissipation channel, and stationary-frictionless interpretation. Both\n  paper contexts own all seven physical selections and expose one exact\n  `selectedModel`; changing any selected value or any of the fifteen relation\n  families fails the original context's exact semantics. Both papers consume\n  that certificate before either route applicability or grounding. Grounding\n  also requires a direct inhabited spectrum-and-subthreshold-motion setup,\n  plus paper-local theory/world use, representation, and conditional-transfer\n  bridges; the positive threshold and every later stability output remain\n  independent. The established endpoint is output-led and reconstructs its\n  implication contracts from direct results. One checked countermodel has\n  complete setup-bounded grounding while the threshold and route fail;\n  another makes the calculation contracts vacuous with no setup while both\n  output endpoints remain false. Mutation countermodels cover all twenty-two\n  retained components. The complete selected route also instantiates\n  `Paradigm.ExplanationModes.StructuralExplanationContext`: its typed energy\n  and excitation-channel constraint structurally explains the scoped\n  stationary-frictionless-motion phenomenon. Both paper adapters realize\n  that explanation. A countermodel keeps every spectrum, threshold,\n  moving-frame, and selected-dissipation calculation true while falsifying\n  the physical interpretation, and therefore blocks the structural\n  explanation. A source-sensitive constraint now pairs the ordinary selected\n  excitation constraint with a typed paper-local derivation and an independent\n  realization relation. Landau's derivation retains the quantum-liquid setup,\n  non-derived potential-vortex ordering, phenomenological phonon-roton\n  spectrum, and absolute-zero wall-flow threshold. Bogoliubov's derivation\n  instead retains the microscopic weak-gas setup, interaction-stability\n  selection, controlled linearization, canonical diagonalization, spectral\n  asymptotics, equilibrium threshold, and relative-motion calculation. Each\n  source theorem reaches `DirectSourceStructuralFrictionlessMotionExplanationAt`\n  before its terminal paper result or any shared established endpoint is\n  available. A finite countermodel preserves the complete common route,\n  established endpoint, and ordinary explanation while falsifying the source\n  relation, so the common conclusion cannot reconstruct which derivation was\n  used. The older terminal-result and ordinary source adapters remain\n  compatibility paths. This adds neither mechanistic explanation nor a\n  universal no-dissipation claim.\n  Phonons, rotons, condensates, Bose gases, walls, vortices, nucleation,\n  hydrodynamics, universal critical velocities, and absence of every\n  dissipation mechanism remain paper-local.\n- `PhysicsLogic/Framework/MomentumResolvedVariationalBound.lean`: the narrow\n  density-mode variational inference independently realized by Feynman 1954\n  and Girvin-MacDonald-Platzman 1986. Its proof-free model retains eleven\n  selected physical indices and all seventeen route-used relation families:\n  setup, density-mode trial construction and admissibility, separate norm and\n  numerator calculations, quotient identification, lowest-sector selection,\n  and the upper-bound comparison. Feynman, GMP, and the dependent\n  Feynman-Cohen 1956 client each assign eleven context-owned values, use the\n  context's unique selected model, certify exact selected semantics, and\n  consume that certificate in applicability. All three clients construct the\n  shared route from direct established physical outputs rather than\n  replaying stored paper-local calculation contracts. The shared established\n  result is output-led: exact selected semantics plus the direct nonvacuous\n  seventeen-relation endpoint. A candidate cannot select itself by supplying\n  alternate indices.\n  Their grounding adapters separately consume exact selected semantics, an\n  inhabited paper-local ground-state/momentum/mode setup, explicit theory use\n  and world representation, and conditional claim transfer. Final paper\n  theorems combine that setup-bounded grounding with the remaining\n  variational route; a typed countermodel has complete grounding and setup\n  while trial construction and every later variational output are false.\n  An inhabited finite witness realizes all seventeen relations with distinct\n  ground/trial states and distinct trial/lowest-sector energies. Direct\n  mutation theorems show that every one of the eleven data and seventeen\n  relation families changes route-used semantics; all three paper adapters\n  derive this nonvacuity from their local technical route. The complete route\n  also realizes a typed structural explanation whose constraint retains all\n  eleven selected data and is satisfied only by the trial, quotient,\n  sector-minimum, and variational-comparison chain. Feynman and GMP now\n  independently derive this explanation directly from their source-facing\n  calculations before any terminal paper result or shared established\n  endpoint exists. Their terminal-result projections remain compatibility\n  adapters. A source-sensitive constraint now additionally retains a typed\n  paper-local derivation. Feynman's unprojected structure-factor quotient,\n  GMP's lowest-Landau-level projected oscillator-strength quotient, and\n  Feynman-Cohen's dependent backflow/correlation refinement have distinct\n  tokens and realization relations. Their source theorems require those\n  relations and raw applicable routes rather than common endpoints or the\n  ordinary explanation. A finite countermodel keeps the complete route,\n  established bound, and ordinary explanation while falsifying provenance.\n  A declared-upper-bound countermodel with no\n  quotient identification blocks the shortcut from inequality to explanation.\n  Helium,\n  Hall liquids, structure factors, oscillator strengths, phonons, rotons,\n  exact-spectrum equality, mode saturation, and gaps remain paper-local.\n- `PhysicsLogic/Framework/HomogeneousCosmicExpansion.lean`: the narrow\n  homogeneous-expansion inference independently realized by Friedmann 1922\n  and Lemaitre 1927. Its proof-free model retains eight selected physical\n  indices and all nine proposition-valued relation families that make those\n  indices a homogeneous cosmology. The route requires exact selected\n  semantics, a paper-local field-equation reduction, a separate increasing-\n  branch calculation that places both selected radius-time points on one\n  nonstationary solution, and an interpretation as cosmic expansion. Stationary\n  and periodic worlds, conserved mass, redshift, observational calibration,\n  and causal explanations remain paper-local. Friedmann's paper-local route\n  now preserves the mixed-equation branch split, the stationary matter\n  contrast, the density and total-mass relations, all three cosmological-\n  parameter root regimes and forbidden radius intervals, the distinct origins\n  of its two monotone worlds, and the periodic world's amplitude and critical-\n  period behavior. These are ten audited routes with independent calculation\n  contracts; only the established monotone assessment feeds the shared\n  expansion adapter. Generic grounding now requires the context's unique\n  `selectedModel`, its homogeneous relativistic setup, and explicit theory-\n  use/world-representation bridges, but no radius evolution, branch\n  calculation, interpretation, or established result. Both paper contexts\n  own all eight physical selections and derive the selected shared setup from\n  their source-local setup. A converse model has setup-complete grounding\n  while radius evolution is false; a false-setup model cannot be grounded. A\n  further countermodel has an evolution relation and an increasing pair but\n  no single selected solution containing both points, so the route is\n  inapplicable. Friedmann's expansion bridge is explicitly marked as a\n  source-anchored reconstruction from increasing homogeneous curvature radius,\n  whereas Lemaitre explicitly interprets expansion of space. His local\n  constant-mass route additionally requires strict numerical radius growth;\n  the original exact period/radius equation then proves positive spectral\n  redshift and positive apparent recession velocity. A contracting-universe\n  countermodel satisfies that same equation while producing blueshift, so\n  neither conclusion is silently imported into the shared framework. Both adapters\n  now retain that interpretation as a callable paper-local bridge and feed it\n  the selected history and increase. Their adapters now construct the\n  source-ordered applicable route directly; that route yields both the\n  output-led established result and a typed structural explanation of the\n  selected expanding history. Its proof-free constraint contains no\n  evolution or expansion output, and neither adapter consumes the established\n  or nonvacuous shared endpoint. A second proof-free source constraint now\n  retains a typed paper derivation and proposition-valued realization relation.\n  Friedmann's token includes the reconstructed interpretation bridge, whereas\n  Lemaitre's token includes the explicit interpretation returned by his\n  constant-mass calculation. Their source-sensitive theorems require both\n  the raw applicable route and the corresponding realized token. A completed\n  expansion with a false derivation relation blocks provenance from being\n  inferred from output equivalence; a declared-output model with false setup\n  separately blocks the physical converse. This is not a causal explanation\n  of expansion, and\n  Lemaitre's radiation-pressure suggestion remains local. The finite audit\n  model has distinct ordered times and radii and realizes the complete route;\n  `NonvacuousHomogeneousCosmicExpansionAt` now states that setup, radius\n  evolution, one selected history, increase, and physical interpretation all\n  hold directly at one model. Both paper adapters expose that proposition.\n  The equation-backed selected history also projects to a neutral radius\n  `Dynamics`, with the ordered endpoint-time pair as evolution parameter.\n  Both papers expose the resulting actual forward-evolution witness. A\n  no-expansion model and a branching established-expansion model prevent this\n  projection from manufacturing either physical interpretation or\n  determinism. The branching model also realizes the structural explanation,\n  proving that it does not imply unique evolution.\n  Every one of the eight index mutations and nine relation mutations destroys\n  the direct result itself; the older seventeen mutation witnesses separately\n  enforce exact semantics.\n- `PhysicsLogic/Framework/NebularDistanceVelocityCalibration.lean`: the\n  qualified observational calibration independently realized by Lemaitre\n  1927 and Hubble 1929. Its proof-free model retains seven selected indices\n  and all ten route-used relation families, including exact universality as a\n  positive predicate whose negation is part of the qualified result.\n  Applicability requires exact paper-local relation semantics plus separate\n  fit, scope-assessment, and interpretation obligations. Both papers\n  construct a unique model from seven context-owned values and consume\n  semantic-retention certificates. Their selected sample and assigned data\n  also construct a named `SelectedCalibrationSetupAt` witness before\n  grounding; mutation countermodels cover all seventeen\n  fields and refute exact semantics after any one-field change. The established\n  result is now exactly selected semantics plus\n  `NonvacuousQualifiedDistanceVelocityCalibrationAt`: valid description,\n  selected sample, both assigned data sets, selected proportional relation,\n  calibrated coefficient, uncertainty, restricted range, non-universality,\n  and rough linearity all hold directly at one model. The implication-valued\n  route is reconstructed from those outputs. Exact selection without the\n  observational setup cannot ground a model, while a selected setup can be\n  grounded without fit or calibration outputs. A setup-free implication\n  model also fails the direct proposition. A separate finite witness\n  and seven index plus ten relation mutations show that every route-used\n  component affects the qualified result itself. Lemaitre and Hubble expose\n  named paper adapters to this same nonvacuous stopping point.\n  The selected sample and assigned distance/velocity datasets additionally\n  form an explicit evidence object supporting the qualified relation and\n  coefficient model. Both papers derive the same\n  `ModelEvidenceContext.SupportsModel` proposition only after fitting and\n  retaining uncertainty, range restriction, nonuniversality, and rough\n  linearity. Accessible obtained data without a fit are a checked\n  countermodel; model truth and theory support remain separate.\n  The finite source-report diagnostic preserves assigned-catalog equality\n  across alternative reductions while comparing their numerical reports.\n  It does not reconstruct actual estimators or assert independent validation,\n  cosmic sampling variation, or a cosmological ensemble target.\n  Cosmological dynamics, numerical fit details, Hubble's downstream NGC 7619\n  consistency check, de Sitter explanations, and modern Hubble-constant\n  semantics remain paper-local.\n- `PhysicsLogic/Framework/StandardCandleAccelerationInference.lean`: the\n  qualified observational-cosmology inference independently realized by\n  Riess et al. 1998 and Perlmutter et al. 1999. Its exact model retains ten\n  selected indices and eighteen relation families covering calibrated\n  magnitude-redshift evidence, a scoped model-family fit, a nonaccelerating\n  reference, a separate acceleration interpretation, and robustness only to\n  assessed systematics. It realizes evidence as model support rather than\n  theory truth and keeps unquantified alternatives explicit. A finite direct\n  model realizes the complete five-stage inference with distinct fitted-family\n  and reference-model roles. Exhaustive activity theorems show that all ten\n  selected data and all eighteen relations affect the realized route, rather\n  than merely changing an exact record. Both paper adapters expose this\n  nonvacuous proposition. Applicability retains the independent paper-local\n  calculations, while established fit, acceleration, and terminal inference\n  objects retain only setup and direct outputs; a vacuity countermodel guards\n  this boundary. The complete route also realizes an ordinary structural\n  explanation. A stronger source-sensitive explanation retains typed,\n  noninterchangeable derivations: Riess starts from classified observations,\n  MLCS/template/snapshot distance reduction, a scoped likelihood, a separate\n  two-component deceleration bridge, and qualified robustness; Perlmutter\n  starts from matched samples, cross-filter/stretch standardization, the\n  A/B/C fit progression, acceleration interpretation, and systematic refits\n  with grey-dust and evolution loopholes open. Neither source theorem accepts\n  an established paper or shared endpoint. A finite converse model completes\n  the route and ordinary explanation while its independent source relation is\n  false. Grounding is bounded by the exact calibrated-evidence and\n  cosmological-comparison setup, excludes every fit and interpretation output,\n  and is independently realized by named Riess and Perlmutter adapters. The\n  neutral route does not identify their samples, light-curve reductions,\n  likelihoods, confidence procedures, ontological interpretations, age\n  calculations, or cross-paper overlap. Separate source-valued controls retain\n  Riess's 10 new/16 total distant and 34 nearby events, 15 spectroscopic\n  confirmations, distinct `Omega_Lambda = 0.68` versus `0.84` flat-prior fits,\n  and `2.8` versus `3.9 sigma` acceleration support. Perlmutter's controls\n  retain the 42+18 sample, 60/56/54 Fit A/B/C cuts,\n  `Omega_M = 0.28 +0.09/-0.08`, separate identified systematic errors,\n  `P(Lambda > 0) = 0.9979`, and unresolved grey-dust/evolution alternatives.\n  Separate searches nevertheless shared nearby Calan/Tololo observations and\n  exactly two distant supernovae, so the teams' evidence is not statistically\n  independent.\n- `PhysicsLogic/Framework/GappedIncompressibleFluid.lean`: the narrow shared\n  inference independently realized by Laughlin 1983 and Haldane 1983. A\n  selected description is valid in a regime and represents a quantum fluid;\n  a paper-local calculation or explicit assumption establishes an excitation\n  gap; and a separate interpretation bridge yields incompressibility and\n  suppressed low-energy dissipation. Its proof-free model retains the three\n  selected indices and all five route-used relation families. The context owns\n  the description, fluid, and regime and constructs one unique\n  `selectedModel`; candidate models cannot select their own indices.\n  Applicability requires exact paper-local selected semantics plus the\n  model-local technical route. Laughlin and Haldane each construct their named\n  shared model from that unique selection and prove a semantic-retention\n  certificate before using it. Model-of and representation grounding retain\n  exact selection and the inhabited pre-gap setup, while model entailment is\n  the shared claim itself. Grounding separately requires only that certificate, the\n  valid selected quantum-fluid setup, and paper-local theory/world bridges; it\n  does not consume the gap or either interpreted output. The output-led\n  established result is exactly selected semantics plus\n  `NonvacuousGappedIncompressibleFluidAt`, where the valid\n  quantum-fluid setup, actual selected gap, incompressibility, and suppressed\n  dissipation hold directly at one model rather than only behind\n  implication-valued clauses; the complete route is reconstructed from those\n  facts when needed. Laughlin and Haldane each expose a named\n  paper-level projection to that direct result. The complete route also\n  instantiates a typed structural explanation of the selected incompressible,\n  low-dissipation fluid phenomenon. Satisfaction requires the gap calculation\n  or assumption and the separate interpretation bridge; a checked\n  gap-without-interpretation model has no such explanation. It defines no Landau\n  level, Hall conductance, hierarchy, fractional charge, disorder, or\n  topological order. Countermodels block setup-to-gap, gap-to-interpretation,\n  incompressibility-to-dissipation, technical-result-to-grounding,\n  grounding-to-technical-route, selection-without-setup grounding, and\n  vacuous implication use. One audit shows\n  that changing the state, fluid, regime, or any retained relation fails exact\n  semantics; a source-shaped direct witness realizes the complete\n  gap-to-incompressibility result, and exhaustive direct mutations make all\n  eight retained components destroy that substantive result.\n- `PhysicsLogic/Framework/SolitaryTravelingWave.lean`: the narrow stationary\n  solitary-wave inference independently realized by Korteweg and de Vries\n  1895 and Zabusky-Kruskal 1965. Its proof-free model retains eleven selected\n  indices and all eleven route-used relation families: validity, system\n  description, nonlinear dispersion, frame selection, asymptotic background\n  condition, nonzero pulse-background contrast, stationary reduction,\n  localized-profile construction, both parameter relations, and shape\n  preservation. Each paper constructs an exact\n  context-derived model whose context owns all eleven selected values, and\n  constructs the established result directly from the inhabited setup,\n  reduction, nontrivial profile, parameter relations, and shape-preserving\n  conclusion. The generic calculation route is reconstructed from those\n  outputs rather than stored inside the result. The same endpoint now yields\n  a typed derivational reduction from the full nonlinear-wave description to\n  the reduced stationary profile and its shape-preserving behavior. Separate\n  countermodels show that a shape label without nontrivial profile support,\n  and complete profile calculations without the physical interpretation,\n  each fail that reduction contract. The complete route also realizes a typed\n  structural explanation whose proof-free constraint retains the full and\n  reduced equations, moving frame, nontrivial profile, and selected pulse\n  parameters, while its distinct phenomenon requires nonzero contrast, both\n  parameter relations, and shape preservation. A terminal-pulse countermodel\n  makes that phenomenon obtain while nonlinear dispersion is absent, so the\n  occurrence does not explain itself. Both papers expose the explanation from\n  their own granular stationary routes. The raw routes now also realize a\n  source-sensitive derivational reduction. Korteweg-de Vries retains the\n  hydrodynamic long-wave setup, successive-approximation deformation-equation\n  calculation, and stationary-profile calculation; Zabusky-Kruskal retains\n  the selected KdV setup, stationary substitution, isolated-pulse calculation,\n  and shape interpretation. Its physical setup now contains the literal\n  normalized equation `u_t + u u_x + delta^2 u_xxx = 0`, with actual temporal\n  and third-order spatial derivatives; its numerical protocol separately\n  contains the period-two profile `u(x,0) = cos(pi x)` and `delta = 0.022`.\n  Source steps make those original equations explicit dependencies, while\n  countermodels reject inviscid steepening, linear dispersion, and a\n  reversed-phase cosine as substitutes. A completed common pulse and ordinary reduction\n  with a false source relation cannot recover either provenance. Theory/model/world grounding\n  requires exact selected semantics together with the true equation,\n  moving-frame, and background setup. Mutation countermodels show that\n  changing any of the twenty-two model components invalidates exact semantics. A\n  dedicated countermodel proves that profile, parameter-relation, and shape\n  labels alone do not exclude a constant-background profile; another proves\n  that a false setup cannot be grounded even when all implication-valued\n  calculations are vacuously true. Korteweg-de\n  Vries's negative and periodic branches and\n  Zabusky-Kruskal's numerical formation, interaction, recurrence, and\n  thermalization routes remain paper-local; the framework defines no generic\n  soliton ontology. Korteweg-de Vries's paper-local scope countermodels now\n  retain actual depth-wavelength and amplitude-depth scale separation,\n  deformation and stationary residuals, cnoidal modulus and closure,\n  third-order support, and a nonvanishing remainder sequence. They separate\n  setup from calculation, localized from periodic stationarity, finite-order\n  support from convergence, and one stationary profile from arbitrary waves\n  without enum-to-Prop truth tables.\n  Separate source-valued controls now retain the original signed coefficient\n  `sigma = l^3/3 - T l/(rho g)`, distinct elevation and capillary-depression\n  pulses, the common critical depth `sqrt(3 T/(rho g))`, and the complete\n  depression profile `-h sech^2(x sqrt(h/(-4 sigma)))`. The elevation and\n  depression witnesses keep the same fluid, gravity, and surface tension but\n  occupy strictly different depths; the original water data give a critical\n  depth strictly between `0.469` and `0.470` cm. Twelve inhabited source and\n  shared-framework boundaries reject a wrong depth, missing surface tension,\n  erased real-valued profile, wrong width, or a solitary branch exactly at\n  zero dispersion. The normalized KdV evolution and period-two cosine protocol\n  remain separate.\n  The 1965 pulse relations `amplitude * width^2 = 12 delta^2` and\n  `speed = background + amplitude/3`, eight observed versus seven compared\n  pulses, exact represented momentum versus nonzero five-digit energy drift,\n  and near-profile return are independently checked. Seventeen mutations\n  reject exact full-state recurrence, exact Euler dynamics, solved close\n  interactions, and exclusion of eventual thermalization without widening\n  the neutral solitary-wave contract.\n- `PhysicsLogic/Framework/LargeComponentSphericalCorrespondence.lean`: the\n  selected infinite-component vector-to-spherical observable agreement\n  independently realized by Stanley 1968 and Wegner-Houghton 1973. Stanley\n  retains the original single global spherical constraint, separate local\n  vector-spin constraint at every lattice site, nonzero finite-spin free-energy\n  correction, equation-(24) remainder accounting, and off-critical\n  temperature scope. Wegner-Houghton separately retains the exact\n  infinite-component critical formulas `y_m = d - 2m`,\n  `nu = 1/(d-2)`, `alpha = (d-4)/(d-2)`, `gamma = 2/(d-2)`, and\n  `beta = 1/2` on `2 \u003C d \u003C 4`. Neither derivation establishes convergence\n  of finite-component critical indices, interchange of the large-component\n  and critical limits, or exact finite-component perturbation theory.\n- `PhysicsLogic/Framework/IncompressibleVelocityCorrelation.lean`: the narrow\n  nonvacuous incompressible velocity-correlation constraint independently\n  realized by Kolmogorov 1941 and Forster-Nelson-Stephen 1977. Kolmogorov\n  retains the original local radial equation\n  `r B_LL'(r) = 2 (B_NN(r) - B_LL(r))`, positive separation, local isotropy,\n  and a high-Reynolds interior. Its adapter now binds the tensor to actual\n  retained-field moment integrals and the radial derivative to the same\n  computed longitudinal profile. Forster instead retains the original Fourier\n  projector `P_ij(k) = delta_ij - k_i k_j / |k|^2`, a nonzero wave vector,\n  positive spectral amplitude, actual tensor transversality, and a\n  long-distance, long-time infrared regime. Lean proves the Fourier tensor\n  is nonzero and rejects a wrong projector cross-term sign. Neither source\n  supplies a shared inertial exponent, proved cascade, whole-flow isotropy,\n  ultraviolet turbulence control, or universality across arbitrary forcing.\n- `PhysicsLogic/Framework/CanonicalGibbsNormalization.lean`: the narrow\n  normalized energy-weight inference independently realized by Jaynes 1957\n  and Metropolis et al. 1953. Jaynes retains the finite enumerated-energy\n  sum, constrained epistemic maximum entropy, the printed exponential,\n  logarithmic normalization, and partition equations, and the absence of\n  inferred microscopic dynamics. Metropolis instead retains positive `kT`,\n  velocity-independent momentum separation, the actual configuration-space\n  measure integral, normalized density, and weighted observable numerator.\n  The shared result neither requires a positive Jaynes energy multiplier nor\n  bounds a continuous probability density by one. It does not infer detailed\n  balance, a finite convergence rate, molecular dynamics, or an exact\n  thermodynamic limit from the canonical target.\n- `PhysicsLogic/Framework/DensityPotentialGaugeDetermination.lean`: the\n  narrow density-to-potential classification independently realized by\n  Hohenberg-Kohn 1964 and Runge-Gross 1984. Its proof-free context retains\n  the selected full description, potential, density, fixed condition,\n  physical system, regime, source-specific gauge, inhabited domain, and\n  separate source calculation. The static branch keeps paired nondegenerate\n  ground states, fixed particle number, strict variational reductio, and an\n  additive spatial constant; the dynamic branch keeps fixed initial state and\n  interaction, time analyticity, current/continuity/boundary reasoning,\n  printed equation (6), and a genuinely time-dependent additive gauge.\n  Neither branch proves literal potential equality, global density\n  representability, an unrestricted initial-state theorem, or a dynamic\n  action minimum.\n- `PhysicsLogic/Framework/DensityFunctional.lean`: the narrow exact\n  ground-density variational inference derived by Hohenberg-Kohn 1964 and\n  explicitly imported by Kohn-Sham 1965. `GroundDensityModel` is proof-free\n  and retains the selected state, potential, derived density, particle number,\n  density and particle-number maps, ground-state and admissible-density\n  predicates, and all three energy functions used by the route. The context\n  owns the selected state, potential, and particle-number sector and exposes\n  their unique `selectedModel`; a candidate cannot select itself by supplying\n  different indices. Route applicability requires exact equality with that\n  model. Theory use and physical representation require the stronger\n  `SelectedGroundDensitySetupAt`: exact selection together with the physical\n  ground-state, derived-density, fixed-particle-number, and selected-density\n  admissibility setup, but no variational output. The route then requires that\n  setup, including explicit\n  admissibility of that selected density in the fixed-particle-number domain,\n  and a selected\n  implication-valued calculation yielding both physical-energy attainment and\n  minimization over the declared fixed-particle-number density domain. A\n  globally quantified paper result may instantiate that calculation but\n  cannot count as an applicable route by itself. Hohenberg-Kohn derives the\n  calculation from its energy and wavefunction-variational premises;\n  Kohn-Sham consumes its imported Hohenberg-Kohn foundation before adding\n  orbital machinery. A typed `GroundDensityVariationalConstraint` now records\n  the selected state, potential, density, and particle-number sector, while\n  `GroundDensityEnergyMinimumPhenomenon` records the selected density, its\n  physical ground energy, and the fixed-number minimum. The complete\n  applicable route realizes\n  `DirectStructuralGroundDensityVariationalExplanationAt`: applying the\n  selected variational calculation to its inhabited setup necessitates both\n  exact attainment and minimization. Both papers expose that explanation\n  directly from their source inputs. A countermodel has exact energy\n  attainment but an admissible lower-energy competitor, so the first output\n  alone is neither the minimum nor its structural explanation. Kohn-Sham\n  retains the exact universal decomposition with\n  that foundation, so the local approximation, nonlocal exact-exchange\n  alternative, and note-added-in-proof exact formulation branch from the\n  exact input without making either alternative inherit the local\n  approximation. Each paper constructs a named exact model, proves a\n  semantic-retention certificate, supplies it independently to\n  `TheoryModelGroundingAt`,\n  and transfers all eight shared claims. The established result is\n  definitionally exact selected semantics together with\n  `NonvacuousGroundDensityVariationalAt`, where selected-density\n  admissibility, energy attainment, and scoped minimization hold together at\n  one model instead of only behind the implication-valued calculation; the\n  complete technical route is reconstructed from those outputs when needed. A\n  pointwise projection to `MathematicalRepresentationContext` additionally\n  proves that the selected admissible density exactly represents a physical\n  ground state at the selected potential and particle number. Hohenberg-Kohn\n  and Kohn-Sham both expose this result. Countermodels separately remove\n  physical ground-state membership and density admissibility, while the\n  framework still makes no converse representability, completeness, density\n  uniqueness, or density-to-state determination claim. A\n  false physical setup cannot be grounded, while a complete setup can be\n  grounded without thereby supplying minimization or a calculation route. A\n  route-shaped finite witness realizes that proposition, and exhaustive direct\n  mutations make all four selected indices and seven retained semantic\n  families destroy it. Further countermodels block vacuous implication use,\n  automatic grounding, and reconstruction from declared theory/world claims.\n  Orbitals,\n  representability beyond the declared\n  domain, exchange-correlation approximations, response kernels, thermal\n  occupations, and spin extensions remain paper-local.\n- `PhysicsLogic/Framework/CongruenceFocusing.lean`: the narrow\n  finite-parameter transverse-collapse route independently realized by\n  Raychaudhuri 1955 and Penrose 1965. Its proof-free model retains eight\n  selected indices and all ten route-used relation families: congruence and\n  positive-profile setup, initial contraction, nonpositive evolution, finite\n  profile collapse, and collapse-to-focusing interpretation. Both papers\n  assign all eight paper-local values to their contexts' explicit selections,\n  use the resulting unique `selectedModel`, prove retention certificates, and\n  consume the certified semantics in applicability. Grounding separately requires\n  only exact semantics, the valid congruence/section/positive-profile setup,\n  and paper-local theory/world bridges. Model use, world representation, and\n  model entailment all retain the exact eighteen-component semantics.\n  The output-led established result is exact selected semantics together with\n  `NonvacuousFiniteParameterCongruenceFocusingAt`, where the setup,\n  contraction, nonpositive evolution, finite separation, profile vanishing,\n  and focusing conclusion hold directly at one model rather than only behind\n  implication-valued calculations. Raychaudhuri and Penrose each construct\n  that direct result from their paper-local inputs, and the complete route is\n  reconstructed afterward.\n  The ordinary structural explanation executes collapse plus interpretation\n  directly without requiring paper provenance. A stricter source-sensitive\n  explanation adds a typed realized derivation, exposes it, and entails the\n  ordinary explanation when provenance is forgotten. Raychaudhuri's\n  zero-lambda timelike-volume derivation and Penrose's temporary-completeness\n  null-area derivation remain distinct. A converse countermodel retains\n  established focusing, the reconstructed route, and ordinary explanation\n  while denying the source derivation, so no source-sensitive explanation\n  follows. Raychaudhuri's separate nonspinning time-scale branch now also\n  retains journal equations (13)-(16) before any interpretation: `rho G^3 = C`,\n  with `G^6 = -g` so `G^3` is the local volume factor, the zero-spin\n  normalized-G equation, its assigned-state first\n  integral, `Q = G/G_A`, the nonnegative anisotropy accumulation `Theta`, and\n  the inverse-square-root proper-time integral. The readout is tied to the\n  selected Einstein system, assigned/comparison states, G-profile,\n  density, anisotropy, interval integral, and elapsed time. The interval\n  inequality and isotropic-maximality reading remain separate calculation and\n  interpretation contracts; a countermodel blocks a named comparison output\n  from manufacturing the displayed formulas.\n  Raychaudhuri supplies a timelike matter congruence and local spatial volume;\n  Penrose\n  supplies an orthogonal null congruence, cross-sectional area, and caustic.\n  Those causal, dynamical, and singularity meanings remain outside the neutral\n  route. Separate source-valued physical controls retain Raychaudhuri's signed\n  `G''/G` equation, rotation and anisotropy branches, independent past\n  contraction, Lambda freedom, and local static balance; Penrose's two null\n  families, exact square-root-area optical chain, separate noncompact Cauchy\n  hypothesis and degree obstruction, and future-null-only conclusion.\n  Countermodels reject promoted curvature divergence, timelike\n  incompleteness, and event-horizon claims. The\n  Raychaudhuri client additionally retains dust stress-energy, density\n  conservation, anisotropy and rotation equality criteria, spin\n  identification, the nonspinning time-bound equality case, and the paper's\n  observational distinction between anisotropy and extra freedom in the\n  cosmological constant. Those details deliberately do not enter the shared\n  focusing model. The\n  grounded form transfers all thirteen shared claims. One eighteen-component\n  audit shows that changing any retained index or relation fails the original\n  context's exact semantics; a separate direct finite model shows that each\n  of the same eighteen changes destroys nonvacuous focusing itself.\n  Countermodels block\n  setup-to-contraction,\n  contraction-to-finite-collapse, profile-collapse-to-focusing, vacuous\n  implication, false-setup grounding, grounding-to-technical-route, and\n  theory/world-to-technical-route shortcuts.\n- `PhysicsLogic/Framework/TrappedSurfaceIncompleteness.lean`: the narrow\n  global-relativity inference derived by Penrose 1965 and reused by Hawking\n  1965 after his independent cosmological trapped-sphere calculation. It\n  separates global causal setup, a closed surface trapped in\n  a selected time direction, finite focusing under temporary directional\n  null completeness, compactness of the associated causal boundary, and the\n  noncompact-Cauchy topology obstruction. The conclusion is directional null\n  geodesic incompleteness. The output-led established proposition retains the\n  exact selected global and trapped-surface setup, all three conditional\n  reductio outputs, and directional incompleteness. A checked theorem\n  reconstructs the complete applicable route instead of storing it.\n  Its proof-free model retains all seven selected physical objects and all\n  twelve relation families used by the route, for nineteen semantically\n  observable components. The eight claims include exact model selection and\n  a direct nonvacuous directional-incompleteness endpoint. That endpoint\n  requires actual global setup, actual trapping, the conditional reductio\n  laws, and rejected directional completeness at one model, without\n  pretending that the discharged complete branch is an actual spacetime.\n  Its structural-explanation projection uses distinct proof-free constraint\n  and phenomenon types. The constraint retains the Cauchy surface, trapped\n  surface, causal boundary, and full reductio scope; the phenomenon retains\n  only the selected spacetime, time direction, and regime. Exact route\n  applicability satisfies the constraint and directly necessitates rejected\n  directional completeness without consuming an established-result wrapper.\n  Penrose realizes this projection for future collapse, while Hawking realizes\n  it for a past-trapped cosmology by applying the imported Penrose global\n  argument. A partial route without the topology obstruction does not explain\n  incompleteness, and incompleteness without trapping or the reductio does not\n  explain itself.\n  A stronger source-sensitive projection now preserves that historical and\n  logical asymmetry. Penrose's typed token requires the granular orthogonal-\n  congruence selection, optical-scalar evolution, finite-affine area collapse,\n  caustic interpretation, compact-boundary calculation, and degree\n  obstruction. Hawking's distinct token requires his flat/open large-sphere\n  convergence calculation and explicitly imported Penrose focusing,\n  compact-boundary, and topology contracts. A completed reductio and ordinary\n  explanation with an unrealized source relation has no source-sensitive\n  explanation, so the common directional conclusion cannot manufacture its\n  derivational history.\n  A finite direct audit makes six realized indices and nine realized\n  relations affect that endpoint; a separate theorem records that the\n  boundary index and three discharged-branch relations are retained but not\n  individually direct facts after completeness is rejected.\n  Distinct calculation, theory, and world roles make transfer explicit.\n  Model membership and world representation require the exact selected model,\n  actual global and trapped-surface setup, and explicit paper-local use and\n  representation bridges.\n  Neither relation assumes focusing,\n  compact-boundary, topology-obstruction, or incompleteness results.\n  `theory_model_inputs_establish_grounding` packages those setup-only inputs,\n  and grounding projects back to that selected setup. A typed countermodel\n  exhibits complete grounding while the topology step and technical route are\n  false; another realizes every direct output on a non-selected model and\n  proves that it cannot ground. Penrose grounds the model in his governed\n  nonspherical-collapse and trapped-surface construction; Hawking grounds it\n  in the expanding flat/open model and large-sphere optical calculation. Each\n  paper has a named adapter proving that its inputs realize the selected\n  incompleteness setup.\n  Penrose names and certifies one collapse model. Hawking separately names\n  and certifies its homogeneous and perturbed cosmological models, preventing\n  the two source routes from sharing an ambiguous selection.\n  Each paper combines that independent grounding with its separately\n  established reductio. The component now conditionally imports\n  `TrappedSurfaceStability`: an output-led established robustness result can supply the\n  target trapped-surface setup only through a paper-local admissibility\n  bridge. The lower component's proof-free model retains all nine selected\n  indices and the five relation families used by that route. Its nine\n  claims include exact semantic selection, the selected realized setup, and the direct\n  `NonvacuousTrappedSurfaceStabilityAt` result. The exact-model mutation\n  audit rejects every changed index or relation, and a separate direct\n  fourteen-component audit shows that each change destroys the inhabited\n  stability proposition itself. Penrose and Hawking each\n  construct the context-derived model, prove exact retention, and ground it\n  from the exact realized reference and controlled-target setup independently\n  of target trapping or the stability calculation. Hawking's grounding\n  therefore explicitly consumes the large-sphere convergence calculation\n  that establishes the reference trapped surface. Both also project their established results to\n  the direct nonvacuous result. Penrose composes controlled nonspherical\n  stability into the future-directed reductio; Hawking composes finite-margin\n  perturbative stability into the past-directed reductio. Global causality,\n  null energy, focusing, boundary compactness, and topology remain independent\n  inputs. The generic direct incompleteness endpoint remains\n  stability-agnostic, while their source-order routes additionally expose\n  `NonvacuousStabilitySupportedDirectionalNullIncompletenessAt`. That\n  composite endpoint retains the direct nonvacuous stability child, exact\n  output-led established stability result, paper-local admissibility bridge, actual upper\n  trapped-surface setup, and direct directional-incompleteness result\n  together.\n  The stronger\n  `SourceSensitiveStabilitySupportedDirectionalNullIncompletenessAt`\n  additionally matches the exact description, target spacetime, trapped\n  surface, direction, and regime across both selected models. It retains the\n  inhabited composition, independent source-sensitive stability and global\n  explanations, and a third paper-local joining derivation. Penrose's\n  adapter exposes his actual optical-scalar equation and future-directed\n  noncompact-Cauchy degree obstruction. Hawking's new perturbed-universe\n  source cannot be replaced by the homogeneous source: its joining adapter\n  retains the literal large-sphere/Friedmann formula, both original and\n  perturbed past-null convergence branches, strict margin and perturbation\n  control, broken exact local symmetry, and the imported perturbed global\n  reductio. A physical countermodel distinguishes future collapse from past\n  open cosmology, direct from covering-space routes, and the unequal `3/2`\n  and `13/2` cosmological convergences while proving that completed child\n  explanations do not manufacture their missing joining derivation.\n  A typed countermodel establishes stability in one context while the upper\n  context rejects target trapping. Other countermodels show that\n  implication-valued reductio bridges can be vacuous without the global\n  causal setup, that a completed reductio does not supply theory/world\n  soundness, and that directional incompleteness at theory and world level\n  does not reconstruct the trapped-surface route. A nineteen-component\n  mutation audit rejects every changed selected object or relation. A finite\n  composed witness realizes stability-supported incompleteness, while a\n  converse model realizes generic incompleteness with a vacuous stability\n  child and rejects the composite endpoint. Lorentzian geometry,\n  Einstein equations, energy tensors, curvature divergence, black holes,\n  cosmic censorship, collapse dynamics, and cosmological optical\n  calculations remain paper-local.\n- `PhysicsLogic/Framework/ValidatedNumericalPrediction.lean`: the lower-level\n  numerical inference independently realized by Fermi-Pasta-Ulam 1955,\n  Zabusky-Kruskal 1965, and Creutz 1980. It separates regime and observable\n  selection, protocol execution, calculated validation checks, the\n  observable-specific reliability bridge, the paper-local numerical\n  calculation, and the bridge identifying its reported value as a physical\n  prediction. Its proof-free calculation model retains the system, run,\n  regime, observable, reported value, and all nine proposition-valued\n  relation families used by the route. The output-led established result\n  retains exact selected setup plus the direct protocol, validation,\n  reliability, calculation, representation, and prediction facts at the\n  model's selected reported value. The complete implication-valued route,\n  both calculations, and both interpretation bridges are reconstructed from\n  those outputs. The component\n  distinguishes the finite calculation model from a theory and represented\n  world. Pre-calculation grounding requires exact retained semantics plus the\n  valid regime and selected observable, but no protocol, validation,\n  reliability, numerical calculation, selected result, or prediction. FPU\n  grounds the finite-chain setup, Zabusky-Kruskal the physical periodic KdV\n  setup, and Creutz the finite-cutoff measured-loop setup. The final grounded\n  result separately combines this certificate with the complete numerical\n  route and selected reported value; all three adapters expose complete\n  theory/world transfers. The established result alone exposes the selected\n  result, realizes every claim, and establishes the direct inhabited route.\n  A countermodel proves that an existential result at a different value\n  cannot establish the selected prediction. The thirteen-claim vocabulary\n  exposes exact semantic selection, setup, protocol, both calculations, both\n  interpretation bridges, validation and reliability outputs, the selected\n  numerical result, prediction, and established route. A sensitivity theorem\n  distinguishes every explicit-index change as a different model and rejects\n  every retained-relation change as a failure of exact semantic retention.\n  The same established output also yields a direct inhabited-route proposition:\n  validity, observable scope and selection, protocol, validation, reliability,\n  calculation, result representation, and prediction all hold at one selected\n  five-index model. An exact finite witness realizes this proposition, while\n  exhaustive activity theorems show that changing any of the five indices or\n  nine relation families destroys it. FPU, Zabusky-Kruskal, and Creutz expose\n  source-anchored adapters to this direct route; the Zabusky-Kruskal adapter\n  preserves its existentially calculated recurrence state.\n  The component now also exposes ordinary and source-sensitive structural\n  explanations of that direct prediction. The ordinary explanation records\n  the applicable selected numerical route and its situated predicted\n  phenomenon. The source-sensitive explanation additionally requires a typed\n  paper-local derivation relation, without consuming an established endpoint\n  or flattening that derivation into generic numerical prose. FPU retains its\n  finite-difference modal-energy validation and one-percent return source,\n  Zabusky-Kruskal retains periodic-KdV validation, soliton focusing, and\n  waveform reconstruction, and Creutz retains equilibrium checks, finite-size\n  Wilson-loop stability, and the selected loop fit. A countermodel realizes\n  the ordinary explanation while refuting the absent source derivation, so\n  the two explanation levels cannot collapse.\n  Countermodels show that a completed numerical route alone does not supply\n  theory/world grounding, that a grounded numerical setup need not complete\n  reliability or prediction, that numerical outputs without the selected\n  physical setup cannot ground a model, and that declared theory and world\n  claims do not reconstruct the numerical route. Discretization, convergence, Monte Carlo,\n  recurrence, finite-size scaling, and continuum semantics remain paper-local.\n- `PhysicsLogic/Framework/ValidatedNumericalNearReturn.lean`: the narrower\n  numerical-evidence inference independently realized by Fermi-Pasta-Ulam\n  1955 and Zabusky-Kruskal 1965. It separates run and regime selection,\n  protocol execution, validation checks, their interpretation as reliability\n  for an explicitly selected return observable-neighborhood criterion, and a\n  paper-local evolution calculation yielding return to that same neighborhood\n  at positive time. FPU selects first-mode energy within one percent;\n  Zabusky-Kruskal selects waveform-profile reconstruction. Its explicit applicability\n  proposition requires all of these inputs together before the established\n  result. The return calculation is indexed by the model's selected final\n  state, and the output-led established proposition directly retains exact\n  selection, setup, protocol, checks, reliability, selected evolution, and\n  selected neighborhood return. Named projections recover the setup,\n  validation calculation, reliability interpretation, return calculation,\n  reconstructed complete route, existential recurrence, and flattened compatibility result. Countermodels prevent\n  implication-valued calculations from becoming applicable when the protocol\n  is absent. `NonvacuousValidatedNumericalNearReturnAt` is now part of the\n  established result itself rather than requiring a second selected-result\n  certificate. A finite witness\n  realizes that proposition, while six index mutations and nine relation\n  mutations show that every route-used component matters; the protocol-free\n  implication model fails the direct proposition. FPU and Zabusky-Kruskal\n  expose named paper adapters to it, with Zabusky-Kruskal preserving its\n  existentially calculated recurrence state. The component now also\n  distinguishes the finite near-return\n  calculation from a theory and represented physical system. Paper-local\n  theory-use and representation bridges are grounded from the exact selected\n  model and physical near-return setup alone. FPU uses its finite-chain setup;\n  Zabusky-Kruskal uses its physical KdV setup and positive recurrence time.\n  Protocol, validation, reliability, evolution, neighborhood return, and the\n  selected final-state result remain downstream. Named paper-local setup\n  adapters certify exactly this grounding boundary. Once separately established,\n  those claims transfer without adding exact recurrence, ergodicity, or\n  thermalization. Exhaustive realization follows from establishment alone.\n  FPU names its\n  reported return state, while Zabusky-Kruskal preserves an existentially\n  selected state. A shared witness bridge now turns either selected\n  near-return result into the lower-level selected numerical result and\n  derives all thirteen numerical-prediction claims without repeating the\n  evolution-and-neighborhood proof. Both paper adapters expose named complete\n  theory/world transfers for all ten near-return claims. Countermodels show\n  that a completed numerical route does not supply semantic grounding, that\n  grounded setup does not supply the numerical route, and that declared\n  theory/world claims do not reconstruct it. They also show that reliability\n  for a foreign observable criterion cannot establish the selected return,\n  and that numerical outputs without the physical setup cannot ground a model.\n  `SourceSensitivePredictionSupportedNumericalNearReturnAt` additionally\n  retains exact lower/upper model selection, their derived-model equality,\n  the inhabited positive-time return, independently sourced prediction and\n  return explanations, and a paper-local joining derivation. FPU's handoff\n  retains its fixed-endpoint quadratic equation, finite chain, Fourier modal\n  analysis, independent total-energy/linear controls, and explicitly\n  neglected nonlinear modal-potential contribution. Zabusky-Kruskal's\n  handoff fixes the actual recurrence state in both models and instead\n  retains the KdV and isolated-pulse equations, period-two cosine profile,\n  exact momentum but approximate energy conservation, unresolved soliton\n  collisions, phase focusing, worsening second return, and open asymptotic\n  scope. A concrete countermodel preserves all physically different FPU/KdV\n  data and both sourced explanations while proving that neither determines\n  a missing joining derivation.\n  Nonlinear-chain, KdV, modal-energy,\n  soliton, mixing, ergodicity, equipartition, and thermalization semantics\n  remain paper-local.\n- `PhysicsLogic/Framework/PowerSpectrumSamplingVariance.lean`: the narrow\n  one-realization estimator inference independently realized by\n  Scott-Srednicki-White 1993 and Knox 1995. Both primary calculations now\n  require actual measured fields: the shared quadratic readout computes the\n  estimator, correlations, and fourth moments from one ensemble and retains\n  a Wick-defect correction until the separate Gaussian moment identity is\n  supplied. The finite-patch route derives its angular variance integral;\n  the full-sky route retains the real-mode count, noise subtraction, and beam\n  calibration while deriving residual variance. Knox's full affine estimator law\n  requires a separate joint Gaussian law and retains negative estimates and\n  general multipoles. Independent equal-area finite fields test variances\n  2 and 1 from different actual correlations. Its proof-free route model retains four\n  selected physical indices plus all ten route-used maps and relation\n  families, including the realization estimator and ensemble target. The\n  context owns all four indices and constructs one `selectedCalculation`, so\n  changing the model, sky, observable, or experiment fails exact semantics. Its\n  explicit applicability proposition requires exact selected semantics, the\n  single-realization setup, and the paper-local calculation, preventing either\n  ambient relation substitution or vacuous use of the calculation implication.\n  The established result is output-led: exact selected semantics plus the\n  actual one-realization setup, estimator outputs, distinct estimates,\n  sampling variation, and failure of exact ensemble recovery. The original\n  implication-valued estimator calculation and complete route are reconstructed\n  from those direct outputs. Generic grounding requires exact model identity\n  and the observed, possible, accessible, noise-free realization setup, but no\n  estimator law, variance calculation, or sampling conclusion.\n  Knox remains experiment-parameterized: each theorem instance owns its\n  selected full-sky experiment rather than imposing one global experiment.\n  Scott-Srednicki-White retain finite coverage, the zero-lag estimator,\n  beam/chopping treatment, the theory-distribution versus realized-value\n  distinction, and Gaussianity in their own named exact model. A first-class\n  exhaustive theorem realizes all seven shared claims, beginning with the\n  selected-semantics certificate; both papers expose named grounded transfers\n  for every claim. Countermodels separate exact selection from inhabited\n  grounding, technical completion from grounding, grounding from the technical\n  route and direct outputs, and declared theory/world claims from reconstruction\n  of the route. Its retained sensitivity model has an actual\n  observed setup and two possible skies with different estimates. A direct\n  activity theorem makes each physical index affect a route-used predicate,\n  while a fourteen-component sensitivity audit checks that every index, map,\n  and relation mutation fails exact semantics. Independent sky patches remain\n  local to Scott-Srednicki-White's later area-scaling approximation. Gaussian\n  and chi-square laws, CMB multipoles, spherical angular kernels, sky fractions,\n  beams, scan geometries, and experiment-specific numerical forecasts remain\n  paper-local. A separate source-valued physical audit nevertheless retains\n  Scott's fourth-moment contraction, `2/A^2` sample-variance integral,\n  `1/(4 pi)` convolved-window normalization, `8/A^3` skewness, distinct small-\n  and large-area limits, qualified independent-patch estimate, correlation-\n  dependent scan area, and variance-versus-temperature distinction. Its Knox\n  witnesses retain `2l+1` Gaussian full-sky modes, strictly positive noise-free\n  cosmic variance, the finite-weight beam-deconvolved noise term, improved\n  resolution at fixed detector weight, conditional `0.016`, `0.11`, and\n  `0.003` forecasts, nuisance dominance, and the cosmological-constant\n  correction to lowest-order tensor consistency. Independent negative controls\n  reject erased premises and formulas; unqualified area laws, complete\n  foreground models, unconditional measurements, universal tensor relations,\n  and resolved cosmological degeneracies are not silently established.\n- `PhysicsLogic/Framework/Conservation.lean`: shared\n  balance-to-conservation semantics extracted from Noether 1918 and Einstein\n  1916. It separates a local or covariant balance equation, the physical\n  scope in which it may be interpreted as conservation, and the explicit\n  paper-local bridge yielding the conservation conclusion. Its proof-free\n  model retains the selected quantity, system, and regime together with the\n  balance, scope, and conservation relation families. The context owns those\n  three indices and exposes their unique `selectedModel`; a candidate cannot\n  select itself by changing them. Noether fixes the represented physical\n  history, while Einstein fixes its unit-typed balance indices around one\n  matter tensor and situation. Both construct named context-selected models\n  and prove exact semantic-retention certificates. Applicability consumes that\n  certificate and retains the\n  balance, scope, and bridge without assuming the conclusion. The established\n  result is output-led: it stores exact selected balance-and-scope setup plus\n  the direct conservation output, while checked theorems reconstruct the\n  implication-valued bridge and complete route. The route also realizes a\n  typed structural explanation whose balance constraint and conserved\n  phenomenon are distinct. Noether and Einstein now derive that explanation\n  directly from their source inputs and the applicable route, before any\n  terminal shared endpoint is consumed. Noether's multidimensional on-shell\n  divergence argument and Einstein's covariant absent-exchange reduction\n  remain different mechanisms; the adapter does not attribute Noether's\n  symmetry derivation to Einstein. A stronger source-sensitive constraint\n  now retains those derivations as different typed values governed by\n  proposition-valued source relations. Its accessor recovers the selected\n  derivation, while a countermodel retains the complete balance route,\n  established conservation, and ordinary structural explanation with every\n  candidate source relation false. The established-result projections remain\n  compatibility paths. It imports `Philosophy/TheoryModel.lean` and\n  `Paradigm/ExplanationModes.lean` and\n  accepts paper-local theory/world interpretations. Grounded conservation\n  requires a separate proof that the exact selected balance model has an\n  actual balance equation and conservation scope, belongs to the selected\n  theory, represents the selected physical case, and transfers soundly. This\n  grounding does not require the interpretation bridge, applicability, or\n  conservation output. Countermodels\n  prevent missing premises or a vacuous implication-valued bridge from\n  silently establishing the route, separate completed conservation from\n  semantic grounding, exhibit a grounded balance-and-scope setup without a\n  bridge or output, reject grounding from an output without that setup, and\n  show that theory/world claims do not reconstruct the balance route.\n  Conservation for an independent reason also fails the structural balance\n  explanation. A\n  complete mutation audit proves that changing any of the three\n  indices or three relation families fails the original context's exact\n  semantics. A separate active finite model makes the selected balance,\n  physical scope, interpretation bridge, and conservation conclusion all\n  true together. Direct route-content theorems show that changing any index\n  or relation destroys this nonvacuous result. Noether's multidimensional\n  `Div B = 0` route and Einstein's absent-gravitational-exchange route each\n  expose the same stronger proposition through named paper theorems.\n- `PhysicsLogic/Framework/ConstraintConsistencyCompletion.lean`: narrow\n  constrained-dynamics semantics extracted from Dirac 1950 and\n  Anderson-Bergmann 1951. Its proof-free model retains the constrained system,\n  selected Hamiltonian dynamics, one actual primary constraint, primary\n  family, completed family, and all six relation families that give those data\n  their shared meaning. Exact eleven-component semantics is required before\n  the route can establish that the selected constraint belongs to the primary\n  family, exclude a contradictory consistency branch, and use a\n  paper-local calculation proving primary inclusion and preservation under the\n  same dynamics. The established result is exact selection plus the direct\n  model-native\n  `NonvacuousConstraintConsistencyCompletionAt` proposition, and derives\n  all ten shared claims and concrete completion and preservation of that\n  selected primary. The ordinary structural explanation retains the complete\n  selected route without requiring paper provenance. A stricter\n  source-sensitive explanation wraps that ordinary constraint, requires an\n  independently realized typed paper derivation, exposes it, and entails the\n  ordinary explanation when provenance is forgotten. Both execute the\n  complete route to obtain primary inclusion and completed-family\n  preservation. Dirac supplies the type-II iterative weak-constraint\n  completion of equations (22)-(25); Anderson-Bergmann supply the canonical\n  primary construction and invariant-generator/Hamiltonian-bracket iteration.\n  Dirac's paper-local module separately retains equations (5)-(11) as a\n  finite-indexed value-level Hamiltonian-construction package: the\n  Hamiltonian definition and variation, weak canonical equality, strong\n  primary-constraint shell equality, and the two coordinate equations. That\n  package remains local because the shared completion component needs only\n  constraint inclusion and preservation, not Dirac's particular variational\n  construction.\n  Anderson-Bergmann's electromagnetic specialization separately retains\n  equations (6.6)-(6.9) as pointwise value-level momentum,\n  primary/secondary surface, generator-density, and bracket-chain\n  propositions over a nonempty field-point domain; a countermodel prevents\n  the final count/algebra labels from standing in for those formulas.\n  Its coordinate specialization likewise retains the structural content of\n  equations (7.1)-(7.7): pointwise Legendre degeneracy and primary surfaces,\n  four distinct primary and four distinct secondary constraints,\n  primary-proportional velocity dependence in the generator, the\n  quasi-inverse identity, velocity-bracket rule, and closing bracket pattern.\n  A second countermodel prevents the eight-count, velocity label, and algebra\n  flag from replacing that package.\n  The shared boundary readout now separately retains an actual preservation\n  transition, constraint values at its endpoints and two candidate orbit\n  points, first-class or invariant-generator bracket closure, independent\n  generator count, orbit dimension, and physical-identification residual.\n  Its checked model bridge ties those values to the same selected system,\n  primary member, completed family, state membership, evolution, and\n  satisfaction relation as the consistency route. A completed constraint\n  without closure, generator, orbit, or identification does not become\n  gauge; generator closure alone does not preserve a constraint; and a\n  positive finite witness shows that consistency and physical gauge\n  identification are compatible when all required data are present. Dirac's\n  first-class solution-orbit witness retains preservation and a nontrivial\n  orbit while withholding physical identification; Anderson-Bergmann's\n  invariant-generator witness retains bracket closure while losing the\n  constraint under canonical evolution.\n  Their classification, function-group, and finite-count conclusions\n  remain outside the shared phenomenon. Dirac\n  and Anderson-Bergmann construct named exact models and ground them through\n  separate paper-local theory-use, world-representation, and claim-transfer\n  predicates plus the inhabited, noncontradictory selected setup. Grounding\n  assumes no completion calculation, inclusion, preservation, route, or\n  result. Countermodels\n  separate setup, inclusion, preservation, technical completion, and semantic\n  grounding; an empty-family model blocks vacuous universal laws, and an\n  eleven-component equality audit detects every retained datum and relation.\n  A stronger countermodel keeps the complete endpoint, reconstructed route,\n  and ordinary structural explanation while falsifying the paper-local\n  derivation relation, so ordinary completion logic cannot manufacture\n  source provenance.\n  A separate finite initial-to-final witness makes all five selected data and\n  six relation families directly active in the nonvacuous completion\n  proposition.\n  Legendre maps, constraint classes, gauge generators, electromagnetic and\n  coordinate canonical formulas, finite counts, and quantization remain\n  paper-local.\n- `PhysicsLogic/Framework/CanonicalGeneratorBracketClosure.lean`: narrow\n  canonical-generator closure semantics extracted independently from Dirac\n  1950 and Anderson-Bergmann 1951. Each paper-local context owns the selected\n  canonical system, admissible-generator family, and bracket relation. Its\n  unique proof-free model retains those data and all three context selection\n  relations. The setup evaluates those retained relations, and each paper\n  proves equality with the exact context model before route applicability, so\n  candidate data cannot select themselves. A separate calculation yields\n  nonemptiness and pairwise admissible representatives. Dirac\n  realizes admissible generators as first-class constraints;\n  Anderson-Bergmann realizes them as generators of infinitesimal invariant\n  canonical transformations. The bracket is relational so linear-combination\n  or equivalent representatives need not be identified syntactically. The\n  established result is output-led: it retains exact selected semantics and\n  the direct nonvacuous closure output. Complete setup, calculation, and route\n  witnesses are reconstructed from those facts, with separate\n  theory/model/world grounding. The model-native\n  `NonvacuousCanonicalGeneratorBracketClosureAt` proposition records the\n  selected system, both selection relations, an admissible generator, and\n  pairwise admissible bracket representatives without relying on an\n  implication-valued calculation. Both paper adapters now expose that direct\n  inhabited result, alongside named certificates transferring all eight\n  retained claims to their selected theory and represented physical system.\n  The complete route additionally realizes a typed structural explanation of\n  the selected nonempty pairwise closure. A finite countermodel retains an\n  inhabited closed family but removes canonical-system selection, proving\n  that algebraic closure alone does not reconstruct the explanation. Dirac\n  and Anderson-Bergmann independently realize the route-bounded endpoint.\n  Grounding uses an actual canonical setup plus pre-calculation theory and\n  world inputs, but no bracket calculation or result. A false-setup model is\n  proved ungroundable; a separate setup-complete nonclosed model is grounded\n  while route applicability remains false. The false-setup calculation also\n  shows why implication-valued calculations cannot stand in for outputs. A\n  concrete finite witness exhibits two admissible inputs and an admissible\n  bracket result. Direct activity theorems make every selected datum and\n  retained selection relation destroy the model-native nonvacuous result when\n  changed, while a separate six-component sensitivity audit checks exact\n  retention.\n  Its three directional shared countermodels now retain canonical phase\n  dimension, admissible-generator count, canonical-selection and left/right/\n  bracket-admissibility residuals, a bracket representative and its distinct\n  constraint-combination value, a Hamiltonian bracket and its separate\n  constraint-combination value, and theory/model/world mismatches. A false\n  canonical selection makes the implication-valued closure calculation\n  vacuous; pairwise closure with Hamiltonian bracket two and constraint\n  combination one blocks compatibility; completed closure with nonzero\n  grounding mismatches blocks physical transfer. A checked positive witness\n  realizes all four boundaries. No proposition-pair truth table replaces\n  these canonical-bracket distinctions.\n  The framework now also composes the independently inhabited\n  `ConstraintConsistencyCompletion` result with actual generator closure\n  through a proof-free, source-order-aware handoff. Dirac's completed-first\n  route retains the selected weak primary, an independently completed\n  first-class representative, and the equation-(43) Poisson-identity\n  calculation. Anderson-Bergmann's generator-first route retains the\n  invariant descriptor extension, quadratic-primary generator ambiguity,\n  equation-(5.6) function-group calculation, separate Hamiltonian-bracket\n  compatibility, and subsequent preservation iteration. A stronger\n  `SourceSensitiveCompletedConstraintGeneratorClosureAt` contract selects\n  both child contexts exactly and independently retains their two\n  source-sensitive structural explanations together with a third typed\n  paper-local handoff derivation. Its projections recover each derivation\n  separately, and its generator-first projection still requires the actual\n  Hamiltonian-bracket calculation. Dirac's handoff explicitly has no such\n  Hamiltonian-bracket premise. An additional inhabited countermodel keeps\n  both completed child results, their two source-sensitive explanations, the\n  completion-first order, and the absence of Hamiltonian-bracket compatibility\n  while withholding the third handoff derivation; the sourced composition\n  consequently fails. Eight finite countermodels distinguish the source\n  orders, reject completed outputs\n  without their paper-local handoff, separate completion from closure in\n  both directions, withhold Hamiltonian compatibility from generator\n  closure, reject route reclassification, and retain a nontrivial\n  constraint-surface orbit without asserting physical gauge identification.\n  Poisson-bracket construction, closure with the Hamiltonian, integrability,\n  orbit dimension, gauge interpretation, and application-specific constraint\n  algebras remain paper-local.\n- `PhysicsLogic/Framework/ProjectorValuationObstruction.lean`: narrow shared\n  complete-projector obstruction semantics extracted from Bell 1966 and\n  Kochen-Specker 1967. Its explicit route requires an actual available\n  projector in a complete compatible context, complete reference contexts for\n  every projector, and a paper-local calculation excluding every global\n  exactly-one coloring. The established result retains those inputs, excludes\n  a context-independent model, and realizes the generic contextuality\n  obstruction. The model-native\n  `NonvacuousProjectorValuationObstructionAt` proposition packages the\n  inhabited complete context, complete reference coverage, no-coloring result,\n  and context-independent-model exclusion directly. One exhaustive theorem\n  realizes all six shared claims, and both paper adapters expose named direct,\n  exhaustive-realization, and grounded-transfer certificates. A data-only\n  calculation model is explicitly separated from the quantum theory using it\n  and the physical measurement situation it represents. Grounding does not\n  consume either no-coloring result. Bell uses only the\n  dimension-greater-than-two condition, his selected projector in a complete\n  reference arrangement, and both real/binary constraint translations;\n  Kochen-Specker's finite 117-direction calculation explicitly retains an\n  inhabited complete projector context before its no-coloring output, then\n  separately uses the commutative-embedding, spin-one, and rhombic-field\n  bridges. Its paper-local spin-one readout additionally retains actual\n  normalized rays, complex angular-momentum commutators, squared-spin\n  projectors and Casimir, all three source Hamiltonian polynomials,\n  distinguishable energy outcomes, and separate adjustable-orthohelium versus\n  fixed-nickel field controls. The displayed source proposition means nonzero\n  spin; a checked complement theorem translates it to the shared zero-spin\n  exactly-one convention. The printed longitudinal-matrix normalization\n  typo is excluded from the physical assumptions. Its ordinary structural\n  explanation now uses only the exact\n  scenario and applicable no-coloring route to derive the conditional\n  contextuality phenomenon. A separate source-sensitive refinement adds a\n  typed paper derivation: Bell retains both real/binary translations and the\n  Gleason obstruction, while Kochen-Specker retains the finite 117-direction\n  calculation. The stronger explanation exposes its derivation and entails\n  the ordinary explanation. Neither route claims indeterminism or a universal\n  hidden-variable impossibility. Countermodels show that an empty declared\n  complete context can satisfy a no-coloring proposition without realizing\n  the direct obstruction,\n  that technical completion does not automatically supply theory/world\n  grounding, that grounding does not supply the obstruction route, and that\n  declared contextuality in a theory and world does not reconstruct the\n  coloring route. A finite logical witness realizes the complete obstruction\n  route together with locally consistent contextual values; with its source\n  derivation relation made false, the same outputs and ordinary explanation\n  have no source-sensitive structural explanation. Direct activity\n  theorems distinguish availability, completeness, assigned values, and\n  reference-context choice: changing assigned values can preserve the direct\n  no-go while breaking local exactly-one satisfaction, because neither paper\n  claims to construct a contextual hidden-variable model. Exact model\n  retention remains a separate four-family audit.\n  Gleason theory,\n  finite coloring constructions, spin realizations,\n  apparatus dependence, and measurement bridges remain paper-local.\n- `PhysicsLogic/Framework/DiscreteSymmetryVacua.lean`: shared finite-symmetry\n  vacuum-counting semantics extracted from Witten 1982 and\n  Seiberg-Witten 1994 formalization. It separates exact law symmetry,\n  spontaneous breaking, parent and residual orders, properness of the\n  residual subgroup, the physical coset-to-vacuum bridge, applicability of\n  the counting route, and an independent vacuum calculation. The output-led\n  established prediction is exact selected semantics together with the direct\n  `NonvacuousSymmetryBreakingPredictionAt` proposition requiring a proper\n  residual subgroup, exact count, and more than one vacuum. Checked theorems\n  reconstruct the complete counting route from those outputs. The agreement proposition\n  separately retains an independent calculation. A\n  proof-free calculation model retains system, regime, parent order, residual\n  order, predicted count, and exactly the five route-used relation families:\n  exact law symmetry, spontaneous breaking, both order readouts, and the\n  vacuum-count readout. Each paper constructs a named context-induced model\n  from five context-owned indices and proves exact ten-component retention\n  before route applicability or grounding. A candidate with a changed system,\n  regime, parent order, residual order, or predicted count cannot certify\n  itself against values read back from that candidate. Paper-local bridges\n  transfer exact symmetry, spontaneous\n  breaking, proper residual order, arithmetic, coset realization, the derived\n  count, and multiplicity to a theory and represented world. Model grounding\n  itself uses only that exact-model certificate and paper-local\n  interpretation; it does not assume any breaking, properness, arithmetic,\n  coset, count, or multiplicity claim. The established result realizes all\n  fourteen shared claims. Exact-retention mutations detect every changed\n  index or relation family, and a positive finite order-four-to-order-two\n  model passes a stronger typed audit: each of the five selected-index\n  mutations and each of the five relation-family mutations destroys the\n  direct nonvacuous endpoint itself. A complete direct output tested against a\n  context selecting another system also fails establishment. A collapsed breaking label with parent\n  order equal to residual order is a checked countermodel: it can satisfy the\n  trivial one-vacuum arithmetic while failing both proper residual order and\n  the direct nonvacuous endpoint. A second countermodel retains the correct\n  count and coset arithmetic while lacking spontaneous breaking, and therefore\n  also fails the direct endpoint. Witten's context selects rank `N`, a\n  four-dimensional\n  regime with infinite spatial volume, and counting data `(2N, 2, N)`, then\n  grounds that conditional count in pure `N = 1` `SU(N)`. Seiberg-Witten\n  selects a four-dimensional, zero-matter `SU(2)`\n  gauge system together with a regime recording the `N = 2` parent, preserved\n  `N = 1`, and preserved `Z4`, followed by the fixed count data `(4, 2, 2)`.\n  It grounds the order-four to order-two count in that distinct mass-deformed\n  `N = 1` theory, then separately checks agreement with the two vacua obtained\n  from its monopole and dyon singularities.\n- `PhysicsLogic/Framework/QuantumCurrentAnomaly.lean`: narrow shared\n  current-level anomaly semantics independently realized by Adler 1969,\n  Witten 1982, and Seiberg-Witten 1994. It separates selection of the physical\n  system and current, classical conservation, the paper-local quantum\n  calculation, the bridge to failed quantum conservation, and the criterion\n  identifying the obstruction as an anomaly. The output-led established\n  proposition retains exact selected classical-current setup, the performed\n  quantum calculation, failed conservation, and identified anomaly. The\n  implication-valued bridge, criterion, and complete route are reconstructed\n  from those outputs. It also projects a direct\n  `NonvacuousQuantumCurrentAnomalyAt` result with the setup, calculation,\n  actual conservation obstruction, and identified anomaly. A finite\n  inhabited model realizes this proposition; exhaustive direct mutations show\n  that either selected index or any of the six relation families destroys it.\n  A proof-free calculation model records\n  the selected system and current together with all six relation families\n  used by the route: system selection, current selection, classical and\n  quantum conservation, the paper-local quantum calculation, and anomaly\n  identification. The context owns the two selected indices and constructs a\n  unique `selectedModel`; exact semantics is equality with that model rather\n  than reconstruction from a candidate's own labels. Checked mutation\n  theorems reject both changed indices and all six changed relation families.\n  Each paper obtains its named model from that context-owned selection.\n  Separate theory and world wrappers\n  and paper-local interpretations control transfer of every shared claim.\n  Grounding consumes exact selected semantics, physical system and current\n  selection, classical conservation, and interpretation bridges; it does not\n  assume the quantum calculation, obstruction bridge, anomaly criterion, or\n  anomaly result.\n  Adler grounds the model in massless spinor electrodynamics, Witten in pure\n  four-dimensional `N = 1` `SU(N)` Yang-Mills at the selected rank, and\n  Seiberg-Witten in pure four-dimensional `N = 2` `SU(2)` Yang-Mills.\n  Their independent original anchors are Adler p. 2434, Witten p. 269, and\n  Seiberg-Witten author TeX §2. Witten p. 297 and Eq. (74) then calculate the\n  residual `2N` subgroup; that result and Seiberg-Witten's `Z8` calculation\n  remain in the downstream anomaly-restriction layer.\n  Every established result realizes all nine shared claims through one\n  exhaustive theorem, and all three paper adapters expose named realization\n  exact-retention, and grounded-transfer certificates.\n  Countermodels show both that vacuous implication-valued bridges cannot\n  replace the physical setup and calculation and that an established anomaly\n  does not automatically supply theory/world grounding. A further typed\n  countermodel grounds the selected classical-current setup while the quantum\n  calculation and established anomaly are false; the converse countermodel\n  supplies all quantum outputs but cannot ground a false selected setup. It does not calculate\n  a residual finite subgroup, spontaneous breaking, or vacuum multiplicity.\n- `PhysicsLogic/Framework/AnomalyRestrictedSymmetry.lean`: narrow shared\n  residual-symmetry semantics extracted from Witten 1982 and Seiberg-Witten\n  1994. It consumes an established shared current-anomaly route, then keeps\n  the anomaly-coefficient calculation, selected nontrivial anomaly sector,\n  residual-order calculation, candidate-subgroup measure invariance,\n  anomaly-phase obstruction of larger candidates, and exact finite-law bridge\n  separate. The established proposition is output-led: it retains exact\n  context selection together with the direct nonvacuous current anomaly,\n  coefficient, sector, order, phase-test, and exact finite-law outputs. The\n  embedded current result, exactness bridge, and full route are reconstructed\n  by checked theorems rather than stored as evidence. A proof-free\n  reduction model stores the selected system, symmetry, and residual order,\n  the complete upstream current-anomaly model, and all six downstream\n  relation families used by the route. The embedded current-anomaly context\n  owns the selected system and current, while this context owns the residual\n  order; together they construct one unique `selectedModel`. Each paper uses\n  that model and proves its exact certificate before applicability.\n  Coefficient, sector, order, phase, and exact-law claims remain\n  proposition-valued applications of those retained relations rather than\n  proof fields. Witten realizes coefficient and exact order `2N` at one\n  `SU(N)` rank; Seiberg-Witten realizes `4N_c-2N_f=8` and exact `Z8` in\n  microscopic pure `N = 2`, `SU(2)`.\n  `NonvacuousAnomalyRestrictedSymmetryAt` now drops exact-record equality\n  while retaining same-system/current ties, the nonvacuous upstream current\n  anomaly, coefficient, sector, order, positivity, both phase tests, and the\n  exact finite-law output directly on one proof-free model. Both paper\n  adapters project their completed calculations to that endpoint.\n  The route now also realizes\n  `DirectStructuralAnomalyRestrictedSymmetryExplanationAt` from its raw\n  applicability proof. The stricter\n  `DirectSourceStructuralAnomalyRestrictedSymmetryExplanationAt` retains a\n  typed paper-local derivation relation in addition to the same route;\n  forgetting provenance yields the ordinary explanation, while a finite\n  false-source countermodel proves that a completed endpoint cannot invent\n  provenance.\n  Witten's full section-8 instanton-phase restriction and Seiberg-Witten's\n  microscopic exact-`Z8` restriction are represented by distinct typed source\n  tokens and relations, separate from their narrower upstream current-anomaly\n  source relations.\n  The independent original anchors are Witten p. 297 and Eq. (74) and\n  Seiberg-Witten author TeX §2. Witten's conjectural condensate breaking and\n  Seiberg-Witten's later mass-deformation restriction remain downstream.\n  Grounding consumes the exact-retention certificate, upstream exact\n  current-model grounding, and paper-local theory/world interpretation; it\n  assumes none of the anomaly-reduction calculations or conclusions.\n  Both adapters expose exhaustive realization and grounded transfer for all\n  fourteen claims. Exact-record mutation theorems reject all three changed\n  indices and all seven changed model families; a separate route-active\n  finite model shows that each of those mutations also destroys the direct\n  nonvacuous endpoint itself. A second countermodel has all direct outputs but\n  fails exact context selection, so it cannot establish a result for the\n  wrong paper-selected system, current, or subgroup order.\n  Further countermodels show that coefficient\n  and order do not select a nontrivial sector, measure invariance does not\n  establish maximality, and complete phase data without an exactness bridge\n  does not establish the quantum law. The component does not identify the\n  surviving subgroup with a spontaneously broken phase; condensates, mass\n  deformations, and vacuum counting remain paper-local.\n- `PhysicsLogic/Framework/AnomalySelectedVacua.lean`: shared composition of\n  anomaly reduction, paper-local selection of the exact finite symmetry used\n  in the vacuum regime, spontaneous breaking, and coset vacuum counting.\n  Witten's selection preserves the anomaly-surviving order `2N`; the\n  Seiberg-Witten mass deformation instead selects `Z4` from `Z8` before\n  `Z4 -> Z2` breaking. Each paper exposes a named complete composite route\n  before the shared deduction. The output-led established result retains exact\n  selection of both child models plus direct anomaly, parent-selection, and\n  vacuum outputs. Named theorems reconstruct the anomaly route,\n  parent-selection interpretation bridge, spontaneous-breaking data, proper\n  residual order, subgroup arithmetic, coset bridge, and complete composite\n  route. It exposes both the child's direct\n  proper-subgroup, multiple-vacuum prediction and a direct composite endpoint\n  requiring nonvacuous anomaly restriction, paper-local parent selection, and\n  the multiple-vacuum prediction together. The implication-valued selection\n  bridge remains a route premise rather than counting alone as physical\n  activity. Its proof-free composite model is grounded through the two\n  setup-only parent model groundings and permits distinct anomaly-source and\n  vacuum-regime theories and worlds. Witten uses the same pure `N = 1` theory\n  for both roles and supplies classical chiral-current conservation;\n  Seiberg-Witten uses microscopic pure `N = 2` plus its classical current for\n  the anomaly role and only the presence of the `N = 1` mass deformation for\n  the vacuum role. Composite grounding fixes both exact context-induced parent\n  models, including the finite-vacuum model's five relation families, and the\n  paper-local semantic bridges; it consumes no anomaly-reduction,\n  parent-selection, breaking,\n  subgroup-arithmetic, coset, or vacuum-count route. Those claims transfer\n  only after the separately established composite result is joined to the\n  grounding. A checked countermodel has a nonvacuous vacuum child but no\n  active anomaly child, so the direct composite endpoint fails; another has\n  complete grounding while the composite route is false. Complete direct\n  outputs under a differently selected anomaly order can be neither\n  established nor grounded. The component keeps\n  currents, deformations, condensates, and vacua paper-local.\n- `PhysicsLogic/Framework/BoundaryGeneratingFunctional.lean`: shared\n  source-indexed functional and correlator-transfer semantics extracted from\n  Gubser-Klebanov-Polyakov 1998 and Witten 1998. Its explicit\n  route-applicability proposition\n  keeps functional equality, source generation, and the differentiation\n  bridge separate and source-specific. The established dictionary instead\n  stores exact model selection and the direct nonvacuous functional,\n  derivative, and correlator outputs; a checked theorem reconstructs the\n  complete route from those outputs. It projects to\n  `NonvacuousFullBoundaryDictionaryAt`, where one actual\n  selected source/bulk pair directly satisfies an inhabited variation scope,\n  admissibility, extension, functional equality, both derivative equalities,\n  and the resulting correlator equality. A finite witness and direct\n  two-index/seven-family\n  mutations make every retained component matter, while a vacuous derivative\n  bridge without a dictionary is explicitly rejected. A\n  proof-free source/bulk model is separately related to a containing theory\n  and represented boundary sector. Grounding fixes exact selection, an\n  inhabited variation sector, source admissibility, and boundary extension,\n  but no functional equality or correlator calculation. GKP grounds it in the D3 near-horizon,\n  leading-large-`N` strong-coupling regime using only the admissible source\n  and selected action-minimizing bulk extension. The Witten adapter grounds\n  its boundary CFT and classical bulk solution from the conformal boundary,\n  regime, source, boundary value, and bulk equation. Proposals, saddle\n  evaluations, source generation, differentiation, and correlator extraction\n  remain in the technical routes. A further countermodel satisfies every\n  direct functional and correlator output while withholding admissibility and\n  extension, so outputs alone cannot supply grounding. Other countermodels\n  separate grounding from both completed and incomplete dictionary\n  calculations. The module does not\n  define a generic holographic duality or import paper-local geometry and\n  spectra.\n  Both adapters expose named certificates transferring every retained\n  source-indexed dictionary claim to their selected theory and boundary\n  sector. Each also exposes the selected boundary source and bulk\n  configuration as direct checked field equalities. GKP's direct adapter is\n  source-anchored in author-TeX lines 484-520; Witten's is anchored in\n  author-TeX lines 612-705 and 772-825.\n- `PhysicsLogic/Framework/BulkBoundaryScalar.lean`: shared scalar\n  mass-dimension semantics extracted from Gubser-Klebanov-Polyakov 1998 and\n  Witten 1998. Paper-local scalar\n  selection and field/operator pairing make the wave-calculation route\n  applicable. The established result is output-led: exact selected semantics\n  plus the directly inhabited scalar/operator mass-dimension result. The\n  complete paper-local wave route is reconstructed from those outputs. Its\n  seven-component proof-free model records the\n  selected field, operator, boundary dimension, both full numerical maps, and\n  the scalar-status and field/operator-pairing predicates. The context owns\n  its field/operator pair and induces one `selectedModel`; changing either\n  object therefore fails exact semantic retention rather than producing a\n  newly self-selected model. Exact equality with that paper-induced model is\n  required by model use, world representation, model entailment, and\n  grounding; grounding also requires the selected scalar/operator pair to be\n  inhabited. It retains relation meanings without supplying the wave\n  calculation or the mass-dimension conclusion. GKP fixes one massless scalar/operator context in its D3\n  strong-coupling sector before applying the flux calculation. Witten retains\n  the source's generality by constructing a context parameterized by each\n  selected massive field/operator pair before applying the larger-root,\n  and source-weight calculations. Witten's two-point calculation remains a\n  separate verification and input to the composed correlator route. Each adapter constructs a named\n  exact model, proves its retention certificate before either the technical\n  route or grounding, and exposes its selected field and operator directly.\n  Countermodels separate numerical agreement and theory/world\n  grounding from completion of the scalar route. A false pair cannot be\n  grounded even if theory/world claims are declared universally true, and a\n  mutation audit detects changes to every retained component. The established\n  result is itself exact selection plus a direct nonvacuous scalar dictionary:\n  GKP author-TeX lines 612-732 and\n  Witten author-TeX lines 1114-1212 anchor the two adapters. A false-setup\n  wave-bridge countermodel and a separate finite witness make both selected\n  indices and all five retained numerical or relation families directly\n  active. Its `PhysicalBranch` is the larger-root choice made in these source\n  arguments, not a universal exclusion of later alternate quantizations.\n- `PhysicsLogic/Framework/ScalarCorrelatorComposition.lean`: narrow checked\n  composition of the boundary generating-functional and bulk-boundary scalar\n  contracts, independently realized by Gubser-Klebanov-Polyakov 1998 and\n  Witten 1998. Each paper first constructs a setup-only composite certificate\n  from exact source/field/operator and bulk-configuration/field links plus the\n  selected setups of both child models; this step consumes no proposal,\n  calculation, or child result. A separate paper-local bridge then\n  identifies the complete selected boundary-correlator map with the scalar\n  two-point power law at the established operator dimension. GKP retains its\n  massless boundary-flux calculation; Witten\n  retains its massive Green-function and on-shell-action calculation. The\n  component does not define holography, functional differentiation, or either\n  explicit correlator formula. The route now requires an inhabited variation\n  scope. Its output-led established result retains the selected composite\n  setup plus a model-native direct nonvacuous composition containing both\n  direct child dictionaries, all three compatibility links, and the realized\n  dimension-indexed two-point statement, but no route or calculation bridge.\n  The complete route is reconstructible from those outputs. An\n  empty-variation countermodel blocks vacuous derivative and bridge contracts,\n  while a direct mutation audit makes both child dictionaries and every added\n  relation physically active. Three additional inhabited composed models\n  separate the actual child dictionaries, source compatibility, and scalar\n  two-point bridge: mass squared one violates the zero-dimension scalar\n  equation, source `false` fails a relation requiring source `true`, and\n  correlator value zero fails a dimension-shifted target one. No\n  proposition-only truth table substitutes for those physical boundaries.\n  Grounding consumes the setup-only composite\n  certificate but remains independent of both child results, both child\n  routes, and the scaling calculation; direct outputs on an unselected model\n  cannot ground it. The complete GKP and Witten routes now also independently\n  realize a typed structural explanation of only the selected dimension-\n  indexed boundary two-point behavior. Its proof-free constraint omits the\n  final two-point predicate, and an inhabited output-without-functional-\n  dictionary model blocks the occurrence-to-explanation converse. No causal\n  mechanism, derivational reduction, or full-duality conclusion is added.\n- `PhysicsLogic/Framework/HolographicRegionEntropy.lean`: shared\n  region/surface entropy semantics extracted from Ryu-Takayanagi 2006 and\n  Lewkowycz-Maldacena 2013. It requires regime-scoped dual descriptions, a\n  selected anchored codimension-two surface, explicit observable\n  translation, a paper-local minimality bridge, and a separate normalized\n  area-to-entropy bridge. Both papers now expose the complete shared bridge\n  and value-calculation applicability proposition before deriving the\n  established entropy. The established result is output-led: exact selected\n  setup plus the direct nonvacuous entropy endpoint. Checked eliminators\n  reconstruct both paper-local bridges and the complete calculation route. Its\n  proof-free model retains eight selected indices and all fifteen route-used\n  semantic families: validity, the four duality-dictionary components, both\n  observable maps, anchoring and selection relations, and all area and\n  entropy maps. RT and LM each construct a named exact model and prove a\n  retention certificate before route applicability. Separate paper adapters\n  combine that certificate with the declared RT or LM region/surface setup.\n  Their grounding proofs use only the selected setup, theory use,\n  boundary-region representation, and conditional transfer of all twenty-five\n  shared claims; they do not use the proposal, replica calculation,\n  minimality, area calculation, bridge, or established entropy result. The\n  established result contains a model-native\n  `NonvacuousHolographicRegionEntropyAt` endpoint that directly retains the\n  exercised setup, dictionary, minimality, area, normalization, and entropy\n  facts without counting exact context equality or implication-valued bridges.\n  Both RT and LM prove that endpoint from their paper-local routes. Each route\n  also projects to an inhabited singleton entropy sector in the neutral\n  duality interface: the translated boundary and bulk observables share the\n  selected entropy prediction. A finite countermodel preserves that common\n  prediction while adding a bulk-only value, proving that the calculation does\n  not establish preservation of the complete prediction relation.\n  The calculation route now also realizes a typed structural explanation of\n  the selected region-entropy equality and matching native boundary/bulk\n  predictions. Its constraint contains physical duality, the exact observable\n  dictionary, selected surface setup, both bridges, area calculation, and\n  normalization, but no final entropy agreement. RT supplies that route from\n  its original proposal; LM supplies it directly from fixed-surface,\n  continuation, Einstein, cone, and AdS/CFT calculations rather than packaged\n  minimal-surface or generalized-entropy outputs. A model with every terminal\n  entropy output at an unselected region has no route or explanation.\n  Countermodels separate technical completion from grounding, grounding from\n  the technical route, declaration from derivation, and vacuous bridges from\n  the direct endpoint. Direct outputs at an unselected region cannot be\n  grounded. A finite model realizes the complete route with\n  distinct boundary and bulk descriptions and observables. Direct mutation\n  theorems make every selected index and semantic family falsify the\n  nonvacuous endpoint, while the older route-fact audit and a twenty-three-field\n  exact-retention audit remain independent checks. Geodesics, replicas,\n  Einstein equations, cone actions, and all proposal or extension statuses\n  remain paper-local. RT now also keeps its original AdS3 vacuum and BTZ\n  interval formulas paper-local: a real-valued readout retains the\n  Brown-Henneaux relation, explicit large/small regime controls,\n  positive-factor cutoff matching, regulated geodesic equations, and\n  vacuum/thermal entropy expressions, while a\n  countermodel prevents named interval outputs from substituting for those\n  formulas.\n- `PhysicsLogic/Framework/SupersymmetricVacuumEnergy.lean`: shared\n  zero-energy-vacuum semantics extracted from Witten 1981 and Witten 1982.\n  Its route separates zero-energy-state evidence, the bridge fixing ground\n  energy, and the global-supersymmetry breaking criterion. The established\n  result is exact selected-regime setup plus a direct nonvacuous unbroken\n  endpoint. Its proof-free model retains the regime, ground energy,\n  zero-energy value, and the complete zero-state, ground-energy, and breaking\n  relation families. A selected-data certificate is one of ten exhaustive\n  claims. Finite witnesses and six-component mutation audits show that every\n  retained value and relation family is active in the endpoint, while direct\n  outputs at an unselected regime do not establish it.\n\n  Witten 1981 constructs one named exact global model and grounds the shared\n  route without a Hamiltonian, ground-state, zero-state, or completed-route\n  premise. Its stronger absence-of-zero-state converse and positive-energy\n  breaking theorem remain paper-local because they have no second independent\n  client. Witten 1982 grounds the shared route from exact model identity and\n  pure `N = 1` `SU(N)` scope together with finite-spatial-volume representation; its\n  supersymmetry-preserving boundary conditions, realized graded\n  trace, nonzero index, zero-state inference, and spectral bridge remain in\n  the technical route. Periodic and twisted routes expose exhaustive\n  realization and transfer independently, while large-volume and\n  boundary-condition principles remain paper-local. Countermodels establish\n  grounding without the technical route, block converse reconstruction,\n  and mutate all three selected values and all three relation families. The\n  shared result is regime-scoped and does not infer infinite-volume breaking\n  from finite-volume breaking.\n  Supercharges, indices, Goldstini, instanton dynamics, and the local-\n  supergravity exception remain paper-local.\n- `PhysicsLogic/Framework/MetricConnectionCurvature.lean`: independently\n  source-qualified contracted-curvature construction shared by Einstein 1916\n  and Rosen 1940. Einstein's direct branch retains the original signed\n  four-index equation (43), the separate `B_mu_nu = R_mu_nu + S_mu_nu`\n  contraction, and `Gamma^tau_(mu nu) = -{mu nu;tau}`. Rosen's distinct\n  Part I branch retains the formal flat auxiliary metric, the nonzero\n  gravitational and flat determinants, the flat connection difference and\n  derivative identity, the rewritten Ricci component, and\n  `kappa = sqrt(g / gamma)`. A flat metric may still have a nonzero\n  connection in curvilinear coordinates. Neither branch supplies a vacuum or\n  sourced field equation; Rosen's formal rewrite does not assign physical\n  geometry to the auxiliary metric or establish background independence.\n  Exact rational metric two-jets now compute both branches, including inverse\n  derivatives, Christoffel symbols, full curvature, source-sign contraction,\n  and auxiliary-covariant derivatives. A genuine Lorentzian-signature\n  condition rejects Euclidean geometry. Kernel-checked flat spherical and\n  Ricci-flat tidal examples distinguish coordinate connection, curvature,\n  vacuum, and pointwise versus chart-wide volume conditions.\n- `PhysicsLogic/Framework/VacuumMetricDynamics.lean`: narrow shared\n  metric/vacuum/free-motion semantics extracted from Einstein 1916 and\n  Schwarzschild 1916. Its proof-free exact model retains the selected metric,\n  situation, worldline, and all nine route-used relation families:\n  physicality, dynamical relevance, non-fixed-background status,\n  field-equation governance, matter absence, vacuum-equation satisfaction,\n  free-worldline status, metric-to-motion-equation selection, and\n  motion-equation satisfaction. Each paper constructs a named model and\n  proves an exact semantic-retention certificate before route applicability.\n  The paper-local context owns all three selected objects, so its `modelAt`\n  is unique rather than being rebuilt from whatever indices a candidate model\n  carries. Theory membership and world representation require\n  `SelectedVacuumMetricSetupAt`: that exact certificate together with the\n  actual physical, dynamically relevant, non-fixed metric, matter-free\n  situation, and selected free worldline. Mutating any selected object fails\n  exact semantics, while a false physical setup cannot be grounded.\n  The route then requires field-equation governance and paper-local bridges\n  separately establishing the vacuum equation and metric-selected free\n  motion. The output-led `EstablishedVacuumMetricDynamicsAt` retains exact\n  selected semantics and the direct realized setup, governance, vacuum\n  equation, metric-selected motion, and all three outputs. It stores neither\n  implication-valued bridge nor route; checked theorems reconstruct both from\n  the direct facts. The ten exhaustive shared claims remain available through\n  that reconstruction. The route also has ordinary and source-sensitive\n  structural explanations. The ordinary explanation executes the raw\n  applicable route into a selected dynamical-vacuum/free-motion phenomenon\n  without first packaging the established endpoint. The source-sensitive\n  explanation additionally requires one typed paper-local derivation relation.\n  Einstein retains metric-as-field meaning, covariance, curvature/contraction\n  selection, and qualified general geodesic extension; Schwarzschild retains\n  the exterior point-mass conditions, determinant-preserving polar construction,\n  exact integration with continuity, and metric-selected orbit calculation. A\n  finite completed-route countermodel has the ordinary explanation but no\n  source-sensitive explanation when the derivation relation is false.\n  A component-wise mutation audit detects every retained index\n  and relation family. A finite logical witness realizes a physical dynamical\n  metric, vacuum solution, and metric-selected free motion. Direct activity\n  theorems make all three selected objects and all nine relations affect the\n  technical route itself, independently of the exact-retention audit. A\n  stronger grounded result distinguishes the selected\n  metric calculation, the gravitational theory using it, and the represented\n  physical situation. Einstein's adapter requires the metric to describe the\n  gravitational field and determine spacetime geometry; Schwarzschild's\n  requires the exact exterior point-mass line element. Both papers expose a\n  named source-local selected-setup theorem used by grounding, independently\n  of their vacuum-equation and free-motion calculations. Curvature, Einstein\n  equations, connections, geodesics,\n  point masses, spherical symmetry, approximations, and observables remain\n  paper-local.\n- `PhysicsLogic/Framework/GravitationalFrequencyShift.lean`: narrow shared\n  local-clock frequency-comparison semantics extracted from Einstein 1911\n  and Einstein 1916. Its explicit route requires regime validity, stationary\n  physically distinct locations, same-kind local clocks, signal transfer, a\n  paper-local frequency calculation, and separate clock-rate and spectral\n  interpretation bridges. The established result is output-led: exact\n  selection plus the direct inhabited setup and three physical outputs. The\n  original calculation and both interpretation bridges are reconstructed by\n  a checked projection rather than stored as premises. Its proof-free model retains six selected physical\n  objects and all seven relation families used by the route. The context owns\n  those six objects, and exact semantics means equality with its unique\n  `selectedModel`, not a model reconstructed from candidate-owned indices.\n  Each paper constructs a named model and proves exact semantic retention\n  before route applicability. Einstein 1916 does so separately at every\n  arbitrary approximation, situation, and redshift, preserving the paper's\n  universal scope. Named paper theorems expose all six selected indices\n  directly in both adapters. The ten exhaustive claims include that\n  certificate, setup, calculation and interpretation bridges, applicability,\n  outputs, and the established result. Its stronger theory-model result\n  distinguishes the comparison model, a paper-local theory role, and a\n  paper-local represented world. Grounding requires the exact selected\n  stationary-comparison setup but remains independent of the shift outputs:\n  Einstein 1911 maps its primitive comparison setup; Einstein 1916 maps the\n  point-mass solution, distinct locations, stationary comparison, same-kind\n  clocks, and transferred signal. Only the combined result adds the technical\n  outputs. The two adapters expose named certificates transferring every shared\n  claim to theory and represented world.\n  The frequency relation transfers to clock-rate and spectral claims only\n  through their separate paper-local interpretation bridges. Vacuous bridges\n  without the setup are rejected and cannot satisfy the direct\n  `NonvacuousGravitationalFrequencyShiftAt` proposition. Every established\n  route projects to that proposition, so validity, distinct locations,\n  stationary comparison, same-kind clocks, signal transfer, frequency\n  relation, clock-rate difference, and spectral displacement all hold at one\n  actual selected model. A finite witness realizes it, and direct six-index\n  and seven-relation mutations make each retained component affect the\n  completed semantics. Its ordinary structural-explanation layer uses exact\n  selected semantics and the pre-endpoint shared route without retaining paper\n  provenance. A separate source-sensitive refinement adds a typed paper-local\n  derivation: Einstein 1911 supplies an accelerated-frame\n  Doppler-plus-equivalence derivation, while Einstein 1916 supplies a\n  static-metric local-clock derivation. The source-sensitive explanation\n  exposes that derivation and entails the ordinary explanation. A converse\n  countermodel proves that the completed phenomenon, an output-reconstructed\n  route, and the ordinary explanation cannot manufacture a missing source\n  derivation. A same-location\n  comparison cannot satisfy the route\n  even when every nominal physical predicate is declared true, a completed\n  technical result need not supply theory/world grounding, exact grounding\n  with complete setup can hold while the route is false, exact selection\n  without setup cannot ground, and declared theory/world claims do not\n  reconstruct the calculation route.\n  Separate six-index and seven-relation mutation theorems, plus their combined\n  thirteen-component audit, detect changes to every selected object and\n  retained relation family.\n  A separate value-bearing shared source readout now also retains Einstein\n  1911's exact equations (2), (2a), and (3), its assumed extension from a\n  homogeneous to a nonuniform field, the distinction between coordinate and\n  locally measured light speed, its `2 / 10^6` solar shift, and explicit\n  pressure/temperature systematics. Einstein 1916 instead retains the\n  equation-(70) temporal metric, equation-(72) local-clock normalization,\n  slower near-source clocks, distinct observer locations, and its explicitly\n  inconclusive stellar-redshift test. Countermodels reject a sign-flipped\n  potential, substituted local light speed, missing Doppler calculation,\n  invented nonuniform-field derivation, discarded spectral systematics,\n  incorrect metric or clock normalization, claimed confirmation, and exact\n  strong-field extrapolation.\n- `PhysicsLogic/Framework/GravitationalRayDeflection.lean`: narrow shared\n  gravitational light-deflection semantics extracted from Einstein 1911 and\n  Einstein 1916. Its explicit route requires a valid description, a selected\n  light ray in a gravitational propagation setup, a paper-local deflection\n  calculation, and a separate assessment that the reported magnitude is\n  nonzero. The output-led established result is exact selected semantics plus\n  a direct nonvacuous proposition requiring validity,\n  gravitational propagation, calculated deflection, and nonzero magnitude at\n  one actual model. The implication-valued calculation and assessment bridges\n  are reconstructed from those outputs. A finite witness realizes it, a countermodel blocks\n  vacuous bridges without setup, and direct four-index/four-relation mutations\n  show every retained component affects the completed proposition. A separate\n  ordinary structural explanation retains the selected propagation problem\n  without a derivation token; the applicable route realizes it. A stronger\n  source-sensitive refinement pairs that constraint with a realized\n  paper-local derivation, exposes the derivation, and entails the ordinary\n  explanation. Einstein 1911 reconstructs its route from a\n  coordinate-light-speed/Huygens token; Einstein 1916 uses a distinct\n  static-metric/null-ray token. A finite countermodel retains the complete\n  phenomenon, a route reconstructed from it, and ordinary explanation while\n  making the source derivation false, so the result cannot manufacture source\n  provenance. The\n  grounded result separately requires exact selection plus the inhabited\n  pre-calculation propagation setup and identifies the theory using the model\n  and the physical world represented by it. A false setup cannot ground, while\n  a grounded setup need not supply the calculation or direct endpoint. Einstein 1911 supplies the\n  position-dependent coordinate-light-speed and Huygens calculation;\n  Einstein 1916 supplies the static point-mass metric calculation and an\n  explicit ray passing the source. A separate source readout now retains the\n  actual original wavefront and potential-gradient formulas, equation-(70)\n  temporal and spatial metric components, equation-(73) null propagation,\n  Huygens' principle in both papers, and equation-(74) full bending.\n  Independent temporal and spatial contributions make the 1916 unrounded\n  prediction exactly twice the 1911 prediction, while the separately rounded\n  original reports `0.83` and `1.7` arcseconds are not exactly related by a\n  factor of two. The 1916 Jupiter prediction is `0.02` arcseconds, and\n  neither paper is credited with a completed eclipse observation.\n  The plus-sign coordinate-speed expansion printed in 1916 is also kept\n  distinct from the opposite-sign expansion implied by the displayed metric\n  and null condition; Lean proves that the two values differ.\n  Countermodels reject omitted Huygens propagation, omitted spatial curvature,\n  a missing null condition, the wrong coefficient, retrofitted 1911 spatial\n  bending, swapped reported angles, and unsupported empirical confirmation.\n  Both adapters expose the four selected model indices;\n  their lifted deflection-calculation relations additionally require the\n  selected description, so a paper calculation cannot silently migrate to a\n  foreign approximation. Grounding consumes the 1911 validity, coordinate-speed,\n  and transverse-ray facts or the 1916 static-solution, point-mass, and\n  ray-passage facts, but no deflection calculation, nonzero result, route, or\n  established endpoint. The direct anchors are Einstein 1911 journal\n  pp. 906-908 and Einstein 1916 journal pp. 819-822. Einstein 1911 now\n  separately retains its p. 907 local Huygens curvature relations, equation\n  (4), p. 908 point-mass `2 k M / (c^2 Delta)` reduction, and\n  `4 / 10^6 = 0.83 arcseconds` report as a paper-local\n  proposition-valued readout package; the companion shared source readout\n  additionally preserves those selected source values without claiming to\n  prove the path integral. A separate composed optical handoff retains both the actual\n  local-clock frequency shift and the actual nonzero ray deflection, exact\n  shared description/regime, the selected signal/ray propagation relation,\n  the paper-local derivation, and a positive solar angle in exact arcsecond\n  hundredths. Einstein 1911 supplies the accelerated-frame, coordinate-speed,\n  and Huygens chain with angle 83; Einstein 1916 supplies the static metric,\n  radial/tangential rod effects, null condition, and its own Huygens\n  calculation with angle 170.\n  Inhabited countermodels separate clock shift from bending in both\n  directions, reject incorrect reported-angle calibration, and prevent one\n  paper's completed outputs or derivation mode from replacing the other's.\n  The source-sensitive optical composition now also exactly selects both\n  child contexts and independently retains the clock derivation, bending\n  derivation, and source-local optical comparison. The 1911 token preserves\n  accelerated-frame Doppler, coordinate-speed/Huygens propagation, and 83\n  hundredths; the 1916 token preserves the static metric, null ray,\n  radial/tangential spatial effects, and 170 hundredths. A calibrated finite\n  countermodel retains both source-sensitive child explanations and ordinary\n  composition while withholding the optical comparison derivation.\n- `PhysicsLogic/Framework/AcceleratedFrameGravity.lean`: narrow shared\n  accelerated-frame comparison semantics extracted from Einstein 1911 and\n  Einstein 1916. Its proof-free exact model retains the reference frame,\n  accelerated frame, experiment, and regime together with the four relation\n  families used by the route: comparison setup, universal free fall,\n  reproduced gravitational motion, and description equivalence. Each context\n  binds one exact four-object selection, and each paper certifies its named\n  model before applicability. The route then requires two distinct paper-local\n  bridges: one from setup and free fall to reproduced gravitational motion,\n  and one from that output to the paper's scoped equivalence conclusion. The\n  established result exposes every stage plus a direct nonvacuous result as\n  ten exhaustive claims. A source-shaped witness and direct eight-component\n  mutation audit show that every retained index and relation family affects\n  that nonvacuous result. Theory/model/world grounding is separately\n  established from exact\n  model identity and interpretation alone; it consumes no setup, free fall,\n  bridge, output, or completed route. The framework does not identify\n  this narrow inference with a general weak, Einstein, or strong equivalence\n  principle, extend mechanical equivalence to all physical processes,\n  eliminate arbitrary gravitational fields, infer the relativity postulate,\n  or construct a gravitational field theory.\n- `PhysicsLogic/Framework/BrokenSymmetrySpectrum.lean`: shared\n  spectrum-scoped Goldstone semantics extracted from\n  Goldstone-Salam-Weinberg 1962, Anderson 1963, Nambu 1960, and Generalized\n  Global Symmetries 2014. It requires a paper-local spectral bridge in\n  addition to spontaneous breaking. The established result retains that\n  complete route and the derived gapless mode in the declared spectrum, so\n  the breaking claim and spectral bridge remain separately projectable. Its\n  stronger semantics distinguish the selected spectral calculation from the\n  theory using it and the physical system or spectrum represented by it. A\n  generic constructor grounds the exactly selected model from explicit\n  theory-use, world-representation, and claim-transfer bridges without\n  assuming spontaneous breaking, the spectral calculation, route\n  applicability, or the gapless-mode result. Goldstone-Salam-Weinberg ground\n  the selected current and physical spectrum without importing current\n  conservation or the spectral calculation; Anderson grounds the selected\n  superconductor and\n  uncoupled matter spectrum without assuming Coulomb absence; Nambu grounds\n  the charge-vertex model with the genuinely representational premise that\n  the quasiparticle vacuum represents the superconductor; and Generalized\n  Global Symmetries grounds each selected current sector and physical photon\n  spectrum without assuming current assignment or photon membership. Each\n  final grounded theorem combines this independent grounding with its\n  separately established technical route. The proof-free calculation model\n  retains the selected symmetry, phase, and spectrum together with the exact\n  continuous-symmetry, law-symmetry,\n  phase-membership, symmetry-action, gapless-mode, and spectrum-membership\n  relations. A finite selected model now realizes the complete route with two\n  distinct in-phase states related by the selected symmetry and a concrete\n  gapless mode in the selected spectrum. Direct mutation theorems show that\n  changing any selected index or any route-used relation destroys the direct\n  `NonvacuousBrokenSymmetrySpectrumAt` proposition itself, rather than merely\n  changing whole-model equality or only a stage predicate. A vacuous spectral\n  bridge without a broken phase also fails that direct endpoint.\n  The complete route now realizes an ordinary typed structural explanation\n  from a proof-free broken-phase constraint distinct from the spectrum-scoped\n  gapless-mode phenomenon. A stricter source-sensitive wrapper adds one\n  paper-selected derivation token and a proposition-valued relation showing\n  that derivation obtains. Source-sensitive explanation exposes its derivation\n  and entails the ordinary explanation, while a countermodel keeps the\n  established spectrum result and ordinary explanation but withholds source\n  provenance. Goldstone-Salam-Weinberg, Anderson, Nambu, and Generalized Global\n  Symmetries each expose both ordinary and source-local adapters while\n  retaining their current calculation, pair dynamics, uncoupled-spectrum\n  restriction, and one-form current matrix elements locally.\n  Each paper's named-model identity fixes its actual physical tuple, and each\n  of the four clients exposes a source-grounded theorem exhibiting the moved\n  state and in-spectrum mode. Only the six shared broken-phase spectral\n  claims transfer. One\n  exhaustive theorem realizes all six from any established result, and all\n  four paper adapters expose named realization and grounded-transfer\n  certificates. Mode conversion, finite-frequency generation, gauge dynamics,\n  and gap calculations remain outside this component. Countermodels reject a\n  vacuous spectral bridge. A nine-component extensional audit observes every\n  selected index and retained relation family, while the direct semantic\n  audit verifies that all nine components affect the route itself. Further\n  countermodels\n  exhibit theory/model/world grounding while the Goldstone route fails, and\n  reject theory/world declarations that do not reconstruct the technical\n  route.\n- `PhysicsLogic/Framework/BrokenSymmetryModeConversion.lean`: shared\n  spectrum-conversion semantics extracted from Nambu 1960 and Anderson 1963.\n  It requires a selected gapless mode in an uncoupled spectrum, interaction\n  absence in that spectrum, interaction activity in a distinct interacting\n  spectrum, a coupling mechanism, and a paper-local conversion calculation\n  before deriving a finite-frequency mode in the interacting spectrum and\n  absence of the original mode there. The generic established result is\n  output-led: exact selected semantics plus the direct\n  `NonvacuousModeConversionAt` endpoint. Its implication-valued calculation\n  and route are reconstructed from the retained setup and outputs. The\n  stronger established result is also output-led, retaining exact selection\n  for the conversion model and Goldstone-spectrum child plus the direct\n  originated endpoint. The complete spontaneous-breaking, scoped-Goldstone,\n  and conversion routes remain reconstructible, preventing conversion alone\n  from reconstructing a symmetry origin. Its direct\n  `NonvacuousGoldstoneOriginatedModeConversionAt` endpoint now contains the\n  nonvacuous Goldstone-spectrum child together with the generic conversion\n  endpoint. The generic endpoint additionally projects to a typed\n  mechanistic explanation. Its component is the original mode in the\n  uncoupled spectrum, its activity is coupling by the selected interaction in\n  the physical system, its organization is the before/after spectrum pair,\n  and its phenomenon is finite-frequency replacement in the interacting\n  spectrum. Both Nambu and Anderson realize this proposition from their\n  distinct Coulomb-polarization and electromagnetic-coupling calculations.\n  A source-sensitive activity now preserves that distinction formally.\n  Nambu's source relation executes the matched Ward-vertex homogeneous\n  zero-mode calculation before assembling the Coulomb pair-process and\n  polarization-resummation setup. Anderson's source relation executes the\n  self-consistent electron-plasma response, undressed-spectrum pole\n  criterion, uncoupled Goldstone calculation, and superconducting gauge-field\n  mixing setup. Neither source theorem consumes an established conversion or\n  ordinary mechanism. A completed common route with an everywhere-false\n  source relation realizes the ordinary explanation but not either\n  source-sensitive explanation.\n  `SourceSensitiveGoldstoneSupportedModeConversionAt` additionally composes\n  exact outer and embedded selected models, the inhabited originated result,\n  independently sourced Goldstone and conversion explanations, and a separate\n  original-paper joining argument. Anderson's join retains printed conductor\n  equations (4), (7), and (8), unequal finite-momentum dispersions,\n  nonrelativistic scope, and the distinction between the normal conductor\n  and broken superconductor without claiming non-Abelian or baryon models.\n  Nambu's join instead retains the matrix Ward identity, the neutral acoustic\n  equation (6.11), the Coulomb-shifted plasma equation (8.11), polarization\n  resummation, distinct neutral/coupled spectra, and unassessed higher-order\n  or beyond-Hartree-Fock corrections. A physical countermodel preserves both\n  sourced children, the complete originated endpoint, different selected\n  systems, Ward and frequency data, and normal versus broken superconducting\n  matter while rejecting a missing source-local handoff.\n  The projection requires actual coupling and all terminal spectrum outputs,\n  but no spontaneous-breaking or Goldstone-origin premise. A finite\n  countermodel retains conversion, finite frequency, final membership, and\n  removal of the original mode while deleting coupling, and therefore refutes\n  the mechanistic explanation. A proof-free selected calculation records\n  both spectra, both modes, the interaction, and the physical system together\n  with the exact six spectrum, interaction-absence, and four conversion\n  relation families. The context owns all eight selected physical indices, so\n  a candidate model cannot select the objects against which its own exactness\n  is judged. Each\n  paper proves an exact retention certificate. A generic constructor grounds\n  the exactly selected physical conversion setup from explicit theory-use,\n  world-representation, and conditional claim-transfer bridges without\n  assuming a calculation, route, or final spectrum. Anderson supplies\n  `SuperconductingConversionSetup`; Nambu supplies `CoulombPlasmaSetup` and\n  the quasiparticle-vacuum representation. The fermion gap,\n  self-energy-kernel equation, resummed-polarization premise, and conversion\n  calculations remain downstream. One exhaustive theorem realizes all\n  nineteen shared claims from an established result. A retained finite model\n  now realizes the full composed route nonvacuously: two distinct phase states witness breaking, the original\n  and converted modes differ, the uncoupled and interacting spectra differ,\n  and every setup and conversion relation is active. Direct stage audits show\n  which part of the route each changed field breaks. A generic typed audit\n  proves that its eight indices and seven conversion relations are active\n  while the four Goldstone-provenance mutations preserve generic conversion;\n  a stronger typed audit proves that every one of the eight index mutations\n  and eleven relation-family mutations destroys the full\n  `NonvacuousGoldstoneOriginatedModeConversionAt` endpoint itself. Both paper\n  adapters now expose named generic-conversion and stronger\n  Goldstone-originated nonvacuity theorems. Countermodels reject an\n  implication-valued bridge that holds only because its physical setup is\n  absent and show that it cannot fake either direct endpoint; another\n  complete generic conversion has no broken-symmetry origin. They also separate\n  uncoupled-spectrum\n  absence from interacting-spectrum activity, exhibit grounding while the\n  composed route fails, reject absent setup, and reject direct\n  Goldstone/conversion outputs under the wrong selected symmetry. They retain\n  a separate nineteen-component extensional\n  audit, and reject theory/world declarations that do not reconstruct the\n  technical route.\n  Polarization tensors, Coulomb equations, gauge fields, and superconducting\n  dynamics remain paper-local.\n- `PhysicsLogic/Framework/CoarseGrainedScaling.lean`: narrow shared\n  coarse-graining and rescaling semantics extracted from Kadanoff 1966 and\n  Forster-Nelson-Stephen 1977. Its explicit route requires a controlled\n  transformation step, an inhabited selected sector, and a paper-local\n  prediction-scaling bridge, then establishes transformed prediction\n  equivalence only throughout that sector. The output-led established result\n  stores exact selected semantics plus the direct nonvacuous controlled-sector\n  result; named projections reconstruct the route, controlled step, bridge,\n  and sector predictions. The ordinary structural explanation retains only the\n  exact selected scaling model and route. A separate source-sensitive\n  refinement pairs that constraint with a typed realized derivation, exposes\n  the derivation, and entails the ordinary explanation. Kadanoff's\n  cell-variable/free-energy/correlation derivation and FNS's infrared\n  momentum-shell velocity-correlation derivation reconstruct the shared route\n  separately and remain distinct. A converse countermodel retains the\n  established output, reconstructed route, and ordinary explanation while\n  denying the source derivation, so no source-sensitive explanation follows.\n  The scaling\n  proof-free model exactly retains six selected data components and ten\n  transformation, prediction, scope, and control families. Kadanoff and FNS\n  prove named exact-model certificates and derive selected controlled setups\n  from `CellModelSetup` and `InfraredRGSetup`. Their theory/model and\n  model/world grounding uses those setups, paper-local interpretation inputs,\n  and conditional transfer, but no scaling bridge, sector calculation, route,\n  or output. Separate final theorems combine grounding with each paper's\n  completed calculation. The exhaustive claim family now has nine members,\n  including the selected setup and direct nonvacuous output.\n  Countermodels block vacuous bridges, control without a prediction\n  calculation, sector widening, transfer across scales, automatic grounding\n  from technical completion, and reconstruction of the controlled route from\n  grounding. Complementary countermodels ground controlled setup without a\n  scaling output and reject grounding from matching output without controlled\n  setup. A sixteen-component mutation audit observes every retained\n  datum, map, and relation extensionally. A separate inhabited finite model\n  realizes the actual two-step transformation, both controls, regime and\n  sector membership, and prediction equivalence for a concrete observable.\n  Direct route-content audits show that changing any of the six selected\n  components or ten map and relation families destroys a transformation or\n  sector subclaim, while a stronger typed audit proves that every mutation\n  destroys `NonvacuousControlledSectorScalingAt` itself. A control-free\n  implication-valued bridge cannot fake that direct endpoint. Kadanoff's\n  singular free energy and FNS's\n  velocity correlation independently witness the selected sectors in named\n  paper theorems.\n  The neutral route remains independent of block spins, shells, exponents,\n  and universality classes. Separate governed source witnesses retain\n  Kadanoff's `a \u003C L \u003C xi`, two-valued cell, `L^(-d)` free-energy factor,\n  nearest-neighbor assumption, conditional exponent relation, and qualified\n  logarithmic branch. FNS witnesses retain the transverse projector,\n  `k . v = 0`, different thermal and constant forcing classes, their\n  dimensions two and four, controlled momentum shell, thermal-only\n  fluctuation-dissipation relation, protected advective vertex, and\n  independently renormalized viscosity.\n- `PhysicsLogic/Framework/ExactRegulatedScaleFlow.lean`: narrow exact-flow\n  contract extracted independently from Wegner-Houghton 1973 and Wetterich\n  1993. A regulated scale-dependent family at an actual selected scale, a\n  paper-local exact full-flow calculation, a selected sector, and a\n  paper-local exact projection\n  calculation establish exact full and projected equations. The established\n  projection also yields a direct\n  `NonvacuousExactProjectedScaleFlowAt` endpoint where the setup, exact full\n  equation, projection setup, and exact projected equation all hold at one\n  model instead of only behind implication-valued calculation contracts. The\n  second-stage adapters now consume that established shared full flow and\n  shared projection setup before replaying only paper-local route content.\n  Separate\n  theory/model/world bridges ground the selected setup. Its proof-free\n  model exactly retains six selected indices, including the actual scale, and\n  the four proposition-valued\n  relation families that interpret their setup, full equation, projection\n  setup, and projected equation. Both paper adapters prove a named retention\n  certificate before applicability and a named direct nonvacuity theorem after\n  the projection is established. Both established results are output-led;\n  checked eliminators reconstruct the calculation contracts and complete\n  route. The 13 canonical claims expose the selected setup, complete route,\n  and direct endpoint. Grounding uses the exact selected model and realized\n  scale-dependent setup, a paper-local theory-use fact, a represented-system\n  fact, and claim-by-claim transfer; it requires no exact flow equation,\n  projection setup, calculation contract, or projection route. The framework\n  does not identify sharp-shell elimination\n  with a modified Legendre transform, and it contains no fixed-point,\n  endpoint, derivative-expansion, epsilon-expansion, large-component, or\n  approximation-control semantics. Countermodels separate implication-valued\n  calculations from applicable routes, show separately that missing full-flow\n  setup and missing projection setup cannot hide behind those implications,\n  separate exact full flow from an exact projection, technical completion from\n  physical grounding, and grounding from a technical route. A setup-complete\n  grounded model with false exact-flow output proves the last separation.\n  Exact-selection and direct ten-component audits make every retained index\n  and relation\n  semantically active.\n- `PhysicsLogic/Framework/NeutralDefectConfiguration.lean`: shared integer\n  defect-charge semantics independently realized by the scalar vortex gas of\n  Kosterlitz-Thouless and the vector dislocation gases of Halperin-Nelson and\n  Young. It retains charge rank, actual integer components, componentwise\n  neutrality, a nonzero opposite-charge pair, and validity scope. The active\n  melting routes now consume rank-two Burgers configurations; rank-one\n  scalar lifting preserves both net charge and the absent transverse\n  component. Checked countermodels separate a lone charge from neutrality, an\n  empty neutral gas from pair presence, and a transverse pair from rank-one\n  admissibility. Its structural explanation retains the selected rank and\n  integer charge list while explaining only an inhabited admissible neutral\n  opposite pair. A source-sensitive refinement keeps KT's neutral unit-vortex\n  premises distinct from the two Burgers-gas routes, and a false-source\n  countermodel prevents the ordinary endpoint from inventing paper\n  provenance.\n- `PhysicsLogic/Framework/LogarithmicDefectThermodynamics.lean`: shared\n  value-level defect thermodynamics independently realized by the original\n  Kosterlitz-Thouless argument and the two active melting papers. It retains\n  two-dimensional validity, core and system scales, core energy, bare and\n  screened logarithmic binding, positional entropy, and the actual\n  `F=E_core+(binding-T*entropy) log(L/a)` competition. Checked theorems\n  separate the cold bound regime, the large-scale hot instability, and the\n  lowering of the bare threshold by screening; countermodels show that a\n  positive core cost can keep a finite system bound above the bare threshold\n  and that logarithmic binding without positional entropy does not unbind.\n  Its structural explanation retains the finite-scale free-energy readout\n  and screened threshold ordering while stopping short of phase\n  interpretation. A source-sensitive refinement keeps KT's finite-area\n  vortex estimate distinct from the two solid-side Burgers routes, and a\n  false-source countermodel blocks provenance from the ordinary endpoint.\n- `PhysicsLogic/Framework/DipoleScreeningResponse.lean`: shared value-level\n  linear response independently realized by the original KT scalar-vortex\n  calculation and Young's vector-dislocation gas. A nonnegative dipole shell\n  raises susceptibility and dielectric response, and\n  `K_eff=K_bare/epsilon` weakens logarithmic binding. Checked countermodels\n  separate density without polarizability, susceptibility without dielectric\n  response, and dielectric response without renormalized binding. Its\n  structural explanation retains the selected shell and binding readouts\n  while explaining only inhabited strict weakening. A source-sensitive\n  refinement keeps KT's finite-core dilute-pair inputs distinct from Young's\n  solid setup, and a false-source countermodel blocks provenance from the\n  ordinary endpoint.\n- `PhysicsLogic/Framework/PhaseWindingCirculation.lean`: shared\n  phase-contour semantics independently realized by KT's planar-spin\n  vortices and Feynman's original helium ring argument. Integer phase\n  winding plus the phase-flow relation quantizes circulation; local\n  irrotationality remains compatible with nonzero circulation in a multiply\n  connected region. Countermodels separate phase winding from flow,\n  circulation from phase consistency, and local irrotationality from sector\n  selection. Its structural explanation retains the selected contour,\n  phase increment, winding, quantum, circulation, and local vorticity while\n  explaining only nonzero quantized locally irrotational circulation. A\n  source-sensitive refinement keeps KT's scoped angular contour distinct\n  from Feynman's many-body phase-gradient ring inputs, and a false-source\n  countermodel blocks provenance from being inferred from the ordinary\n  endpoint.\n- `PhysicsLogic/Framework/CorrelationDecayChannel.lean`: shared\n  large-distance channel semantics independently realized by KT's spin-wave\n  factor and Hastings-Koma's ground-sector-corrected bosonic correlation.\n  Positive algebraic exponents or exponential rates suppress the selected\n  channel; they do not suppress an unrelated raw or full correlator without\n  its paper-local bridge. Countermodels separate zero exponent/rate and a\n  finite-separation bound from genuine asymptotic decay. The explicit\n  envelope-indexed structural constraint retains the selected norm readout,\n  cutoff, and branch parameters, while its phenomenon is only the\n  nonvacuously suppressed selected channel. A source-sensitive refinement\n  keeps KT's scoped spin-wave power law distinct from Hastings-Koma's printed\n  corrected-correlation formula; a false-source countermodel prevents the\n  ordinary asymptotic endpoint from manufacturing paper provenance.\n- `PhysicsLogic/Framework/DefectUnbindingTransition.lean`: narrow shared\n  transition semantics extracted from Halperin-Nelson 1978 and Young 1979.\n  It separates the bound, rigid low-temperature phase and its suppressed\n  defect fugacity from the high-temperature recursion calculation, then\n  requires an explicit paper-local bridge before deriving defect unbinding\n  and lost long-distance rigidity. Its output-led established proposition is exact\n  selected semantics together with the direct\n  `NonvacuousDefectUnbindingTransitionAt` endpoint, where the ordered phase,\n  both flow outputs, unbinding, the unbound phase, and lost rigidity all hold\n  at one selected model rather than merely behind an implication-valued\n  bridge. The complete route is reconstructed from those outputs rather than\n  stored in the result. Both paper adapters expose named route-applicability\n  and direct\n  nonvacuity theorems, and a countermodel prevents a vacuous interpretation\n  implication from replacing the actual flow calculation. The complete route\n  also realizes a typed mechanistic explanation whose component, activity,\n  organization, and phenomenon roles retain the bound defect, selected flow,\n  ordered-to-unbound phase data, and unbinding with rigidity loss. A model\n  with the flow and all terminal outputs but no ordered bound-defect\n  organization blocks the converse. A source-sensitive refinement now keeps\n  Halperin-Nelson's smooth-substrate elastic decomposition and quadratic-\n  fugacity recursion distinct from Young's self-consistent vector-gas\n  screening and independent periodic-substrate consistency check. Both are\n  reconstructed from raw paper-local premises; a checked forgetful theorem\n  recovers the ordinary unbinding mechanism from either source-sensitive\n  explanation, while a completed common route and ordinary mechanism with a\n  false source relation blocks provenance recovery.\n  Its independently audited composition now consumes the actual nonvacuous\n  `NeutralDefectConfiguration` and `LogarithmicDefectThermodynamics` outputs\n  before a separate original-paper screening/flow handoff and the direct\n  unbinding result. Kosterlitz-Thouless preserves a scalar neutral vortex gas,\n  the selected integer vortex charge, dielectric breakdown, and a distinct\n  dissociation bridge; Halperin-Nelson retains vector Burgers charges, finite\n  dislocation core energy, quadratic-fugacity recursion, and equations\n  (3)-(5); Young retains the different self-consistent physical and general\n  radial/angular vector-gas recursions and equations (25). Inhabited models\n  distinguish screened from bare binding and cold from hot regimes, and prove\n  that completed neutrality, thermodynamics, and unbinding do not supply the\n  independent calculation handoff.\n  A stronger source-sensitive composition now retains the ordinary composed\n  endpoint, source-sensitive neutral, logarithmic, and transition\n  explanations, and a separately typed cross-stage handoff derivation. KT\n  supplies its original dielectric-breakdown/dissociation transition token\n  and scalar-vortex composition token; Halperin-Nelson retains its\n  smooth-solid quadratic-fugacity equations-(3)--(5) join; Young retains its\n  self-consistent physical/general vector-gas equations-(25) join. A\n  countermodel has the ordinary composition and all three child source\n  explanations but no handoff derivation, so provenance cannot be recovered\n  merely by composing completed stages.\n  The module also imports\n  `Philosophy.TheoryModel`: the proof-free model retains all eight selected\n  indices and all eight relation families used by the bound-phase and\n  recursion-flow route. Each paper constructs one named exact model and proves\n  a definitional semantic-retention certificate before route applicability.\n  The 17 canonical claims expose every setup premise, calculated flow output,\n  bridge, interpreted output, direct endpoint, and final transition. Grounding\n  consumes the exact\n  selected, inhabited bound-defect phase plus paper-local use and\n  representation bridges, but no high-temperature recursion flow, unbinding\n  bridge, phase-occurrence output, or rigidity-loss result. Halperin-Nelson\n  retain the two-dimensional triangular\n  system and smooth substrate; Young retains the triangular lattice,\n  continuum-elastic description, and vector-Coulomb-gas description. Their\n  quadratic-fugacity and self-consistent triangular recursions remain in the\n  technical routes. At the paper level, Halperin-Nelson now retains its\n  distinct equations (3)-(5), following inverse-elastic-coupling definition,\n  critical value, and equation (7), while Young retains equations (25a)-(29);\n  the shared framework does not identify those different recursion systems.\n  Typed countermodels show that exact selection without an\n  inhabited bound phase cannot ground, while an inhabited bound phase can be\n  grounded with the unbinding route and direct endpoint false. Further\n  countermodels show both that a\n  completed technical transition need not supply theory/world grounding,\n  selected-regime validity does not become global validity, and declared\n  theory/world transition claims do not reconstruct the missing bound-phase\n  and flow route. One 16-field mutation audit prevents any route-used relation\n  from becoming semantically inert in the exact selected semantics; a second\n  direct 16-component audit shows that changing any selected index or relation\n  destroys the nonvacuous endpoint. Dislocations, Burgers vectors, vector Coulomb\n  gases, elastic constants, correlation laws, hexatic phases, critical\n  exponents, and later defect transitions remain paper-local.\n- `PhysicsLogic/Framework/InfraredOrderSuppression.lean`: narrow shared\n  no-order semantics extracted from Mermin-Wagner 1966,\n  Kosterlitz-Thouless 1973, and generalized global symmetries 2014. A selected\n  valid system, symmetry, charged order\n  parameter, explicit real expectation and infrared-limit filter, actual\n  suppression, and a separate physical no-breaking bridge yield a checked\n  unbroken result while retaining an independent other-order value. The three\n  adapters preserve the genuinely different limits and calculations:\n  Mermin-Wagner uses the post-thermodynamic small-field magnetization limit;\n  KT uses the positive-field ordinary-magnetization limit while retaining\n  rigidity as other order;\n  the higher-form route uses large separation, divergent Coulomb potential,\n  and the exponential loop law. Value-bearing countermodels show that charged\n  scope without suppression and suppression without the physical bridge do\n  not forbid breaking. Full theory/model/world transfer is explicit for all\n  three clients. Separate source-valued witnesses now retain the Mermin-Wagner\n  positive-temperature isotropic scope, uniform versus staggered channels,\n  actual finite Bogoliubov denominator, ordered thermodynamic/zero-field\n  limits, surviving unrelated order, divergent susceptibility, and the\n  independently calculated axial exception.\n  Mermin-Wagner's paper-local setup additionally retains its complete\n  matrix-valued exchange-plus-ordering-field Hamiltonian, noncommuting\n  spin-S algebra and Casimir, both direct/inverse spin and exchange Fourier\n  transforms, finite Gibbs partition function and Boltzmann weights,\n  equal-energy exclusion in the spectral inner product, equations (4)-(6),\n  and exact selected raising/lowering operators. Its physical `J(0)` is the\n  dimension-correct zero lattice vector, not an empty displacement; eight\n  independently inhabited boundaries prevent these source formulas from\n  collapsing back into names. The KT witness separately\n  distinguishes logarithmic energy from positional entropy, positive versus\n  negative vortex free energy, neutral bound pairs, surviving topological\n  order, screened stiffness, an approximate bare upper bound, and the\n  excluded superconducting/Heisenberg cases. The higher-form witness keeps\n  `q \u003C= d`, continuous `d-q \u003C 3`, discrete `d-q \u003C 2`, the genuine\n  `exp(-V)` Wilson-loop value at finite separation, independent surviving\n  order, and the separate compact Ward-selection bridge.\n  The framework now also exposes ordinary and source-sensitive structural\n  explanations. Its ordinary constraint retains the selected system,\n  symmetry, charged order parameter, regime, and infrared filter; typed\n  source tokens separately preserve Mermin-Wagner's Bogoliubov/ordered-limit\n  chain, KT's quoted ordinary-order input without its vortex route, and the\n  higher-form dimension/Coulomb/Ward chain. A false-source countermodel shows\n  that a completed no-order endpoint cannot manufacture provenance.\n- `PhysicsLogic/Framework/AdiabaticCyclePhase.lean`: weak shared closed-cycle\n  phase semantics extracted from Berry 1984 and\n  Arovas-Schrieffer-Wilczek 1984. It retains a parameter-dependent family, a\n  closed sufficiently slow cycle, a transported sector, and a paper-local\n  calculation of an additional non-dynamical, duration-independent phase.\n  The proof-free context owns the five selected objects and all nine relation\n  families used by the route. Exact semantics identifies a candidate with that\n  one context-selected model, so the candidate cannot select its own physical\n  indices. The output-led established result is exactly selected semantics\n  plus `NonvacuousAdiabaticCyclePhaseAt`, in which all six setup\n  relations and all three phase outputs hold at one model rather than behind\n  an implication-valued calculation contract. A finite Bool witness realizes\n  it, and exhaustive five-index and nine-relation mutation theorems destroy\n  the direct proposition under every selected-value or relation-family\n  change. The older fourteen-component exact-semantics audit remains separate.\n  Both papers name the exact model, prove a definitional retention\n  certificate, construct named paper-local selected-setup adapters, and\n  expose named nonvacuity projections before using the shared inference.\n  The selected calculation model is distinct from its containing theory and\n  represented physical system. Exact selected semantics plus the inhabited\n  slow closed-cycle setup is required in theory membership and world\n  representation. The generic grounding constructor uses that selected setup,\n  explicit theory use,\n  explicit world representation, and conditional claim transfers. Berry and\n  Arovas-Schrieffer-Wilczek delegate to it through separate paper-local\n  interpretation inputs before combining grounding with their technical\n  calculations. Exact selection without setup cannot ground, while a selected\n  setup can have complete grounding with the phase outputs false. Further\n  countermodels block\n  automatic theory/world grounding and reconstruction of a missing technical\n  route from declared final claims. The complete route also realizes a typed\n  structural explanation whose constraint retains the selected family,\n  parameter space, cycle, sector, and phase and whose phenomenon retains the\n  additional nondynamical, duration-independent phase. Both papers expose\n  named projections. A finite model with all three phase outputs but no\n  parameter-dependent setup makes the phenomenon obtain without explaining\n  it.\n  Curvature, gauge representation, interference, charge, and statistics\n  remain in stronger shared components or paper-local routes.\n- `PhysicsLogic/Framework/PlanarExchangeStatistics.lean`: narrow shared\n  winding-to-exchange semantics extracted from Wilczek 1982 and\n  Arovas-Schrieffer-Wilczek 1984. It retains an identical planar pair, full\n  winding and exchange paths, both calculated phases, their two-exchange\n  composition, and a separate fractional-statistics bridge. Wilczek grounds\n  the model in charge-flux-composite quantum mechanics and a selected planar\n  composite pair; Arovas-Schrieffer-Wilczek grounds it in Hall-quasihole\n  exchange statistics and a selected separated two-quasihole configuration.\n  Wilczek's Bose/Fermi endpoints and continuous interpolation in the\n  charge-flux parameter remain paper-local: the shared layer keeps only the\n  selected fractional phase classification independently supplied by both\n  papers. Wilczek's independently sourced interpolation conclusion now\n  requires an actual typed charge-flux composite, pair state, flux tube,\n  potential, and winding/exchange paths for every `0 \u003C= Delta \u003C= 1/2`.\n  Each member retains `q(Delta) Phi(Delta) = 2 pi Delta`, exchange phase\n  `2 pi Delta`, full-winding phase `4 pi Delta`, and its own weak-force,\n  fixed-product approximation. Lean derives genuine continuity and proves\n  that the Bose and Fermi composites have different charge-flux products;\n  holding one product fixed across the entire family cannot interpolate.\n  Independent countermodels distinguish three selected composites from the\n  full continuum, formal phases from physical composite realization, wrong\n  charge-flux or exchange laws, parameters outside the strict open interval,\n  and complete two-anyon interpolation from unresolved many-anyon dynamics.\n  The established endpoint is output-led and reconstructs both\n  implication-valued contracts. Each paper has a named adapter from its\n  identical planar-pair and path premises to the selected shared setup;\n  grounding requires that setup but no phase or classification output.\n  Countermodels separate the technical route from theory/world grounding and\n  prevent declared final claims from reconstructing the calculation. They\n  also show that exact selection without setup cannot ground and that the\n  selected setup can ground while every exchange output is false. The\n  synthetic sensitivity model makes every setup and phase relation depend on\n  its physical arguments. `NonvacuousPlanarExchangeStatisticsAt` now keeps\n  the identical planar pair, both paths, winding relation, both phases,\n  composition, and fractional classification together at one model. Both\n  paper adapters expose that direct result. Every one of the seven selected\n  values and nine relation families falsifies the direct result when changed;\n  the older sixteen-component audit still separately enforces exact model\n  semantics. The complete route additionally realizes a typed structural\n  explanation whose constraint retains the selected system, pair, two paths,\n  two phases, and regime, and whose distinct phenomenon retains the\n  fractionally classified exchange phase. Wilczek and\n  Arovas-Schrieffer-Wilczek independently expose that projection. A finite\n  model with declared fractional classification but no exchange-phase\n  calculation makes the phenomenon obtain without explaining it. This adds\n  no generic anyon, gauge, braid, Hall-charge, Chern-Simons, or\n  topological-order ontology.\n- `PhysicsLogic/Framework/FieldFreeMagneticInterference.lean`: shared\n  magnetic-flux interference semantics extracted from Aharonov-Bohm 1959 and\n  Berry 1984. It retains coherent alternatives in a field-free accessible\n  region, a closed circuit around excluded field support, the\n  circulation-to-flux and phase calculation, coherent phase readout, and the\n  bridge to flux-dependent interference. Its established result is output-led:\n  it stores the exact selected model, an actual field-free setup, and the\n  realized circulation, phase, recombination, and readout outputs, while the\n  implication-valued proof route is reconstructed. Both clients prove\n  setup-bounded theory/model/world grounding from their paper-local physical\n  setups without consuming a circulation or interference calculation.\n  Countermodels show that exact selection alone cannot ground the model, that\n  grounding can precede all interference outputs, and that declared\n  theory/world conclusions do not reconstruct the interference route. The\n  established result also yields a direct nonvacuous interference model once\n  explicit distinct-path and selected gauge-orbit witnesses are supplied.\n  That direct route now projects the selected vector-potential orbit to\n  `SymmetryAndGauge.RepresentationContext`: the closed-loop phase is a\n  representative-independent value of one inhabited field-free flux\n  configuration. Interferometric phase and flux readouts remain separate\n  conjuncts. A countermodel retains the representative-independent value but\n  has no readout, so gauge invariance is not conflated with interferometric\n  significance or with an ontology of local potentials. This endpoint is a\n  prediction/readout relation, not a performed-observation claim.\n  The route also has ordinary and source-sensitive structural explanations.\n  Aharonov and Bohm's typed source token retains the shielded-solenoid\n  split-beam, branch-phase, recombination, and flux-interpretation route.\n  Berry's distinct token retains the exact single-valued transported-box\n  Dirac-phase construction, its explicit nonnecessity of adiabaticity, and\n  reference-box readout. Neither source relation stores a shared endpoint.\n  A finite model with complete ordinary interference but a false source\n  relation proves that the common output cannot recover either derivation.\n  Aharonov-Bohm pp. 486-487 and Berry pp. 52-54 anchor the two adapters; a\n  separate twelve-index/seventeen-family direct activity audit prevents\n  collapsed alternatives, vacuous gauge orbits, or inactive semantics from\n  counting as physical interference.\n- `PhysicsLogic/Framework/AdiabaticHolonomy.lean`: narrow shared cycle\n  semantics extracted from Berry 1984 and Hannay 1985. Its proof-free exact\n  model retains eight selected indices, all three maps of the representation\n  context, and all eleven relation families used by the route. The context\n  owns the eight indices, and selected semantics compares candidates with that\n  one exact model. A sensitivity theorem rejects direct mutations of every one\n  of these twenty-two components. A separate inhabited finite witness makes\n  those same twenty-two components directly active in\n  `NonvacuousAdiabaticHolonomyAt`, rather than only visible through exact\n  record equality. The\n  route requires a parameter-dependent family, a slow closed cycle, local\n  continuation data, a convention-dependent connection calculation, and a\n  `Philosophy.SymmetryAndGauge.RepresentationContext` for local\n  representatives, convention redundancy, and convention-indexed curvature\n  values. The route requires an actual representative of the selected\n  physical sector, curvature invariance on redundancy orbits, and the premise\n  that all representatives of that sector lie in one orbit; the established\n  theorem then derives a physical\n  representative-independent curvature value. It also retains the same cycle\n  invariant, traversal-duration independence, and a paper-specific\n  physical-significance bridge. The established route projects to the direct\n  nonvacuous proposition. The output-led established result is exactly that\n  proposition plus selected semantics, and the implication-valued significance\n  bridge and complete route are reconstructed from its facts. Berry and Hannay\n  each expose the result from their paper-local inputs. Each paper names its exact model and proves by\n  definitional equality that no retained component was changed in the adapter.\n  Nine exhaustive claims include the exact selected semantics and route\n  applicability as well as setup, calculation, significance, curvature, and\n  the direct nonvacuous and established results. The module also imports\n  `Philosophy.TheoryModel` and\n  keeps the selected calculation, its containing theory, and its represented\n  physical system distinct. Theory membership and world representation require\n  exact selected semantics plus the inhabited slow closed-cycle setup. A\n  generic grounding constructor adds explicit theory use, world\n  representation, and conditional claim transfers; it contains no connection,\n  curvature, duration-independence, significance, route-applicability, or\n  established-result premise.\n  Berry and Hannay delegate to this constructor through separately stated\n  paper-local interpretation bridges before combining grounding with their\n  technical routes. Berry's\n  interference significance and Hannay's generally nonzero angle remain\n  downstream technical conclusions. Exact selection of an open cycle cannot\n  ground a model; a separate inhabited setup can be grounded while curvature\n  construction, the holonomy route, and the direct endpoint remain false.\n  Further countermodels separate existence,\n  invariance, and orbit completeness, block a vacuous significance bridge,\n  show that the vacuous bridge fails the direct nonvacuous proposition,\n  show that a completed calculation does not supply theory/world grounding,\n  and show that declared theory/world claims do not reconstruct the technical\n  route.\n  The framework now also separates ordinary and source-sensitive structural\n  explanations. `AdiabaticHolonomyConstraint` retains only the selected\n  proof-free shared model, while `AdiabaticHolonomySourceConstraint` adds a\n  typed paper-local derivation relation. Berry and Hannay each expose an\n  ordinary raw-input adapter and a separate source-sensitive adapter; the\n  latter retains Berry's instantaneous-eigenstate/spectral/interference route\n  or Hannay's action-averaging/angle-curvature route without consuming an\n  established or nonvacuous endpoint. A countermodel realizes complete\n  ordinary holonomy explanation while its source relation is false, so the\n  common physics output cannot manufacture paper provenance.\n  Quantum eigenstates, classical\n  action-angle coordinates, spectral formulas, Liouville conservation,\n  integrability, and concrete observables remain paper-local.\n- `PhysicsLogic/Framework/EquilibriumNoiseDissipation.lean`: narrow shared\n  equilibrium-noise semantics independently realized by Nyquist 1928,\n  Callen-Welton 1951, and Kubo 1957. Each paper independently constructs the\n  direct established result from equilibrium and dissipative setup, separate\n  dissipation, fluctuation, and relation calculations, represented physical\n  readouts, its selected spectrum convention, and the sector-wide value\n  equality. The setup also requires an actual member of the selected\n  frequency sector. The output-led established proposition retains exact\n  selected semantics plus those direct nonvacuous outputs; implication-valued\n  readout and relation bridges are reconstructed only when a complete\n  technical route is requested. The complete route also realizes a typed\n  structural explanation of the represented, convention-indexed relation.\n  Each paper now reaches that explanation directly from source-facing inputs,\n  before an established shared relation or nonvacuity endpoint is consumed.\n  Callen-Welton's theorem explicitly reconstructs its packaged generalized\n  relation from the perturbative dissipation, zero-force fluctuation, and\n  common-spectral-sum stages. The older terminal projections remain\n  compatibility routes;\n  a finite equation-only countermodel retains the calculation flags and\n  numerical equality but removes both physical readouts, blocking the\n  explanation. This adds no causal-production or observation claim and does\n  not identify the three papers' spectrum conventions. Its proof-free\n  source constraint now also retains a typed paper-local derivation. Nyquist's\n  second-law/filter and transmission-line route, Callen-Welton's two quantum\n  spectral sums, and Kubo's response/correlation conductivity theorem each\n  realize distinct tokens before entering the same shared explanation. A\n  complete-route countermodel with a false derivation predicate proves that\n  matching noise/dissipation output cannot reconstruct source provenance. The\n  separate proof-free calculation model retains the\n  selected system, regime, temperature, force, frequency sector, validity and\n  equilibrium predicates, force and fluctuation relations, value and\n  prediction maps, physical readout relations, and all three calculation\n  predicates. Each paper proves that its named model contains exactly those\n  nineteen semantic components. Exact selected semantics and a model-native\n  technical route are separate premises of applicability, while the direct\n  established result realizes ten exhaustive claims, including the active\n  frequency sector. The model is distinct from the equilibrium theory using it and the\n  physical fluctuating system it represents. Nyquist grounds this separation\n  through equal-temperature\n  exchange, matched-line theory, and a pure fluctuating resistance;\n  Callen-Welton through perturbative setup, zero applied force, equilibrium,\n  and spontaneous fluctuations; Kubo through application setup and the\n  selected near-equilibrium conductor. None of these grounding proofs assumes\n  the established shared relation or its paper-local calculation package.\n  A generic constructor requires the exact selected model and complete\n  inhabited equilibrium linear-dissipative pre-output setup before\n  transferring claims, so model grounding cannot be manufactured from a bare\n  interpretation declaration.\n  Countermodels block both automatic theory/world grounding from technical\n  completion and reconstruction of the technical route from declared\n  theory/world relations; a positive countermodel also constructs grounding\n  while both the technical route and direct established endpoint are false. A\n  separate empty-sector countermodel\n  makes all three calculation flags true but blocks establishment. An\n  nineteen-component sensitivity theorem shows that changing any selected\n  index, relation, or value map changes the exact model. A finite established\n  witness and direct activity theorems further show that every one of those\n  changes destroys the nonvacuous sector-wide output; Nyquist, Callen-Welton,\n  and Kubo derive that output independently. Circuits, quantum\n  transition sums, conductivity tensors, correlation functions, oscillator\n  factors, and application formulas remain paper-local. Callen-Welton also\n  retains its conclusion as a separate two-system interpretation: an\n  initially isolated coherent periodic source supplies the selected force to\n  the dense-spectrum generalized system, later coupling lets equilibrium\n  fluctuations act back on the source, and the resulting loss of periodic\n  motion, coherence, and ordered energy supports only the paper's scoped\n  macroscopic interpretation of dissipation.\n  Separate source-valued witnesses now retain those deliberately omitted\n  physical distinctions without widening the generic contract. Nyquist keeps\n  frequency-local second-law filtering, matched-line mode counting, the\n  one-sided `4 R k T` voltage spectrum, current-transfer convention, indirect\n  carrier dependence, and a zero-point-free Planck replacement. Callen-Welton\n  keeps conjugate generalized force, separate transition and equilibrium\n  spectral sums, the half-quantum oscillator factor, qualified classical\n  limit, Brownian/radiation/acoustic applications, wall/volume factor two, and\n  a future-scoped coherence-loss interpretation. Kubo keeps symmetrized rather\n  than ordered current correlation, qualified observation, exact conductivity\n  relation, classical recovery, conditional static/isothermal comparison,\n  time-reversal-qualified reciprocity, full-spectrum sum-rule scope, and\n  independent interacting Einstein relation. Thirty-three controlled\n  mutations reject formula, convention, approximation, application, and\n  epistemic-scope collapses among the three original papers.\n- `PhysicsLogic/Framework/LinearResponseTransport.lean`: narrow shared\n  response-to-transport semantics extracted from Nakano 1956 and Kubo 1957.\n  It requires explicit equilibrium and linear-response setup, separate\n  calculations and bridges for causal response, equilibrium-correlation\n  representation of a kernel sector, and transport extraction from the\n  kernel family. Both papers expose a separate theorem proving the complete\n  shared route-applicability proposition before deriving the established\n  transport result. That result is output-led: it retains exact selected\n  semantics, the inhabited setup, the three supplied calculations, causal\n  response, sector-wide equilibrium-kernel representation, and the transport\n  readout. The three paper-local bridges and complete route are reconstructed\n  from those direct facts. The same source-ordered premises also project to a\n  scoped `Paradigm/ReductionAndEmergence` derivational reduction with distinct\n  equilibrium-response, driven-transport, and represented-behavior types.\n  Realization requires the inhabited setup, microscopic support retains the\n  three calculations, bridges, causal response, and equilibrium kernel, and\n  macroscopic exhibition retains the actual transport readout. Nakano and\n  Kubo expose direct paper adapters that do not consume the terminal shared\n  result. A source-sensitive refinement additionally records Nakano's\n  pulse-response/thermal-kernel/static-conductivity derivation and Kubo's\n  canonical-response/relaxation/correlation-admittance derivation as distinct\n  typed sources. Kubo's raw-input theorem now constructs the route directly\n  rather than passing through its ordinary reduction wrapper. Countermodels\n  separately block recovery of source provenance from a completed route,\n  recovery of the derivation from a\n  readout without an equilibrium kernel and from an equilibrium kernel without\n  transport extraction. Kubo's shared premise stops before its paper-local\n  zero-Planck and classical-correlation recovery, so the projection is neither\n  a classical-limit theorem nor a reduction of complete theories. Its\n  proof-free calculation\n  model retains six physical indices and all fifteen route-used relation,\n  value-map, and calculation fields. Each paper constructs a named exact\n  model, proves a semantic-retention certificate, and consumes that\n  certificate in the applicability theorem. Named field-equality theorems\n  expose all six indices in each adapter; Kubo's frequency-domain kernel and\n  admittance relations are additionally scoped to its selected force and\n  near-equilibrium regime. The calculation model, containing\n  response theory, and represented driven equilibrium system are separate\n  Lean objects. All eight claims, including exact selected semantics, setup,\n  and the three calculation claims, transfer only through explicit theory and\n  world bridges. These calculation claims mean applicability and soundness,\n  not literal calculation by the conductor. Generic theory/model membership\n  and world representation now require both exact model selection and the\n  complete equilibrium linear-response setup. A shared constructor then\n  establishes grounding from those premises plus theory use, world\n  representation, and conditional claim-transfer bridges. Nakano and Kubo\n  delegate to that constructor. Kubo's paper-local operational assessment\n  separately retains continuous observation of one particular macroscopic\n  system, the unproved ensemble-to-observation identification, its unknown\n  exact condition, and the unresolved optical readout bridge; none of those\n  qualifications are promoted into shared transport semantics. Nakano uses\n  only his arbitrary-field response\n  setup, while Kubo adds his operational assessment, including the unproved\n  observation bridge and unknown exact macroscopic condition. Neither proof\n  assumes a response, kernel, or transport calculation or any established\n  result. Countermodels block both automatic theory/world grounding from a\n  completed calculation and reconstruction of the technical route from\n  declared theory/world claims; a positive countermodel has exact selection\n  and complete setup-grounding while the response calculation and route are\n  false, while a false-setup model is explicitly ungroundable. A 21-component\n  mutation audit shows that changing any retained field invalidates exact\n  model selection.\n  The causal-response bridge is now semantically grounded rather than trusted\n  by name. Each paper constructs a paper-local\n  `Paradigm.ResponseCausality.ResponseCausalityContext`; its pulse calculation\n  exposes past kernel support, exact dependence representation, and a\n  nonvacuous stimulus-response witness, and the shared paradigm theorem\n  derives retarded response. This temporal result is kept distinct from\n  interventionist influence, no-superluminal signalling, deterministic\n  uniqueness, and Kubo's unresolved ensemble-to-observation bridge.\n  The kernel index is neutral so that Nakano's time-domain route and Kubo's\n  selected frequency-domain route do not get falsely identified. Hamiltonians,\n  operators, integrals, transforms,\n  spectral sums, relaxation models, conductivity tensors, susceptibilities,\n  and Green functions remain outside the neutral shared inference.\n  Separate source-valued controls retain Nakano's strictly retarded pulse\n  convolution, `beta = 1/(k T)`, positive normalized thermal trace,\n  imaginary-time kernel, Boltzmann energy-gap quotient,\n  `pi hbar/(k T)` conductivity factor, and explicitly assumed one-relaxation\n  approximation. Kubo independently retains the Poisson-bracket sign,\n  static oscillator continuation, both symmetric and antisymmetric tensor\n  channels, and even-real/odd-imaginary frequency reflection. Seventeen\n  mutations reject source, formula, universal-Markovianity, and strong-drive\n  collapses while preserving the paper-independent transport route.\n- `PhysicsLogic/Framework/RemoteCorrelationPrediction.lean`: narrow shared\n  correlation-to-remote-prediction semantics independently realized by EPR\n  1935, Bohr 1935, and Bell 1964. Its exact proof-free model retains twelve\n  semantic components:\n  experiment, local and remote subsystems, regime, the two operational\n  observation relations, selected quantity, procedure assignment, preparation,\n  separation,\n  procedure availability, and correlation calculation. An exact selected\n  setup additionally requires preparation and a witness that at least one\n  quantity is selected. That setup, the paper-local calculation,\n  prediction-readout bridge, and distinct non-disturbance bridge establish the\n  direct nonvacuous output. The twelve-claim vocabulary also records model\n  selection, inhabited setup, route applicability, and the output-led\n  established result. EPR, Bohr, and Bell each construct a named exact model\n  and inhabit it with, respectively, EPR's first remote quantity, Bohr's\n  double-slit position branch, or an explicit Bell spin component. Their\n  separate grounding theorems consume only that\n  exact inhabited setup plus theory/world bridges, not the correlation route.\n  The complete route also realizes a typed structural explanation. Its\n  constraint retains the experiment, distinct subsystem roles, selected\n  quantity sector, local procedure assignment, and regime, and requires the\n  prepared separated setup, actual correlation calculation, both bridges,\n  and a nonempty selected sector. Its distinct phenomenon is certainty and\n  non-disturbance for every selected remote quantity. A correlation without\n  the readout bridge and declared certainty/non-disturbance without a\n  correlation calculation both fail to explain that phenomenon.\n  Reality criteria, completeness, predetermination, hidden variables, and\n  Bell's no-go route remain outside the common prediction model and inference.\n  EPR separately supplies a compatible reality interpretation and an explicit\n  sufficient-reality premise. Bohr supplies no arrangement-independent\n  reality field, and Bell's exact model is provably unchanged under arbitrary\n  admissibility assignments. Separate\n  source-valued controls retain EPR's `x_2 = x_1 + x_0`, `p_2 = -p_1`,\n  nonzero commutator, distinct incompatible local procedures, explicit common\n  remote-reality assumption, and only sufficient reality criterion. Its ideal\n  continuum state is distributional rather than square-normalizable, with no\n  derived finite-resolution regularization. Bohr separately retains two\n  distinct separated particles, measured double-slit preparation-diaphragm\n  momentum, the source equations `q2=q1-(q1-q2)` and\n  `p2=(p1+p2)-p1`, mutually exclusive later arrangements, and no jointly\n  performed procedures. His source-sensitive route accepts remote certainty\n  and mechanical nondisturbance while rejecting EPR's arrangement-independent\n  completeness inference; a physical countermodel supplies both alternative\n  prediction values but neither joint measurement nor a common-reality\n  identification. Bell's\n  controls retain same-axis singlet anticorrelation, normalized local hidden\n  variables, the original three-setting bound with quantum values `1 > 1/2`,\n  a locally incomplete illustrative model, and an allowed nonlocal\n  completion. They explicitly reject operational-signalling and all-hidden-\n  variables-excluded overclaims, and distinguish a possible future\n  fast-setting experiment from one already performed. Countermodels separate setup from output and\n  grounding in both directions, block reconstruction of the technical route\n  from output declarations, and prevent semantic erasure of any retained\n  model component.\n- `PhysicsLogic/Framework/SelfConsistentSpectralGap.lean`: narrow shared\n  inference extracted from BCS 1957 and Nambu 1960. A description must be\n  valid in a declared regime, a paper-local self-consistency problem must\n  receive a nontrivial calculated solution, and a separate paper-local bridge\n  must identify a finite gap in a selected excitation spectrum. BCS and Nambu\n  each expose a named theorem establishing the complete shared route before\n  deriving the spectral result. Their final shared theorems establish direct\n  output facts rather than invoking the generic route constructor. The\n  established proposition is exact selected semantics plus the direct\n  inhabited-gap proposition; the paper-local solution calculation and\n  spectral interpretation contracts are reconstructed from those outputs.\n  The proof-free model retains the selected description, gap,\n  excitation, spectrum, and regime together with validity, self-consistency,\n  nontrivial-solution, spectrum-membership, finite-gap, and spectrum-gap\n  relations. BCS and Nambu each construct one named exact model and prove its\n  semantic retention. A `TheoryModel` interpretation keeps that calculation\n  distinct from the theory using it and the represented superconductor;\n  grounding requires the exact selected, inhabited unsolved setup but not the\n  solution calculation or spectral bridge. BCS explicitly supplies its\n  paired-state-to-metal representation bridge, and Nambu supplies its\n  quasiparticle-vacuum-to-superconductor bridge. Countermodels show both that\n  implication-valued calculations can hold vacuously and that neither an\n  established technical gap nor physical spectral truth reconstructs the\n  missing route. The established result also yields a direct inhabited-gap\n  proposition in which validity, the posed self-consistency problem, its\n  nontrivial solution, excitation membership, gap finiteness, and the\n  spectrum-gap relation all hold at the same five selected objects. An exact\n  finite model realizes this proposition, and exhaustive activity theorems\n  show that changing any of the five indices or six relation families\n  destroys it. BCS anchors its adapter to pp. 1182-1183; Nambu anchors its\n  adapter to pp. 652-653. BCS additionally retains its equation-(2.40)\n  epsilon_0 value, equation-(2.50) square-root dispersion, and selected\n  equation-(2.49) threshold locally. Their Lean deductions prove a strictly\n  positive gap, exclude selected subgap quasiparticles, and show that the\n  two-particle energy attains its minimum of 2 epsilon_0 at the Fermi\n  surface; a positive-energy subgap countermodel separates a merely named\n  threshold from that minimum. The shared endpoint does not collapse those\n  formulas into Nambu's distinct source calculation. The earlier\n  eleven-component equality audit remains\n  as a separate exact-retention check. A source-sensitive structural\n  projection distinguishes BCS's coherent variational paired-state\n  derivation from Nambu's anomalous-self-energy derivation. Nambu's later\n  Ward-identity and collective-mode routes are policy-excluded from that\n  token. A complete ordinary route and all gap outputs can coexist with a\n  false source relation, so result equivalence does not reconstruct\n  derivational provenance.\n  The gap is scoped to the selected quasiparticle excitation spectrum, not\n  every excitation: Nambu separately has a gapless collective branch, and\n  BCS leaves other spin sectors open.\n  The complete direct route now also realizes the mature structural-\n  explanation interface through distinct proof-free constraint and\n  phenomenon types. BCS and Nambu consume their respective route-applicability\n  theorems directly; pairing and anomalous self-energy remain paper-local. An\n  output-only invalid-setup model blocks a gap label from explaining itself,\n  while a second finite model proves that a structurally explained selected\n  quasiparticle gap can coexist with an ungapped collective spectrum.\n  Superconductors, pairing, anomalous self-energies, variational states,\n  quasiparticles, and particular gap equations remain paper-local.\n- `PhysicsLogic/Framework/TransverseMeissnerScreening.lean`: narrow shared\n  response-to-screening inference extracted from BCS 1957 and Nambu 1960.\n  A description must be valid in a declared regime, a selected field must be\n  static and transverse, and the paper-local calculation must produce an\n  induced current whose long-wavelength response opposes that field. A\n  separate physical bridge identifies this response with exclusion of the\n  selected field from the bulk. Its proof-free model retains all six selected\n  objects and all six route-used relation families. BCS and Nambu each\n  construct a named exact model and prove a semantic-retention certificate\n  before route applicability. The established result is output-led: exact\n  selected semantics plus the direct setup, calculated current, sign relation,\n  and bulk field exclusion. The calculation and bridge are reconstructed. A\n  shared induced-current adapter must replay the model-native setup before\n  rerunning its paper-local calculation: BCS rebuilds validity, linear\n  response, and current decomposition with its coherence factor, while Nambu\n  rebuilds the Ward result, longitudinal defect, collective state, and\n  transverse response with its local Ward-vertex setup. A\n  `TheoryModel` interpretation keeps the response model distinct from the\n  electrodynamic theory and represented superconductor. Grounding requires the\n  selected physical response setup, model use, representation, and conditional\n  transfer, but no response calculation, bridge, or result. BCS supplies its\n  `MeissnerSetup`; Nambu supplies its `GaugeInvariantMeissnerSetup`. All thirteen claims\n  transfer only after that independent\n  grounding is combined with technical establishment. The established result\n  is exact selected semantics plus the model-native\n  `NonvacuousTransverseMeissnerScreeningAt` proposition that requires an\n  actual setup and the calculated current, screening sign, and bulk exclusion\n  together, while storing neither implication-valued obligation; this makes the shared\n  claim family thirteen claims. The generic endpoint remains gap-agnostic.\n  The source-order BCS and Nambu adapters additionally expose\n  `NonvacuousGapSupportedTransverseMeissnerScreeningAt`, which retains the\n  direct nonvacuous self-consistent-gap child, exact established gap route,\n  paper-local admissibility bridge, selected response setup, and direct\n  screening endpoint together. The stronger source-sensitive composition\n  additionally requires independently realized gap, screening, and joining\n  derivations. BCS's join retains its original gap/dispersion/pair-breaking\n  formulas, coherence case II, printed London-current equations, Pippard\n  kernel, and penetration depth. Nambu's join instead retains anomalous\n  nonperturbative pairing, gauge phase, the matrix Ward identity, the\n  Coulomb-omitted collective intermediate, longitudinal cancellation, and\n  the surviving physical transverse response. An inhabited countermodel\n  distinguishes gap values, quasiparticle versus collective excitations,\n  opposing versus aligned currents, and applied versus residual fields while\n  proving that completed child explanations cannot supply a missing joining\n  source. BCS realizes the route\n  through its paramagnetic-plus-diamagnetic response calculation; Nambu\n  realizes it after collective vertex corrections cancel the unphysical\n  longitudinal response while retaining the transverse BCS response. The\n  complete route now also realizes a typed mechanistic explanation: the\n  system-current-field component undergoes a calculated induced and opposing\n  current activity in the valid static transverse response organization,\n  producing bulk field exclusion. Both papers derive this explanation from\n  their full source-stage gap, response, and interpretation inputs before any\n  established shared endpoint exists. A countermodel keeps bulk exclusion\n  true while deleting the current activity, so the phenomenon cannot explain\n  itself. The\n  component composes with the established\n  self-consistent-gap route only through a paper-local admissibility bridge:\n  BCS uses the gapped spectrum in its coherence-factor calculation, while\n  Nambu uses the nonperturbative anomalous solution to establish the Ward\n  identity, continuity equation, and conserving current. Ward constructions,\n  Pippard kernels, penetration depths, and superconductivity mechanisms\n  remain paper-local. Countermodels block inference from a completed gap to\n  a transverse setup, from a calculated current to its screening sign, from\n  an opposing current to bulk field exclusion, and from physical exclusion\n  or theory/model grounding back to the missing response route. They also\n  reject absent-setup grounding and output-only grounding at a non-selected\n  model. A finite\n  positive model realizes the complete screening route and the direct\n  nonvacuous endpoint, and a finite composed witness realizes the\n  gap-supported endpoint. A complementary countermodel realizes generic\n  screening without a nonvacuous gap, proving that screening alone is not\n  gap-supported screening. Direct endpoint-falsification tests cover all six\n  selected indices and all six relation families. A\n  separate twelve-field exact-model audit rejects every changed component.\n  Separate source-valued witnesses now retain the actual BCS equations\n  (5.22), (5.25)-(5.29), case-II coherence channel, London endpoints,\n  gapless normal-current cancellation, Pippard scale, and independent\n  field-expulsion bridge. Nambu's witness retains its noncommuting two-by-two\n  Ward matrix identity, matched self-energy kernel, charged-line insertions,\n  nonzero longitudinal defect, collective cancellation with unchanged\n  transverse response, Coulomb-omitted gapless pair, Coulomb-shifted plasma\n  frequency, and exchange between quasiparticle core and collective cloud.\n  Thirty-one controlled mutations reject altered formulas, mistaken gauge\n  representatives, erased transverse screening, interacting zero modes, and\n  unsupported transport, strong-coupling, or all-orders claims. These source\n  witnesses strengthen fidelity without broadening the generic screening\n  contract or treating local gauge redundancy as a broken physical symmetry.\n- `PhysicsLogic/Framework/RGEndpointMonotonicity.lean`: narrow shared\n  renormalization-group irreversibility contract extracted independently from\n  Zamolodchikov 1986 and Komargodski--Schwimmer 2011. It retains a selected\n  nontrivial ultraviolet-to-infrared fixed-point flow, ordered scale\n  evolution, a running quantity with endpoint identifications, weak\n  monotonicity, strict endpoint ordering, an output-led direct result, and\n  setup-bounded `TheoryModel` grounding. Zamolodchikov's stress-tensor and\n  positive coupling-metric calculation and Komargodski--Schwimmer's dilaton,\n  anomaly-matching,\n  dispersion, optical-theorem, and positive-cross-section calculation remain\n  paper-local. Zamolodchikov's adapter now replays the selected shared flow\n  setup into its stronger paper-local setup before either the conformal\n  endpoint bridge or the running-monotonicity calculation is used; the\n  beta-vanishing and critical-CFT premises remain local rather than being\n  smuggled into the shared vocabulary.\n- `PhysicsLogic/Framework/EffectiveInteractionDynamics.lean`: narrow shared\n  organization extracted from Ordonez-Ray-van Kolck 1995 and independently\n  tested by both parts of Epelbaum-Gloeckle-Meissner 1998/1999. It separates\n  perturbative finite-order\n  construction of an effective interaction from nonperturbative full\n  dynamics generated by iteration. The retained model now contains its\n  selected interaction, generated dynamics object, order, and regime together\n  with exactly the seven\n  semantic families used by the shared route. The context owns the low-energy\n  dynamics object, regime, and truncation order and derives the selected\n  interaction from that order, producing one unique `selectedModel`; a\n  candidate model cannot choose a different dynamics object, EFT regime, or\n  order and certify itself. Each paper constructs\n  its named exact model from that unique selection and proves that it retains\n  the paper adapter's semantics before applying the route. The established\n  result has a checked projection back to the exact selected dynamics and\n  retains that certificate and the complete route directly together\n  with an explicit proposition stating the\n  perturbative-interaction/nonperturbative-dynamics organization. An\n  exhaustive twelve-case technical semantics checks every part of that\n  model-local route in the framework and in each paper adapter. A\n  finite model realizes a direct nonvacuous route that requires the selected\n  order to induce the selected interaction and uses all seven relation\n  families. Exhaustive activity theorems prove that changing any of the four\n  indices or any of the seven relation families destroys that direct route;\n  the eleven-component mutation audit separately checks exact semantic\n  retention.\n  The same raw route now also realizes a structural explanation of the\n  selected mixed organization. A proof-free constraint selects the exact\n  finite-interaction/iteration model, while a separate phenomenon retains\n  the selected interaction, generated dynamics, order, and regime. The\n  source-sensitive form adds an independently realized typed paper\n  derivation without consuming the established endpoint, ordinary\n  explanation, or existing derivational-reduction wrapper. Ordonez-Ray-van\n  Kolck, EGM Part I, and EGM Part II provide distinct source explanations\n  for irreducible-potential iteration, unitary-projected formal iteration,\n  and regulated NNLO Lippmann-Schwinger solution. A finite false-source model\n  keeps the complete route, established organization, and ordinary\n  explanation while denying provenance.\n  A separate theory-model interpretation now treats the\n  finite-order interaction as a mathematical model, keeps each paper's\n  effective theory and represented low-energy dynamics distinct, and\n  transfers only the claims that full dynamics require nonperturbative\n  treatment and are generated by iteration; every adapter proves this\n  exhaustive two-claim transfer. Each transfer is indexed by the pair of the\n  selected dynamics and regime rather than by regime alone. Grounding uses\n  only exact model retention,\n  explicit theory use and world representation, and conditional claim\n  transfer; it consumes no power-counting, construction, iteration, route, or\n  established-result premise. Perturbative construction\n  through a finite order is a model condition, not a property asserted of\n  nature. Countermodels show both that a complete technical route need not\n  supply the interpretation bridges, that exact grounding can hold while the\n  technical route is false, and that even theory-and-world truth of\n  both physical dynamics claims does not reconstruct the finite-order\n  interaction route. Nucleons, pions,\n  potentials, projectors, diagrams, regulators, and scattering equations\n  remain paper-local. The term-level data underlying power counting also\n  remain paper-local; the shared model retains only soundness and completeness\n  through the selected order. The 1999 calculation paper adds a third adapter from\n  its imported NNLO potential through regulated Lippmann-Schwinger iteration,\n  without promoting its cutoff choices or numerical observables into the\n  shared interface. No adapter claims regulator-independent observables, and\n  KSW's amplitude-first resummation is intentionally outside this component.\n- `PhysicsLogic/Framework/RenormalizedPrediction.lean`: narrow shared\n  renormalization inference extracted from KSW 1998 and\n  Bedaque-Hammer-van Kolck 1998. It keeps the paper-local parameter-flow\n  calculation separate from the all-scale matching calculation and derives\n  scale-to-scale prediction invariance only through explicit bridges to the\n  mature RG semantics. The technical route also requires one actual target\n  prediction in the selected sector and projects to a direct nonvacuous\n  proposition containing the selected setup, both calculations, running\n  parameters, all-scale matching, and a witnessed common effective prediction\n  at two distinct scales. The established proposition stores exact semantic\n  selection, that direct nonvacuous output, and cross-scale agreement; its\n  complete implication-valued route is reconstructed from these outputs. A\n  separate empirical interpretation distinguishes\n  the target description, each scale-indexed effective description, and the\n  physical system. Only target empirical adequacy plus representation of that\n  same system at every scale yields empirically adequate effective\n  predictions. Both paper adapters first prove a named complete\n  renormalization-route proposition, and the established result exposes its\n  complete setup, both calculations, both exact interpretation bridges, and\n  the reconstructed route. The stronger grounded result retains an independent\n  empirical route as well. The exact proof-free calculation model retains the\n  selected system, target, regime, and observable sector together with the\n  scale-indexed effective descriptions, running parameters, prediction\n  relations, selection predicates, and both calculation predicates. KSW and\n  Bedaque-Hammer-van Kolck each construct a named model from their paper-local\n  context and prove exact semantic retention before either route applies. An\n  explicit theory/model/world interpretation states when a theory uses that\n  same model and when it represents a physical world. Generic grounding\n  requires only exact model selection, setup, and those paper-local bridges;\n  it consumes neither renormalization calculation nor the empirical route.\n  KSW grounds the selected pion-inclusive two-nucleon EFT\n  and scattering problem through effective-range matching;\n  Bedaque-Hammer-van Kolck ground the selected leading-order short-range\n  three-body EFT and low-energy system through the paper's cutoff-correction\n  representation predicate. Every empirically grounded result\n  realizes all eighteen shared claims, including exact semantic selection,\n  through one exhaustive theorem, and\n  both paper adapters expose named realization and theory/world transfer\n  certificates. Countermodels show why vacuously true implication bridges,\n  target mismatch, effective-representation failure, or theory/world claims\n  without the technical route cannot be repaired by all-scale matching. A\n  predictionless countermodel keeps both calculations, both bridges, running\n  parameters, all-scale matching, and extensional cross-scale agreement while\n  blocking both route applicability and the direct endpoint. A separate\n  countermodel grounds the selected setup while parameter flow and route\n  applicability are false, while another proves that false setup cannot be\n  grounded even under universally permissive theory and world claims. A\n  stronger sourced two-body/prediction composition retains exact selection of\n  both independent child contexts, their distinct source explanations, and a\n  third paper-local joining derivation. KSW's joining source preserves the PDS\n  loop, bubble summation, unitarity recovery, pion-inclusive mixed expansion,\n  and full-amplitude RG cancellation; BHvK's preserves the dressed dibaryon,\n  effective-range amplitude, three-body integral equation, individually\n  UV-finite diagrams, cutoff-sensitive sum, one running counterterm, and the\n  original equation-(12) limit-cycle sine ratio. An inhabited countermodel\n  keeps the successful ordinary composition, distinct systems/regimes/targets,\n  and both child source explanations but rejects a missing joining derivation.\n  A\n  fifteen-component mutation audit changes every\n  retained index, scale map, prediction relation, selection relation, and\n  calculation predicate independently, and a completed finite model repeats\n  that audit directly against the nonvacuous endpoint. Beta functions,\n  subtraction schemes, cutoffs, counterterms, amplitudes, and truncation\n  errors remain paper-local.\n- `PhysicsLogic/Framework/PostCalibrationPrediction.lean`: narrow shared\n  inference from a completed calibration to a separately calculated target\n  excluded from that calibration and requiring no additional fitted input.\n  KSW 1998 realizes it with a fitted coupled-channel S-wave phase and an\n  unfitted mixing angle; Bedaque-Hammer-van Kolck 1998 with one fitted\n  three-body datum and the remaining energy dependence; and\n  Epelbaum-Gloeckle-Meissner 1999 with nine low-wave contact parameters and\n  the unfitted three-D-one phase shift. Its exact proof-free model retains\n  four selected indices and all five route-used relation families. Each\n  paper adapter proves that this complete model retains its paper-local\n  semantics before applicability. The established result is output-led:\n  exact selected semantics are conjoined directly with validity, calibration,\n  target exclusion, no-extra-input status, and target prediction. The setup,\n  target-calculation contract, and route are reconstructed from those facts.\n  The raw applicable route now also realizes an ordinary structural\n  explanation of the exact calibrated-description/uncalibrated-target\n  phenomenon. Its source-sensitive form additionally requires a typed\n  paper-local derivation relation. KSW retains the coupled S-wave fit and\n  parameter-free mixing prediction; Bedaque-Hammer-van Kolck retain the\n  one-datum limit-cycle-scale fit and cutoff-insensitive energy dependence;\n  Epelbaum-Gloeckle-Meissner retain the low-wave contact fit and parameter-\n  free three-D-one calculation. All three source theorems reconstruct the raw\n  route without consuming the established endpoint or ordinary explanation.\n  A completed-prediction countermodel has the ordinary explanation but no\n  source-sensitive explanation when the derivation relation is false.\n  Grounding instead uses the same exact model plus only the paper-local\n  description-validity facts; it does not\n  require the calibration, target exclusion, no-extra-input claim, or target\n  calculation. A nine-component mutation audit prevents altered calibration\n  or prediction semantics from passing as the selected model. A finite witness\n  realizes the direct endpoint, while a\n  countermodel blocks a vacuous implication-valued calculation with no setup;\n  direct mutations show all four indices and five relations affect that\n  completed proposition. An invalid selected description cannot be grounded,\n  while exact valid grounding need not supply the target calculation or route.\n  The established route also projects to a neutral active prediction sector:\n  its calibrated description and singleton unfitted target are observable only\n  under the complete valid post-calibration setup, and prediction separately\n  requires the actual target calculation. All three clients realize this\n  interface. Countermodels reject a calculated target reused in the fit and a\n  parameter-free target that was never calculated; no empirical-adequacy or\n  probability-role conclusion is added.\n  Parameter-free status, calculation, empirical agreement, and\n  theory/model/world grounding remain distinct. A checked empirical boundary\n  now retains the selected description/calibration/target/regime,\n  calibration and target-calculation residuals, predicted and observed\n  target values, observation tolerance, and truncation allowance. Its exact\n  model bridge retains completed validity, calibration, target exclusion,\n  no-extra-input status, and target prediction without assuming agreement.\n  KSW and Bedaque-Hammer-van Kolck realize completed predictions whose\n  hypothetical target discrepancy exceeds both allowances;\n  Epelbaum-Gloeckle-Meissner realize bounded target agreement while retaining residual cutoff\n  dependence. No constant empirical-agreement predicate substitutes for the\n  prediction, observation, or error budget.\n- `PhysicsLogic/Framework/ThreeBodyPairwiseInputInsufficiency.lean`: narrow\n  shared three-body obstruction extracted from Thomas 1935 and\n  Bedaque-Hammer-van Kolck 1998. A calibrated pairwise two-body input is used\n  without an independent short-distance three-body ingredient; a paper-local\n  calculation establishes an instability; explicit bridges say that\n  pairwise sufficiency would imply stability and that the instability\n  excludes stability. The checked reductio derives pairwise-input\n  insufficiency. The established endpoint is output-led: exact selected\n  semantics plus direct validity, calibration, pairwise-only construction,\n  instability, excluded stability, and excluded sufficiency. The complete\n  implication-valued route can be reconstructed from those outputs. Its proof-free model\n  carries four selected indices and all six route-used relation families;\n  each paper-local context owns those indices and exposes one\n  `selectedModel`, so a candidate cannot select itself by changing them;\n  exact paper-local retention is required independently by model use,\n  representation, model entailment, grounding, and route applicability.\n  Model use, representation, and grounding additionally require the actual\n  selected validity/calibration/pairwise-only setup, but no instability or\n  insufficiency output. A\n  retained finite audit model realizes an actual calibrated setup and\n  instability and has a nonempty off-route sufficiency/stability case. Direct\n  audits now prove that every selected index and relation family changes the\n  nonvacuous endpoint containing validity, calibration,\n  pairwise-only construction, instability, excluded stability, and excluded\n  sufficiency. A false-setup countermodel separates that proposition from\n  vacuous implication bridges, while a mutation audit proves that changing\n  any component fails the original context's exact semantics. The paper\n  interpretations retain the selected indices and pre-calculation setup but\n  do not duplicate the six relation families. Thomas realizes the\n  instability as absence of a lowest three-body energy in the singular\n  limit; Bedaque-Hammer-van Kolck realize it as nonuniqueness and cutoff\n  sensitivity of the resummed amplitude. Thomas's setup-indexed singular\n  calculation replays the shared calibrated boundary and pairwise-only\n  construction facts into `SingularPairwiseSetup` before it is applied;\n  Bedaque names completed two-body resummation plus the pairwise-only integral\n  equation as a source-native setup that excludes the later cutoff outputs.\n  The ordinary structural-explanation projection executes the instability\n  calculation plus both reductio bridges from the selected pairwise-only\n  setup, without treating provenance as physics. A source-sensitive\n  refinement additionally requires an independently realized typed paper\n  derivation. Thomas supplies a singular-boundary variational derivation;\n  Bedaque-Hammer-van Kolck supply a resummed-equation asymptotic cutoff\n  derivation. A complete endpoint with that derivation relation false still\n  has the ordinary explanation but cannot manufacture a source-sensitive one.\n  Both adapters provide named retention certificates, construct the direct\n  endpoint from their source routes, and recover their source-native setup\n  from any established endpoint. A setup-complete/no-instability\n  countermodel grounds the selected model while falsifying the obstruction.\n  A typed projection into `Philosophy/Determination.lean` treats the pairwise\n  input as the reduction of the exact selected model and admits that model\n  only when its calibrated setup and stable prediction both hold. The two\n  paper-local instabilities therefore refute nonvacuous stable-prediction\n  determination through an empty admissible domain, without asserting a\n  shared noninjective family. A stable countermodel remains inhabited and\n  determined even with the opaque pairwise-sufficiency predicate false.\n  Finite range, neutron-neutron repulsion, symmetry\n  restrictions, and a running three-body force remain paper-local possible\n  responses, not conclusions of the shared framework. A checked remedy\n  boundary now retains the selected system/input/observable/regime,\n  two-body-calibration, short-distance-instability, and pairwise-prediction\n  residuals, counts of finite-range, repulsive, symmetry, and running-force\n  alternatives, actual selection, two cutoffs and predictions, and the repair\n  residual. Its exact bridge ties the quantitative obstruction to the same\n  calibrated pairwise-only model. Thomas realizes three candidate revisions\n  with none selected; Bedaque-Hammer-van Kolck realize a selected running\n  counterterm and matching running formula while withholding phase locking\n  and two-cutoff prediction agreement. A positive witness supplies the\n  missing agreement and zero repair residual.\n- `PhysicsLogic/Framework/FinitePrecisionTrajectoryPredictability.lean`:\n  narrow shared route independently realized by Miller 1964, Portegies\n  Zwart-Boekholt 2014, and Lorenz 1963. A paper-local deterministic\n  classification, an explicit realization of that classification as forward\n  uniqueness of the selected trajectory relation at the reference state and\n  time, two initial states\n  compatible with one finite-resolution input, a paper-local selected-time\n  divergence calculation, and an explicit\n  reliability-exclusion bridge establish only failure of the selected point\n  prediction. The calculated reference trajectory then makes the retained\n  evolution nonvacuously unique at the selected state and time. The\n  established endpoint is output-led: exact selected semantics together with\n  the actual nearby-state setup, a separated selected-time trajectory pair,\n  nonvacuously unique reference evolution, and point-prediction failure. The\n  implication-valued calculation and reliability contracts can be\n  reconstructed from those direct facts. Its exact\n  proof-free model retains seven selected indices and\n  eight route-used relation families. The seven indices are owned by the\n  paper-local context, and every adapter defines its named model through the\n  resulting `selectedModel`, proves semantic retention, and consumes it in\n  route applicability. A candidate cannot change an index and certify itself\n  by passing that changed value back to `modelAt`. Generic theory/world\n  membership and grounding require one complete selected pre-output setup:\n  exact selection, valid deterministic evolution, two admissible compatible\n  finite-resolution state descriptions, and the explicit realization of the\n  deterministic classification. They consume no trajectory divergence,\n  reliability exclusion, or established prediction limit. A setup-complete\n  countermodel with identity evolution and no state separation is grounded\n  while failing the direct endpoint. An\n  inhabited finite model realizes a direct\n  `NonvacuousFinitePrecisionPredictabilityAt` proposition with distinct\n  compatible initial states, unique deterministic trajectories, a calculated\n  separated final-state pair, and point-prediction failure. Direct activity\n  theorems prove that each of the seven selected indices and each of the eight\n  relation families changes that route-used proposition. A separate\n  fifteen-component mutation audit proves that every changed index or relation\n  fails the original exact semantics. Each paper constructs the direct\n  endpoint from its source route rather than using the generic route-to-\n  endpoint theorem as the source analysis. Lorenz's adapter consumes the shared\n  setup directly; Miller and Portegies Zwart-Boekholt replay shared trajectory\n  facts into their stronger local numerical setups before divergence and\n  reliability are calculated. The complete route also realizes a typed\n  structural explanation. Its constraint retains the selected system, both\n  finite-resolution-compatible initial states, time, resolutions, regime,\n  realized deterministic dynamics, actual divergence, and the reliability-\n  exclusion bridge. Its separately typed phenomenon is nonvacuously unique\n  forward evolution together with failed selected point prediction. One\n  countermodel has deterministic nearby trajectories but no divergence;\n  another has deterministic divergence but declares point prediction reliable\n  and lacks the bridge. Neither structurally explains prediction failure.\n  A source-sensitive variant keeps three distinct typed derivations: Lorenz's\n  central nonperiodic-instability argument plus an explicit finite-witness\n  bridge; Miller's controlled parallel `n`-body protocol and measured\n  separation; and Portegies Zwart-Boekholt's raw arbitrary-precision Brutus\n  validation followed by the same-realization Hermite disagreement. The 2014\n  source theorem constructs the converged reference and comparison setup\n  internally. A finite countermodel has the complete route, established\n  output, and ordinary explanation but no source explanation, so provenance\n  cannot be inferred from prediction failure.\n  Ontic indeterminism, ensemble\n  failure, numerical convergence, entropy growth, irreversibility, stability\n  topology, return-map evidence, and atmospheric extrapolation are not\n  consequences of the shared component. Its checked value-bearing\n  scope-boundary readout now retains distinct nearby inputs and separated\n  outputs, both positive resolutions and actual distances, two candidate\n  successors of the same reference input, successor count, realization\n  count, two bounded ensemble fractions, and statistical tolerance. The\n  deterministic witness has exactly one realized successor and therefore no\n  ontic branching. The 2014 three-body client realizes pointwise divergence\n  together with agreement of 10,000 ensemble realizations; Lorenz and Miller\n  retain zero tested realizations, so their pointwise limits do not silently\n  establish ensemble reliability.\n- `PhysicsLogic/Framework/CosmologicalPerturbationCollapse.lean`: narrow\n  exact collapse-criterion route independently realized by Weinberg 1987 and\n  Press-Schechter 1974. Its proof-free model retains the selected background,\n  perturbation, and regime together with all five relation families used by\n  the route. The ten-claim vocabulary separately exposes exact model\n  selection, the three setup premises, their conjunction, the paper-local\n  calculation, applicability, exact collapse equivalence, the direct\n  nonvacuous model-native criterion, and the established criterion. Both\n  papers construct this exact model and prove a named selected-setup\n  certificate consumed by applicability and grounding. The established result\n  is output-led: it retains that setup and the direct exact equivalence, while\n  checked theorems reconstruct the implication-valued calculation and route.\n  Their concrete grounding theorems use only that selected setup, theory use,\n  world representation, and claim-transfer bridges, never the collapse calculation\n  or result. A converse model has complete grounding with no collapse route,\n  while an output-only model has the exact equivalence but cannot ground\n  without the setup. Eight independent mutations show that no retained\n  component is inert.\n  A finite scoped witness realizes the exact criterion with both the criterion\n  and collapse satisfied. The established route and both paper adapters also\n  project to `NonvacuousExactCollapseCriterionAt`, which requires the setup\n  and exact criterion directly without asserting collapse. A false-setup\n  countermodel separates it from vacuous implication bridges, and direct\n  activity theorems make all three indices and five relations affect that\n  proposition itself.\n  The framework also projects a satisfied exact criterion into the mature\n  structural-explanation contract using distinct criterion and phenomenon\n  roles. Exact equivalence alone is insufficient: a checked false/false\n  countermodel has an exact criterion but no explanation of actual collapse.\n  Press-Schechter discharges satisfaction from the positive overdensity in\n  its selected setup. Weinberg must receive its paper-local\n  `NonlinearCondensationBound` as an explicit additional premise.\n  Press-Schechter's adapter consumes its terminal\n  `EstablishedSphericalBoundCondensation` and extracts the direct setup and\n  exact criterion instead of replaying the spherical calculation.\n  A checked value-bearing distribution boundary now retains the selected\n  background and perturbation, nonnegative strength and collapse threshold,\n  distribution support, selected density, normalization, maximum strength,\n  distribution residual, raw collapsed-tail fraction, and abundance\n  residual. Press-Schechter realizes a satisfied positive-overdensity\n  criterion while withholding distribution support and abundance; Weinberg\n  realizes a normalized supported perturbation distribution while withholding\n  the nonlinear threshold and abundance. The two converse directions and a\n  positive criterion-plus-tail witness prevent an exact collapse test,\n  distribution existence, and thresholded abundance from being conflated.\n  Weinberg's adapter now consumes\n  `EstablishedNonlinearSphericalCollapse`, which retains the spherical setup\n  and calculated vacuum-energy/collapse equivalence without retaining the\n  implication-valued `NonlinearCollapseCalculation`. A staged countermodel\n  blocks a vacuous calculation implication from satisfying this boundary.\n  Weinberg's paper-local downstream logic keeps the nonlinear threshold\n  upstream of the maximum-perturbation anthropic cap, and keeps that cap\n  upstream of both the redshift-calibrated quasar lower bound and the\n  cap-indexed intrinsic-vacuum-distribution expectation. The perturbation\n  distribution that supplies the maximum is now a distinct typed object from\n  the intrinsic vacuum-energy distribution assumed smooth and featureless\n  below that cap; neither the empirical route nor a Planck-scale premise can\n  manufacture the missing distributional hypothesis. The complete paper\n  conclusion also retains the calculated missing-mass and cosmic-age\n  assessments rather than dropping them after the near-bound expectation.\n  Vacuum-energy bounds, observer selection, Gaussian statistics,\n  virialization, missing-mass corrections, and abundance spectra remain\n  paper-local.\n- `PhysicsLogic/Framework/ThresholdedCollapseAbundance.lean`: narrow shared\n  cosmological-abundance inference extracted from Press-Schechter 1974 and\n  Bond-Cole-Efstathiou-Kaiser 1991. A threshold setup licenses separate\n  paper-local raw-count and missing-mass calculations; a final calculation\n  consumes both outputs and supplies a normalized differential spectrum.\n  Press-Schechter uses initially underdense accretion; Bond et al. use prior\n  first crossings. The proof-free model retains the field, population,\n  raw fraction, completed fraction, spectrum, regime, and all four route-used\n  relation families exactly. Both papers\n  certify that exact model before applicability and ground its actual\n  threshold-counting setup through theory use and world representation without\n  assuming any raw-count, missing-mass, or spectrum output. Their stronger\n  source-input adapters instead execute the paper-local calculations before\n  constructing the shared route: Press-Schechter applies its Gaussian-tail,\n  underdense-accretion, and analytic-spectrum calculations in source order,\n  while Bond et al. execute the sharp-`k` first-crossing calculation and\n  project its raw tail, prior-crossing completion, and equation-(3.9)\n  spectrum. A typed source-sensitive reduction now records these as distinct\n  derivations: Press-Schechter's maximum-variance Gaussian-tail, accretion,\n  and spectrum route cannot be inferred from Bond et al.'s absorbing-barrier\n  first-crossing route, or conversely, merely because both reach the same\n  normalized abundance. Neither source path assumes a terminal paper result\n  or a shared abundance endpoint. A completed-route countermodel keeps the\n  source relation false and therefore blocks provenance reconstruction.\n  Press-Schechter's paper-local terminal result now also retains the actual\n  displayed maximum-variance chain: equations (7)-(11) for variance,\n  the initial spectrum's second moment, Gaussian density, density-contrast\n  width, and erfc tail; a\n  separate factor-two collapsed-mass equality; and equations (12)-(13) for\n  the differentiated tail and `M^(-3/2)` exponential number-density\n  spectrum. These are explicit imported calculus equalities, not proofs of\n  the Gaussian integral or derivative. Checked projections and countermodels\n  prevent the named Gaussian, doubling, and spectrum predicates from standing\n  in for those value-level formulas. The source map now also projects their\n  conjunction as a checked analytic-formula output after the terminal\n  spectrum result.\n  Its downstream self-similar endpoint now likewise retains equations\n  (14a)-(14b) for the later density and sigma-squared moments of the derived\n  spectrum. Lean proves the paper's equal-scale reproduction consequence from\n  those formulas, and the self-similarity bridge consumes that conditional\n  formula rather than leaving it inert. A countermodel prevents the older named\n  moment-reproduction predicate from supplying them by itself.\n  Typed countermodels exhibit a raw fraction without missing-mass accounting,\n  setup-licensed accounting without a raw fraction, completed accounting\n  without a differential spectrum, and all three outputs without the\n  threshold setup that would justify them. Technical completion and\n  theory/model/world grounding are independent in both directions: false setup\n  cannot be grounded, but setup-complete grounding still need not supply the\n  raw calculation or route. True theory/world claim tables likewise cannot\n  reconstruct the route. A\n  six-value/four-relation exact-retention mutation audit prevents inert selected data\n  or relations. The model now also has a direct nonvacuous proposition\n  requiring setup, raw count, missing-mass accounting, and normalized spectrum\n  at one selected model. A false-setup countermodel separates that proposition\n  from vacuous implication bridges; a finite witness makes all six selected\n  values and four relation families affect the direct proposition. The\n  established result is exactly the selected direct proposition, and the\n  complete implication-valued route is reconstructed from its direct setup and\n  outputs. Both paper routes reach it from their source-local results.\n  The realized raw count also projects to a typed\n  `EnsembleProbabilityContext`; the completed fraction and differential\n  spectrum remain downstream roles. Countermodels show that raw ensemble\n  probability supplies neither completion nor the spectrum and does not imply\n  an observed frequency.\n  The same complete route now projects to a typed\n  `ReductionAndEmergence.RealizationContext`: a proof-free threshold-counting\n  and mass-accounting description realizes a distinct normalized-abundance\n  description, source support retains the raw count, missing-mass accounting,\n  and spectrum-conversion calculation, and the target exhibits only the\n  selected differential spectrum. Countermodels block reduction when spectrum\n  conversion is absent and when matching outputs lack the threshold setup.\n  This is a scoped statistical-to-abundance derivation, not reduction of\n  cosmological dynamics, halo identity, or galaxy formation.\n  Press-Schechter's\n  projection consumes only `EstablishedAnalyticMassSpectrum`, reconstructing\n  the shared calculation stages from its retained direct outputs. Bond et\n  al.'s projection analogously consumes only\n  `EstablishedSharpKMassSpectrum`; neither adapter replays a paper-local\n  implication-valued calculation.\n  A separate source-valued physical readout now also retains the two original\n  mechanisms without imposing either on the generic route: Press-Schechter's\n  maximum-variance equation, erfc tail, separately assumed spherical accretion,\n  factor-two completion, equation-(13) density, uncontrolled boundary overlap,\n  and two finite 1000-body experiments; Bond et al.'s independent sharp-`k`\n  increments, absorbing barrier, reflection, prior crossings, derived\n  factor-two completion, both equation-(3.9) forms, correlated Gaussian and\n  top-hat filter bounds, an at-most-20-percent sharp-`k` peak discrepancy and\n  comparable general-filter underestimates, failed\n  low-mass particle identification, separate halo calibration, and\n  additional two-barrier merger history. Countermodels distinguish equal\n  normalized abundances with different physical mechanisms and reject\n  invented Press-Schechter first crossings, exact general-filter formulas,\n  particle-level identity from a mean fit, uniquely derived calibration,\n  filter selection from limited simulations, and merger histories without a\n  second barrier. Gaussian-field and first-passage mathematics, spherical\n  dynamics, simulation outputs, and galaxy formation remain paper-local\n  imported or unresolved physics rather than generic framework theorems.\n- `PhysicsLogic/Framework/InflationaryPatch.lean`: narrow shared cosmology\n  inference extracted from Guth 1981 and Albrecht-Steinhardt 1982. It\n  requires an admissible selected model and an applicable selected mechanism,\n  then separates initial patch homogeneity, accelerated expansion,\n  observed-region containment, and paper-local bridges to homogeneity and\n  flatness production. Its proof-free calculation model retains the selected\n  model, initial condition, region, mechanism, both targets, and the six\n  proposition-valued relation families used by the deduction. The output-led\n  established result retains exact selected setup, distinct target roles,\n  expansion, coverage, and both produced targets; the implication-valued\n  transfer route is reconstructed from those direct facts. Guth and\n  Albrecht-Steinhardt each define a named paper-local calculation model and\n  prove that it is exactly the model selected by the shared context. The patch\n  calculation, containing cosmological theory, and represented expanded region\n  are separate Lean objects. Model membership and world representation retain\n  the exact selected pre-output setup plus explicit paper-local use and\n  representation bridges. That setup includes admissibility, mechanism\n  applicability, initial homogeneity, and distinct target roles, but excludes\n  accelerated expansion, observed-region coverage, either transfer bridge,\n  and either produced target. A generic setup-only theorem constructs\n  grounding, and a typed countermodel grounds that setup while the\n  patch-expansion route is false. Each paper\n  combines this independent grounding with its separately established route.\n  The model now also exposes\n  `NonvacuousInflationaryPatchAt`: a direct endpoint that drops exact-record\n  equality and requires the actual setup, both produced targets, and an\n  explicit proof that homogeneity and flatness are distinct targets, without\n  storing either implication-valued bridge. Twelve exhaustive claims expose\n  selected data,\n  admissibility, applicability, the three patch facts, both transfer bridges,\n  both target-production conclusions, target distinctness, and the direct\n  endpoint. Transition completion, graceful exit, reheating, monopoles,\n  deferred curvature physics, and global viability remain outside this\n  framework. The raw applicable route plus distinct targets now also realizes\n  an ordinary structural explanation of the situated expanded patch. A\n  source-sensitive explanation additionally retains one typed paper-local\n  derivation relation: Guth's local sub-horizon patch, expansion, coverage,\n  and horizon/flatness transfer source; or Albrecht-Steinhardt's homogeneous\n  fluctuation region, continued expansion, observed-region containment, and\n  separate homogeneity/flatness bridges. Albrecht-Steinhardt's paper-local\n  thermal setup now also retains equation (1) as a value-level\n  positive-temperature family with the Coleman-Weinberg polynomial/log terms\n  and explicit positive-half-line thermal integral. Its old-inflation setup\n  separately retains p. 1221 equation (2): the vacuum-dominated Friedmann\n  chain, explicit density/GUT-temperature approximations, expansion-time\n  definition, and approximate exponential scale factor. Neither source theorem consumes an\n  established patch, bubble-completion result, defect-formation result, or\n  global-viability conclusion. A countermodel gives the completed ordinary\n  explanation while falsifying the source relation.\n  Countermodels block route-to-grounding and grounding-to-route shortcuts,\n  reconstruction of the route from declared theory/world claims, and treating\n  any context-selected model, mechanism, target, or physical relation as\n  semantically inert. Initial condition and region remain explicit route\n  parameters. A separate finite interpretation now realizes the complete\n  direct endpoint with distinct homogeneity and flatness targets. A\n  coincident-target countermodel can make the older route shape applicable\n  while failing both output-led endpoints, and a false-setup model blocks\n  vacuous implication bridges. Direct activity theorems make every one of the six selected objects\n  and six relation families affect the direct proposition before the\n  independent exact-record mutation audit is applied. Its exact solution\n  context has no consequence type and no naturalness, side-effect, or\n  unacceptability payload.\n- `PhysicsLogic/Framework/BubbleTransitionCompletion.lean`: independent\n  shared old-inflation obstruction extracted from the same two papers. It\n  separates bubble-mediated first-order transition, cosmologically\n  sufficient expansion, the paper-local calculation that expansion outpaces\n  bubble formation and connected completion fails, and the bridge to an\n  incomplete-transition side effect. Both papers first prove named selected-\n  setup adapters, then complete their distinct routes. The output-led\n  established obstruction retains exact selected data, the inhabited setup,\n  expansion dominance, failed connected completion, and the side effect. It\n  stores neither implication-valued paper-local contract; checked exposure\n  theorems reconstruct the competition calculation and interpretation bridge\n  from the direct outputs. It also projects to\n  `NonvacuousBubbleCompletionObstructionAt`, where the setup and three direct\n  outputs hold on one model. Its proof-free\n  calculation model retains the\n  selected model, initial condition, regime, phase, mechanism, consequence,\n  and exactly the five proposition-valued relations used by the route. Guth\n  and Albrecht-Steinhardt each construct a named paper-local model and prove\n  exact retention before any technical inference. Albrecht-Steinhardt's\n  regime is its selected bubble-nucleation rate, and its lifted expansion and\n  completion relations are guarded by that rate and the broken phase. One\n  exhaustive theorem realizes all nine shared claims, including selected-\n  data identity, and both\n  paper adapters expose named exhaustive-realization and grounded-transfer\n  certificates. A countermodel prevents the\n  implication-valued calculation and bridge from counting when the bubble\n  setup is absent, including at the direct endpoint. The framework also\n  imports `Philosophy.TheoryModel` and\n  distinguishes the selected competition calculation from its containing\n  cosmological theory and represented universe. Model grounding retains only\n  exact selected data, an inhabited first-order expansion setup, and explicit\n  paper-local theory/world roles; it assumes no competition calculation,\n  failed completion, or side effect. Each final paper theorem combines this\n  setup-bound grounding with its separately completed technical route.\n  Further countermodels separate route completion from grounding, grounding\n  from route applicability, output claims without selected setup, and declared\n  theory/world claims from the route.\n  A mutation audit changes the selected model, mechanism, consequence, or any\n  one of the five retained relations and refutes exact selected semantics.\n  A separate finite interpretation realizes the complete obstruction, direct\n  nonvacuous endpoint, and scoped viability-failure route. Direct activity\n  theorems make all six selected objects and all five retained relation\n  families affect the direct endpoint itself, while the older route-fact and\n  exact-record audits remain separate.\n  Initial condition, regime, and phase remain explicit route parameters.\n  Potentials, tunneling rates, percolation thresholds, thermalization, and\n  consequence-acceptability judgments remain paper-local. Its exact viability\n  context has no target type and no naturalness, target-realization, or\n  target-production payload. A separate composed inflation/bubble handoff\n  now retains an actual expanded patch, an actual incomplete-transition\n  obstruction, exact selected model and initial condition, an independent\n  source-local expansion/transition calculation, and either literal mechanism\n  identity or literal mechanism inequality. Guth realizes patch success and\n  graceful-exit failure for the same mechanism; Albrecht-Steinhardt realize a\n  successful fluctuation replacement while the distinct standard-bubble\n  mechanism remains obstructed. Finite countermodels prevent relabeling one\n  mechanism as the other, manufacturing the paper-local handoff from the two\n  endpoints, or transferring the old mechanism's side effect to its\n  replacement. Its source-sensitive composition also exactly selects both\n  child contexts and independently retains the patch derivation, bubble\n  derivation, and paper-local comparison derivation. Guth's token keeps the\n  same-mechanism slow-nucleation/percolation route; Albrecht-Steinhardt's\n  token explicitly requires unequal replacement and standard-bubble\n  mechanisms. An inhabited finite countermodel has ordinary composition and\n  both sourced child explanations while withholding the comparison source.\n- `PhysicsLogic/Framework/CausalDomainDefectFormation.lean`: narrow shared\n  defect-formation route realized in Kibble 1976 and reused in Guth 1981's\n  explicitly imported Kibble argument. It separates a nontrivial family of sufficiently separated domains\n  from its selected local order-parameter assignment, requires uncorrelated\n  assigned values, threads the same assignment through collective assembly,\n  and retains a paper-local calculation excluding its global extension and\n  identifying an obstruction before a separate physical-defect\n  interpretation. Its proof-free context owns eight selected values and all\n  ten route-defining relation families and constructs one unique\n  `selectedModel`. Each client proves exact paper-context retention before\n  applicability. Guth's context is parameterized by the selected bubble\n  family, phase, and defect, so those values cannot be read back from a\n  candidate model. The output-led established result stores exact selection\n  plus direct setup, assembly, failed extension, obstruction, and defect\n  production; it reconstructs the implication-valued route. Both clients provide explicit theory/model/world\n  grounding and exhaustive transfer of seventeen claims. The completed route\n  also projects to a direct nonvacuous formation proposition requiring setup,\n  assembly, failed extension, obstruction, and defect production at one model.\n  The complete route additionally realizes a typed structural explanation.\n  Its constraint retains the exact description, transition, domain family,\n  local assignment, assembly, obstruction, and regime, and is satisfied only\n  by the full selected technical route including the physical-defect\n  interpretation. Kibble's protodomain/vertex/surface route and Guth's\n  bubble/coalescence/Higgs-knot route realize the same scoped endpoint. A\n  countermodel retains a calculated topological obstruction while deleting\n  the interpretation and defect production, and therefore refutes the\n  structural explanation. A converse countermodel declares defect production\n  after collective assembly but omits the global-extension failure and\n  topological route, so the output alone also fails to reconstruct the\n  explanation.\n  The generic grounding constructor requires exact selected-model semantics\n  and an inhabited independent-domain setup but consumes none of those route\n  conclusions. A setup-complete countermodel still lacks assembly and every\n  formation output. Mutation countermodels\n  prove that changing any selected value or relation family fails the original\n  context's exact semantics; a separate finite direct audit shows that all\n  eight selected values and all ten relations affect realized formation, and\n  a physical countermodel shows that changing only the assignment can change\n  whether the route is established. The finite causal witness selects two\n  distinct domains with opposite local order-parameter values while\n  explicitly excluding a third exterior domain; domain membership and causal\n  separation are not constant truth-status predicates.\n  Vacuum manifolds, homotopy groups, walls, strings, monopoles, magnetic charge,\n  production estimates, annihilation, network evolution, and inflationary\n  suppression remain paper-local.\n- `PhysicsLogic/Framework/FiniteRegulatorGaugeInvariance.lean`: narrow shared\n  finite-cutoff gauge semantics extracted from Wilson 1974 and Creutz 1980.\n  It separates the regulated lattice setup, exact action and closed-observable\n  invariance, and the compact-integration bridge making gauge fixing\n  unnecessary. Each paper proves the complete route-applicability proposition\n  before deriving the shared result. The established proposition is\n  output-led: it retains the exact selected finite-regulator setup, both\n  invariance outputs, and the no-gauge-fixing output. The calculation and\n  interpretation bridge are reconstructed from those facts when the complete\n  route is requested. Implication-valued calculations and bridges do not count\n  when the finite-regulator setup is absent. It requires orbit\n  completeness before invariant values become representative-independent\n  physical quantities and contains no continuum transfer, simulation, or\n  confinement claim. Its proof-free model retains all four physical indices\n  and all nine semantic relation families used by the route. Wilson and Creutz\n  each name an exact model, prove its retention, and derive a direct\n  `NonvacuousFiniteRegulatorGaugeInvarianceAt` proposition containing the\n  realized finite setup, both invariance outputs, compact integration, and\n  no-gauge-fixing output. The raw applicable route now also realizes an\n  ordinary structural explanation of the exact selected action-and-closed-\n  observable phenomenon. Its constraint requires exact selected-model identity\n  as well as the complete route, so a record with the same four indices but\n  different relation fields cannot masquerade as the explained calculation.\n  The source-sensitive form additionally requires one typed paper-local\n  derivation. Wilson retains the angular-link gauge transformation, plaquette\n  action, closed-path product, compact periodic integral, and no-gauge-fixing\n  argument; its local route now also retains equations (3.4), (3.6), and\n  (3.8) as selected real-valued link/plaquette propositions before forgetting\n  to the shared endpoint. Creutz retains pure `SU(2)` links, the Wilson\n  action, invariant group measure, exact local symmetry, and\n  gauge-fixing-independent correlations. A completed-route countermodel has the ordinary explanation\n  but no source-sensitive explanation when its derivation relation is false.\n  A separate direct physical-value proposition requires\n  an actually represented physical state and scoped orbit completeness. A\n  theory/model/world layer grounds the exact selected model together with an\n  actual finite-regulator setup, independently of the invariance calculation\n  and outputs; the\n  final theorem then combines grounding with the technical route. Its\n  two-tier claim semantics transfers ten base claims, including exact model\n  selection, selected setup, and the complete route, or all fourteen claims after orbit\n  completeness is added. Countermodels establish independence in both\n  directions. A finite direct model shows every selected index changes the\n  realized regulated route and every retained relation changes the represented\n  physical-value lane, so the audit does not rest only on record inequality.\n- `PhysicsLogic/Framework/LoopAreaConfinement.lean`: narrow shared\n  loop-area-to-confinement inference extracted from Wilson 1974 and Creutz\n  1980. Its proof-free model retains six selected physical indices and all\n  seven relation families used by the route. Wilson and Creutz each name an\n  exact model and prove its retention before any setup or calculation is\n  assumed. The established proposition is output-led: exact selected setup,\n  area law, linear potential, and confinement are retained directly, while\n  the paper-local area-law calculation and both interpretation bridges are\n  reconstructed by checked eliminators. Eleven exhaustive claims cover exact\n  selection, selected setup, each calculation or bridge, applicability, the\n  three outputs, and the established result. Theory/model/world grounding uses\n  exact selection plus the valid loop/surface/source/positive-tension setup,\n  theory use, world representation, and conditional claim transfer; it uses\n  no area-law or interpretation output. The final paper\n  theorems combine this independent grounding with their separately completed\n  routes. The established result also yields a direct\n  `NonvacuousLoopAreaConfinementAt` proposition at one actual calculation\n  model. The generic endpoint remains regulator-agnostic, while Wilson's and\n  Creutz's source-order routes additionally expose\n  `NonvacuousFiniteGaugeSupportedLoopAreaConfinementAt`. That\n  composite keeps the direct finite-gauge child, established gauge route,\n  admissibility bridge, loop setup, and confinement endpoint together.\n  Countermodels establish independence in both directions: setup-bounded\n  grounding can hold while the area law is false, and all three outputs cannot\n  ground a model whose selected setup is false. A finite\n  direct witness shows every one of the six indices and seven relations\n  changes realized route semantics, rather than merely changing record\n  equality. A finite composed witness realizes the regulator-supported\n  endpoint, while a converse model realizes generic confinement with a\n  vacuous gauge child. The complete selected route now also instantiates the\n  mature structural-explanation contract: its typed constraint requires the\n  actual loop setup, area-law calculation, and both physical interpretation\n  bridges, and its phenomenon contains both the rising static potential and\n  confined sources. A countermodel retains all three outputs while deleting\n  selected-regime validity, so output labels alone do not explain them.\n  Wilson and Creutz independently derive this explanatory endpoint from their\n  different calculations. Continuum confinement is not a transferable claim.\n- `PhysicsLogic/Framework/EquilibriumSampling.lean`: narrow shared\n  equilibrium-targeted update inference extracted from Metropolis 1953 and\n  Creutz 1980. It keeps detailed balance, the paper-local convergence\n  calculation, equilibrium interpretation, and selected finite-run\n  convergence logically separate. Creutz's adapter now mirrors Metropolis's\n  separation: its imported heat-bath result supplies repeated-update\n  convergence first, and only a distinct interpretation bridge consumes that\n  convergence under the same heat-bath setup to identify the ensemble used\n  for equilibrium measurements. A\n  countermodel blocks the heat-bath setup plus convergence from supplying\n  that interpretation by themselves. Its proof-free exact model retains the\n  selected description, regime, update, and ensemble together with the\n  validity, equilibrium-target, detailed-balance, target-space-accessibility,\n  asymptotic-convergence, and equilibrium-production relation families. The\n  Metropolis adapter supplies target-space accessibility only through its\n  paper-local calculation consuming the certified finite periodic cell,\n  positive proposal width, periodic wraparound, successive particle attempts,\n  finite-probability allowed moves, and the selected update's implementation\n  of that proposal; the shared framework receives only the resulting\n  accessibility fact. Metropolis's paper-local balance route separately\n  retains actual positive canonical state probabilities, symmetric proposal\n  probabilities, the acceptance-weighted uphill transition, and the\n  unsuppressed downhill transition. Lean derives the original directional\n  equality `p_r T_rs = p_s T_sr` from equation (2), preserves it in the\n  completed sampling result, and supplies normalized physical countermodels\n  showing that discarded rejected attempts or non-Boltzmann population\n  weights destroy that equality. None of these Metropolis-specific transition\n  formulas is imposed on Creutz's distinct heat-bath mechanism. The\n  context owns all four selected indices, and `selectedModel` fixes their\n  unique combination rather than reading a candidate model's own indices back\n  into the semantics. Both paper adapters construct and certify that exact\n  context-selected model before exposing a complete route-applicability\n  theorem. The established proposition is output-led: it stores exact\n  selection together with the direct `NonvacuousEquilibriumSamplingAt`\n  proposition, where validity, target,\n  balance, accessibility, asymptotic convergence, and equilibrium production\n  all hold at one selected model. It stores no calculation or applicability\n  proof; the selected setup, calculation contract, interpretation bridge, and\n  complete route are reconstructed from those direct relations. Metropolis\n  and Creutz each derive the output from their source-local route without\n  asserting selected finite-run convergence. A ten-part mutation audit shows\n  that changing any of the four\n  indices fails the original context's exact-selection proposition and that\n  changing any of the six relations invalidates exact retained semantics. A\n  finite source-shaped witness realizes the complete asymptotic route while\n  its selected finite run remains unestablished; direct activity theorems\n  make all four indices and six relations affect route-used propositions, and\n  a second direct mutation audit makes every such change falsify the\n  nonvacuous proposition itself. A\n  separate\n  paper-local theory/model/world grounding treats convergence as a conclusion\n  of the algorithmic model and equilibrium production as a conclusion of the\n  theory and represented sampling process. Grounding requires the exact\n  selected model plus the inhabited pre-convergence setup: validity, target,\n  balance, and accessibility. It assumes neither the convergence calculation\n  nor convergence nor equilibrium production. Metropolis grounds representation\n  with configuration-space accessibility; Creutz grounds it with successive\n  entire-group heat-bath updates and single-link Boltzmann weight. The shared\n  theory/model context requires that exact selected setup in theory\n  membership, world representation, and grounding.\n  The shared layer only combines an established technical route with such\n  independently proved grounding. Balance and target-space accessibility are\n  separate shared premises. Countermodels show that completed equilibrium\n  sampling does not manufacture grounding and that declared theory/world\n  equilibrium claims do not reconstruct the sampling route. A false-setup\n  countermodel cannot be grounded even though both implication-valued\n  calculation contracts hold, while a setup-complete no-convergence model can\n  be grounded without acquiring a route or output. Proposal and\n  acceptance rules,\n  accessibility, heat-bath replacement, Markov kernels, mixing rates,\n  finite-run convergence, physical-time dynamics, and observables remain\n  paper-local.\n  The complete route now additionally realizes a typed structural explanation\n  of the selected asymptotic algorithmic-sampling phenomenon. Its proof-free\n  constraint and phenomenon retain the same four indices but no proofs;\n  satisfaction requires exact selection, the inhabited target/balance/access\n  setup, the convergence calculation, and the interpretation bridge.\n  Metropolis reaches this endpoint by reconstructing its finite model,\n  canonical target, modified update, pairwise balance, and accessibility from\n  source-local calculations. Creutz reaches it with the regulated heat-bath\n  setup while keeping equilibration and equilibrium interpretation distinct.\n  Countermodels exhibit the output without valid setup and convergence without\n  interpretation; a positive model realizes the explanation while finite-run\n  convergence remains false. Thus this is neither physical dynamics nor a\n  mixing-time or finite-run certificate.\n  A stronger source-sensitive explanation retains one typed paper-local\n  derivation. Metropolis's token expands to the pp. 1088-1089\n  finite-periodic/canonical reductions, symmetric local proposal,\n  downhill-or-Boltzmann acceptance, repeated rejected configurations,\n  reachability, pairwise population flow, equilibration, and interpretation.\n  Creutz's distinct token expands to the regulated SU(2) predecessor,\n  conditional entire-group single-link heat bath, detailed balance,\n  accessibility, equilibration, and interpretation on p. 2309. A countermodel\n  preserves the common route, established endpoint, and ordinary explanation\n  while falsifying the source relation, so common outputs cannot reconstruct\n  either algorithm's derivation.\n- `PhysicsLogic/Framework/ReciprocalTransport.lean`: narrow shared\n  Onsager-Casimir semantics for parity-sensitive field-reversed transport.\n  Near-equilibrium fluctuations do not suffice: microscopic reversal must\n  relate the selected dynamics at `H` to reversed dynamics at `-H`, and the\n  macroscopic regression law is restricted to an explicit intermediate-time\n  window. A separate ensemble-regression hypothesis and paper-local\n  correlation and coefficient calculations are required to derive\n  `L_ij(H) = epsilon_i epsilon_j L_ji(-H)`. Both paper adapters first prove\n  the complete `RouteApplicableAt` proposition, and established transport\n  retains that complete route, including both paper-local calculations.\n  The context owns one exact evaluation field and a literally distinct\n  selected transport-variable pair, and separately records the\n  paper-admissible field family. Its unique proof-free model retains the\n  selected process, evaluation field, both selected variables,\n  field-reversal map, time-reversal parity assignment, and kinetic-coefficient\n  family together with all seven route-used relation families. Named\n  projections expose those exact selections, field-paired microscopic\n  reversal, the intermediate regression window, the macroscopic regression\n  law, calculations, correlation result, and reciprocal relation. A\n  selected projection exposes an actual off-diagonal coefficient relation;\n  a singleton variable type cannot realize the route through diagonal\n  identity alone. A separate finite model realizes the direct route with two\n  opposite-parity variables, positive-to-negative field reversal, and\n  asymmetric off-diagonal coefficients satisfying the Onsager-Casimir sign\n  rule. Its `NonvacuousReciprocalTransportAt` proposition retains the actual\n  setup, regression premise, correlation result, universal relation, and\n  selected cross-variable instance without using exact-record equality.\n  Changing any of the four selected indices or any of the three functions and\n  seven physical relation families destroys that direct proposition. Both\n  paper adapters derive it from their source-local calculations. A stronger\n  structural projection explains the universal field-reversed relation and\n  its selected off-diagonal instance from the exact reversible setup,\n  intermediate-window regression premise, correlation calculation, and\n  coefficient calculation. Its proof-free constraint retains the process,\n  field pair, variables, reversal map, parities, and coefficient family but\n  no reciprocal equality. Onsager realizes it through the zero-field heat\n  route; Casimir realizes it from granular parity, reversal, regression-scope,\n  correlation, and coefficient premises. Reciprocal coefficient outputs in a\n  model with false physical setup do not reconstruct this explanation.\n  The separate theory-model-grounded result distinguishes that exact\n  calculation from the theory using it and the represented transport system.\n  Onsager proves that zero field is fixed under reversal, specializes the\n  shared parity assignment to time-even variables, and obtains ordinary\n  same-field reciprocity. Casimir grounds both declared zero- and\n  magnetic-field routes as distinct exact contexts with their intermediate-\n  time regression scope. A\n  first-class exhaustive theorem realizes all thirteen\n  shared claims, and both paper adapters expose named grounded transfers for\n  every claim.\n  Countermodels show that a completed technical route need not be semantically\n  grounded, that fixed-field reversibility does not supply the `H` to `-H`\n  relation, that regression without its time window is inapplicable, that\n  changing any of the fourteen model components changes the selected model,\n  that a second admissible field still fails exact selection, and\n  that even declaring all thirteen theory/world claims true does not reconstruct\n  the regression-and-correlation route.\n  A checked field-reversal boundary now retains the exact selected process,\n  field pair, variables, nonzero field values, forward/same-field/paired\n  trajectory weights, time-reversal parities, and three cross-coefficient\n  values. Its model bridge ties the paired trajectory balance and coefficient\n  entries to the selected calculation. Onsager realizes same-parity magnetic\n  reciprocity at `-H` while both fixed-field balance and reciprocity fail;\n  Casimir independently realizes the mixed-parity minus sign at `-H` with the\n  same fixed-field failures. No constant reversibility predicate substitutes\n  for the field values, trajectory weights, parity signs, or coefficients.\n  Thermodynamic variables, dissipation principles, response functions,\n  four-poles, and Hall applications remain paper-local.\n- `PhysicsLogic/Framework/FinitePartitionNonvanishing.lean`: narrow shared\n  finite-system induction semantics independently realized by\n  Liu-Sinclair-Srivastava 2018 and Peters-Regts 2017. A proof-free\n  calculation model retains the selected interaction or assignment together\n  with the admissible finite-system class, graph-indexed parameter domain,\n  natural-number complexity measure, and partition-nonzero relation. Each\n  paper supplies that relation through an actual complex-valued finite\n  configuration sum rather than an uninterpreted conclusion. The shared\n  edge-indexed configuration kernel computes hard-core independent-set sums\n  and pinned zero-field Ising sums separately, retains actual graph degree and\n  prescribed spins, enforces constant hard-core activity at every vertex, and\n  calculates the Ising unpinned-vertex induction complexity. One-edge graph\n  witnesses preserve three versus four hard-core occupations, site-dependent\n  cancellation, the original vertex split, disagreement-weighted Ising sums,\n  exact pinning restrictions, and the original pinned-spin partition split.\n  The two independent paper certificates retain seventeen graph- and\n  value-bearing fidelity boundaries.\n  Each\n  adapter fixes the arbitrarily quantified interaction or assignment as the\n  context-owned `selectedParameter`, constructs the unique `selectedModel`,\n  and proves exact equality with it. Grounding requires those exact semantics\n  together with an actual admissible complexity-zero graph in the selected\n  parameter domain, while assuming no nonzero base value, induction step, or\n  uniform conclusion. Explicit theory-use and finite-world representation\n  bridges then transfer the selected setup and downstream claims. The\n  Ising adapter uses bounded-degree arbitrarily pinned graphs and unpinned\n  vertex count; the hard-core adapter uses bounded-degree graphs, complex-tube\n  assignments, and vertex count. The established result is output-led and\n  stores selected data, base, step, and uniform nonvanishing directly. An\n  eighth direct\n  `NonvacuousFinitePartitionNonvanishingAt` claim additionally requires an\n  actual admissible complexity-zero graph with nonzero partition value. Both\n  paper adapters expose that endpoint from explicit zero-complexity graph\n  witnesses and thread the witness through named grounded transfers for every\n  claim. The shared component now also has ordinary and source-sensitive\n  structural projections. Peters-Regts supplies the typed\n  `doubleLogInvariantDomainVertexSubsetInduction` derivation, whose relation\n  retains the threshold setup, coordinate/contraction calculations, complex\n  invariant domain, occupation-ratio recurrence, final-root cancellation,\n  and empty-graph witness. Liu-Sinclair-Srivastava supplies the distinct\n  `correlationDecaySawTreePinnedSpinInduction` derivation, retaining the tree\n  uniqueness and correlation-decay route, complex extension, SAW recurrence,\n  pinned cancellation, and zero-unpinned witness. Each source theorem rebuilds\n  the shared base/step route from those paper-local premises; neither source\n  relation stores the shared route, established result, or explanation. A\n  countermodel establishes the ordinary explanation while making the selected\n  derivation relation false, proving that provenance is additional logical\n  content. No finite-regularity or\n  thermodynamic-limit claim is transferable. Countermodels show both that a\n  completed induction does not supply theory/world grounding and that even\n  universal declarations of all eight theory/world claims do not reconstruct\n  the induction route. An empty selected parameter domain can satisfy the\n  universal induction vacuously but fails the direct endpoint and cannot be\n  grounded because it lacks the selected finite-base scope. A finite direct\n  witness separately proves that changing the selected parameter or any\n  selected system class, parameter domain, complexity, or partition relation\n  falsifies the nonvacuous endpoint itself, alongside the exact-selection\n  audit. A separate size-family\n  scope and `FiniteRegularityBridgeAt` remain necessary even for finite-stage\n  regularity, which still does not imply regularity of the limiting\n  description.\n- `PhysicsLogic/Framework/RandomDisplacementDiffusion.lean`: narrow shared\n  stochastic-spread inference extracted independently from Einstein 1905,\n  Smoluchowski 1906, and Linde-Linde-Mezhlumian 1993. It requires a\n  regime-scoped controlled step\n  description, a paper-local directional-bias control, and a paper-local\n  control of inter-step dependence. Independent calculations establish\n  linear mean-square and root-time rms spreading and diffusive transport;\n  the framework imposes no common order on those calculations. A distinct\n  typed constraint and phenomenon now expose the corresponding structural\n  explanation: the complete controlled-step route necessitates all three\n  outputs. This theorem uses route applicability directly rather than the\n  established or nonvacuous endpoint. A finite all-outputs-but-biased model\n  blocks the occurrence-to-explanation converse, while a second model shows\n  that both spread laws without transport do not constitute the selected\n  phenomenon. All three papers additionally realize a source-sensitive\n  explanation whose typed derivation distinguishes Einstein's transition\n  expansion and point-source solution, Smoluchowski's persistent collision\n  flight and gas-kinetic analogy, and the Linde-Linde-Mezhlumian random-phase\n  Hubble-step and Langevin/Fokker-Planck route. These theorems consume raw\n  paper inputs and route applicability, not an established endpoint or the\n  ordinary explanation. A complete common route with a false derivation\n  relation proves that shared diffusion semantics do not reconstruct source\n  provenance. All three papers\n  now establish an explicit shared route-applicability proposition before\n  deriving the established diffusion result. That result is output-led: it\n  retains exact selected semantics, every inhabited setup relation, and all\n  three direct outputs, but no implication-valued calculation or paper-local\n  route order. Named theorems reconstruct the stochastic setup, spread\n  calculation, diffusive-transport calculation, and complete route when\n  needed, preserving the papers' different logical order and mechanisms. A\n  proof-free model records the selected description,\n  system, step model, time, and regime together with the exact validity,\n  step-control, directional-bias, inter-step-dependence, spread, and transport\n  predicates. Each paper proves that this full relation family is the one\n  selected by its adapter. The context owns all five physical indices and\n  exposes one exact `selectedModel`; changing any physical index or any of the\n  seven retained relations fails that context's exact semantics. Separate\n  direct semantics require all four setup relations and all three outputs to\n  hold at that same model. A finite witness inhabits the complete route, and\n  exhaustive five-index and seven-relation mutations each destroy this\n  route-used proposition. All three paper adapters derive it from their\n  independently anchored established routes. Separate\n  paper-local interpretations state which theory uses that model, which\n  physical process it represents, and what each calculated claim means in the\n  theory and represented world.\n  Einstein grounds the model in molecular-kinetic theory and the selected\n  suspended-particle process; Smoluchowski grounds it in kinetic collision\n  theory and the selected suspension process; Linde-Linde-Mezhlumian ground\n  it in semiclassical stochastic inflation and the selected coarse-grained\n  inflaton process. Only an established technical result plus those explicit\n  bridges yields the stronger grounded result. Grounding itself consumes the\n  exact inhabited pre-output stochastic setup and the conditional theory/world\n  bridges; it consumes neither spread nor transport calculation and no\n  established result. A selected model with false validity or stochastic\n  controls therefore cannot be grounded.\n  Einstein, Smoluchowski, and Linde-Linde-Mezhlumian each also expose the\n  direct structural explanation from their own granular route. Gaussianity,\n  collision geometry, gas analogy, physical-volume branching, stationarity,\n  objective chance, and a common microscopic mechanism remain outside it.\n  Model-level diffusive transport is the actual transport conclusion, not a\n  disguised setup predicate. Transition laws, persistent collision geometry,\n  Gaussianity, drag, diffusion coefficients, osmotic pressure, and numerical\n  factors remain paper-local. The established result realizes four shared\n  claims, including exact selected-model data. Countermodels separate\n  dependence control from\n  directional-bias control, stochastic setup from spread, spread from\n  transport, completed diffusion from theory/world grounding, declared\n  theory/world claims from reconstruction of the stochastic route, vacuous\n  implication-valued calculations from an applicable route, and one-regime\n  validity from transfer. A further pair proves that exact selection without\n  an inhabited setup cannot ground a model, while a complete pre-output setup\n  can be grounded before spread or transport is obtained.\n- `PhysicsLogic/Framework/ThermalDragBrownianTransport.lean`: the narrower\n  Einstein-Smoluchowski composition requiring established stochastic diffusion\n  together with thermal setup and sibling hydrodynamic-drag/coefficient and rms-\n  spread calculations. Einstein obtains the coefficient before point-source\n  spread, while Smoluchowski obtains relaxation spread before his later\n  gas-kinetic coefficient; the shared route no longer invents one universal\n  order. Its proof-free model retains the complete nested\n  stochastic model, six additional selected data components, and all four\n  thermal/drag/spread relation families. The nested context owns its five\n  stochastic selections and the parent owns six transport selections; their\n  unique composed `selectedModel` is required by route applicability and the\n  model judgment. Both papers construct named exact models and expose complete\n  theory/world transfers for all nine claims. Grounding requires exact model\n  selection plus the established nested diffusion, drag-regime validity, and\n  paper-local thermal drive, but no child drag/coefficient calculation, spread\n  calculation, output, or transport route. Countermodels prove both that exact\n  selection alone cannot ground a model and that an inhabited setup can be\n  grounded while the child route remains false. The output-led established\n  result is exact selection together with the direct\n  `NonvacuousThermalDragBrownianTransportAt` proposition: the nested\n  stochastic controls, drag-regime validity, thermal drive, drag law,\n  coefficient relation, and rms spread all hold at one selected model rather\n  than only through implication-valued calculation contracts. A finite Bool\n  witness realizes that proposition, and exhaustive mutation theorems show\n  that changing any of the eleven selected physical values or eleven\n  route-used relation families destroys it. The older exact-semantics audit\n  still shows that seven top-level data components and four parent relations\n  cannot be erased from the selected model. Both paper adapters bind every\n  parent relation to their selected description, carrier, medium, drag\n  convention, coefficient, spread, time, and regimes, unpack the shared\n  thermal setup to recover the paper-local calculation setup they actually\n  use, then delegate named nonvacuity theorems to the generic projection. The\n  endpoint additionally realizes a typed mechanistic explanation of the rms\n  spread from thermal drive, drag, and coefficient organization. A finite\n  no-thermal-drive model retains stochastic spreading but refutes that\n  explanation, and the projection does not infer ontic randomness. A second,\n  source-sensitive mechanistic projection retains a typed paper-local\n  derivation and its independent proposition-valued realization. Einstein's\n  raw constructor derives osmotic pressure before dynamic equilibrium and\n  independently constructs transition-law/point-source diffusion;\n  Smoluchowski's derives equipartition from collision imbalance before\n  constructing its small-particle diffusion and large-particle\n  relaxation/Stokes branches. Neither source theorem accepts established\n  diffusion, established thermal-drag transport, or the ordinary mechanism as\n  an input. A checked forgetful theorem strips only source provenance from\n  any source-sensitive explanation and recovers the ordinary thermal-drag\n  mechanism from the same physical witnesses. A finite countermodel completes\n  the shared route, established output, and ordinary mechanism while\n  falsifying the source relation, proving that common transport behavior does\n  not reconstruct either derivation. A stronger composed endpoint now requires\n  both child source explanations, their actual two-regime physical handoff,\n  and a third independently realized joining derivation. Einstein's join\n  retains the original transition/Gaussian formulas, both stationary balance\n  equations, and exact coefficient; Smoluchowski's retains both particle-size\n  setups, his original persistent-flight and relaxation/Stokes formulas,\n  different numerical prefactor, and explicit failure of exact agreement.\n  An inhabited distinct-regime countermodel completes both child sources\n  and transport while withholding that joining derivation. Separate\n  source-valued witnesses now\n  retain Einstein's osmotic force balance, actual `6 pi eta a` drag,\n  exact scoped diffusion coefficient, normalized symmetric-step variance,\n  Gaussian point-source density, and molecular-count inference; Smoluchowski's\n  distinct witnesses retain noncancelling finite collision counts, the\n  `8/3` persistent-flight prefactor, exponential relaxation, distinct\n  near-agreeing coefficients, unresolved aggregation, and incomplete direct\n  experimental verification. No universal numerical coefficient or\n  common microscopic derivation is asserted, and Einstein's\n  mobility convention is not identified with Smoluchowski's resistance\n  convention.\n- `PhysicsLogic/Framework/LowEnergyEffectiveRangeReduction.lean` and\n  `PhysicsLogic/Framework/EffectiveRangeBoundStateExtraction.lean`: the Bethe\n  and Blatt-Jackson low-energy reduction and its deuteron-data extraction\n  composition. The reduction model retains five selected physical indices and\n  all eleven relation families used by the route. Each paper names its exact\n  context-owned `selectedModel`, proves a selected-semantics certificate,\n  realizes all thirteen shared claims, including the separately established\n  two-parameter endpoint, and transfers them through theory and\n  represented-world judgments.\n  The zero-energy stage returns controlled reference data together with the\n  scattering-length definition; the reduction consumes both and returns the\n  effective-range definition and phase law as sibling outputs. Bethe and\n  Blatt-Jackson keep\n  their distinct comparison-wave and variational calculations as explicit\n  route hypotheses. Their completed paper-local and shared results retain only\n  the inhabited setup and realized physical outputs; checked reconstruction\n  theorems recover the calculation functions when a source-order or adapter\n  proof needs them. The same output-led boundary applies to both higher-order\n  assessments.\n  Bethe's neutral branch now additionally retains the literal equations\n  (7), (10), (11), (13), and (14): the sine-normalized comparison wave,\n  its explicit `k cot(delta)` origin-derivative readout, the\n  comparison-minus-exact radial overlap, the zero-energy scattering length,\n  and the energy-dependent/effective-range integrals. Lean checks that\n  equation (7) really normalizes the comparison wave at the origin, that its\n  phase function is tied to the same `k` and `delta`, and\n  that equations (10), (11), and (13), together with `k_1^2 = 0`,\n  produce the exact energy-dependent phase relation before the controlled\n  equation-(14) replacement is used.\n  At the separately selected observable energy, actual `k^2 = k * k`,\n  nonzero `sin(delta)`, and the same-energy `k cot(delta)` readout allow Lean\n  to derive both original equation-(17) forms:\n  `4 pi sin(delta)^2 / k^2 = 4 pi / (k^2 + (k cot(delta))^2)`.\n  The physical S-wave maximum is characterized by `cos(delta) = 0`;\n  concrete positive-domain countermodels show that neither the wave-square\n  identity nor the physical phase readout can be dropped.\n  Their complete shared reduction now imports the effective-theory\n  truncation vocabulary: the selected two-parameter law is calculation-complete\n  only with its calculated higher-order term and is controlled only when that\n  correction is small. Both papers derive the same `ControlledAt` proposition\n  through their distinct local mechanisms. A calculated but nonsmall\n  correction is a checked countermodel, and neither empirical adequacy nor\n  potential-shape determination is inferred.\n  The complete route also realizes a typed derivational reduction from the\n  selected short-range scattering description to the two-parameter effective\n  description and its controlled phase behavior. Realization requires the\n  inhabited low-energy setup; source support requires the controlled\n  zero-energy reference and scattering-length definition; macro exhibition\n  requires the effective-range definition, phase law, calculated small\n  correction, and unresolved detailed shape. Both paper adapters consume\n  their applicable routes directly. A non-small-correction model and an\n  output-only false-setup model block promotion of a bare law or declared\n  reduced behavior to derivational reduction. No unique potential recovery or\n  multiple-realizer universality follows.\n  A second, source-sensitive projection pairs the exact model with a typed\n  paper-local derivation token. Blatt-Jackson's stationary-functional and\n  zero-energy-trial route is distinct from Bethe's comparison-identity and\n  interior-replacement route even though both realize the same shared\n  behavior. Their adapters start from raw paper premises, and a finite\n  countermodel proves that a complete route and complete output cannot supply\n  a missing source derivation.\n  The downstream bound-state extraction now also projects its complete\n  parent-and-child route to the mature model-evidence core. A typed\n  channel-parameter estimate is supported only when the selected aggregate\n  evidence package is accessible, both binding and scattering measurements\n  obtain, the parent two-parameter law is active, the bound-state relation is\n  calculated and controlled in the uncoupled scope, and the estimate is both\n  extracted and qualified. Bethe and Blatt-Jackson independently realize this\n  endpoint through their distinct comparison-wave and pole-continuation\n  calculations. A no-data countermodel keeps extraction and qualification\n  labels true but refutes evidence support. No exactness, prediction,\n  potential-shape determination, or theory truth follows.\n  The extraction now also has route-only and source-sensitive structural\n  explanations of that same qualified estimate. Bethe's typed source requires\n  the raw comparison identity, controlled interior replacement, ground-state\n  specialization, and empirical extraction contracts. Blatt-Jackson's typed\n  source instead requires the stationary functional, zero-energy trial\n  reduction, scattering-matrix continuation to `k = -iγ` with\n  `S(-iγ) = 0`, and its empirical extraction. Neither source theorem consumes\n  an established shared extraction, nonvacuous endpoint, ordinary\n  explanation, or evidence-support endpoint. A finite converse model retains\n  the complete route, estimate, ordinary explanation, and evidence support\n  while falsifying the source relation.\n  Bethe's observable S-wave cross-section calculation remains a separate\n  paper-local child of the established phase law. At explicitly positive\n  `k^2`, the printed formula proves cross-section positivity and the\n  `4 pi / k^2` unitarity bound; saturation holds if and only if the actual\n  phase vanishes, and every nonzero phase gives strict suppression.\n  Zero-wave-number and nonzero-phase countermodels block both shortcuts.\n  The need for the next term near that maximum remains separate; neither\n  the phase law alone nor the bound alone licenses the low-order truncation.\n  Blatt-Jackson additionally realizes a paper-local universality explanation\n  from explicitly unequal square and Yukawa wells with shared low-energy\n  parameters and controlled selected phase behavior. Its conclusion retains\n  unresolved detailed shape and higher-order dependence; it is not an\n  arbitrary-potential or all-energy universality claim.\n  The same restricted context has an explicit derivation bridge and checked\n  robust realization, so Lean derives compatible reduction and autonomous\n  emergence without treating the low-energy macrodescription as a unique\n  reconstruction of the potential.\n  Model and represented-world membership require the exact selected\n  low-energy setup: exact context selection, validity, neutral S-wave scope,\n  short range, and low energy relative to the interaction range. Grounding\n  uses only that setup, physical representation, and conditional transfers,\n  never the controlled reference, two-parameter outputs, higher-order outputs,\n  technical route, or established reduction. Each paper supplies its own\n  setup proposition before invoking the generic constructor. One countermodel\n  proves that a false low-energy setup cannot ground even an exactly selected\n  model; another has a complete setup and grounding while the first calculated\n  output and the technical route are false.\n  A 16-component mutation audit proves that every index or relation\n  substitution fails the original context's exact semantics.\n  A finite inhabited witness independently realizes the direct reduction;\n  changing any of the five indices or eleven relations destroys its active\n  setup, output, or unresolved-shape content. The shared established result is\n  definitionally exact selected semantics together with\n  `NonvacuousEffectiveRangeReductionAt`; it stores neither\n  `TechnicalRouteApplicable` nor any implication-valued calculation contract.\n  The downstream extraction embeds this exact parent model but depends only on\n  its established order-`k^2` endpoint, before either paper's later\n  higher-order analysis. It adds three context-owned selections and eight\n  extraction-specific relation families, including uncoupled S-wave scope and\n  qualification of the reported estimate. Its unique `selectedModel` exposes\n  all twelve extraction claims. Each paper again\n  supplies that named exact model and exhaustive transfer. Bethe's adapter\n  uses a separate bound-state-relation control proposition at the deuteron\n  energy; policy forbids substituting its positive-energy scattering-accuracy\n  assessment. Both clients explicitly retain deferred tensor-force scope and\n  the qualified status of the reported range. Bethe's paired\n  relation/extraction contracts and\n  Blatt-Jackson's continuation/extraction contracts are consumed to produce\n  direct terminal relation, control, empirical-input, and parameter outputs.\n  Separate theorems reconstruct those contracts when the embedded parent and\n  child routes are replayed; the terminal propositions themselves do not store\n  them. Model and represented-world membership require the exact selected\n  child setup: exact child selection, the established parent two-parameter\n  law, the selected bound state, uncoupled S-wave scope, and both measured\n  inputs. The selected experiment is an aggregate evidence package and can\n  combine several measurements. Grounding delegates to a\n  generic constructor using only that setup, physical representation, and\n  conditional transfers, never the bound-state relation calculation, its\n  control output, the parameter extraction, or the established child result.\n  One countermodel proves that a false parent setup cannot ground the child;\n  another has the complete parent/bound-state/data setup and grounding while\n  the relation calculation and child route are false. A\n  twelve-component child audit proves that changing the parent reduction, any\n  child selection, or any child relation fails the original context's exact\n  semantics, without identifying the papers' comparison-wave and\n  analytic-continuation calculations.\n  The stronger composed audit opens the parent rather than treating it as one\n  opaque field: all thirteen order-`k^2` parent components and all eleven child\n  additions are\n  necessary for the direct nonvacuous extraction. Blatt-Jackson's explicit\n  warning that approximate equation (5.3) should not be solved exactly is\n  preserved, as are Bethe's shape qualification and both papers' singlet-range\n  limitations. The established child result is definitionally exact child\n  selection together with the direct composed nonvacuous extraction. Bethe's\n  accuracy result separately retains that a square well\n  would require different triplet and singlet intrinsic ranges, a long-tailed\n  potential can accommodate a common range, and one channel's energy\n  dependence does not select the shape. Bethe's pp. 41 singlet-data limitation\n  is now a separate paper-local route: it combines the failure of\n  neutron-proton singlet data to fix the range with distinct assumptions of\n  approximate proton-proton/neutron-proton singlet-force equality and a\n  borrowed proton-proton effective range. The later charge comparison consumes\n  that qualification without falsely depending on the deuteron\n  triplet-extraction route. Its proton branch also retains the direction and\n  anomalous size of the high-energy departure, the failed tensor-force account,\n  and the unresolved status; its final small force difference is robust only\n  across the considered shapes and supports conditional approximate, not exact,\n  charge independence under a common range-and-shape comparison.\n  KSW 1998 is explicitly rejected as a third client: it imports the standard\n  effective-range expansion to calibrate PDS couplings and RG boundary\n  conditions, but does not perform the controlled zero-energy-reference and\n  small higher-order-correction stages required by this route.\n- `PhysicsLogic/Framework/LargeScatteringLengthResummation.lean`: the narrow\n  large-length, low-energy all-orders two-body resummation route independently\n  realized by KSW 1998 and Bedaque-Hammer-van Kolck 1998. Its exact proof-free\n  model retains five selected objects and all five route-defining relations,\n  including an all-orders requirement indexed by the selected resummed\n  object. Its output-led endpoint retains exact selection and the actual\n  setup, requirement, obtained description, and recovered target. Both\n  adapters construct theory/model/world grounding from the inhabited\n  pre-calculation setup only. A positive setup-complete countermodel has full\n  grounding but no applicable resummation route, and a\n  finite positive model realizes the complete technical route. Direct tests\n  make all five selected indices and all five relation families route-active,\n  while a separate ten-component exact-model audit detects every changed\n  field. PDS bubble sums and dressed-dibaryon calculations remain distinct\n  paper-local mechanisms. The applicable route also realizes a typed\n  derivational reduction from the selected large-length two-body description\n  to the selected low-energy target. Realization retains the valid anomalous-\n  length setup and actual all-orders requirement; source support requires the\n  obtained resummed description; macro exhibition requires its recovered\n  target. KSW supplies the PDS loop, bubble sum, and unitarity recovery,\n  whereas Bedaque-Hammer-van Kolck supply the dressed-dibaryon and\n  effective-range recovery. A second source-sensitive projection retains the\n  exact proof-free model plus a typed paper derivation: KSW's PDS-loop/bubble-\n  chain/unitarity token and BHvK's self-energy/dressed-dibaryon/effective-range\n  token have distinct raw realization relations. The generic constructor and\n  both paper adapters consume the applicable route directly, not an\n  established, nonvacuous, or ordinary derivational endpoint. One countermodel\n  has a declared recovered target but no valid source setup; another has the\n  complete technical route and ordinary reduction but a false derivation\n  relation, and therefore no source-sensitive reduction. Its seven directional\n  shared countermodels now use a reduced value-level readout: `Q R \u003C 1`,\n  `Q |a| = 1`, inverse-length and\n  cutoff scales, a retained graph order and unsuppressed first omitted graph,\n  complex bare/loop/resummed inverse values, the leading\n  scattering-length-amplitude equations, normalization, target comparisons,\n  and separate theory/model/world mismatches. A checked positive readout has\n  `R = 1`, `|a| = 4`, `Q = 1/4`, an unsuppressed omitted graph, resummed\n  inverse `(-1/4,-1/4)`, and target amplitude `(-2,2)`. Directional changes\n  then separately block the requirement, resummation, recovery, route\n  reconstruction, and grounding. No proposition-pair or `Unit` truth table\n  replaces these distinctions. The result asserts\n  neither full-theory reduction, universality, equivalence of the two\n  mechanisms, nor unique microscopic recovery.\n- `PhysicsLogic/Framework/FiniteVelocityCommutatorCone.lean`: the\n  interaction-dependent commutator-cone route independently realized by\n  Lieb-Robinson 1972, Nachtergaele-Sims 2006, and Hastings-Koma 2006. Its\n  proof-free model retains nine selected physical indices and eleven semantic\n  relation families. Each paper names its exact model, proves semantic\n  retention, and transfers all ten claims through theory and represented-world\n  judgments. Mutation countermodels detect changes to every one of the 20\n  retained components. Exponential suppression remains distinct from exact\n  microcausality and a universal light speed. Its explicit exact-signal bridge\n  is refuted by an inhabited effective-cone countermodel and is independently\n  consumed by Lieb-Robinson and Nachtergaele-Sims, so the distinction is\n  kernel-checked paper logic rather than an import-only qualification.\n  Lieb-Robinson's paper-local\n  source graph now supplies each basis, differential, Green-function, contour,\n  interpretation, and imported-theorem contract independently before applying\n  it to certified inputs. Its exponential- and slower-tail remarks remain\n  separate class-qualified roots with omitted calculations, while only the\n  actual finite-range result feeds the shared cone and downstream clustering\n  composition. The complete applicable route now also realizes a typed\n  structural explanation. Its constraint retains the exact selected local\n  system, interaction, observables, regions, bound, and regime, whereas its\n  distinct phenomenon retains only finite information propagation. All three\n  papers realize the explanation directly from their route inputs. One\n  countermodel has the velocity phenomenon without the commutator route; a\n  second has the full state-independent cone calculation without the physical\n  velocity interpretation. Neither case counts as this explanation, and no\n  strict no-signalling, relativistic microcausality, universal light speed, or\n  spectral-gap clustering conclusion is added.\n  Its two directional shared countermodels now retain finite interaction\n  range, separated supports, exterior interaction norm, commutator norm and\n  bound, propagation velocity, and interpretation residual. A range-one\n  setup with commutator norm one and claimed bound zero blocks the estimate;\n  a valid bound with nonzero interpretation residual blocks the velocity\n  conclusion. Source-valued witnesses additionally retain the positive\n  finite-time Lieb-Robinson exterior commutator, the sharper metric bound\n  that vanishes at initial time, separate spectral-gap and ground-projection\n  premises, and Hastings-Koma's distinct exponential and power-law tails.\n  The power-law branch has no shared exponential-cone model; odd fermions use\n  an anticommutator, and connected decay does not erase a nonzero\n  ground-sector correction.\n- `PhysicsLogic/Framework/SpectralGapClustering.lean`: the corrected\n  correlation-decay route independently realized by Nachtergaele-Sims 2006\n  and Hastings-Koma 2006. Its proof-free model retains fifteen physical\n  indices and sixteen route-defining relation families. Both papers name the\n  exact selected model, prove semantic retention, and transfer all thirteen\n  claims through full theory-entailment and represented-world judgments.\n  The established route also projects to a direct model-native clustering\n  proposition; a false-setup model blocks vacuous calculation contracts, and\n  separate direct mutations make all 31 components active in that proposition.\n  A typed structural-explanation projection treats the complete gapped-local\n  setup plus propagation, filtering, correction, bound, and decay calculations\n  as the necessitating constraint for the selected corrected-correlation\n  phenomenon. Both papers realize it independently. A countermodel retains a\n  real gapped setup and declared correction, bound, and decay but rejects\n  finite propagation, so neither the gap nor the output label explains the\n  phenomenon alone.\n  A stronger finite-velocity-supported endpoint now retains the direct\n  commutator-cone child, exact cone route, admissibility bridge, gapped setup,\n  and completed clustering together for the paper routes that actually use\n  that source order; generic clustering remains propagation-source agnostic.\n  The exponential routes consume a shared commutator cone only through\n  explicit model-specific admissibility; Hastings-Koma's power-law branch\n  remains direct. The framework does not identify the papers' filter\n  calculations or ground-sector corrections.\n  Its four directional shared countermodels now retain a positive gap and\n  distance, interaction/propagation norms and bounds, frequency-filter and\n  ground-sector-separation residuals, symmetric forward/reverse ground\n  contributions, and an all-distance exponential profile. They exhibit a\n  gap without propagation, propagation without filtering, corrected decay\n  with raw correlation one, and `(1/2)^distance` clustering at zero gap. No\n  proposition-pair truth table replaces these distinctions.\n- `PhysicsLogic/Framework/NonequilibriumWorkIdentity.lean`: narrow shared\n  nonequilibrium-work semantics independently realized by Jarzynski 1997 and\n  Crooks 1999. A declared finite classical process, positive inverse\n  temperature, canonical initial preparation, equilibrium reference free\n  energies, and defined work observable make the identity calculation\n  applicable. A paper-local calculation establishes the exact exponential\n  work identity; a separate mean-work definition and convexity bridge\n  establish the average-work bound. The identity-only and final established\n  propositions are output-led: they retain exact selected setup and direct\n  physical outputs, while checked theorems reconstruct the identity and bound\n  routes. Its proof-free model retains\n  six selected data components: the process, inverse temperature, trajectory\n  work assignment, ensemble-average functional, free-energy-difference\n  assignment, and mean-work assignment. It also retains the five setup\n  relation families used by the route. Jarzynski and Crooks each construct a\n  named exact model and prove that it retains the paper-local semantics before\n  applicability is established. The context owns the selected process and\n  constructs one unique `selectedModel`; the process-indexed `modelAt` family\n  remains only for the neutral paradigm view. Exact model identity is required\n  by theory membership and world representation; grounding additionally\n  requires the complete positive-temperature physical setup but no calculated\n  identity, convexity bridge, or bound.\n  Their Hamiltonian phase-space and forward/reverse stochastic path\n  derivations remain paper-local, as do\n  weak-coupling reductions, steady-state relations, sampling claims, and\n  approximations. Jarzynski's paper-local Hamiltonian route additionally\n  requires strictly positive `Z_0,Z_1,Y_0,Y_1`, proves that its system and\n  full-reservoir canonical densities are positive and integrate to one, and\n  derives positive `Z_1/Z_0` and `Y_1/Y_0` ratios. Proof-free scalar\n  countermodels separate physical canonical normalization from source-shaped\n  equations satisfied only through totalized zero-partition inverse or\n  division. This Hamiltonian phase-integral machinery remains paper-local\n  rather than becoming a requirement of Crooks's stochastic-path route.\n  Crooks's distinct source-sensitive readout additionally retains positive,\n  normalized forward and reverse three-state transition kernels, actual\n  reversed-protocol path equalities, normalized stationary populations, and\n  the physical same-protocol detailed-balance equation. Its circulating\n  witness has transition probabilities 1/2 and 1/6 and probability\n  current 1/9; its independent balanced witness has zero current and\n  satisfies the same fluctuation route. A Boolean balance report is accepted\n  only when it agrees with the actual transition probabilities, and the\n  common finite-time fluctuation contract neither assumes detailed balance\n  nor assumes its failure. These source-valued checks do not widen the\n  neutral work-identity interface or burden Jarzynski's independent client.\n  Countermodels independently mutate all eleven retained\n  components, and every mutation fails semantic retention, including a changed\n  switching protocol. The final established result is exact selected semantics\n  conjoined with the direct\n  `NonvacuousNonequilibriumWorkIdentityAndBoundAt` proposition, where the\n  positive-temperature setup, exact identity, mean-work definition, and bound\n  hold together at one selected process. A false-setup countermodel keeps the\n  implication-valued calculation contracts true but fails this proposition.\n  That false setup also cannot be grounded merely by declaring every theory\n  and world claim true.\n  A separate finite witness has positive temperature and nonzero work,\n  free-energy difference, and mean work; exhaustive direct mutation theorems\n  make every one of the eleven retained components destroy the direct complete\n  route itself. The countermodels also block reconstruction of either route\n  from its conclusion and block theory/world declarations from replacing the\n  technical calculation. Both adapters construct the direct proposition from\n  their distinct paper-local outputs and transfer every retained claim to their\n  selected theory and represented process.\n  The same source-ordered route now realizes a typed derivational reduction\n  from a proof-free exact-ensemble work description to a distinct\n  average-work description and scoped free-energy/mean-work inequality.\n  Source support retains the actual identity calculation and identity, the\n  ensemble-mean definition, and the convexity bridge; target exhibition is\n  only the mean-work bound. Jarzynski and Crooks realize this projection\n  directly from granular paper inputs, without consuming the established\n  terminal wrapper. A source-sensitive refinement additionally pairs the\n  exact selected model with a typed paper-local derivation token. Jarzynski's\n  token is realized only by its canonical-Hamiltonian, Liouville,\n  partition-ratio, and Jensen route; Crooks's token is realized only by its\n  forward/reverse path-weight, entropy-work, and Jensen route. Thus the same\n  identity and bound do not erase how either paper obtained them.\n  Countermodels block an identity-plus-coincidental-bound shortcut, a\n  bound-without-identity shortcut, and reconstruction of derivation provenance\n  from an otherwise complete physical route. The projection adds\n  no pathwise law, entropy increase, arrow of time, autonomy, emergence, or\n  complete-theory reduction.\n- `PhysicsLogic/Papers/GoldstoneSalamWeinberg1962.lean`: paper-local\n  symmetries, vacua, fields, currents, particles, and spectra, with distinct\n  perturbative, general-current, charge, composite, and outlook deductions.\n  Its shared spectral adapter separately grounds the current calculation in\n  the selected theory current and represented physical spectrum, with\n  an exact paper-data retention certificate plus exhaustive realization and\n  transfer certificates for all six shared claims.\n- `PhysicsLogic/Papers/Anderson1963.lean`: paper-local plasma,\n  superconductor, gauge-field, mode, and two-spectrum semantics, including\n  a bare-response pole criterion that places zero-mass support only in the\n  undressed matter spectrum, and checked separation of an uncoupled zero mode\n  from the finite-frequency interacting plasmon. The uncoupled spectral\n  adapter requires absence of long-range Coulomb interaction, certifies every\n  shared spectrum claim, and does not transfer the later conversion.\n- `PhysicsLogic/Framework/CollisionlessKineticPoisson.lean`: shared\n  collisionless electrostatic kinetic-Poisson self-consistency, independently\n  realized by Landau 1946 and Bernstein-Greene-Kruskal 1957. Its proof-free\n  physical context separately selects the plasma, primary and background\n  distributions, electrostatic potential, regime, equation branch, and\n  ion-background treatment; a nonvacuous result requires the collisionless\n  kinetic equation, Poisson closure, and their independent coupling. Landau\n  selects a fixed-ion linear Fourier initial-value problem and retains its\n  printed one-sided formulas (6)-(10); BGK selects a stationary nonlinear\n  electron-ion wave and retains its printed equations (1)-(4). Concrete\n  countermodels reject incorrect Poisson signs, restored collisions,\n  substituted background distributions, negative trapped populations, false\n  velocity-distribution damping, unsupported actual-plasma existence, and\n  source explanations without their separate derivation. Damping, trapping,\n  analyticity, and physical realization are not shared conclusions.\n- `PhysicsLogic/Framework/ControlledResonanceModelTest.lean`: narrow shared\n  experimental-gravitation logic, independently realized by Pound-Rebka 1960\n  and Hughes-Robinson-Beltran-Lopez 1960. Its proof-free context retains the\n  actual resonance, distinct configurations, protected reference, finite\n  sensitivity, observed readout, independent model calculation, and distinct\n  affirmative-versus-null branches. Source-valued witnesses separately retain\n  the 74/148-foot gamma reversal, inversion-stability assumption,\n  `-(5.13 +/- 0.51)` versus `-4.92` redshift comparison, 22/104-degree\n  galactic orientations, protected Atomichron/proton references, original\n  `P2(x) = (3 * x^2 - 1) / 2`, separate nuclear-structure conversion, and\n  finite `10^-20` bound. Exact isotropy, unrestricted angular coverage, exact\n  redshift equality, and whole-theory support remain unestablished.\n- `PhysicsLogic/Papers/LandauDamping1946.lean`: paper-local collisionless\n  kinetic setup, normal-mode obstruction, arbitrary-initial-data Laplace\n  solution with value-level equations (6)-(10) for the one-sided transform,\n  inverse contour, transformed distribution, and three-dimensional-to-\n  longitudinal potential reduction, nonvacuous deterministic evolution,\n  analytic continuation, collective-field damping, long- and short-wave\n  asymptotics, initial-data regularity sensitivity, a logically independent\n  moving-pole route to persistent velocity-resolved oscillations, and a\n  separate causal half-space penetration calculation retaining source\n  equations (24)-(26), (35), (37), (39), (41), and (44)-(46): actual\n  dielectric response, reflecting-wall and bulk boundaries, sign-dependent\n  resonant contours, Fourier integration, `x^(2/3)` far attenuation,\n  distinct below-/above-plasma-frequency profiles, the positive spatial\n  decrement, and the nonexact approximate wall values. The module\n  deliberately derives no entropy-production or microscopic-irreversibility\n  claim. Its seventeen paper-local countermodel theorems now retain actual\n  right-half-plane\n  transform parameter and longitudinal velocity, long-wave formula and\n  residual data, field/distribution amplitudes, wave-number and decrement\n  comparisons, initial-data and moving-pole values, real-valued evolution and\n  response amplitudes, branching alternatives, distinct below-/above-pole\n  contour orientations, sub-/super-resonance frequencies and dielectric\n  values, exact bulk amplitudes, the zero-mode identity, the physical `2/3`\n  exponent, actual positive spatial damping, and separate approximate versus\n  exact wall fields. No `Unit`/`Bool` truth table replaces those distinctions.\n- `PhysicsLogic/Papers/BernsteinGreeneKruskal1957.lean`: the original\n  stationary nonlinear plasma construction, retaining trapped/passing\n  populations, direct quadrature, inverse trapped-population calculation,\n  nonnegativity, arbitrary-profile scope, singular moment surrogate, and\n  open collision/stability obligations. Its actual stationary equation (4)\n  retains separate positive/negative velocity-direction energy branches;\n  passing populations may therefore be unequal even at the same energy.\n  The distribution also retains its connected orbit component, so distinct\n  trapped wells are not collapsed while passing populations remain common\n  across potential intervals.\n  Electron and ion orbit results retain opposite charge-signed trapping\n  thresholds, real turning roots, a forbidden separating barrier, equal\n  occupation within each trapped well, independently adjustable disconnected\n  wells, and freely assignable passing-direction populations. Seven inhabited\n  countermodels keep these physical implications distinct without imposing\n  trapped-orbit assumptions on Landau's independent plasma route. Its four\n  printed-formula\n  countermodels now retain meaningful setup domains: positive charge and\n  species masses with nonnegative densities/distributions for equations\n  (1)-(4), a signed quadrature and zero turning derivative for equations\n  (6)-(8), and an in-range potential with zero endpoint trapped density for\n  equations (9)-(12). Those domains withhold the corresponding stationary,\n  direct, inverse, and substituted calculations; no constant named-output\n  predicate replaces these BGK distinctions.\n- Printed-formula countermodels across the active paper library now retain\n  source-shaped physical domains rather than constant named-output predicates.\n  The cross-disciplinary audit spans axial anomalies, black-hole mechanics\n  and entropy, hidden-variable dynamics, boundary layers, excursion sets,\n  gauge and string mass/charge formulas, path amplitudes, helium and Hall\n  response, CMB spectra, renormalization, nebular and stellar dynamics,\n  nonlinear waves, stochastic inflation, and transport. Positive scales,\n  regularity, nonzero denominators, selected directions and cycles, and\n  value-level formula failures remain separate checked facts; no truth-status\n  pair replaces those distinctions.\n- `PhysicsLogic/Papers/PoundRebka1960.lean`: the original terrestrial\n  gravitational-redshift experiment, including recoil-free resonance,\n  opposite-Doppler calibration, temperature and monitor controls,\n  source-absorber reversal, offset diagnosis, the explicit inversion-stability\n  premise, separate observed/predicted shifts, and finite-uncertainty model\n  support. It independently realizes the shared controlled-resonance model\n  test without identifying redshift agreement with a nuclear null bound.\n  Its earlier eleven paper-local countermodel theorems retain actual\n  Table-I readings and corrections, 74-foot tower, 148-foot two-way, and\n  six-inch close-baseline values, distinct direction/record alternatives,\n  reported shift and ratio uncertainties, and evidence transfer with zero\n  model-support residual but nonzero theory-support residual. No all-true\n  framework record or enum truth table replaces those distinctions.\n  The counting refinement computes response convolutions, quarter-cycle\n  gates, calibrated gain, thermal shifts, normalized period estimates,\n  reversal residuals, and actual sampling moments. The expanded fidelity\n  matrix has 33 boundaries. The first-four-day table is distinct from the\n  final ten-day result; `513/492` is not the separately printed ratio `1.05`.\n  A possible unrounded reconstruction explains why the last displayed row's\n  nonexact arithmetic alone is not evidence of an error in the raw reduction.\n- `PhysicsLogic/Papers/KolmogorovLocalStructure1941.lean`: the original local\n  turbulence argument, including conditional velocity-increment laws, local\n  homogeneity and isotropy, high-Re interior scope, two similarity hypotheses,\n  viscous normalization, inertial two-thirds scaling, and longitudinal/\n  transverse ratios. Its increment-law and derivative countermodels use\n  actual random fields, probability laws, and computed moment profiles.\n  The conditional-law comparison uses two positive-mass base-velocity\n  events, not arbitrary values of a conditional kernel on null events.\n  A constant drift has isotropic increments but anisotropic absolute\n  velocity; `R=10^6` does not remove a boundary;\n  `lambda=1` and `r=L=2` fail the upper inertial bound; and a two-thirds\n  second moment supplies neither the later five-thirds spectrum nor the\n  four-fifths law. No status-enum truth table replaces those distinctions.\n  The technical turbulence semantics remains paper-local until an independent\n  primary-paper client demonstrates genuine reuse.\n- `PhysicsLogic/Papers/Jaynes1957.lean`: the complete two-part\n  maximum-entropy, thermodynamic-dictionary, density-matrix, information-loss,\n  and controlled-relaxation argument. Its sixteen paper-local countermodel\n  theorems now retain actual probability, constraint, entropy, variance,\n  canonical-weight, trial-count, population, propagator, rate, correlation,\n  and approximation values. In particular, a broad two-state maximum-entropy\n  assignment has variance `1/4`; the array/eigenstate witness checks the\n  measurement formula `1/2 + s^2/4` and equality criterion `s=0`; identical\n  instantaneous densities admit\n  rates zero and `1/4`; an approximate propagator composition has residual\n  `1/20`; equal positive rates at a nonzero energy gap fail finite-temperature\n  detailed balance; and the same reduced mean permits global variances four\n  and sixteen across the reliability threshold. No `Unit`-carrier truth table\n  replaces those distinctions. The exact Jaynes normalization and relaxation\n  semantics remain paper-local until an independent primary-paper client\n  demonstrates genuine reuse.\n  The independent fidelity matrix now has twenty-five physical boundaries:\n  its source-valued thermometer keeps `Z_joint=Z_system Z_bath`,\n  `p_ij=p_i p_j`, and `lambda=dS_bath/dE_bath=1/T`; its rotating nuclear\n  spin has `omega=1`, `lambda=-1`, zero energy transfer, zero magnetic\n  field, and the proved `\u003Cm>=-(1/2)tanh(lambda/2)` polarization. Distinct\n  normalized arrays `(1,0),(0,1)` and `(3/5,4/5),(-4/5,3/5)` give the same\n  density matrix, while removing correlations changes entropy from `log 2`\n  to `2 log 2` without changing the exact unitary entropy or additive mean.\n- `PhysicsLogic/Papers/Nambu1960.lean`: paper-local generalized\n  Hartree-Fock self-consistency, nonperturbative gap, gauge-phase family,\n  Ward-identity vertex, gauge-invariant Meissner response, collective pair\n  dispersion, nonlocal quasiparticle charge cloud, Coulomb plasma shift, and\n  explicit approximation-boundary semantics. The paper-local routes now retain\n  value-level equations (2.15), (2.20), (4.4b), (5.9), (6.11), and (8.11):\n  quasiparticle energy and twice-pairing-scale gap, circular anomalous\n  self-energy components, a noncommutative two-by-two Ward matrix relation,\n  selected longitudinal cancellation, the Coulomb-omitted gapless dispersion,\n  and the distinct Coulomb plasma frequency. Its shared screening adapter\n  rebuilds the corrected response antecedent from shared Ward-result,\n  collective-state, and transverse-field facts before rerunning Nambu's\n  paper-local calculation. Its ladder-spectrum grounding\n  requires an explicit representation of the superconductor by the selected\n  quasiparticle vacuum and transfers the complete shared spectrum vocabulary.\n  Its source-sensitive gap-to-screening composition separately preserves the\n  anomalous gap, gauge-phase family, matrix Ward identity, Coulomb-omitted\n  gapless collective intermediate, longitudinal cancellation, and surviving\n  physical transverse current.\n- `PhysicsLogic/Papers/Nakano1956.lean`: paper-local arbitrary-time electric\n  field response, pulse and thermal-trace kernel calculations, exact static\n  conductivity extraction, typed equations (1)-(5) with explicit causal and\n  positive-time integrals, beta normalization, thermal trace denominator,\n  Boltzmann spectral weights, current matrix elements, phase, and\n  energy-delta conductivity sum, subsystem decomposition, perturbative pair\n  interaction, one-relaxation-time approximation, and explicit separation of\n  exact result, typical-case approximation, and suggested broader scope.\n  Infinite-sum convergence, integral evaluation, the equal-energy continuation\n  of equation (4), and the delta distribution remain explicit imported\n  mathematics rather than being silently totalized or hidden behind a named\n  output. Explicit representation bridges tie the real/complex formula\n  readout back to the selected current, electric field, kernel family, and\n  static transport value. Formula atoms are projected from the response and\n  static calculation premises, and a finite countermodel blocks named\n  current/conductivity outputs from supplying equations (1)-(5).\n- `PhysicsLogic/Papers/Ramsey1950.lean`: paper-local two-state molecular beam,\n  pulse/free/pulse evolution, fixed-field phase accumulation, space-mean\n  energy detuning, fixed apparatus dimensions with selected pulse/free transit\n  times inverse to molecular velocity, distribution-level transit-time\n  variation, exact- versus off-resonant reinforcement, velocity-averaged\n  separated-field resonance, the spin-one-half magnetic-moment specialization\n  and imported Majorana higher-spin extension, calculated limiting regimes versus an\n  interpolated middle interval, pulse-strength and width calculations,\n  reported potassium comparison, two separate probable interpretations,\n  field-uniformity and precision scope, proposed applications, and operational\n  access to the intermediate-region mean splitting. Thirteen checked routes now\n  preserve these stages separately. Nonzero coupling now proves actual\n  two-state mixing normalization, and the full equation-(12) expression is\n  proved to lie in `[0,1]`. The paper's velocity average retains positive\n  selected and most-probable speeds, both inverse-speed transit times, the\n  original normalized molecular-beam weight `2*y^3*exp(-y^2)` on `y > 0`,\n  and the actual continuous integral of the coherent response at every\n  positive speed. Lean proves normalization, integrability, and the averaged\n  probability bounds. Explicit near-error and weighted dephasing estimates\n  derive separate inhabited frequency sweeps. The doubled harmonic derived\n  from equation (15) remains distinct from the half harmonic literally\n  printed in equation (18), with an actual-integral counterexample to their\n  identification. The averaging contract supplies these physical inputs,\n  not the desired final conclusions.\n  Together with Rabi 1939 it realizes a direct nonvacuous shared\n  resonant-transition spectroscopy route whose ten selected objects and nine\n  relation families are all directly active, together with a stronger\n  normalized two-outcome endpoint independently realized by Rabi's actual\n  equation-(2) transition and Ramsey's actual beam average. Its adapter\n  replays the shared\n  controlled setup, driven transition, and resonance readout through retained\n  pulse/free/pulse, resonance, averaging, interpolation, and line-shape\n  contracts supplied as independent hypotheses. Established physical results\n  do not cache those implication-valued contracts. The shared terminal result\n  is output-led and reconstructs its route. Rabi's resonance-dynamics setup\n  and Ramsey's separated-field setup independently realize the shared\n  pre-output boundary used by both route assembly and grounding; no frequency,\n  response, readout, or quantity output is a grounding premise. No field-free\n  or coherence/decoherence framework is imported.\n  The source-sensitive projection now keeps Rabi's one-region\n  gradient-refocusing and cross-molecule moment extraction distinct from\n  Ramsey's pulse/free/pulse interference and velocity-averaged fringe route.\n  Both source theorems begin with raw paper-local stages rather than complete\n  paper conclusions. A finite converse model has completed spectroscopy, its\n  route, and the ordinary explanation but no source explanation, so a\n  resonance-based extraction cannot certify its own apparatus derivation.\n  A separate source-valued AMO framework audit now retains Rabi's printed\n  Larmor and weak-field transition formulas, opposite deflection gradients,\n  detector minimum, cross-molecule Li-7 assignment, imported spin `3/2`,\n  frequency/field-to-`g` coefficient, exact magnetic moment, and the fact that\n  the displayed values `2.167 * 3/2` and `3.250` are not an exact equality.\n  The journal pp. 527-528 rotating-versus-oscillating distinction is now\n  physical rather than an opaque sign flag: the measured positive magnitude is\n  `|mu_signed|`, so two genuine moments `+mu` and `-mu` retain the same field,\n  Larmor frequency, and nonzero transition probability. A pure oscillating\n  field contains both opposite rotation senses and cannot identify the sign;\n  one selected rotating sense distinguishes them, but that contrast is not\n  represented as a measurement performed by Rabi's oscillating apparatus.\n  Absolute calibration and the hyperfine discrepancy remain qualified. Ramsey's\n  separate witnesses retain both pulses, the drive-free intermediate phase,\n  exact equation-(12) interference, inverse-velocity transit times, positive\n  distribution weights, explicit beam averaging, and an interpolated rather\n  than calculated middle interval. The `0.600 pi` selected pulse area,\n  `0.200` weaker comparison, `0.64`, `1.23`, and `1.4` width coefficients,\n  and distinct `0.6` same-length improvement remain separately active.\n  Longitudinal field averaging does not erase transverse uniformity, and a\n  proposed shielded-region application is not an already performed\n  measurement.\n- `PhysicsLogic/Papers/BardeenCooperSchrieffer1957.lean`: paper-local\n  phonon/screened-Coulomb competition, coherent pair variational state,\n  a separately qualified common-pair-momentum persistent-current argument,\n  self-consistent quasiparticle gap with local equation-(2.40),\n  equation-(2.50), and pair-breaking-threshold values, near-critical square-root and continuous\n  thermal gap closure, explicit weak-coupling thermodynamic relations,\n  case-I/case-II coherence-factor matrix elements, Meissner and Pippard\n  response, empirical bridges, and unresolved model extensions. Its shared\n  screening adapter rebuilds the local response antecedent from shared\n  validity, static-field, transverse-field, linear-response, and\n  current-decomposition facts plus the paper-local case-II classification and\n  factor before rerunning the BCS calculation. Its source-sensitive\n  gap-to-screening composition retains the actual variational gap, selected\n  coherence channel, original London-current formulas, Pippard response,\n  penetration depth, and field-expulsion bridge as an independently checked\n  joining derivation.\n- `PhysicsLogic/Papers/Kadanoff1966.lean`: paper-local cell variables,\n  scale separation, reduced temperature, weak external field, cell site\n  count, two-valued cell-spin sum, effective magnetic field,\n  nearest-neighbor effective Ising description, explicit free-energy and\n  correlation comparisons, critical-exponent consequences, and the separately\n  qualified effective-coupling regularity extension. The shared\n  coarse-grained-scaling route now consumes the established paper-local cell\n  construction rather than a bare cell label.\n- `PhysicsLogic/Papers/ForsterNelsonStephen1977.lean`: paper-local stochastic\n  fluid models A, B, and C; momentum-shell elimination and rescaling;\n  dimension-dependent fixed-point behavior; long-time tails; infrared\n  universality; a nonvacuous transverse-momentum slow-mode reduction from\n  Model C to the Model A infrared description; Galilean Ward-identity\n  reasoning; and explicit perturbative and ultraviolet limitations. Its\n  thirty-two inhabited Forster-Nelson-Stephen fluid boundaries retain\n  `P_12=-12/25` and `C_12=-12` at `k=(3,4,0)`, genuinely distinct shell\n  and time rescalings, `D_A(k)=2k^2`, `D_B(k)=2`, a Model C pulse supported\n  only for `1\u003C|k|\u003C4`, generated infrared forcing `1/2`, critical dimensions\n  two and four, `z_A=2`, and `z_B=5/3`. The Model A all-order argument does\n  not prove the Model B result, and a selected finite-band flow does not\n  establish universality for every finite-band force.\n- `PhysicsLogic/Papers/Mori1965.lean`: paper-local orthogonal projection,\n  exact generalized Langevin dynamics, force-memory correlation, the distinct\n  ordinary-force secular cancellation tail, complement-propagator exclusion of\n  that tail from the projected damping kernel, and plateau-value avoidance.\n  The central exact-memory package now retains equations (3.3), (3.8), and\n  (3.10)-(3.12) as componentwise complex-valued propositions: a finite\n  frequency-matrix action, an actual derivative, a causal interval integral,\n  a nonempty selected-component domain with a genuine two-sided covariance\n  inverse, explicit differentiability/\n  integrability hypotheses, force orthogonality, and both covariance-matrix\n  correlation identities.\n  Plateau resolution and qualified short-memory localization are now sibling\n  consequences of the exact force-memory route rather than an artificial\n  chain. Sections 4-8 are represented directly: canonical scalar-product\n  selection and proposed typicality, time-reversal reciprocity, the good-\n  variable criterion, hydrodynamic slow modes, spin/oscillator/fluid examples,\n  exact projected thermal after-effect dynamics, distinct aged-regression and\n  local-equilibrium transport routes, thermal/mechanical response comparison,\n  ordered-limit qualifications, explicit projected transport coefficients,\n  and the open Mori-Zwanzig comparison. Calculation and assessment contracts\n  remain independent theorem premises; none of the fifteen established-result\n  families stores one as proof payload. Fourteen inhabited fidelity boundaries include a\n  false-setup projection chain in which every implication-shaped calculation\n  is vacuously true but no reduction is established. The shared memory-kernel\n  adapter retains the certified direct-output route, while a separate adapter\n  now applies the projection, orthogonal-dynamics, exact-equation, and force-\n  correlation calculations in source order and realizes the mature\n  derivational-reduction interface before a completed endpoint exists. This\n  does not promote the later short-memory approximation, or assert autonomy\n  or multiple realization. The adapter remains narrow, while the\n  thermal convolution nonvacuously realizes shared retarded-response semantics.\n  Its finite real-sector model now computes the Gram projector and vertical\n  force, solves the full and complementary oscillator generators, and checks\n  the exact causal memory equation. The constant projected correlation and\n  oscillating ordinary correlation are provably different; exact projection\n  alone does not make memory decay.\n- `PhysicsLogic/Papers/Zwanzig1973.lean`: the complete nonlinear generalized-\n  Langevin argument through generalized conservative dynamics, the symmetric\n  nonsingular shifted quadratic bath, the solved and integrated bath\n  trajectory, exact history-dependent elimination, conditional canonical bath\n  moments, Gaussian fluctuation-dissipation, the exact particle-plus-\n  oscillator specialization, a distinct Debye-continuum/sinc-kernel route,\n  and the later slow-system delta-localization route.\n  Equations (17) and (19) now remain value-level propositions over nonempty\n  finite system/bath component domains: equation (19) exposes an actual\n  derivative, the nonlinear A-W-L-W-transpose history convolution, and A-W-F\n  noise action, while equation (17) exposes conditional-canonical zero mean\n  and kT-times-kernel covariance with explicit thermal positivity and positive\n  bath quadratic form. The same matrix propagator now defines the shifted\n  initial force, inverse-bath covariance, memory kernel, and equation (18).\n  The particle route retains equations (22)-(24) as actual derivatives,\n  convolution, finite cosine sum, and covariance. Equations (25)-(30) retain\n  the distinct continuum and local models, including the original printed\n  cutoff-squared convention and its separately checked normalization mismatch.\n  Thirteen calculation or\n  interpretation contracts are independent hypotheses rather than outputs of\n  their setups. None of the nine established-stage families stores those\n  contracts as proof payload. The shared adapter retains that direct-output\n  path and now also constructs the exact shared route from exact-elimination,\n  conditional-canonical, bath-moment, and noise calculations before a\n  canonical-noise endpoint is packaged. Eleven inhabited fidelity boundaries include a\n  staged false-setup chain that makes every calculation through exact\n  elimination vacuously true without establishing the result, while\n  preserving the special-bath, distribution-role, exact/local, and\n  continuum/Markov distinctions. The\n  exact elimination also realizes the mature derivational-reduction interface,\n  independently of the continuum and Markov approximations. The strengthened\n  paper also independently uses the shared finite residual-covariance\n  operation. An actual positive oscillator bath realizes fluctuation-\n  dissipation, while a nonsingular negative-energy bath excludes a physical\n  canonical covariance and a finite bath retains nonzero-lag correlations.\n- `PhysicsLogic/Papers/OrdonezRayVanKolck1995.lean`: paper-local low-energy\n  field selection, the original equations-(1)-(3)/(14) chiral-index chain\n  `nu = 4 - A + 2 L - 2 C + sum_i V_i Delta_i`,\n  `Delta_i = d_i + f_i / 2 - 2`, `Delta_i >= 0`, and\n  `A = 2, C = 1 => nu = 2 L + sum_i V_i Delta_i`,\n  irreducible-potential construction, reducible dynamical iteration,\n  third-order momentum-space potential, regularization and coordinate\n  conversion, radial solution, empirical fit, and explicit short-range and\n  higher-order limitations. The finite vertex-list readout keeps the source\n  sum structural, checks the two-nucleon specialization and nonnegative index,\n  and includes a negative-index countermodel when equation (3) is omitted;\n  none of that widens the shared effective-interaction contract. The\n  momentum route now also retains preprint p. 10 equations (15)-(16) as a\n  selected scalar matrix-element package: the literal static\n  `-(2 g_A/F_pi)^2` one-pion-exchange coefficient, isospin and spin-momentum\n  factors, pion denominator, `C_S` and `C_T` contacts, and the parity-forbidden\n  zero first correction. The package is tied to the selected leading and\n  first-order potential objects through their matrix-element map; a\n  name-only countermodel blocks replacing those equations by order labels.\n- `PhysicsLogic/Papers/Zamolodchikov1986.lean`: the original two-dimensional\n  c-theorem route through stress-tensor correlations, the trace identity,\n  Callan--Symanzik evolution, separately established positivity of both the\n  coupling-space metric and the running c-function, strict differential\n  decrease away from fixed points, explicit RG integration, and fixed-point\n  identification with the Virasoro central charge. The printed normal\n  coordinates and no-linear-term expansion in equations (11)-(12) separately\n  establish stationarity of every c-gradient component at both fixed points;\n  inhabited countermodels reject deriving that claim merely from vanishing\n  beta, a vanishing directional derivative, or central-charge matching.\n  Its complete\n  route realizes the shared RG endpoint-monotonicity framework while keeping\n  the local field-theory calculation explicit. The shared adapter reconstructs\n  the paper-local selected-flow setup from the shared flow facts plus the\n  retained beta-zero and conformal-endpoint facts before invoking either\n  endpoint identification or the c-theorem calculation.\n- `PhysicsLogic/Papers/KomargodskiSchwimmer2011.lean`: the four-dimensional\n  a-theorem route through anomaly matching, the spectator dilaton,\n  low-energy scattering, the forward amplitude, a dispersion relation, the\n  optical theorem, and positivity of the total cross section. Separate routes\n  retain the moduli-flow argument, general-flow extension, running\n  a-function, free-scalar check, and stated open questions; the general\n  unitary flow realizes the shared RG endpoint-monotonicity framework. Its\n  forward-positivity adapter reconstructs the low-energy dilaton theorem from\n  the supplied shared coefficient assignment before building the dispersion\n  sum rule.\n- `PhysicsLogic/Papers/Heisenberg1927.lean`: operational quantity definition,\n  stationary-state position and momentum restrictions, gamma-ray microscope\n  accuracy and recoil, energy-time resolution, an independent selected\n  Gaussian transformation whose equations (3)-(6) now retain the printed\n  position Gaussian, Jordan integral, exponential q-p kernel, transformed\n  momentum Gaussian, and selected `p_1 q_1 = h/(2 pi)` product,\n  experiment-relative value partitions, coherent versus intermediately\n  measured transitions, the high-excitation obstruction, observation-defined\n  trajectories, exact and finite free packets, the grating and radiative-jump\n  thought experiments, causal interpretation, qualified resonance\n  fluorescence, weak quantization, and the coupled rotor-rack energy\n  distinction. Its 53 claims and 18 semantically certified routes retain every\n  proof-stage correction while its direct measurement adapter proves\n  disturbance without identifying that claim with prepared-state dispersion.\n- `PhysicsLogic/Papers/Kennard1927.lean`: transformation-related coordinate\n  and momentum probabilities with pointwise `M M*` density formulas,\n  Kennard's doubled-variance precision,\n  Gaussian saturation, the general equation-(27) positivity route,\n  alternative and joint observation interpretations, and simple-motion\n  scope. Its adapter constructs an exact shared model, proves semantic\n  retention, directly packages the shared state-dispersion outputs, and\n  realizes and grounds both the shared state-dispersion route\n  and the independent amplitude-derived exact-observation probability route.\n  Its state-dispersion provenance theorem starts from the general amplitude\n  factorization and nonnegative remainder rather than an established shared\n  inequality, keeping the pp. 338-339 derivation distinct from Robertson's.\n- `PhysicsLogic/Papers/BornCollisions1926.lean`: the full original collision\n  paper's discrete and continuum frequency rules, asymptotic flux balance,\n  directional elastic and inelastic scattering, excitation thresholds,\n  qualified dipole and evidence assessments, practical-indeterminism\n  interpretation, and open radiation extension. Its elastic route supplies\n  the scattering realization of the shared amplitude-to-outcome-probability\n  component without exporting Born's paper-local channel meanings.\n- `PhysicsLogic/Papers/RocekVerlinde1991.lean`: the original-author v1 routes\n  for bosonic parent-action reduction, one-loop dilaton correction, compact\n  holonomy completion, vector/axial quotients, mode and singularity\n  interpretation, and the N=2 Legendre extension. Only the first local\n  reduction route feeds the shared parent-action component.\n- `PhysicsLogic/Papers/DeLaOssaQuevedo1992.lean`: the earliest available\n  author revision's abelian review, non-abelian parent path integral,\n  determinant and dilaton correction, SO(N) examples, leading black-hole\n  applications, and explicit unresolved global-equivalence assessment. Its\n  local parent route now retains value-level equations (3.2), (3.3), (3.10),\n  and (3.15): a finite Lie-index curvature with actual partial derivatives\n  and commutator sum, the multiplier-curvature worldsheet integral, the\n  selected bar-h/f-inverse/h predual-action integral, and the real logarithmic\n  determinant shift of the dilaton.\n  Functional path integration and determinant evaluation remain explicit\n  source contracts rather than invented internal mathematics. Its\n  adapter shares the local reduction route while preserving the unknown\n  multiplier range, duality group, and global CFT relation.\n- `PhysicsLogic/Papers/HamiltonGeneralMethod1834.lean`: the original 1834\n  varying-action calculation, positive final and negative initial endpoint\n  momentum readouts, separate parameter/energy derivative recovery of\n  complete motion integrals, initial and final characteristic equations,\n  transformed and relative coordinates, explicit selected-to-relative,\n  relative-to-binary, and binary-to-Newtonian system links, the general\n  three-point pairwise-force specialization with nine full and six relative\n  endpoint-integral counts, centre/relative action and energy splitting,\n  translation/rotation constraints, ternary pentagon and four-point heptagon\n  geometry counts, the stated arbitrary-multiple-system extension, arbitrary\n  binary quadrature, Newtonian conic and Lambert specialization, exact and\n  first-order action corrections, and time principal function. The perturbation\n  branch now retains Hamilton's printed p. 296 equations (O5) and (P5) as\n  paper-local real-valued formulas: the rigorous correction keeps the\n  second-part living-force term, the approximate expression drops it, and\n  explicit imported integral linearity identifies their difference as the\n  higher-order remainder. A checked countermodel blocks the printed pair from\n  making the first-order expression exact without remainder control.\n  Characteristic-equation\n  verification now branches from signed endpoint derivatives without\n  inheriting the stronger complete-recovery route. Its shared adapter\n  combines the positive final derivative route with the later\n  first-order-equation verification while leaving living force, the initial\n  endpoint sign, the system-specialization chain, ternary recovery,\n  invariant multiple-system geometry, binary motion, Kepler formulas, and\n  perturbations local. Its twelve directional paper-local countermodels are\n  now value-bearing: stationary action fixes both endpoint displacements and\n  energy variation while remaining dynamically impossible; varying action\n  retains `5=4-1+2*1`, conservation, and a dynamically possible neighbor;\n  signed endpoint derivatives are `(2,-3)`, complete recovery requires six\n  parameters and the energy derivative `2=t`, the ternary counts are\n  `(9,9)/(6,6)`, and the pentagon reduction is `10-1=9`. Binary quadrature\n  leaves a three-body problem unsolved, and exact correction reuses the\n  checked nonzero-remainder model. No proposition-pair or action/variation\n  status truth table replaces these Hamilton distinctions. The\n  predominant-mass approximation now consumes the\n  established multiple-system geometry route instead of depending on varying\n  action alone.\n- `PhysicsLogic/Papers/JacobiPDEReduction1837.lean`: the original 1837 theorem\n  that any complete integral of the time-dependent principal equation\n  recovers mechanical motion, together with constrained and explicitly\n  time-dependent scope, autonomous reduction, the critique of Hamilton's\n  second equation, homogeneous-force stability tests, the Kepler example,\n  general characteristic-system reduction and converse, and the broader\n  Pfaff comparison. The endpoint-defined principal function and the arbitrary\n  complete integral remain separate selected scalar functions; only the\n  arbitrary complete-integral reconstruction feeds the shared component.\n  The p. 104 Hamilton-Jacobi relation and pp. 107-109 derivative recovery\n  relations are retained as paper-local value packages with explicit\n  evaluation points and name-only countermodels.\n- `PhysicsLogic/Papers/AlbrechtSteinhardt1982.lean`: the original\n  new-inflation argument, including the radiative finite-temperature\n  potential, exact versus near-Coleman-Weinberg tuning, the trusted\n  `T^4 exp(-F_bubble/(kT))` saddle rate, independently supplied bubble\n  percolation, saddle breakdown above strong coupling, multiple thermal\n  fluctuation paths, order-one `phi ~ T` and `R_initial ~ 1/T` scaling,\n  the full `phi_ddot + 3 H phi_dot + V' = 0` Klein-Gordon equation,\n  `N = H tau`, `R_final = R_initial exp(N)`, and\n  `delta_H \u003C 3.6e-11`. Thirty-three\n  inhabited physical boundaries separate a large converted fraction from\n  bubble connectivity, full accelerated field dynamics from an unsupported\n  overdamped truncation, sixty exact exponential e-foldings from observed\n  containment, nonthermal-monopole suppression from allowed thermal\n  monopoles, unobserved from globally absent domain walls, and selected\n  cosmological success from deferred thermalization, baryogenesis,\n  curvature, and perturbation-spectrum calculations. The concrete paper\n  witnesses agree with the independent reusable bubble-transition framework.\n- `PhysicsLogic/Papers/Robertson1929.lean`: Hermitian means and rms\n  deviations, the one-particle Schwarz-commutator proof, conjugate-variable\n  specialization, angular-momentum inequality and extremal saturation, and\n  the author's polynomial-operator scope statement. Actual complex `2 x 2`\n  observables and normalized state vectors verify `[X,Y] = 2 i Z`; the same\n  observables produce either a saturated bound of one or a zero bound with\n  dispersions `4/5` and `3/5`. Hermitian `3 x 3` integer-spin generators\n  realize the original `l=1,m=0` and `l=1,m=1` branches, including their\n  component variances, `J^2 = 2`, and exact extremal saturation. Thirty-four\n  inhabited physical boundaries prevent loss of conjugation, normalization,\n  Hermiticity, centered moments, ordered commutators, absolute values,\n  state dependence, angular assumptions, or the distinction between state\n  dispersion and apparatus disturbance. Its adapter constructs an\n  exact shared model, proves semantic retention, and grounds the same shared\n  route while keeping commutator analysis local. Its shared established\n  result is constructed directly from the retained rms, commutator-bound, and\n  product outputs. The terminal general result\n  retains the scoped setup, direct commutator-bound outputs, and the printed\n  real-valued normalized-wavefunction, doubled Schwarz overlap, mean/rms,\n  and `h |C0| / (4 pi)` formulas. The source's bilinear pairing is checked\n  pointwise against the conjugate-first convention. Its two norm factors\n  give `|\u003C[A,B]>|^2 \u003C= 4 (Delta A Delta B)^2`; nonnegative rms values\n  then give the product bound. That inequality is no longer a supplied\n  calculation conclusion. Calibration connects the numerical inequality to\n  the selected product relation. The conjugate\n  branch checkedly substitutes unit coefficient magnitude to obtain\n  `h / (4 pi)`; the angular branch retains `M_z`, `M^2`,\n  the `M_x M_y - M_y M_x = -h M_z / (2 pi i)` action formula,\n  transverse rms squares, `Delta M_z = 0`, the oriented component\n  bound, and `l(l+1) >= m(m+1)`, with `m = l` checked as\n  equality of the reduced relation. All shared endpoint consumers accept the\n  terminal result instead of replaying the Schwarz calculation, and none of\n  these source-specific formulas is promoted into the neutral shared\n  framework. A separate source-sensitive adapter intentionally starts earlier,\n  from the one-particle setup and raw integration-by-parts,\n  Schwarz-commutator calculation, so the terminal result cannot manufacture\n  derivational provenance.\n- `PhysicsLogic/Papers/WittenIndex1982.lean`: proposition-valued index model and\n  the actual `c -> c + 2*pi/L` gauge identification and periodic physical\n  wavefunction, identity-connected Gauss-law/Weyl constraint, terminating\n  `U^p|Omega>` tower, `UV=VU=0`, `V^2 ~ U^r`, exclusion of the cubic\n  invariant by two spinor components, distinct pseudo-invariant `V|Omega>`\n  multiplet, unresolved signed branches, and fixed-theta `(T_z)^N=T` orbit\n  with unit winding and one index contribution from every parallel flux\n  eigenvalue. Its independent physical boundaries also distinguish\n  nonadmissible large-field deformations, missing gauge quotients,\n  incomplete operator algebra, finite-volume limits, and sector sums.\n- `PhysicsLogic/Papers/WittenDynamicalBreaking1981.lean`: global\n  vacuum-energy and the printed `E=f^2` Goldstino current-algebra residue,\n  finite-order nonrenormalization, equations (28)-(31) with both\n  supersymmetric-mechanics supercharges and their actual Pauli axes, the\n  spin-dependent Hamiltonian,\n  an arbitrary growing two-zero superpotential, its integral solution,\n  the source's `W~x^4`/`integral W~x^5` illustration, and the opposite-tail\n  normalizability obstruction. Its\n  `2+1`-dimensional sixth-order scalar potential, Higgs-triplet\n  `SU(2)->U(1)` vacuum, unresolved symmetric vacuum, and monopole pair\n  retain charges `+1/-1`, magnetic flux, the Bianchi-reduced\n  `(2*pi*a/e)*Q`, exact two-zero-mode saturation, undeformed signed\n  cancellation, mixed-species zero modes, and genuine discrete-breaking\n  unequal weights. Twenty-nine\n  physical fidelity boundaries also preserve the four-dimensional zero-mode\n  obstruction, gravitational and technicolor qualifications, and explicit\n  unresolved four-dimensional conclusion.\n- `PhysicsLogic/Papers/Adler1969.lean`: paper-local axial current, Ward\n  identity, loop diagram, regulator prescription, anomalous term,\n  renormalization, neutrino-scattering, massless-symmetry, conserved-generator,\n  and PCAC semantics. Six checked routes distinguish formal field equations\n  from the linearly divergent triangle calculation, physically select the\n  vector-gauge-invariant prescription, derive the vertex and scattering\n  consequences, establish current nonconservation despite gamma-five\n  invariance, and retain the controlled two-photon extrapolation and\n  note-added all-orders qualification. The paper-local value layer retains\n  equation (30) and now also Appendix A equations (A11) and (A22): the\n  formal equation-of-motion sigma-model PCAC divergence and the actual\n  anomaly-modified quantum divergence are distinct selected values. A\n  nonzero electromagnetic anomaly proves their inequality before, and\n  independently of, the controlled two-photon decay approximation; inhabited\n  countermodels also separate vector gauge invariance, the real-photon spin\n  restriction, and heavy-fermion decoupling.\n- `PhysicsLogic/Papers/SeibergDuality1994.lean`: the conjectural magnetic SQCD\n  dictionary, six anomaly checks, conditional conformal-window bound,\n  dual-of-dual test, one-flavor mass deformation, and a grounded qualified\n  assessment that never promotes consistency evidence into a duality proof.\n  Its shared mass-flow adapter now establishes exact selected semantics plus\n  the direct nonvacuous endpoint requiring the selected setup, calculations,\n  outputs, evidence, and nonproof boundary together; the complete route is a\n  checked reconstruction from that output-led result. Its seven directional\n  paper-local countermodels are now value-bearing: `(N_c,N_f)=(3,6)` gives\n  magnetic and second-dual rank three, the proposed charges and six anomaly\n  coefficients `(3,-3/2,3,-10,7/2,-18)`, `D(M)=3/2`, the second-dual\n  F-terms, and a one-flavor condensate `-1` with reduced magnetic rank two.\n  The separate `(3,5)` boundary retains the broken-`SU(2)` instanton\n  coefficient, `Lambda_L^(2N_c-1)=m Lambda^(2N_c-2)`, and the matched\n  confining coefficient; it is not incorrectly left as an open case.\n  Completed checks still do not prove duality or supply grounding. No\n  proposition-pair truth table replaces these magnetic-SQCD distinctions.\n- `PhysicsLogic/Papers/KutasovSchwimmer1995.lean`: the original adjoint-SQCD\n  proposal parsed into adjoint-superpotential, stability, magnetic-dictionary,\n  anomaly, one-flavor mass, polynomial-vacuum, and qualified self-dual routes.\n  Imported SQCD results, expected exact marginality, and unresolved free-field\n  questions remain explicit. Together with Seiberg 1994, only its narrow\n  magnetic mass-deformation consistency route enters the shared framework,\n  including the same direct nonvacuous endpoint. Its six directional\n  paper-local countermodels are now value-bearing: `(k,N_c,N_f)=(2,3,4)`\n  gives magnetic rank five, meson/trace counts `(2,1)`, baryon occupations\n  `(1,2)->(2,3)`, and all six normalized anomaly coefficients; a one-flavor\n  mass has F-term values `(0,-1)`, condensate `-1`, two-color Higgsing, and\n  reduced rank three. The polynomial witness retains four stable vacua out of\n  six magnetic candidates and `det M-B*Btilde=1`; the self-dual witness\n  retains expected marginality but no established fixed point. Completed\n  consistency routes still do not prove duality or supply grounding. No\n  proposition-pair truth table replaces these adjoint-SQCD distinctions.\n- `PhysicsLogic/Papers/Bell1964.lean`: proposition-valued Bell framework and\n  concrete singlet directions, checked derivation and violation of the\n  original inequality, plus checked EPR, exact no-go, robustness, and\n  nonlocality deductions. Bell's first section-III illustration now retains\n  the pure-spin polarization, uniform hidden hemisphere, sign response,\n  zero-weight boundary, spherical-average calculation, rotated-direction\n  calibration, and derived `cos theta` expectation before concluding that a\n  single-spin hidden-variable account exists. Bell's section-II\n  predetermination now requires an actual hidden-state value and two distinct\n  magnet settings, not merely response functions on a possibly empty domain.\n  The candidate model's\n  equation-(1) responses are\n  now explicitly required to realize the outcomes inferred by the EPR route;\n  a countermodel shows that abstract predetermination alone does not localize\n  an unrelated candidate model. Three further inhabited boundaries reject\n  empty hidden-state, empty-setting, and singleton-setting response domains.\n  A composed paper theorem connects the nonvacuous remote-prediction result\n  to the nonvacuous shared local-response result through Bell's explicit\n  EPR and candidate-realization bridges. Its shared deterministic-response\n  adapter now\n  requires an actual local functional representation and establishes generic\n  factorization at every hidden state. The adapter now also distinguishes the\n  response-function calculation from the candidate deterministic completion\n  using it and the separated spin-pair experiment it represents. Dichotomic\n  outcomes and normalization occur in the theory-use bridge, while separation\n  and operational locality occur in the world-representation bridge. A named\n  paper certificate fixes the exact unrestricted and proposed local response\n  functions together with a nonempty hidden-state domain and two distinct\n  settings independently of both bridges; the shared semantics require that\n  setup in model use, representation, and model entailment.\n  At fixed settings, an explicitly supplied hidden-state value also realizes\n  witnessed common-cause support screening; this is not hidden-state-averaged\n  probabilistic independence. The established response directly stores the\n  nontrivial domain, exact and generic factorization, total support, and\n  no-signalling outputs; a theorem reconstructs its complete route. Its\n  exhaustive certificate covers all six shared claims, and the grounded Bell\n  adapter transfers that vocabulary to the candidate theory and represented\n  experiment.\n  Framework countermodels show that determinism and rectangular singleton\n  support alone do not establish Bell locality, and that a completed technical\n  route does not itself supply theory/model/world grounding. A two-field\n  mutation audit rejects changes to either retained response object.\n  The direct response proposition now also requires one actual setting pair\n  and hidden-state value, realizing screening, total support, and\n  possibility-level no-signalling at that same witness. Universal\n  factorization over an empty setting scope is a checked countermodel, while a\n  finite inhabited model makes both response-function fields directly active.\n  Complete factorization outputs over a singleton setting type still cannot\n  establish theory/model/world grounding.\n  Hidden-parameter\n  generality and probability normalization are separate premises. A\n  signed-average countermodel isolates positivity\n  as an essential input to Bell's hidden-state averaging step; a finite-speed\n  countermodel separately shows why spacelike separation is required before\n  remote influence is classified as instantaneous. The final Lorentz route\n  stores the signal's temporal and spatial separation and checks the reversal\n  of causal order under a suitable subluminal boost.\n- `PhysicsLogic/Papers/EPR1935.lean`: the original completeness argument with\n  separate reality and completeness criteria, single-system and\n  separated-system routes, an explicit single-system joint-representation\n  obstruction from which Lean derives the paper's first alternative,\n  conditional remote states, and the concrete position-momentum calculation.\n  Its pp. 779-780 equations (7)-(18) are now retained as a value-level\n  conditional-wavefunction package: two basis expansions of one joint state,\n  continuum momentum and position branches, phase factors, Dirac-delta\n  position localization, selected eigenvalue shifts, and the noncommutator.\n  The Planck constant is strictly positive, and the displayed delta is\n  interpreted operationally by its evaluation action on test functions.\n  The position eigenstate and its remote conditional partner retain their\n  distinct distributional actions, including the printed factor of `h`; the\n  joint continuum state has an explicitly nonzero distributional pairing.\n  The exact state is not square-normalizable, and no finite-resolution\n  regularization is silently supplied. The sum and integral evaluations\n  remain imported mathematics. Independently inhabited countermodels show\n  that all twelve printed equations can still hold for a zero fake delta and\n  zero joint state unless those operational requirements are stated.\n  The actual paper calculation now realizes the shared framework's EPR\n  idealization control directly, with the physical conversion\n  `hbar = h / (2 pi)` rather than identifying the two Planck constants.\n  The remaining route keeps\n  checked wave-function incompleteness, the simultaneous-measurement\n  objection, and the explicitly unconstructed alternative theory. Its remote\n  certainty-and-non-disturbance step realizes\n  the narrow shared framework also used by Bell 1964. The established shared\n  result retains EPR's named exact correlation model, prediction-readout\n  bridge, non-disturbance bridge, and complete selected route, while the\n  completeness reductio remains paper-local.\n- `PhysicsLogic/Papers/Bohm1952.lean`: both original 1952 papers parsed into\n  separate Schrödinger-decomposition, configuration-guidance, one-particle,\n  many-body transition, apparatus measurement, equilibrium, contextual\n  observable, EPR, radiation-field, and completion/scope routes. The module\n  distinguishes the continuity and Hamilton-Jacobi calculations from the\n  added actual-configuration and guidance postulates; proves only\n  equivariance from the shared flow while retaining general relaxation as an\n  author expectation; derives effective packet selection without fundamental\n  collapse; and realizes supplemented deterministic completion and\n  predictive-versus-ontic probability through the mature philosophy and\n  paradigm layers. Its selected electron gives the universal completion law\n  a concrete governed-system witness; an empty-system countermodel blocks a\n  vacuous completion. Its certified source routes additionally retain\n  `p = grad S`, `v = grad S / m`, stationary zero particle motion\n  with positive total energy and balanced classical/quantum forces, one\n  actually occupied apparatus packet with two squared-amplitude Born\n  weights, distinct apparatus-hidden-variable distributions, and EPR\n  correlations with changed remote motion but unchanged operational\n  marginal. Twenty-five physical fidelity boundaries block the corresponding\n  invalid substitutions. The polar formulas now use actual coordinate fields\n  and derive the local Born current from the source certificate; a nodal-wave\n  boundary prevents upgrading a conserved density to a node-free polar chart.\n  The equilibrium certificate now retains almost-everywhere trajectories of\n  the very map used for Born transport: actual derivatives equal the current\n  divided by positive density, with initial values and calibrated coordinates\n  and clock. A normalized endpoint-only loop fails this guidance condition.\n  Normalization, existence of regular flow, and common measure pushforwards\n  remain separate explicit analytic inputs; global existence is not claimed.\n  The deterministic-motion route now also derives actual coordinate continuity\n  and uniqueness on a regular interval from the guidance ODE and an explicit\n  uniform spatial Lipschitz bound. Selected-state evolution is identified with\n  all such trajectories, and state decoding recovers their actual configurations.\n  Its universal determinism premise remains separate from this interval result.\n  Its explicitly nonlocal configuration-space dynamics is\n  not mapped to the shared deterministic-local-response framework. Comparison\n  with Dürr-Goldstein-Zanghì 1992 earns only the narrow guided-density\n  equivariance component. That component retains both density maps and the\n  common guided-evolution relation in a named exact model. Its established\n  result is defined by the direct initial-agreement, common-evolution, and\n  later-agreement endpoint. The two paper adapters ground the selected\n  pre-output setup without using propagation, later agreement, or the\n  completed technical route, and transfer all nine shared claims only after\n  the separate route and grounding certificates are combined. Each of\n  the five selected physical indices now changes the direct nonvacuous\n  equivariance proposition, as does each of the three retained semantic\n  families. Bohm's wave density is computed through `densityOfWave`, and\n  both adapters bind common evolution to their exact wave, ensemble, times,\n  and regime.\n  The original Durr-Goldstein-Zanghi author TeX and PDF now also ground the\n  paper-local equations (3.8)-(3.18) at the actual value level:\n  `v_k = (hbar / m_k) Im(grad_k psi / psi)`, `rho = |psi|^2`, both printed\n  complex-current forms, ensemble continuity, and the exact current-flux\n  substitution. Equations (5.17)-(5.19) retain the occupied disjoint\n  environment branch and `psi_Y(x) = Psi(x,Y)`, while equation (6.1) keeps\n  normalized conditional Born probabilities distinct from an actual unique\n  configuration and ontic chance. Physical witnesses realize traveling,\n  time-reversed, and stationary waves, exact `(9/25,16/25)` conditional\n  probabilities, environment selection, and wave-rescaling invariance.\n  Sixteen inhabited fidelity boundaries exclude wrong mass/current/Born\n  formulas, zero-wave nodes, missing flux substitution, incorrect environment\n  conditioning, overlapping branches, autonomous conditional evolution, and\n  multiple actual configurations. None of this paper-specific physics is\n  inserted into the shared guided-density framework.\n- `PhysicsLogic/Papers/GRW1986.lean`: the original objective-localization\n  model parsed into separate random individual-process, deterministic\n  ensemble master-equation, free-particle suppression, selective trajectory,\n  constituent amplification, rigid-body, parameter-calibration, scoped\n  measurement, energy-increase, phase-space diffusion, and limitation\n  routes. Free, trajectory, constituent, rigid-body, and energy routes keep\n  independent local setups, including the necessary master-equation physics.\n  Calibration consumes the free, trajectory, amplification, and rigid results;\n  measurement consumes amplification and calibration, while phase space uses\n  the free result. These are certificate dependencies, distinct from the\n  physical assumptions within each local setup. Its amplification calculation\n  also requires the sourced\n  macroscopically distinct pointer-branch pair and one-localization\n  coherence-destruction premise before it can conclude selected branch\n  decorrelation; the shared Zeh/GRW adapter reconstructs and replays that\n  local setup. The parameter route also realizes the neutral unification\n  contract: one GRW dynamics acts on microscopic constituents and the derived\n  macroscopic center of mass, while one admissible parameter choice yields\n  practical microscopic agreement and rapid, time-scoped macroscopic\n  classical behavior. Its phase-space route also realizes exactness-aware\n  recovery: retained stochastic diffusion prevents the approximate\n  phase-space description from becoming exact deterministic classical\n  mechanics. The module realizes the mature\n  objective-stochastic-localization paradigm while distinguishing\n  statistical-mixture formation from the additional definite-pointer bridge.\n  The selected apparatus and pointer record make universal dynamics and\n  macroscopic definiteness nonvacuous; an empty-scope model satisfies only the\n  weaker law package.\n  Comparison with Bohm 1952 does not earn a shared technical measurement\n  framework because the two papers use physically different\n  outcome-selection mechanisms.\n  The original selective operation (2.7) now restricts the same Gaussian\n  integral to a result region, and (2.8) computes its weight from the kernel's\n  coordinate trace. Complementary regions recover the nonselective map.\n  Positive-weight conditioning has unit trace; a half-weight subensemble\n  and a zero-probability selection cannot be passed off as normalized states.\n  Positivity and trace-class operator interpretation are not inferred from\n  unit trace, and no actual individual record follows from this bookkeeping.\n  Equation (3.3) now uses the squared norm of the actual nonselective kernel,\n  with a positive normalized density expansion and physical endpoint states.\n  Trace-square differentiation and Hamiltonian trace cyclicity are separate\n  mathematical inputs; strict Gaussian purity loss and final mixedness are\n  derived. Mixedness is not called a proper stochastic ensemble or an actual\n  outcome. The finite diagnostics also compute purity and coherence from\n  positive density matrices: a mixed state can retain coherence 1/4 and have\n  purity 5/8. Unit trace supplies neither purity nor positivity. These matrix\n  controls also exhibit different pure-preparation supports with the same\n  mixed density. They are not solutions of the continuous GRW evolution.\n  The trajectory route now retains the forward selective equation (5.1),\n  actual trace loss (5.2), and the common finite-window Gaussian estimate\n  (5.3). It derives the exponential survival bound and long-time extinction,\n  with survival probability computed from a measure on ordered real jump\n  times and localization centers. Actual Hamiltonian conjugation and Gaussian\n  jumps determine each branch kernel. The history law is weighted by that\n  branch's trace; normalization, positivity/regularity, Poisson counts,\n  projectivity, and selected-kernel representation remain explicit mathematics.\n  The probability-to-trace equality is then derived by integral interchange.\n  A positive no-test probability gives a lower survival bound, and three\n  concrete history controls separate counts, test-time survival, and continuous\n  confinement. Full continuous stochastic existence is not proved.\n  Practical accuracy is an independent approximation input: a\n  near-one upper bound does not prove high survival. The fixed-diffusion\n  infinite-frequency limit and the nonselective full-region control remain\n  distinct, and an expected localization count is not a realized count.\n  Its directional paper-local countermodels are value-bearing.\n  They retain `N=100`, elementary rate one and amplified rate 100, branch\n  separation two against localization distance one, the coordinate damping\n  exponent `-4`, localized kernel `exp(-4)` for input kernel one, and the\n  reduced evolution relation\n  `density derivative=-(1-exp(-4))=Hamiltonian term 0+localization term -(1-exp(-4))`\n  with zero residual. Finite Gaussian localization suppresses a nonzero\n  coordinate kernel but cannot erase it exactly. A separate exact-erasure\n  control satisfies the algebraic master term but violates equation (2.10).\n  These numbers are illustrative test values, not the paper's calibration.\n  The named-equation converse keeps a valid reduced evolution\n  relation while withholding the printed localization formulas. Spontaneous\n  localization requires stochastic outcomes and the printed formulas; the\n  complete witness has equal mixture weights, energy-increase rate one from\n  `hbar^2 lambda alpha/(4m)`, internal spread `1/2` against localization\n  distance one, and exactly one realized pointer record. Rate\n  addition without differently located constituents blocks branch\n  decorrelation; a center-of-mass-localized but internally broad body blocks\n  rigid protection; and a definite pointer leaves the exhaustive measurement\n  residual nonzero. No proposition-pair, status-enum, or `Unit`-carrier truth\n  table replaces these GRW distinctions.\n- `PhysicsLogic/Papers/Wilson1974.lean`: paper-local link, plaquette, loop,\n  surface, quark-path, transfer-matrix, coupling-regime, and continuum-limit\n  semantics. The finite-gauge route now retains selected equation-(3.4),\n  equation-(3.6), and equation-(3.8) link/angle/plaquette values with explicit\n  site, boundary-link, configuration, and finite-gauge-coupling relations.\n  Its nine directional paper-local countermodels are now value-bearing: the\n  selected gauge pair has zero orbit residual while equation (3.4) fails, the\n  compact angular link and plaquette action with phase one respectively\n  withhold equations (3.6) and (3.8), and the tiled-area witness retains\n  `A/a^2=4` against leading power three. The normalized isolated loop is\n  `1/2`, while a unit-separation vacuum loop shields area four down to one;\n  hopping and vacuum-loop weights one withhold the no-free-quark inference.\n  Positive strong tension, zero weak tension, and an uncontrolled mean-field\n  jump do not establish transition order, and nonzero scaling, Euclidean,\n  and Lorentz residuals withhold continuum confinement. No proposition-pair\n  or finite-gauge status truth table replaces these Wilson distinctions.\n  Exact finite-spacing gauge invariance is separated from the\n  representative-to-physical interpretation bridge; the strong-coupling\n  plaquette expansion is separated from the area-law-to-confinement bridge;\n  and the regulated no-free-quark result is not promoted to continuum QCD,\n  restored Lorentz invariance, or continuum string equivalence. Together with\n  Creutz 1980, it exposes a complete finite-regulator gauge-route\n  applicability theorem. Its shared gauge adapters reconstruct the local\n  lattice setup from the shared finite-regulator setup, then apply the retained\n  compact-integration bridge to the calculated action and loop invariance\n  proofs; no-gauge-fixing is not a cached sibling output. Its strong-coupling\n  setup also realizes a complete\n  shared loop-area setup and applicability theorem before deriving the narrow\n  inference from a calculated area law through a linear-potential bridge to\n  regime-scoped confinement. That complete route now also proves the direct\n  nonvacuous shared loop-area proposition and the stronger finite-gauge-\n  supported endpoint at Wilson's named model. It separately realizes the\n  shared structural explanation only after the spanning-surface calculation\n  and binding interpretation are both present; the lattice construction and\n  strong-coupling calculation remain paper-local.\n- `PhysicsLogic/Papers/Creutz1980.lean`: paper-local pure SU(2) lattice\n  construction, heat-bath Boltzmann update, independent-start and\n  finite-size checks, Wilson-loop fit, confinement-based scale setting, and\n  qualified asymptotic-freedom comparison. The numerical reliability route is\n  required before the fitted area law is used, and neither perturbative\n  scaling agreement nor absence of an observed transition is promoted to a\n  continuum proof. Its regulated gauge inputs separately establish the\n  complete shared gauge-route applicability proposition. The shared gauge\n  adapters rebuild Creutz's local SU(2) setup from shared finite-regulator\n  input and apply the invariant-group bridge to the calculated action and loop\n  invariance proofs. Its loop-fit route\n  separately exposes the full selected loop/surface/source/tension setup and\n  shared applicability proposition. It independently realizes the narrow\n  shared loop-area confinement inference and proves the direct nonvacuous\n  shared proposition and stronger finite-gauge-supported endpoint at Creutz's\n  named finite-cutoff model. Its fitted area law and separate potential and\n  confinement interpretations also realize the structural-explanation\n  endpoint. The paper-local fit now retains\n  `ln W(C) = -K A(C) + O(P(C))`, its lattice-unit rewrite,\n  `W(S) = exp[-(A + B S + C S^2)]`, and `C = a^2 K`; these displayed\n  formulas do not widen the shared loop-area contract. Its\n  equilibrium-sampling provenance theorem separately retains\n  the p. 2309 conditional entire-group single-link heat bath, detailed\n  balance, accessibility, equilibration, and interpretation instead of\n  inferring that route from the common sampling endpoint. Its algorithm,\n  fitting procedure, and evidential conclusion remain local.\n- `PhysicsLogic/Papers/Stanley1968.lean`: paper-local spherical and\n  finite-component vector-spin models, normalized-partition reduction,\n  stationary-point and normalization calculations with a distinct finite\n  site-count index, equation-(24)'s explicit\n  `-beta psi_infty = -1/2 - 1/2 ln(2K) + F/N + remainder` accounting with its\n  separately vanishing normalized-log remainder, a noncritical free-energy\n  limit, ten-term free-energy and susceptibility support, an exact\n  linear-chain check, a qualified\n  `m`-spherical heuristic, and the appendix's unresolved critical-index order\n  of limits. It realizes the neutral large-parameter paradigm without\n  importing gauge-theory coupling or diagram topology. The linear-chain route\n  now retains equation (28)'s finite-spin Gamma/Bessel formula and equation\n  (29)'s limiting square-root/log free energy, explicitly identified with the\n  selected spherical free energy, in its checked endpoint. Its\n  paper-local countermodel theorems retain actual scope and value data:\n  a one-dimensional Bessel witness with nonzero two- and three-dimensional\n  residuals, tenth-order free-energy/susceptibility agreement with an\n  eleventh-order departure, actual uniformly convergent free energies with\n  unequal critical indices, a stable family with uniform free-energy and\n  entropy convergence but no specific-heat transport, and a converged\n  noncritical free energy with vanishing remainder but failed equation-(24)\n  stationary accounting.\n- `PhysicsLogic/Papers/THooft1974.lean`: paper-local color-index surfaces,\n  the journal-p. 465 chain\n  `r = g^(V3 + 2 V4) N^I`, `F = L + I`,\n  `2 P = 3 V3 + 4 V4`, `V = V3 + V4`,\n  `r = g^(2 P - 2 V) N^(F - L)`,\n  `F - P + V = 2 - 2 H`, and\n  `r = (g^2 N)^(V3 / 2 + V4) N^(2 - 2 H - L)`,\n  with the pointwise `g^2 N` identity kept separate from the\n  large-rank/small-bare-coupling trajectory, Euler-characteristic rank\n  exponents, fixed-rescaled-coupling trajectory retained in the specialized\n  asymptotic-organization conclusion, planar one-boundary dominance,\n  conditional dual-string comparison,\n  light-cone block representation, planar Hamiltonian reconstruction, and\n  unresolved discrete-spectrum binding criterion. It realizes the mature\n  large-rank paradigm and, with Witten 1979, the narrow shared planar-diagram\n  route with actual nonplanar and additional-boundary correction witnesses.\n  Checked specializations retain the planar one-boundary rank power and\n  fixed-rescaled-coupling rewrite; a separate checked theorem reconnects that\n  pointwise rewrite to the fixed trajectory only when both hypotheses are\n  supplied, while a finite countermodel prevents\n  equations (3.2), (3.4), (3.5), and (3.7) from manufacturing equation (3.6)\n  without the vertex/dot count in equation (3.3). Its five directional\n  paper-local countermodels are now value-bearing: the rank-four witness\n  keeps `g^2 N=1`, the exponents `(1,0,-1)` for planar one-boundary,\n  extra-boundary, and one-handle diagrams, and the corresponding relative\n  corrections `(1/4,1/16)`. A planar two-boundary diagram has exponent zero\n  and is not leading; the topological string analogy retains a mesh but no\n  continuum bridge, and the planar Hamiltonian retains continuous free\n  spectrum but no established discrete interacting spectrum. The finite-rank\n  witness gives `N=3` and `1+1/3+1/9=13/9`, so leading order is not exact.\n  No proposition-pair truth table replaces these planar-gauge distinctions.\n  That shared framework now projects its fixed-coupling nonplanar sector back\n  into the mature large-rank paradigm only after explicit varying-family and\n  planarity-classification premises. Constant-family and overlapping\n  planar/nonplanar countermodels prevent a technical selection from\n  masquerading as nonvacuous topological organization.\n- `PhysicsLogic/Papers/SeibergWitten1994.lean`: concrete electromagnetic\n  charge vectors and Dirac pairing; exact BPS charge-period logic; conditional\n  singularity and monodromy reconstruction with three pairwise-distinct named\n  singularities and explicit exclusion of additional selected singularities;\n  effective-theta/Witten-charge\n  preservation under the `T^{-2}` relabeling and the separate `P T^{-2}`\n  infinity-matrix factorization; the elliptic curve, differential, and period\n  solution; checked monopole-vacuum equations; and explicit\n  condensation-to-Higgs-to-gap-to-confinement reasoning. The infrared\n  monopole is connected to a finite-energy semiclassical gauge-Higgs soliton\n  with degree-one asymptotic Higgs winding and nonzero quantized flux, while\n  the real-axis continuation now retains path connection, real electric\n  periods, imaginary magnetic periods, and nonreal period ratios before its\n  no-jump conclusion; wall crossing remains an explicit scope limitation.\n  This independent active client now realizes the shared charge and\n  discrete-vacuum frameworks.\n- `PhysicsLogic/Papers/GeneralizedGlobalSymmetries2014.lean`: paper-local\n  higher-form defect, charged-operator, Maxwell-current, background-field,\n  loop-order-parameter, infrared-no-order, and photon-spectrum semantics.\n  Six checked routes\n  derive positive-form Abelianity from continuous defect-exchange witnesses\n  and faithful fusion, plus linking action, a compact-spacetime\n  selection rule, electric and magnetic Maxwell one-form symmetries, their\n  mixed anomaly, and the photon as a Goldstone mode of both broken\n  symmetries. The sixth route captures the generalized\n  Coleman-Mermin-Wagner argument: continuous `d-q\u003C3` or discrete `d-q\u003C2`\n  scope, a charged order parameter, divergent infrared potential, and the\n  source's `exp(-V)` expectation law yield a checked zero-expectation limit\n  and an unbroken symmetry. Countermodels retain the dimension, form degree,\n  potential, expectation, breaking, and other-order values, separating low\n  dimension from actual divergence, divergence from suppression without the\n  loop law, and selected no-order from absence of other transitions. The\n  Maxwell line operators realize the shared charge framework,\n  while the final spectral conclusion realizes the shared broken-symmetry\n  spectrum framework with separate theory/model/world grounding for the\n  electric and magnetic current sectors and paired exhaustive certificates.\n- `PhysicsLogic/Papers/MerminWagner1966.lean`: the original magnetic\n  no-order argument with value-bearing spin, exchange, Brillouin-zone,\n  field, magnetization, and susceptibility semantics. Two checked routes\n  separate the Bogoliubov/operator estimate, finite mode and denominator\n  bounds, uniform equation-(11) family, thermodynamic equation-(12) transfer,\n  logarithmic two-dimensional and arctangent one-dimensional infrared bounds,\n  distinct small-field scalings, and post-thermodynamic spontaneous limit\n  from the source's finite-second-moment qualification, precise axial\n  anisotropic exception, open nonmagnetic transitions and susceptibility,\n  and distinct crystalline and classical comparisons. Countermodels block\n  finite-zero-to-thermodynamic inference, generic-anisotropy extrapolation,\n  and promotion of magnetic no-order to absence of every order channel.\n  The magnetic route now realizes the shared infrared-order-suppression\n  framework using its actual post-thermodynamic small-field limit and an\n  explicit spontaneous-breaking bridge.\n- `PhysicsLogic/Papers/KosterlitzThouless1973.lean`: the original\n  finite-core, dilute neutral-vortex and iterated-dielectric argument, with\n  fifteen source claims and five checked routes for microscopic setup,\n  original screening/phase classification, factorized conventional-order\n  suppression, solid and material-dependent scope qualifications, and\n  winding-barrier metastability. It distinguishes original equation (19)\n  from the rescaled equation (21), proves the solid's `L` versus `sqrt(L*r)`\n  contour scalings, excludes charged-superfluid protection through its\n  finite-energy vortex free energy, and explicitly contracts Heisenberg\n  winding through the third spin component. Eighteen inhabited fidelity\n  boundaries retain these exclusions, separate shell density,\n  polarizability, dielectric response, and renormalized binding. Its\n  microscopic route retains integer phase winding and local irrotationality\n  away from vortex cores; its metastability route derives thermodynamic\n  protection from the positive logarithmic vortex-pair barrier rather than\n  assuming divergence. It does not substitute a later BKT recursion.\n- `PhysicsLogic/Papers/Maldacena1997.lean`: D3 stack dimension, charge and\n  five-form flux; explicit four-dimensional `N = 4` `U(N)` worldvolume data\n  with six real adjoint scalars at the superconformal point; explicit\n  `alpha' -> 0` scaling with distinct bulk-radial and inter-brane separation\n  data; fixed stretched-string and Higgs scales followed by an independent\n  coincident-brane conformal specialization; the full equation-(2.2) D3\n  metric with positive-radial scope, physical harmonic readout, and separate\n  worldvolume, radial, and sphere warp coefficients; checked disappearance\n  of its constant term only after that formula is supplied; radius and explicit\n  `AdS_5 x S^5` near-horizon metric coefficients; proper-energy redshift\n  equations; fixed positive near-extremal worldvolume energy density, the\n  displayed `U_0^4 = (2^7/3) pi^4 g^2 mu` relation, the separate fixed-`U_0`\n  limit input, a checked finite-horizon deduction, and an explicit\n  finite-temperature premise before Hawking flux;\n  boundary data; and compositionally checked sector, duality, calculational,\n  and interpretive routes. Its local supergravity result now separately\n  realizes prediction-grounded classical recovery: a controlled singleton\n  observable approximation is not treated as classical until the proper-energy\n  window, local calculation, and correctness bridge supply the behavior.\n- `PhysicsLogic/Papers/GubserKlebanovPolyakov1998.lean`: point-indexed\n  boundary source/operator coupling and its exponentiated CFT expectation;\n  admissible bulk extension and proposed on-shell functional dictionary;\n  controlled leading-large-`N` correlator transfer; asymptotic conformal\n  symmetry; massless scalar, graviton, higher-partial-wave, and massive-string\n  dimension routes; and separately retained expectations, deferrals, regime\n  limits, and open leg-factor obligations. Its inhabited variation-sector\n  approximation now also realizes prediction-grounded classical recovery only\n  through the separate leading-large-`N` classical-supergravity reading.\n- `PhysicsLogic/Papers/WittenHolography1998.lean`: Witten's original\n  source-indexed CFT/bulk generating-functional proposal, controlled\n  classical-saddle correlator prescription, general massive-scalar\n  mass-dimension route, three protected Kaluza-Klein spectrum families,\n  spin-structure-sensitive Hawking-Page transition, and conditional\n  Hamiltonian state/operator extension. The proposal, controlled\n  approximation, imported calculations, quantitative evidence, and\n  additional Hamiltonian assumptions remain logically distinct. Its thermal\n  branch now retains the original section-3.2 `beta(r_+)` and\n  `I(X_2)-I(X_1)` formulas as selected scalar readouts; Lean\n  checks their small/large-radius signs before the action crossing enters the\n  spin-selected saddle route.\n- `PhysicsLogic/Papers/AMPS2012.lean`: complementarity postulates with\n  physical content, including a unitary black-hole S-matrix, exterior\n  semiclassical equations, `dim H_M = exp(S(M))`, and quantitative no drama;\n  entropy data, explicit `B(omega)`/`C(omega)` Bogoliubov kernels whose\n  creation strength is evaluated from the stored `C(omega)` itself,\n  operational infalling-vacuum annihilation conditions, transmission,\n  creation-norm and eigenstate-defect data; separate projection,\n  prediction, measurement-performance, and number-state propositions; a\n  countermodel excluding prediction-to-state conflation; distinct ordinary\n  low and mined high modes; distinct Page-time and scrambling-extension ages;\n  mining premises, scrambling expectation, and compositionally checked\n  incompatibility, extension, and resolution deductions.\n- `PhysicsLogic/Papers/Jarzynski1997.lean`: paper-local switching protocols,\n  trajectory work, Hamiltonian and density data, partition functions, and\n  ensemble averages. The isolated route selects the initial point on the\n  unique trajectory through each final phase point, uses that same\n  final-to-initial correspondence in Liouville transport and work-energy\n  balance, checks the pointwise Boltzmann cancellation, and derives the\n  partition ratio from explicit integral obligations; an exact full-reservoir\n  route repeats the checked correspondence and derivation in the combined\n  phase space. Full-ratio endpoint invariance yields path/rate independence\n  before a dependent quasistatic-reference route derives the central law;\n  direct weak-coupling partition reduction depends only on the exact\n  full-ratio route, not the quasistatic transfer. The\n  limiting identities are checked separately. The Jensen route is stated on\n  the actual trajectory-work ensemble and must consume the explicit\n  mean-work definition before deriving the average-work bound. The\n  Gaussian cumulant calculation yields an exponential-average formula that\n  must be combined with the certified Jarzynski equality; countermodels\n  delimit trajectory-level, mean-label, and free-energy-identification\n  overclaims. Proof-free numerical countermodels retain selected initial and\n  final phase points, forward flow, inverse selection, transported densities,\n  thermal versus interaction energy, reservoir degrees, and the canonical\n  marginal residual; equal endpoint densities do not select an inverse\n  trajectory, weak coupling does not make a small reservoir canonical, and a\n  large reservoir alone does not establish canonical system sampling.\n- `PhysicsLogic/Papers/Onsager1931.lean`: paper-local coupled-process,\n  chemical-transition, anisotropic-crystal, fluctuation-regression,\n  dissipation, stationary-flow, magnetic-field, and approximation-regime\n  semantics. It proves the Part I reciprocal heat-conduction conclusion only\n  from explicit regression, correlation, and coefficient-identification\n  calculations. The fluctuation branch now also retains equations\n  (4.3)-(4.10) as a represented real-valued readout and checks that its\n  opposite-sign delayed correlations plus microscopic-reversal symmetry force\n  `omega_3 = 0`; an explicit countermodel keeps (4.3)-(4.9) with nonzero\n  `omega_3` while denying (4.10). Countermodels separate entropy positivity from reciprocity,\n  equilibrium from detailed balance, microscopic reversibility from its\n  macroscopic bridge, zero-field from magnetic same-field reciprocity, and\n  the anisotropic result from the deferred general transport theorem. With\n  Casimir 1945 it realizes the narrow shared reciprocal-transport inference.\n  The source-sensitive structural layer now retains this as Onsager's\n  reversal-fixed zero-field heat/fluctuation route, distinct from Casimir's\n  parity- and field-paired route with an independently assessed regression\n  hypothesis. A completed reciprocal relation and ordinary structural\n  explanation cannot reconstruct either source token.\n- `PhysicsLogic/Papers/Casimir1945.lean`: paper-local equilibrium fluctuation\n  statistics, velocity-parity and magnetic-field reversal, the explicitly\n  independent ensemble-regression hypothesis, thermomolecular pressure,\n  heat-current representative ambiguity, electrical four-poles, resistance,\n  and Hall parity. Its general reciprocity result now retains Casimir's\n  selected equations (18a)-(18c) and `(18 prime)` as value-level even-even,\n  odd-odd, and mixed-parity coefficient equalities; zero-field equalities use\n  an explicit `reverseField zeroField = zeroField` premise, and a reduced\n  countermodel rejects name-only reciprocity. Its zero- and magnetic-field\n  adapters construct distinct exact selected contexts; Onsager's\n  independently checked heat adapter, each construct the complete shared\n  reciprocal-transport applicability proposition before deriving a\n  coefficient relation. Its thirty-three inhabited Casimir transport\n  boundaries retain `Delta S=-3`, Gaussian covariance values `1/2` and\n  `1/4`, an independent `1\u003C2\u003C10` regression window, zero instantaneous\n  derivative with nonzero lagged displacement, `Q_small=8`, `Q_large=10`,\n  Knudsen pressure values `3` and `6`, and\n  `R_12(+H)=2=R_21(-H)` with field-odd Hall values `+1` and `-1`.\n  Virtual entropy cancellation does not eliminate irreversible entropy\n  production. Broader linear-response machinery remains paper-local or\n  unformalized.\n- `PhysicsLogic/Papers/LeeYang1952.lean`: the paired original partition-zero\n  papers, with finite positive-coefficient partition polynomials separated\n  from the thermodynamic limit; zero-free analyticity separated from its\n  single-phase interpretation; nonvacuous zero accumulation separated from\n  both a possibly vacuous universal neighborhood law and the physical\n  singularity bridge; and the Ising/lattice-gas dictionary, circle theorem,\n  one-dimensional root gap, two-dimensional exact transition, and unresolved\n  finite-field/root-distribution scope represented as distinct checked\n  routes. It exercises `Paradigm/ThermodynamicLimit.lean` but does not by\n  itself earn a shared partition-zero or phase-transition framework. Together\n  with BBCKK 2004, it now realizes the narrower shared\n  `Framework/PartitionZeroPhaseBoundary.lean` result. That established result\n  stores the actual finite-family, boundary, accumulation, and singularity\n  outputs; its full implication route is reconstructed by theorem. The p. 406\n  transition adapter reaches it only after an actual selected transition is\n  supplied; conditional zero localization alone does not create one. Its finite-volume setup also\n  requires an actual finite-size witness, so an empty size family cannot make\n  the universal finite-stage claims vacuous. Its theory/model/world\n  grounding uses only the selected finite family, finite pressure and density\n  definition, regularity, and explicit interpretation bridges; it does not\n  assume zero accumulation, singularity, or a phase boundary.\n  A separate one-way ordinary structural-explanation route stops before the\n  converse singularity-to-boundary bridge: the actual transition and finite\n  regular family explain accumulated zeros and the singular limit. A stronger\n  source-sensitive route adds the typed Lee-Yang localization derivation and\n  reconstructs raw applicability from it. A completed correspondence plus\n  ordinary explanation with the derivation relation set false cannot recover\n  the source-sensitive explanation.\n- `PhysicsLogic/Papers/BiskupBorgsChayesKotecky2004.lean`: the original\n  Pirogov-Sinai paper on first-order partition-function zeros. It keeps\n  Assumption C, contour representation, cluster expansion, metastable free\n  energies, distinguishable Gibbs phases, the periodic torus phase sum, and\n  the imported preceding zero theorem as separate propositions and routes.\n  Theorem B retains its actual `L >= L_0` threshold, `kappa = tau / 4`,\n  phase-subset-dependent `U_{kappa/L}(Q)` region, exclusion of the closed\n  half-width regions for competing phases, analyticity on the larger complex\n  domain, nonzero analytic finite metastable weights, their distinct\n  `exp(-tau L/8)` logarithmic and derivative corrections,\n  `(ell!)^2 M_0^ell` normalized derivative bounds,\n  `alpha - 2 exp(-tau/2)` overlap nondegeneracy, and the original\n  `ell! (C_0 L^d)^(ell+1) zeta(z)^(L^d) (sum q_m) exp(-tau L/16)`\n  remainder bound. The unrestricted regular finite family at physical\n  controls comes from the finite lattice model, not from applying the\n  restricted complex phase-sum theorem to every torus or control.\n  Standard Ising, perturbed Ising, and Blume-Capel consequences consume the\n  general zero-control result explicitly. With Lee-Yang it earns only the\n  finite-family, zero-accumulation, limiting-singularity, and physical\n  phase-boundary correspondence; all contour and model-specific machinery\n  remains paper-local. Its direct shared-result adapter combines the actual\n  physical-coexistence boundary on pp. 109-110 with the zero route on\n  pp. 112-115; the controlled phase sum alone still does not create a\n  boundary. Its ordinary explanation uses the one-way route and actual\n  boundary; a stronger typed source derivation combines the controlled phase\n  sum, distinguishable-phase coexistence, physical boundary, and imported\n  zero-location control to reconstruct that route and source-sensitively\n  explain accumulation and singularity without consuming the converse\n  physical bridge. Its selected finite size\n  supplies the shared nonempty-family premise. Its paper-local\n  `FinitePartitionFamilySetup` supplies shared\n  grounding with finite partition definition and regularity, not the\n  controlled torus phase sum or the subsequent zero-location calculation.\n  Seven additional inhabited boundaries reject a below-threshold phase sum,\n  an ambient complex domain without the required phase-subset exclusion, an\n  incorrect `kappa/L` width, thermodynamic regularity inferred from a\n  complex phase sum, nonzero finite phase weights inferred from partition\n  analyticity, the identification of the `1/8` and `1/16` suppression\n  exponents, and overlap nondegeneracy inferred from a single-phase\n  derivative bound.\n- `PhysicsLogic/Papers/LiuSinclairSrivastava2018.lean`: the original\n  correlation-decay route to a Fisher-zero-free complex neighborhood for the\n  bounded-degree zero-field Ising model. It separates the imported regular-tree\n  uniqueness theorem, real contraction calculation, complex invariant-domain\n  construction, Weitz self-avoiding-walk recurrence, pinned-spin induction,\n  final cancellation exclusion, and external deterministic-approximation\n  bridge. Its finite pinned-graph induction explicitly realizes the base,\n  step, selected-model-data, and route-applicability semantics of the narrow\n  shared `Framework/FinitePartitionNonvanishing.lean` interface. It now\n  exposes the output-led established shared result before the\n  Fisher-zero theorem projects uniform nonvanishing. The framework imports\n  `Paradigm/ThermodynamicLimit.lean`, but reaches finite-description\n  regularity only through a separately supplied size-family scope and\n  interpretation bridge; neither finite regularity nor nonvanishing implies\n  regularity of the limiting description. Its finite induction model now\n  retains the exact bounded-degree pinned-graph class, complex-neighborhood\n  interaction domain, unpinned-vertex complexity, and pinned-partition\n  relation selected by the source. It is grounded separately in the\n  zero-field Ising theory and represented finite Ising graph family for each\n  nearby interaction and explicit zero-unpinned base graph. Grounding remains\n  independent of the nonzero base calculation and induction step, with\n  exhaustive realization and transfer certificates for all eight shared\n  finite claims. The same witness\n  projects the established induction to the direct nonvacuous endpoint.\n- `PhysicsLogic/Papers/PetersRegts2017.lean`: the original hard-core\n  occupation-ratio proof of the strong univariate Sokal conjecture. It\n  separates the elementary angle theorem, regular-tree rational dynamics,\n  parabolic optimality input, double-log coordinate, uniform real\n  contraction, complex invariant domain, unequal-input convex reduction,\n  vertex-subset induction, final-root cancellation argument, univariate\n  exhaustion, external interpolation consequence, and the appendix\n  counterexample to a literal multivariate product domain. Its empty-graph\n  base and vertex-subset step explicitly realize the same shared route\n  contract as Liu-Sinclair-Srivastava. It likewise exposes the established\n  shared result before the multivariate tube theorem projects uniform\n  nonvanishing; both papers keep their correlation, recurrence, and domain\n  physics local. Its finite induction model is grounded separately in the\n  hard-core theory and represented finite hard-core graph family using an\n  explicit vertex-count-zero graph in the selected tube. The model\n  exactly retains the bounded-degree graph class, graph-indexed complex-tube\n  assignment domain, vertex-count complexity, and multivariate partition\n  relation at the selected assignment. Grounding is independent of the\n  empty-graph nonvanishing calculation and vertex-subset step. The paper\n  adapter exposes exhaustive realization and grounded transfer certificates\n  for all eight shared finite claims once an explicit vertex-count-zero graph\n  in the selected tube is supplied, and it projects the route to the direct\n  nonvacuous endpoint.\n- `PhysicsLogic/Papers/EinsteinBrownian1905.lean`: the original molecular-\n  kinetic Brownian-motion argument, with independent osmotic-pressure and\n  transition-law routes joined only when the diffusion coefficient is\n  eliminated to recover the molecular count. Its first route explicitly\n  retains the contrast between the classical no-wall-force prediction and\n  molecular-statistical osmotic pressure. Its original equations (1) and (2)\n  now genuinely determine the following unnumbered diffusion-coefficient\n  display by cancelling an explicitly nonzero concentration gradient; a\n  uniform force-free equilibrium satisfies both equations without determining\n  that coefficient. The formalization keeps external Stokes transport,\n  continuum reduction, point-source solution, and numerical calculations\n  explicit, derives actual Gaussian moments and interval probabilities, and\n  preserves Einstein's unresolved identification of the\n  prediction with observed Brownian motion. Its shared stochastic model is\n  grounded from Einstein's inhabited mesoscopic symmetric-step setup in\n  molecular-kinetic theory and the selected suspended-particle process before\n  the Taylor and point-source calculations transfer diffusion claims. Its\n  selected-data theorem retains Einstein's symmetric displacement law,\n  independent-step control, coefficient-dependent moment laws, and diffusion-\n  equation transport predicate in the shared model. Its source-sensitive\n  diffusion/thermal-drag composition additionally exposes the original\n  transition and Gaussian formulas, both force/flux balances, and exact\n  inverse-Stokes diffusion coefficient through an independent joining source.\n  Its predictive route retains disjoint measured intervals and actual\n  history-event probabilities. Its prospective molecular-count method\n  retains finite-sample moments, separate calibration and sampling errors,\n  and derived uncertainty intervals instead of assuming experimental recovery.\n  Its actual mesh process also gives an exact finite-step second moment and\n  conditional readout inference at the selected observation time without\n  assuming an exactly Gaussian finite-step law. Clock separation, joint\n  increment independence, aligned population models, and conditional\n  finite-to-continuum error transfer remain distinct obligations.\n- `PhysicsLogic/Papers/SmoluchowskiBrownian1906.lean`: the independent\n  collision-imbalance and persistent-direction account, separating empirical\n  exclusions, equipartition, microscope-visible averaged motion,\n  small-particle and large-particle regimes, relaxation and Stokes drag,\n  diffusion, and suspension stability. It preserves the explicit numerical-\n  factor disagreement with Einstein, treats agreement as strong support\n  rather than proof, and leaves aggregation unresolved. Together with\n  Einstein 1905 it realizes the narrow shared stochastic-diffusion interface\n  and its source-sensitive thermal-drag composition without identifying\n  their historical derivations. The third joining source retains the original\n  persistent-flight and relaxation formulas, both particle-size regimes, and\n  the logically explicit failure of exact coefficient agreement. Its model is grounded\n  from the inhabited small-particle collision setup and diffusion-regime\n  validity in kinetic collision theory and the selected suspension process;\n  that interpretation is not manufactured by the completed random-flight\n  calculation. Its selected-data theorem retains the collision and persistence\n  controls, path-dependent spread laws, and coefficient-bearing transport\n  predicate.\n- `PhysicsLogic/Papers/LindeLindeMezhlumian1993.lean`: the stochastic-inflation\n  argument now includes the original paper's controlled ordinary-diffusion\n  route before its branching extension. Random-phase Hubble-time field steps\n  yield linear variance and root-time rms spread in the flat-potential\n  regime. Its separate Langevin/Fokker-Planck calculation now retains the\n  literal beta-dependent Langevin, comoving Fokker-Planck, and continuity\n  formulas over a typed `P_c` readout, with Hubble positivity,\n  differentiability, and the Ito/Stratonovich convention boundary explicit.\n  The physical-volume branch separately retains the selected Stratonovich\n  backward generator, adjoint generator, expected-volume equation, endpoint\n  derivative, and backward/forward branching equations over distinct `u`\n  and `P_p` readouts; the initial-field and final-field reproduction terms\n  are not interchanged. Projection theorems expose both formula bundles from\n  their calculation contracts, and a finite countermodel blocks named\n  diffusion or branching outputs from supplying the displayed equations.\n  This is the third realization of\n  `Framework/RandomDisplacementDiffusion.lean`, grounded from the inhabited\n  flat-potential random-phase Hubble-step setup in semiclassical stochastic\n  inflation and the selected coarse-grained inflaton process; it\n  remains logically distinct from physical-volume branching and stationary\n  measure claims. Its selected-data theorem retains the flat-potential\n  validity and drift restriction, random-phase and independent-step controls,\n  field-variance laws, and ordinary comoving diffusion relation.\n- `PhysicsLogic/Papers/BondColeEfstathiouKaiser1991.lean`: the original\n  excursion-set analysis, separating a typed continuous resolution history\n  from its selected scale and threshold interpretation, exact sharp-`k`\n  first-passage logic along that history, numerical general-filter histories,\n  qualified N-body comparison, two-barrier merger and bias calculations, and\n  explicit low-mass and galaxy-formation limits.\n  The sharp-filter route retains the unrestricted Gaussian, the reflected\n  absorbing density in equation (3.1), independent increments, equations\n  (3.5)-(3.7), the Langevin force covariance and power spectrum, and the\n  prior-crossing origin of the factor of two. The original equation (3.9)\n  contains an apparent printed threshold-power mismatch; the formalization\n  preserves that literal typography separately from the physically\n  reflection-derived Gaussian result, and a nonunit-barrier countermodel\n  rejects both their identification and the previously accepted hybrid.\n  For Gaussian and top-hat filters it additionally distinguishes the\n  unrestricted drift-only one-point Gaussian from the non-Markov absorbing\n  survival process and retains the source's integer upcrossing, downcrossing,\n  first-crossing, and rate inequalities.\n  All four established stages retain setup plus direct physical outputs, not\n  proof-carrying calculation wrappers. The N-body assessment additionally\n  records the original quantified peak comparison: at most 20 percent\n  sharp-`k` overestimate and comparable Gaussian/top-hat underestimates.\n  Together with Press-Schechter 1974 it realizes only the narrow thresholded\n  collapse-abundance route; its stochastic process, filtering, halo\n  calibration, simulation, and merger semantics remain paper-local.\n- `PhysicsLogic/Papers/FermiPastaUlam1955.lean`: the original finite nonlinear-\n  chain numerical experiment, with the weakly nonlinear fixed-end setup,\n  finite-difference and modal-analysis protocol, the printed equation-(4)\n  discrete sine transform and original equations (5a)/(5b), repeated as (5a) in the reprint,\n  particle/modal energies, independent total-energy and linear-control\n  checks, quadratic-mode transfer and near return, cross-force finite-time\n  nonmixing evidence, and the conjectural quasi-state proposal represented as\n  separate routes. Figure 1 supplies the distinct selected values `N=32`,\n  `alpha=1/4`, `(delta-t)^2=1/8`, approximately 30,000 cycles, five displayed\n  modes, and higher-mode energy bound 20. The omitted nonlinear potential is\n  retained as a separately evaluated correction, so the reported modal-energy sum is not\n  identified with the separately checked conserved total. First-mode return\n  is the numeric inequality `|E_return-E_initial| \u003C= E_initial/100`, derived\n  independently of the equipartition interpretation. The formalization\n  distinguishes this modal return from exact full-state recurrence, finite\n  observed failure of equipartition from asymptotic nonthermalization, and\n  validated numerical evidence from an analytic theorem. Together with\n  Zabusky-Kruskal 1965, it\n  realizes the narrow `Framework/ValidatedNumericalNearReturn.lean`\n  interface; with Zabusky-Kruskal and Creutz 1980, it also realizes the\n  lower-level `Framework/ValidatedNumericalPrediction.lean` interface. Its\n  near-return adapter grounds the finite calculation separately in the\n  weakly nonlinear chain theory and selected finite physical chain. The same\n  raw finite-difference/modal-energy source derivation also realizes the\n  lower-level source-sensitive numerical-prediction explanation without first\n  packaging an established prediction.\n  Its 37 fidelity boundaries now include actual cycle-indexed phase\n  histories. Modal energies are computed from coordinates and velocities;\n  the mean and high-mode tail use the declared active mode set. A strict\n  tail bound proves finite non-equipartition; individual high-mode bounds\n  alone do not. Figure 9 separately averages kinetic energy over cycles\n  `1..nu` for modes `1,3,5,7` of the Figure 6 broken-linear case, with reported\n  effective N=16, squared step `1/64`, cutoff `5/128`, and a 25-percent\n  slope increase. Its numeric test is independent of the mixing assessment.\n  The validation uses optional linear controls and a separate energy-drift\n  tolerance, not a universal one-percent control log. The weak nonlinear\n  force bound is evaluated on the actual bond force, not fixed to one tenth.\n  Equal finite phase records with conserved modal energy can have a\n  continuation whose kinetic averages converge to equipartition. A harmonic\n  flow preserves energy while reversing the phase-space state. These\n  diagnostic histories are not solutions of the nonlinear FPU equations.\n  Long observation times now compare the actual cycle clock to a selected\n  characteristic linear period. The p. 987 positive-matrix analogy has an\n  independent imported-result route with normalized eigenrays, not raw-vector\n  convergence. The nonlinear proposal uses actual quadratic iterates and\n  cone-occupation averages over every nonvanishing initial orbit. A weak\n  quadratic map has only zero-or-one limiting values per cone but no uniform\n  finite partition of initial directions, so the two source formulations are\n  not silently equated. Both remain conjectural. The public dynamics API and\n  a nine-theorem independent quadratic client separate unique evolution,\n  fixed direction, and decay of the actual vector.\n  A separate consumer constructs its own frequency-two oscillator and\n  applies the shared exact-return-to-observable-return theorem without\n  importing this paper or its control witnesses.\n  The reported effective N is no longer identified with active cardinality.\n  A positive energy calibration now relates reported modal sums to total\n  energy; the velocity projection is retained separately from the\n  displacement projection. The literal sine formula loses a terminal\n  coordinate if all listed coordinates are free, and its boundary at N\n  differs from the chosen N+1 interior-count convention. A nonzero fixed-end\n  example derives the conversion from two explicit Parseval calculations\n  and distinguishes the printed particle-energy sum from the Hamiltonian.\n  The checked relative one-percent return survives common positive\n  calibration; an unconverted absolute bound need not. The independent\n  oscillator client checks that distinction in rescaled energy units too.\n  The original report explicitly distinguishes the squared step in its\n  captions from the positive cycle duration. The checked clock now has\n  `delta-t=sqrt(1/8)` and `t_n=n*delta-t`; it rejects the earlier unsquared\n  `1/8` reading, a negative step, and exact elapsed time inferred from a\n  rounded cycle report. The `30,017`-cycle control is constructed diagnostic\n  data, not a recovered original computation log. Four independent internal\n  client theorems exercise the clock with their own `sqrt(2)/4` step.\n  The additional force-derived energy refinement computes the Hamiltonian\n  from the same quadratic, cubic, or broken-linear potential and actual\n  phase samples, counting each bond once. Explicit component evaluation\n  inputs, not an assigned energy-conservation flag, connect reported modal\n  and nonlinear readouts to that Hamiltonian. The validation route requires\n  the resulting sampled drift bound with both endpoint errors. Relative\n  precision needs a resolved positive physical reference. Neither energy\n  constancy nor small net nonlinear potential supplies Newton's law or\n  weak bond forces. An independent three-moving-site cubic client computes\n  `H=41/8` with unequal readouts `83/16` and `81/16`; its combined bound is\n  `163/640`, not the reported-drift budget `83/640`. These remain paper-local\n  semantics, not a new shared framework or reconstruction of the original runs.\n- `PhysicsLogic/Papers/ZabuskyKruskal1965.lean`: the original KdV numerical\n  experiment introducing solitons, with the isolated pulse calculation,\n  checked finite-difference evolution, pulse-train identification through\n  measured width and speed, nonlinear identity-preserving interactions,\n  unresolved close-overlap mechanism, phase-focusing near recurrence, and\n  qualified long-time thermalization expectation represented as distinct\n  routes. It distinguishes near profile reconstruction from exact state\n  recurrence and realizes the same narrow validated-near-return interface as\n  Fermi-Pasta-Ulam while keeping KdV and soliton physics paper-local. Its\n  validated run also realizes the lower-level numerical-prediction interface.\n  Its near-return adapter separately grounds the finite-difference\n  calculation in the KdV theory and represented periodic KdV system. Its\n  periodic-KdV validation, soliton-focusing, and waveform-reconstruction\n  source derivation is also retained by the lower-level source-sensitive\n  numerical-prediction explanation.\n  Its six directional paper-local countermodels are now value-bearing: an\n  isolated pulse with positive dispersion, peak contrast three, and width one\n  withholds equations (2)-(4), whereas the calculated witness retains width\n  two and speed one. The eight-pulse train satisfies separate percent-level\n  width and one-fifth speed checks but leaves the close-interaction residual\n  nonzero; exact momentum coexists with\n  energy drift `1/100000`, first-profile residual `1/100` and poorer second\n  residual `2/100` withhold exact state recurrence, and finite recurrence\n  does not exclude later equipartition. No proposition-pair or pulse/status\n  truth table replaces these Zabusky-Kruskal distinctions.\n- `PhysicsLogic/Papers/Miller1964.lean`: the original parallel-trajectory\n  stellar-system experiment, retaining deterministic reversible equations,\n  first-integral and reduced-step controls, exponential phase-space\n  separation, encounter amplification, inverse-square collective scaling,\n  qualified irreversibility, individual prediction limits, and the unresolved\n  ensemble question as distinct routes. Its narrow point-predictability route\n  realizes the shared finite-precision trajectory component. The parallel\n  branch now retains p. 253 equation (2) as the literal logarithm of the\n  summed squared position and velocity differences, while the encounter\n  branch retains p. 251 equation (1), the angular-error amplification factor,\n  and the stated `tau / ln f` e-folding time. Lean checks the unit-distance\n  normalization, strict amplification, and positive e-folding consequence;\n  countermodels prevent named separation or encounter calculations from\n  manufacturing those formulas.\n- `PhysicsLogic/Papers/PortegiesZwartBoekholt2014.lean`: arbitrary-precision\n  validation and approximate-versus-converged resonant three-body comparison,\n  separating convergence, individual trajectory disagreement, the first\n  integral-time dissolution criterion's independent energy/radius/outward-\n  motion conditions and surviving bound binary, all four 10,000-member\n  initial-condition classes, majority-only energy control, tested timestep\n  thresholds, four distinct survival half-lives, selected ensemble recovery,\n  and untested extrapolations. Its individual-comparison route realizes the\n  same shared finite-precision trajectory component while its physical\n  escape and ensemble conclusions remain paper-local.\n- `PhysicsLogic/Papers/Lorenz1963.lean`: finite deterministic dissipative\n  flow, separate central and noncentral instability deductions, bounded\n  finite-memory numerical integration, Saltzman's original dimensional\n  convection equations, both distinct temperature Fourier modes, the exact\n  Rayleigh threshold `27 pi^4/4`, and the severe three-mode reduction.\n  Its complete Jacobian, both characteristic polynomials and equilibria,\n  separate convection-instability threshold `470/19`, and exact\n  `exp(-287/30)` volume factor distinguish shrinking phase volume from\n  converging trajectories. Lorenz's idealized two-branch return map retains\n  its undefined midpoint, opposite slopes, distinct preimages, and every\n  printed periodic cycle; exact surrogate calculations and finite numerical\n  evidence still do not prove nonperiodicity of the physical flow.\n  Atmospheric predictability remains conditional. Its selected\n  nearby-state divergence route is the third independent realization of the\n  shared finite-precision trajectory component; the real atmosphere is not\n  identified with the finite model.\n- `PhysicsLogic/Papers/Noether1918.lean`: paper-local variational problems,\n  finite-parameter, infinitely-many-parameter, arbitrary-function, and mixed\n  transformation groups, exact calculation\n  interfaces for both theorems and converses, a theorem-II route deriving\n  selected Euler-Lagrange equations from the remaining equations, and checked\n  theorem-I divergence relations in both the finite and non-arbitrary-function\n  infinite-parameter cases. The finite coefficient contract now retains\n  equation (13) as a value-level sum of selected Euler expressions times\n  generator variations equaling the selected current divergence, with a\n  projection theorem and countermodel separating that formula from a relation\n  label. The theorem-II calculation now supplies the exact intermediate\n  variational and integration-by-parts inputs, not equations (15) or (16).\n  `Noether1918/ArbitraryFunctions.lean` derives the weighted divergence\n  formula for every smooth compactly supported test family, proves vanishing\n  boundary jets, and uses an explicit Gauss formula plus Mathlib's fundamental\n  lemma to derive the pointwise adjoint identities. The coefficients are\n  actual ordered derivatives of coefficient times Euler expression on the\n  same history. The source certificate exposes those same pointwise identities.\n  Operator independence, a positive function count, and an inhabited regular\n  history are explicit; stronger differential irreducibility remains separate.\n  `Noether1918/EulerDependence.lean` replaces opaque remaining/dependent\n  equation predicates by actual selected Euler expressions. Its reduction\n  supplies a universal reconstruction on smooth trial fields, zero-preserving\n  recovery maps, and explicit initial or boundary jets, not the desired\n  equations. Lean derives their vanishing from the same history's identities\n  and remaining equations. Each theorem-I case retains a separately qualified converse.\n  Mixed-group output explicitly records that its\n  divergence relations are independent of its theorem-II identities.\n  Both consequence routes inherit\n  their forward-theorem outputs through semantic route certificates; separate\n  multidimensional-conservation and one-dimensional-first-integral routes,\n  plus the philosophy-layer Noether bridge, consume the certified finite\n  relation output at the retained parameter count rather than recomputing a\n  one-generator surrogate;\n  the mixed-group result, Hilbert's improper energy criterion with its\n  Euler-expression/derivative current construction and identically\n  divergence-free remainder, and\n  countermodels delimit the theorem's scopes. The thirteen algebraic countermodels\n  retain value-bearing Euler expressions, generator variations, alternating\n  derivative coefficients, injective parameter modes, distinct histories,\n  current decompositions, and equation residuals. They explicitly separate\n  sourceful from zero divergence, mixed outputs from their independence,\n  nonlinear first-integral dependence, and conservation from impropriety;\n  no `Unit`-carrier truth table replaces those distinctions.\n  Four coordinate-current controls and two actual adjoint-identity controls\n  are joined by two equation-recovery controls and three first-integral\n  controls, bringing the fidelity matrix to twenty-four boundaries. An independent kinetic\n  gauge client verifies the density invariance for arbitrary local shifts,\n  operator independence, and all inputs before using the library to derive\n  an off-shell identity and residual balance. It also constructs an actual\n  differential recovery, realizes a nonconstant on-shell history, and checks\n  that reversing the selected equation requires an initial value. A remaining\n  equation at just one point does not supply the neighborhood needed to\n  differentiate its vanishing.\n  `Noether1918/FirstIntegrals.lean` now derives constancy of the actual\n  selected currents on connected open one-dimensional history domains using\n  Mathlib's mean value theorem. No supplied integral-existence predicate or\n  mandatory nonlinear-dependence flag remains. A free-particle family has\n  independent space and time translations but the nonlinear relation\n  `2E = P^2`; different histories have different conserved values. Actual\n  derivative controls exclude a single constant across disconnected regions,\n  a compulsory zero value, and empty-domain realizations. An independent\n  harmonic-oscillator client derives conserved nonzero energy even though\n  its boundary term and Lagrangian density vary with time.\n  `Noether1918/FiniteCurrents.lean` defines the corrected\n  variation, `B = A - f delta x`, and actual coordinate divergence on the same\n  history. The finite on-shell and sourceful routes use that identity and\n  regularity to derive zero divergence or source balance, respectively.\n  An independent free-scalar client checks gradient energy and the negative\n  Laplacian before deriving a nonzero, nonconstant, divergence-free current.\n  The coordinate-current API is now shared with Einstein 1916 through\n  `Framework/Conservation.lean`. Their different source arguments separately\n  derive its nonvacuous result. An external transport client imports neither\n  paper and tests continuity, uniform production, domain restriction, and\n  background-current subtraction through six public-API proof uses.\n- `PhysicsLogic/Papers/HohenbergKohn1964.lean`: paper-local potentials,\n  nondegenerate ground states, densities, universal and decomposed energy\n  functionals, with the universal term explicitly equal to fixed kinetic plus\n  mutual Coulomb-repulsion energy rather than an opaque internal-energy\n  label, and a theorem-I route that derives both strict variational\n  inequalities, potential-difference antisymmetry, and the reductio from\n  explicit principles. Additive-constant transport and nondegenerate state\n  uniqueness are separate inputs. Its theorem-I route independently realizes\n  the shared density-potential gauge determination framework without\n  conflating static constant shifts with time-dependent gauges. Its\n  theorem-II route proves exact\n  ground-energy attainment and a bound over every representable density,\n  rather than only one selected competitor. A separate footnote-11 route\n  proves that positivity and integer normalization alone do not logically\n  establish representability, without asserting a physical counterexample.\n  The remaining routes cover\n  the corrected equation-(35) momentum-kernel/polarizability equality\n  `K(q) = (2 pi / q^2) (1 / alpha(q) - 1)`, equation (36)'s\n  dielectric definition, the checked equation-(37) dielectric rewrite on\n  its explicit common denominator domain, equations (38)-(40)'s small-`q`\n  polarizability series, derivative singularity at `2 k_F`, and `q^-4`\n  large-momentum decay, and equations (44)-(46)'s transferred small-`q`\n  kernel series, derivative singularity, and `q^2` large-momentum growth.\n  Equation (47) then retains the position-space kernel as a distribution on\n  test functions, with the origin delta and distributional Laplacian\n  explicit, while equation (48) retains `G[n]-G[n0]`, the\n  perturbation-square integral, the gradient-square integral, and the\n  higher-gradient remainder.\n  These limit formulas feed the explicit `2 k_F` nonanalyticity and\n  inverse-cube Friedel profile, the checked\n  finite-gradient obstruction, and the conditional gradient expansion with\n  equation (63)'s divergence-reduced local energy density: one second-order\n  gradient-square term, three distinct fourth-order invariants, an explicit\n  sixth-order remainder, and equation-(64) integration to the global value.\n  Equation-(83) partial summation then has an explicit\n  three-dimensional local energy density, local-density kernel, opposite\n  half-displacement density differences, divergence/higher-order remainder\n  channels, and equation-(64) integration back to the global residual\n  functional. Equation (84) now fixes that local-density kernel through a\n  summable countable reciprocal-momentum Fourier series with positive box\n  volume, nonzero momentum and dielectric denominators, and the complex\n  `exp(-i q . r')` plane wave. The equation-(84) `1/epsilon`\n  subseries remains distinct from equation (37)'s\n  `1/(epsilon - 1)` exact-kernel rewrite. Scope countermodels include failure of\n  universality when internal energy depends on the varied external potential,\n  failure of a named gradient expansion to supply equation (63), failure of a\n  named kernel to supply equation (84), and failure of a named\n  partial-summation label to supply equation (83).\n- `PhysicsLogic/Papers/RungeGross1984.lean`: the fixed-initial-state,\n  gauge-qualified time-dependent density-functional argument, including the\n  Taylor-current, continuity, equation-(6) density-separation, boundary,\n  hydrodynamic, stationary-action, and effective-orbital routes.\n  It independently realizes the shared density-potential gauge determination\n  framework while retaining fixed initial conditions, the original\n  equation-(6) derivation, and open representability and practical scope.\n  Its six paper-local countermodel theorems now retain actual density, potential-jet,\n  divergence, gauge-shift, phase, action/Hessian, functional-residual,\n  approximation, initial-state, and derivation values. In particular, the\n  equation-(6) witness has a nonzero right-hand side but zero density\n  derivative; spatial potentials `(0,1)` and `(2,3)` are gauge-equivalent\n  without literal equality; and a zero first variation with Hessian values\n  `2,-2` is stationary but not minimal. No `Unit`-carrier or status-enum\n  truth table replaces those distinctions.\n  Its independent fidelity matrix now has twenty-one physical boundaries.\n  The original `k+1` current and `k+2` density derivatives, occupied-support\n  integral `-18`, zero boundary flux, both fixed hydrodynamic initial\n  conditions, and `A[n]=B[n]-int(nv)` are retained inside the certified\n  source routes. The exact Kohn-Sham witness has density two, external\n  potential one, Hartree term two, exchange-correlation derivative three,\n  and effective potential six; Taylor-flat nonanalytic futures, nonzero\n  boundary flux, zero occupied support, missing initial current, and\n  omitted exchange-correlation terms are independently ruled out.\n- `PhysicsLogic/Papers/LandauSuperfluidity1941.lean`: paper-local\n  quantum-liquid operators, the explicitly supposed potential-below-vortex\n  ordering, phonon-roton spectrum, low-temperature excitation\n  thermodynamics, zero-temperature wall-excitation threshold derived from\n  both actual branch dispersions, an explicitly attained quadratic-roton\n  minimum and proven-positive critical speed,\n  rotating-vessel two-motion statistics, nonliteral two-fluid interpretation,\n  two-velocity hydrodynamics, and second sound. The spectrum first feeds a\n  separate dilute-gas heat-capacity route; the absolute-zero flow branch\n  remains independent of it, while the later rotating-vessel route consumes\n  the thermodynamic result before reaching two motions. The low-temperature\n  statistical regime is kept distinct from the lambda-point endpoint. Its selected wall-channel\n  result realizes the shared subthreshold-excitation component through an\n  exact paper-context model-retention certificate, without claiming exclusion\n  of vortices or every dissipative process. A source-facing theorem starts\n  from the operator/spectrum premises and direct wall-flow calculation rather\n  than accepting `EstablishedSubthresholdFlow`.\n  Its thermal and normal-density routes now use actual momentum integrals\n  through the shared excitation-response component, deriving heat from\n  energy families and equation (3) from radial moment identities. Explicit\n  quantum-statistics bounds preserve the dilute approximation's scope.\n- `PhysicsLogic/Papers/BogoliubovSuperfluidity1947.lean`: paper-local weak\n  Bose gas formalized in 24 source atoms and 13 certified routes. It keeps the\n  exact pair-potential Hamiltonian, interaction-sign stability restriction,\n  weak-excitation linearization, commutation-preserving canonical\n  diagonalization, and phonon-to-molecular spectral asymptotics separate\n  before deriving equilibrium occupations, the positive velocity threshold,\n  and stationary frictionless condensate-quasiparticle motion. A sibling\n  threshold branch derives the molecular momentum distribution and\n  zero-temperature depletion; only then are the small-depletion,\n  weak-coupling, low-temperature, and excluded-short-range-repulsion\n  conditions assessed. The later exact zero-density two-body scattering\n  replacement, free-energy and virial-pressure calculation, hard-sphere and\n  weak-attraction comparison, and semi-phenomenological real-liquid proposal\n  remain distinct downstream routes. Its complete motion route independently\n  realizes the unchanged shared subthreshold-excitation component through an\n  exact paper-context model-retention certificate. A source-facing theorem\n  executes the complete microscopic-to-threshold chain and motion calculation\n  without accepting `EstablishedFrictionlessMotion`; molecular depletion and\n  real-liquid extensions remain outside that route.\n- `PhysicsLogic/Papers/FeynmanTwoFluid1954.lean`: paper-local liquid-helium\n  density-mode ansatz, variational energy, phonon-roton interpretation,\n  dilute-excitation thermodynamics, moving two-fluid description,\n  current-conservation diagnosis, impurity mass estimate, and qualified\n  scope. Its fixed-momentum upper-bound route independently realizes the\n  shared momentum-resolved variational component through an exact\n  paper-context model-retention certificate, a direct nonvacuity theorem, and\n  a structural explanation of only the selected upper-bound relation. The\n  structural route executes the ansatz and Eq. (18) calculation directly;\n  it does not consume the terminal established spectrum.\n  The thermodynamic and moving-fluid stages additionally retain selected\n  Eq. (25)-(26) and Eq. (39)-(43) formula packages rather than only named\n  outputs; all established stages avoid storing implication-valued\n  calculations. Its moving-fluid result now also retains Feynman's\n  multiply connected ring argument: integer phase winding and locally\n  irrotational flow can carry nonzero permanent circulation. The original\n  expectation of accuracy near\n  the structure-factor maximum and the appendix's experimental impurity-mass\n  disagreement are explicit.\n  Its actual Bose-current derivative now consumes the shared excitation\n  response with the original number normalization. The literal `n^2`\n  coefficient and differentiated `n(1+n)` response remain distinct.\n- `PhysicsLogic/Papers/FeynmanCohen1956.lean`: paper-local return-flow\n  construction across eighteen source-distinct routes: Landau and simple-mode\n  benchmarks, localized continuity failure, foreign-atom mechanism, exact\n  symmetrization and controlled linearization, qualified vortex picture,\n  diffraction and identity scope, corrected Kirkwood and residual integrals,\n  separate norm and numerator calculations, variational quotient,\n  optimization, momentum regimes, error budget, and thermodynamic scope. It\n  also carries typed equation-(9), equation-(61), and equation-(63) scalar\n  packages tied to the selected momenta, structure factor, corrected\n  correlation data, return-flow strength, energies, and reported gaps. The\n  staged packages survive into the simple benchmark, improved spectrum, and\n  optimized gap, and a countermodel blocks a named output from replacing the\n  printed formulas. It has twelve formal nonimplications and uses the shared\n  variational component as a dependent refinement of Feynman 1954 while\n  supplying its own exact paper-context model-retention certificate and direct\n  inhabited-route theorem.\n- `PhysicsLogic/Papers/GirvinMacDonaldPlatzman1986.lean`: paper-local\n  lowest-Landau-level projection with exact Gaussian cyclotron subtraction,\n  actual noncommuting complex density matrices and exponential commutator,\n  a positive finite spectral measure with evaluated zeroth and first moments,\n  oscillator-strength rather than static-weight fractions, an unsaturated\n  98% density mode, and explicit density-dark excitations below every\n  proposed gap. Its remaining paper-local semantics retain the qualified gap\n  condition, magneto-roton dispersion, crystallization interpretation,\n  large-wave-vector scope, finite-thickness and disorder assessment, and\n  static response. Its projected single-mode\n  upper bound independently realizes the shared momentum-resolved\n  variational component through an exact paper-context model-retention\n  certificate, a direct nonvacuity theorem, and a structural explanation of\n  only the selected upper-bound relation. The structural route executes the\n  unprojected diagnosis, projected construction, and projected energy\n  calculation in source order before any terminal projected bound exists.\n  Nine established stages retain\n  only named direct outputs; the source graph explicitly certifies the\n  unprojected diagnosis and projected trial before the energy quotient, and a\n  staged countermodel blocks all nine vacuous calculation contracts. Twenty\n  inhabited fidelity boundaries additionally separate incorrect operator\n  order, commuting densities, unprojected structure factors, filled Landau\n  levels, negative spectral weights, zero denominators, exact first moments,\n  invisible lower states, incomplete saturation, and false many-body gaps.\n- `PhysicsLogic/Papers/Laughlin1983.lean`: paper-local odd-Jastrow state\n  selection, independent variational evidence, plasma mapping, two\n  fractional-charge calculations, excitation algebra, compression-gap\n  reasoning, localization, and scoped Hall response. It realizes shared\n  charge assignment, evidence semantics, and the gapped-fluid route without\n  promoting a generic quantum Hall framework.\n- `PhysicsLogic/Papers/Haldane1983.lean`: paper-local spherical monopole\n  geometry with literal radial-field, Dirac-flux, angular-momentum,\n  lowest-Landau-level energy/degeneracy, and magnetic-length formulas; finite\n  `2S=m(N-1)`, finite `N/(2S)`, and explicit thermodynamic\n  `nu -> 1/m` formulas; operator flux/angular-momentum shifts, fixed-field\n  `m`-hole production, `N+1` degeneracy, and opposite `e/m` charge\n  formulas; hard-core exact versus general variational state assessment,\n  conditional hierarchy recursion, continued-fraction observables, and the\n  unresolved interaction-dependent existence problem. The readouts are tied\n  to the selected sphere, radial field, electron gas, parent state, operators,\n  excitations, and charge assignments; countermodels block merely named\n  monopole, parent-filling, or fixed-field outputs from supplying those\n  equations. It realizes grounded shared charge assignment, the exact\n  fractional-Hall quasihole-charge route, and the gapped-fluid route. The\n  fixed-field charge calculation remains independent of the parent gap, which\n  is retained as an explicit author assumption only in the gapped-fluid and\n  hierarchy routes. Its thirty-two inhabited Haldane hierarchy boundaries\n  include an actual six-flux monopole with seven Landau states, finite filling\n  `1/2` versus thermodynamic `1/3`, three fixed-field holes of charge `e/3`,\n  parent/child fluxes `15`, `19`, and `11`, and the separate continued\n  fractions `[3,+2]=2/7` and `[3,-2]=2/5`. Their charges and Hall\n  resistances are respectively `e/7`, `e/5`, `7/2`, and `5/2`; all printed\n  hierarchy formulas remain compatible with zero child gap.\n- `PhysicsLogic/Papers/Kitaev2001.lean`: paper-local Majorana-chain semantics\n  for the exactly solvable endpoint modes and parity doublet, boundary-root\n  phase distinction, exponentially small finite-chain splitting, parity-\n  resolved `2pi` cycle, `Z2` Majorana number and loop diagnostic, quadratic\n  Pfaffian formula, weak-pairing odd-Fermi-point criterion with explicit gap\n  opening, and the qualified `4pi` Josephson-current proposal. Material\n  realization and fault-tolerant gates remain open. Together with\n  Oreg-Refael-von Oppen 2010, its boundary calculation now independently\n  realizes the narrow shared `Framework/BoundaryMajoranaMode.lean` route.\n  Its source-anchored adapter also projects the completed route to a direct\n  nonvacuous boundary-mode proposition and to a structural explanation whose\n  constraint includes the actual boundary calculation. Its separate grounding\n  path consumes only `BoundaryMajoranaGroundingSetup`, before bulk\n  classification or boundary-mode outputs.\n  Together with Fu-Kane 2009, its localized parity branch independently\n  realizes `Framework/ParityResolvedFractionalJosephsonResponse.lean` and\n  projects its completed response to the direct nonvacuous shared endpoint.\n- `PhysicsLogic/Papers/FuKane2009.lean`: paper-local quantum-spin-Hall\n  semantics for the superconducting-magnetic interface Majorana mode, BdG and\n  Andreev spectrum, protected parity crossing, bulk parity-transfer\n  interpretation, fixed-parity fractional Josephson response,\n  finite-temperature switching rate, telegraph-noise spectrum, and proposed\n  HgCdTe probe. The junction result retains the original magnetic-barrier\n  transmission, `epsilon_0(phi) = sqrt(D) Delta_0 cos(phi/2)`, both\n  occupation energies `epsilon_0(phi) (N_0 - 1/2)`, and the exact\n  `I_0(phi) = (1/2) sqrt(D) e Delta_0 sin(phi/2)` current. Its thermal\n  result separately retains the two printed switching rates, conditional\n  bath symmetry, quasiparticle versus two-dimensional variable-range-hopping\n  activation, the two-pi thermal equilibrium current, and the Lorentzian\n  noise spectrum; the zero-frequency formula is derived rather than assumed.\n  Concrete transparent and magnetic junctions, two different thermal baths,\n  and nineteen inhabited fidelity boundaries prevent these source equations\n  from collapsing into named predicates. Its interface route makes the known\n  SSH zero-mode result an\n  explicit imported theorem hypothesis, keeps the subsequent BdG\n  self-conjugacy inference separate, and is a third independent client of\n  `Framework/BoundaryMajoranaMode.lean`. Its later Josephson route separately\n  realizes the shared parity-resolved fractional-response component without\n  promoting the QSHI anomaly or noise calculation into generic semantics. Its\n  interface adapter also exhibits the direct nonvacuous shared mode, and its\n  interface route realizes the shared structural explanation. Its Josephson\n  adapter exhibits the direct nonvacuous shared response. The shared\n  mode grounding consumes `MajoranaInterfaceSetup`, not the completed\n  interface result.\n- `PhysicsLogic/Papers/Gamow1928.lean`: paper-local semantics for the\n  nuclear potential and classical obstruction, rectangular-barrier\n  calculation, damped outgoing state and decay constant, radial barrier\n  transfer, qualified Geiger-Nuttall comparison, and the unknown-potential\n  and gamma-preparation scope. Actual waves and currents distinguish standing\n  amplitudes, leading tunneling factors, and exact scattering probabilities.\n  Complex-energy time evolution derives damping and finite-region survival;\n  conservation and leading normalization derive equation (5). The separate\n  Coulomb model derives a base-corrected log slope and combines model-transfer\n  and Taylor errors without identifying the conflicting printed exponents.\n  The normalized survival curve gives correctly conditioned\n  future escape probabilities; the damped and radial routes jointly realize\n  the nonvacuous shared memoryless-decay endpoint. Its named setup bridge\n  maps two local nuclear\n  barrier setups, comparable potential profiles, and energy ordering to the\n  shared pre-output grounding boundary. Its source-facing mechanism theorem\n  reaches both selected decay explanations before constructing the\n  Geiger-Nuttall comparison. Its stronger source-sensitive theorem records\n  separate lower and higher damped-outgoing radial-transfer derivations and\n  exposes either derivation from the resulting explanation.\n- `PhysicsLogic/Papers/GurneyCondon1928.lean`: paper-local semantics for\n  chance-governed radioactivity, overlapping interior and exterior\n  wavefunctions, overlap-sensitive rates, the conditional energy-rate trend,\n  incoming-alpha scattering consistency, and the field-emission analogy.\n  Because the original letter prints no tunneling integral, its local value\n  layer retains source-faithful inequalities instead: positive overlap below\n  an explicit selected smallness scale, a positive decay rate and observation\n  duration, the corresponding escape probability in `(0, 1)`, and\n  conditional strict energy/overlap/rate ordering with equal-duration\n  probability comparisons. The letter's explicitly recalled exponential law\n  receives normalized survival and correctly conditioned age-independent\n  future-probability semantics, with countermodels separating positive rate,\n  survival, conditioning, and positive observation duration.\n  Its independent setup bridge preserves the two selected potential pictures,\n  comparable profiles, and energy ordering without assuming wave-overlap or\n  decay outputs. Its source-facing mechanism theorem executes the two\n  setup-and-overlap routes without using the conditional comparison or the\n  objective-chance classification. Its source-sensitive theorem records the\n  two interior/exterior wave-overlap derivations separately rather than\n  identifying them merely because they realize the same shared route.\n  Together these two papers independently realize\n  `Framework/FiniteBarrierMetastableDecay.lean`.\n- `PhysicsLogic/Papers/OregRefaelVonOppen2010.lean`: paper-local\n  spin-orbit-coupled quantum-wire semantics retaining the perpendicular wire\n  axes, four-term BdG Hamiltonian, homogeneous spectrum and two gapped phases,\n  distinct `4e^2/h` and `2e^2/h` transport plateaus, Zeeman- and\n  pairing-interface gradient matrices and oscillator branches,\n  chemical-interface decay and wavefunction-matching coefficients, the\n  weakly split pairing-sign Majorana doublet, and fractional `h/e` versus\n  conventional `h/(2e)` Josephson flux periods. Fifteen inhabited fidelity\n  boundaries keep those physical distinctions independent. Vortex\n  action remains an expectation, detailed braiding remains deferred, and\n  material realization and fault tolerance remain open. Its chemical\n  interface independently realizes the shared boundary-Majorana route\n  without promoting semiconductor, Zeeman, Josephson, or braiding vocabulary\n  into the framework. Its source-anchored adapter projects that route to the\n  same direct nonvacuous boundary-mode proposition and structural\n  explanation. Its separate\n  `ChemicalInterfaceGroundingSetup` contains only the shared pre-output\n  physical setup.\n- `PhysicsLogic/Papers/Parker1969.lean`: paper-local quantum-field theory in\n  an expanding universe, separating canonical commutator propagation,\n  continuity-based scalar statistics, Bogoliubov pair production and\n  infinite-volume representation change, adiabatic invariance, Parker's\n  minimization postulate for physical particle operators, radiation- and\n  dust-era no-creation conditions, heuristic backreaction, the rough\n  present-epoch estimate, and conformal no-creation for massless nonzero-spin\n  fields. Together with Hawking 1975 it realizes the narrow shared\n  Bogoliubov particle-production inference, while Parker's time-local\n  particle definition and cosmological conclusions remain paper-local. Its\n  Bogoliubov route retains equations (13), (28), (39), (40), (52), and (55):\n  the selected operator ansatz, hyperbolic coefficient parameterization,\n  unitary implementation, normalization, occupation, and density formulas.\n  It keeps the production calculation without silently manufacturing Parker's\n  later physical particle criterion. A separate\n  downstream route realizes the neutral description-relative particle-content\n  paradigm only after consuming the minimization-selected observation-time\n  operator: the same scalar-field state is initially vacuum and has positive\n  nonvacuum content under that physically selected description. A separate\n  bridge still prevents positive occupation from silently becoming nonvacuum\n  status. Its\n  shared context owns six selected indices and all seven route-used relation\n  families and constructs one named model, with an exact paper-semantics\n  certificate consumed by applicability. Its output-led established result\n  retains exact selection plus the directly realized vacuum-to-production\n  facts and reconstructs the calculation route. Grounding uses the same exact\n  model, Parker's actual incoming-vacuum setup, and his explicit theory/world\n  bridge without assuming mode mixing or any later production output. Its\n  pp. 1061-1062 adapter now projects the route to a direct nonvacuous result\n  containing the actual incoming vacuum, selected coefficient relation,\n  positive occupation, and produced-particle conclusion. The same granular\n  inputs now realize a typed structural explanation: its proof-free constraint\n  retains Parker's selected creation coefficient, while its distinct\n  phenomenon contains the incoming vacuum, represented positive occupation,\n  and produced particles. A shared countermodel with that terminal phenomenon\n  but no selected mode expansion blocks the converse. A stronger\n  source-sensitive explanation now retains Parker's typed canonical\n  transformation/vacuum/creation-coefficient derivation. Parker's full\n  calculation first projects to a narrower source calculation that omits\n  vacuum persistence, pair statistics, stimulation, and density; the source\n  theorem then starts from that setup, calculation, and interpretation rather\n  than a terminal production result.\n- `PhysicsLogic/Papers/Hawking1975.lean`: paper-local semiclassical collapse,\n  asymptotic in/out mode mixing, nonzero negative-frequency production,\n  a selected last-escaping horizon ray trace with logarithmic phase,\n  selected late-time wave packets dominated by high incoming frequencies,\n  greybody thermality, spin and mass extensions, Kerr-Newman shifts and\n  superradiance, renormalized integrated flux, quasi-stationary evaporation,\n  black-hole thermodynamics, and the qualified Planck endpoint. Its heuristic pair picture is kept\n  separate from the derivation. It realizes the exact Bogoliubov production\n  inference shared with Parker and the compensation-to-generalized-entropy-\n  nondecrease inference shared with Bekenstein. Its beta-row model carries the\n  same context-owned exact-retention certificate, while a thirteen-component\n  framework mutation audit makes every index or relation change fail the\n  original exact semantics. A nonvacuous finite witness realizes the complete\n  vacuum-to-positive-occupation route and its direct realized result, with\n  direct component-activity checks. Its pp. 206-207 adapter projects the\n  beta-row route to that result without absorbing collapse or\n  future-null-infinity interpretation into the shared component. Those same\n  source-local inputs realize the shared structural mode-mixing explanation,\n  without identifying Hawking's collapse and ray tracing with Parker's\n  expansion mechanism. The stronger source-sensitive explanation records a\n  distinct asymptotic in/out beta-row derivation. It stops at equations\n  (2.5)-(2.10) and excludes the later ray-tracing, thermal, greybody, and\n  evaporation routes. A complete shared route with a false source relation\n  has the ordinary explanation but neither paper's source-sensitive one.\n  The collapse route also realizes description-relative particle content for\n  the same incoming-vacuum field state under the asymptotic outgoing\n  description, without treating particle descriptions as conscious observers\n  or arbitrary relabellings.\n  Bogoliubov grounding uses Hawking's actual incoming-vacuum setup and explicit\n  theory/world bridge without assuming the beta-row calculation or particle-\n  production result. Its\n  p. 203 thermodynamic route now branches from steady thermality and explicit\n  entropy bookkeeping without absorbing the later p. 219 renormalized-flux\n  calculation; backreaction remains the separate premise for evaporation. Its\n  separate generalized-entropy model retains the process, both entropy-change\n  functions, and all five route-used predicates; its exact certificate is\n  consumed by route applicability and by exact theory/model membership. Its\n  context fixes `generalizedEntropyProcess` before constructing the unique\n  `selectedModel`, so a candidate cannot change the process and remain exact.\n  Its shared compensation adapter rebuilds the local thermodynamic setup from\n  shared process, account, horizon-exchange, and fluctuation facts plus the\n  paper-local mechanical and area-law analogies before invoking the thermal\n  interpretation.\n  Entropy-model grounding delegates to the generic route-independent\n  constructor using the certificate, Hawking's pre-compensation thermodynamic\n  setup, and explicit theory/world bridges, without assuming the compensation\n  calculation or nondecrease. The completed Hawking route separately proves\n  direct nonvacuous generalized-entropy balance at that named process.\n- `PhysicsLogic/Papers/Bekenstein1973.lean`: paper-local black-hole entropy\n  logic from the Kerr mechanics analogy and inaccessible information through\n  merger-based area scaling, the semiclassical one-bit coefficient estimate,\n  the statistical generalized second law, oscillator and beam tests,\n  fluctuation resolution, individual-quantum accounting, and the finite-box\n  Geroch engine. Together with Hawking 1975 it realizes only the narrow\n  generalized-entropy balance inference; information loss, area coefficients,\n  radiation, and all example calculations remain paper-local. Its named\n  Section V route branches from the inaccessible-information result without\n  consuming the tentative one-bit normalization; the oscillator, beam, and\n  Geroch tests explicitly rejoin the coefficient route where they use\n  Eqs. (15)--(18). Its named\n  eight-component shared model is constructed from a context that fixes\n  `bodyCaptureProcess`, then certified against that context before the\n  compensation route can be used. Its shared compensation adapter rebuilds\n  the local body-capture setup from shared process, account, horizon-exchange,\n  and fluctuation facts plus the paper-local horizon-crossing fact before\n  invoking the information calculation. Theory/world grounding delegates to the\n  generic constructor using the certificate, Bekenstein's pre-compensation\n  body-capture setup, and explicit bridges, without assuming compensation or\n  nondecrease. The completed capture route separately proves direct nonvacuous\n  generalized-entropy balance at that named process. Its typed entropy source\n  separately reconstructs the mechanics, inaccessible-information, actual\n  body-capture, compensation, and statistical-interpretation chain before\n  realizing the source-sensitive explanation. A completed common balance and\n  ordinary explanation cannot reconstruct either paper's missing source.\n- `PhysicsLogic/Papers/KaplanSavageWise1998.lean`: paper-local scattering\n  channels, subtraction scales, scale-indexed coupling and amplitude values,\n  scale-weighted coupling derivatives, beta-formula and running-solution\n  values, interaction terms, regimes, and fits; checked PDS, literal\n  complex-valued equation-(5) loop and equation-(6) bubble-amplitude\n  readouts with on-shell, zero-power-loop, and non-pole obligations,\n  value-level RG matching, a loop-to-resummation-to-unitarity chain, a separate\n  minimal-subtraction scope theorem contrasting natural `p/Lambda` counting\n  with the large-length `p \u003C\u003C 1/|a|` window, mixed resummation,\n  explicit-pion, and a `D2` chain whose requiredness is derived from\n  scale-indexed amplitudes with and without the term, whose same-order\n  contribution uses shared power counting, and whose Weinberg inconsistency\n  is a checked contradiction rather than an imported obstruction;\n  scale-cancellation,\n  empirical-support deductions through an explicit author-interpretation\n  bridge, and coupled-channel deductions with explicit matrix\n  components, observable values, mixed calculation orders, fit-parameter\n  status, and scope countermodels. Its pion-inclusive running-coupling and\n  full-amplitude matching route realizes the shared renormalized-prediction\n  component.\n- `PhysicsLogic/Papers/BedaqueHammerVanKolck1998.lean`: paper-local\n  short-range three-body EFT, large-scattering-length, resummation, integral-\n  equation, distinct intermediate-asymptotic and on-shell momentum roles,\n  asymptotic-phase, Lambda-star phase locking, two-cutoff solution agreement,\n  datum-to-Lambda-star calibration, cutoff, running-force, prediction,\n  numerical-check, and bound-state semantics. The original author source fixes\n  the exact `3 sqrt(3)/(4 pi)` channel threshold, distinguishes the bosonic\n  channel from the protected spin-3/2 quartet and coupled spin-1/2 nucleon\n  equations, and separates the exact characteristic root from the quoted\n  `s0 ~= 1.0064`. Its sine-ratio coupling repeats after\n  `Lambda -> Lambda exp(pi/s0)` without becoming constant or admitting its\n  poles. One fitted `a3 = 1.56 a2` datum yields the distinct\n  `r3 = 0.57 a2` and `B3 = 1.5/(M a2^2)` predictions; the independently\n  rounded helium values retain their nonzero `0.468 A` and `0.079 A`\n  residuals. Twenty inhabited countermodels reject stronger false readings.\n  Five checked routes establish\n  the nonperturbative cutoff\n  obstruction, the leading one-parameter running three-body force,\n  low-momentum prediction invariance, one-datum predictive consequences, and\n  the qualified shallow-state and triton extensions. Its\n  pairwise-only cutoff obstruction independently realizes\n  `Framework/ThreeBodyPairwiseInputInsufficiency.lean`, while its promoted\n  running-force route realizes `Framework/RenormalizedPrediction.lean`.\n  Its pairwise-input context fixes the dressed dibaryon description, on-shell\n  amplitude observable, and low-energy regime before constructing the shared\n  model. Its grounding boundary additionally requires completed two-body\n  resummation and the pairwise-only three-body equation, but no nonuniqueness,\n  cutoff sensitivity, or insufficiency output.\n  Its ordinary shared explanation starts from the pairwise-only route; its\n  source-sensitive refinement additionally retains the resummation,\n  three-body equation, and asymptotic cutoff derivation and stops before the\n  running-force remedy.\n- `PhysicsLogic/Papers/Thomas1935.lean`: paper-local finite-range and singular\n  neutron-proton interaction models with the original finite-support\n  potential, exterior `A exp(-lambda r)/r` deuteron, exact signed binding\n  relation, and both pair potentials. The singular route retains the genuine\n  `A(1/r-lambda)` contact limit, `4 pi A^2=2 lambda`, two distinct\n  neutron-proton coincidence channels, the mixed three-body kinetic term,\n  and the explicitly absent triple-contact condition. Its separate\n  variational input retains both contact-surface corrections rather than\n  reusing a divergent finite-range quadratic form. Physically inhabited\n  countermodels share identical deuteron data while producing distinct\n  double-contact amplitudes and three-body energies. The paper retains its\n  observed-mass constraint, disjunctive physical alternatives, and\n  numerical-scope qualifications. Its singular route proves absence of an\n  algebraically least three-body energy and realizes the shared pairwise-input\n  insufficiency framework without selecting one remedy. Its shared context\n  fixes the singular interaction, triton binding observable, and nuclear\n  regime before constructing the model, and its calibrated relation retains\n  both physical contact equations. The shared instability adapter\n  reconstructs the singular local setup from the supplied shared calibration\n  and pairwise-construction facts before invoking the variational calculation;\n  the reverse adapter recovers that source setup from the output-led endpoint.\n  An ordinary theorem explains the instability from the shared route, while\n  a distinct source-sensitive typed theorem retains that setup and\n  calculation without consuming the endpoint or selecting a remedy.\n- `PhysicsLogic/Papers/EpelbaumGloeckleMeissner1998.lean`: paper-local\n  chiral pion-nucleon Hamiltonians, eta/lambda projection,\n  Bloch-Horowitz energy-dependent reduction, Okubo unitary decoupling,\n  pion-number recursion, finite-order potential construction, complete\n  two-nucleon term accounting through the first correction, leading\n  three-nucleon cancellation, and explicit regularization, Delta, and\n  numerical open obligations. Its certified routes retain orthogonal\n  complementary projector actions; the original `kappa_i` and `nu_A`\n  counting formulas; the full spin/isospin pion-exchange potential and\n  independent scalar/tensor contacts; projection graphs without nucleon-only\n  denominators; and the equal-and-opposite rational three-body contributions.\n  Twenty-two physical countermodels reject formula substitutions and preserve\n  the distinction between internal unitary cancellation and iterated\n  old-fashioned recoil.\n- `PhysicsLogic/Papers/EpelbaumGloeckleMeissner1999.lean`: paper-local\n  realization of the Part-II two-nucleon calculation: imported and\n  renormalized NNLO potential, sharp and exponential regulation,\n  Lippmann-Schwinger iteration, all nine published NNLO coefficients and\n  their explicit `4 + 4 + 1` S/P/S-D projected contact formulas, distinct\n  NLO/NNLO fit windows and sharp/exponential cutoffs, an unfitted three-D-one\n  prediction, the complete selected NLO/NNLO/experimental deuteron table,\n  nonobservable D-state probabilities, the actual `47.1/2.5 GeV` spurious\n  state scales, and an explicitly incomplete Delta extension. Lean checks\n  that binding-energy improvement need not improve the quadrupole moment.\n  It independently realizes both finite-order-interaction plus iterative\n  dynamics and post-calibration prediction, with separate theory/model/world\n  grounding.\n- `PhysicsLogic/Papers/Einstein1916.lean`: paper-local coordinates, metrics,\n  metric connections, equations of motion, curvature tensors, bodies,\n  sources, energy tensors and traces, field equations, coordinate-dependent\n  total matter-plus-gravity energy complexes, approximation regimes, and\n  phenomena;\n  checked routes from Einstein's two motivations through covariance, metric\n  interpretation, connection-built geodesic motion with the original\n  `Gamma^tau_(mu nu) = -{mu nu;tau}` Christoffel index order, the complete\n  signed four-index equation-(43) metric-curvature formula, and\n  a separately checked curvature-contraction dependency retaining the original\n  upper-to-last-lower trace, the geometric and coordinate vacuum equations,\n  the trace-adjusted sourced equation under its displayed\n  `sqrt(-g) = 1` condition, separated from its relativity limitation, and\n  its separately checked coordinate-scoped conservation validation, the\n  covariant matter balance, the explicit frictionless-fluid Euler\n  specialization that consumes that preceding balance certificate, the\n  generalized Maxwell systems with value-level covariant equations\n  (59), (60), (62), (63), (65), (66), and (66a), explicit coordinate-derivative\n  laws and a checked potential-curl-to-cyclic-identity step, plus the separate\n  three-dimensional dictionary (61), (60b), (64), (63a), and (65a),\n  field-current force density, electromagnetic energy balance, and free-charge\n  recovery of the matter balance with open matter-ontology scope, the Newtonian\n  limit, and\n  the scoped redshift, 1.7-arcsecond\n  solar-deflection, and 43-arcsecond-per-century Mercury conclusions.\n  Seventeen inhabited fidelity boundaries now include computed Lorentzian,\n  spherical-coordinate, Ricci-flat tidal, source-sign, and volume-derivative\n  controls. These pointwise witnesses do not assert global solution existence.\n- `PhysicsLogic/Papers/Rosen1940.lean`: paper-local formal-versus-physical\n  two-metric semantics across Rosen's paired Parts I and II. Part I now\n  retains equations (7)-(10) as a selected four-coordinate component package:\n  the gravitational/flat connection difference, its metric-derivative\n  formula, the Ricci rewrite, and `kappa = sqrt(g / gamma)`, tied to the\n  selected metrics and tensors. Both metric determinants must be nonzero,\n  without requiring either Lorentzian determinant to be positive; a checked\n  degenerate-metric countermodel separates this from the square-root domain.\n  Part II independently retains the exact printed motion formulas\n  `m=m_0*d_sigma/ds=m_0/w=m_0*sqrt(gamma_44/g_44)` and the separately\n  qualified weak-field approximation `m approximately m_0*(1-phi)`.\n  Equal inertial and gravitational masses need not be constant: the same\n  reference rest mass two gives proper masses two and one when the selected\n  gravitational metric changes. Sixteen physical countermodels additionally\n  separate a fixed physical flat background from dynamical gravitational\n  fields, shared coordinate motion from identical physical intervals,\n  force-free potential from the proposed absolute-frame light-drag effect,\n  and matter expansion in fixed flat space from expanding geometry. The\n  physical-flat-background, empirical-agreement, absolute-frame,\n  cosmological, and open foundational routes remain separate and do not\n  turn covariance into background independence or Rosen's deferred Miller\n  proposal into established evidence. A computed metric-jet adapter supplies\n  the actual equations-(7)-(10) package and independently realizes the shared\n  geometry contract; flat auxiliary curvature neither erases its coordinate\n  connection nor imposes vacuum on the gravitational metric.\n- `PhysicsLogic/Papers/Schwarzschild1916.lean`: paper-local coordinate\n  systems, exact point-mass metric, reduced vacuum equations, integration\n  constants, approximation, worldline, orbit, and frequency-law semantics;\n  checked exact integration and uniqueness, finite-order nonuniqueness\n  assessment, Mercury and circular-orbit deductions, and a separately\n  qualified molecular expectation. Equation (14)'s areal-radius line element\n  and equations (15)-(18)'s equatorial first integrals and reciprocal-radius\n  orbit equation are value-level paper-local formulas; a named orbit output\n  cannot replace the latter package. Its exact-solution and orbital routes\n  realize the shared vacuum-metric-dynamics interface without importing\n  post-1916 horizon semantics.\n- `PhysicsLogic/Papers/Nordtvedt1968.lean`: paper-local test-element and\n  self-gravitating-body scopes, operational mass-ratio calibration, general\n  weak-field metric coefficients, stationary two-body cancellations,\n  Brans-Dicke comparison, virial sphere reduction, and nonstationary\n  oscillatory terms. It realizes the existing equivalence-principle semantics\n  while keeping the paper's coefficient calculations and unresolved\n  coordinate interpretation local.\n- `PhysicsLogic/Papers/HughesRobinsonBeltranLopez1960.lean`:\n  paper-local finite evidence logic for a selected galactic `P_2`\n  inertial-mass anisotropy model. The chlorine and lithium observations now\n  retain the printed 22/104-degree sidereal comparison, 9190-Mc/sec and\n  30-kc/sec atomic readout, 4.3-ppm versus `5.0 +/- 1`-ppm nuclear\n  widths, 8-cycles/sec residual allowance, and the `10^-10` and\n  `10^-20` ratios as proposition-valued data tied to the selected\n  objects; the oxygen `10^-10` comparison remains its own branch.\n  Lean checks the finite ratio hierarchy while the Coulomb and\n  central-potential conversions remain explicit imported physical hypotheses.\n  It independently realizes the shared controlled-resonance model test using\n  the bounded selected `P2` model, protected references, finite nuclear\n  sensitivity, and separate source-calculation branch.\n  Its seven paper-local countermodel theorems now retain actual P2, angular,\n  frequency, field, linewidth, ratio, conversion, scope, and evidence data:\n  a 22/22-degree collapsed pair with zero prediction/rotation residuals still\n  fails both scans; equal finite bounds cannot establish stronger nuclear\n  sensitivity; and the evidence witness has zero bounded-model-support\n  residual but nonzero theory-support residual. No `Unit`/`Bool` framework or\n  constant relation replaces those distinctions.\n- `PhysicsLogic/Papers/Penrose1965.lean`: paper-local nonspherical collapse,\n  positive-area future trapping with both independent null expansions\n  negative, future-directed optical-scalar focusing, compact-boundary\n  construction, and the original signed-degree transport contradiction on a\n  noncompact Cauchy surface. The checked degree argument derives the shared\n  topology obstruction. Sixteen inhabited fidelity boundaries distinguish\n  one-sided convergence, marginal trapping, finite caustics, signed\n  preimage counts, physical alternatives, and stronger singularity claims.\n- `PhysicsLogic/Papers/HawkingOpenUniverses1965.lean`: paper-local expanding\n  equation-(1) Robertson-Walker metric with all three `K=-1,0,+1` branches,\n  a separate flat/open theorem scope, compact hyperbolic quotient\n  with a noncompact deck-translation cover and explicit incompleteness\n  descent, and both original large-sphere past-null convergences. Its\n  `0 \u003C= delta \u003C epsilon` perturbation calculation proves strict positivity\n  independently for both null families, while the weaker global alternative\n  retains the unique timelike Ricci eigenflow, noncompact causal cover,\n  complete spatial hypersurface, pointwise positive density bound, and\n  uniform flow-tilt bound. Twenty\n  inhabited fidelity boundaries preserve compact-versus-cover topology,\n  strict trapping, two-sided control, curvature-divergence nonimplication,\n  and the deferred closed-universe extension.\n- `PhysicsLogic/Papers/Friedmann1922.lean`: paper-local homogeneous-curvature\n  cosmology, the stationary/nonstationary split, Einstein and de Sitter\n  stationary cases, radius-equation reduction, monotone first- and\n  second-kind worlds, periodic worlds, an `actualWorldKindAt` relation with\n  existence-plus-uniqueness determination, a checked open-alternatives\n  adapter, and explicit cosmological-constant and illustrative-period\n  qualifications. Its ten directional paper-local countermodels are now\n  value-bearing: equations (4)-(5) can hold at `R=1`, `c=kappa=1`,\n  `lambda=0`, `R'=0`, `R''=-1/2`, and `rho=3` while equation (6) fails for\n  `A=2`; positive mass can fail equation (9); the subcritical witness has\n  roots one and two with a negative between-root radicand; the monotone\n  creation radii are zero and two. Period identification retains an integer\n  multiple of a calculated period and finite existence, whereas the\n  unbounded-time witness retains genuine recurrence. The calculated period\n  selects neither temporal reading, and the original `5*10^21`-solar-mass,\n  `10^10`-year illustration leaves actual-world determination open. No\n  proposition-pair or temporal-status truth table replaces these Friedmann\n  distinctions.\n- `PhysicsLogic/Papers/Lemaitre1927.lean`: paper-local homogeneous\n  variable-radius cosmology, field equations and energy conservation,\n  constant-total-mass expansion, exact radius-ratio redshift, the near-source\n  velocity-distance approximation, and original 43-object velocity catalog\n  with 42 selected nebulae after excluding NGC 5194 because of its NGC 5195\n  association. Its value-bearing calibration retains absolute magnitude\n  `-15.2`, `log_10(r/parsec) = 0.2m + 4.04`, declining\n  `1/sqrt(1+r^2)` distance weights, directed `300 km/s` solar motion,\n  asymmetric `0.4`-to-`2.5` distance uncertainty, distinct weighted `625`\n  and unweighted `575 km/s/Mpc` estimates, and their nonzero `6.25` and\n  `3 km/s` rounded-mean residuals. The Einstein static, current expanding,\n  and asymptotic initial radii are respectively `2.7e10`, `6e9`, and\n  `2.7e8` parsecs, while the separately rounded `y = 0.0465` is not falsely\n  identified with their exact ratio. Twenty inhabited fidelity boundaries\n  retain these distinctions and leave the radiation-pressure origin as a\n  suggestion rather than a result. The original scan corrects the archived\n  OCR's erroneous 48-object catalog reading.\n- `PhysicsLogic/Papers/Hubble1929.lean`: paper-local construction of the\n  selected nebular distance sample, the literal p. 170\n  `rK + X cos(alpha) cos(delta) + Y sin(alpha) cos(delta) +\n  Z sin(delta) = v` equation of condition with the fit residual kept\n  explicit at the data boundary, individual and grouped proportional fits,\n  residual and independent pre-conclusion validation checks, a roughly linear\n  first-approximation conclusion over a restricted range, a downstream NGC\n  7619 consistency check, and a possible but unestablished de Sitter\n  interpretation. A proof-free observational readout retains the actual\n  24-object and 9-group samples, 465/513 fits with 50/60 uncertainties,\n  500 adoption boundary, 150/110 residuals, four-object Virgo scope,\n  all-22 1.4-million-parsec/745-km/s mean check, downstream 7.8 versus 7\n  million parsecs, and separate de Sitter prediction residual without\n  replacing observational distinctions by enum-to-Prop truth tables.\n- `PhysicsLogic/Papers/RiessEtAl1998.lean`: paper-local classified supernova\n  sample, cross-band and light-curve distance reductions, scoped FRW\n  likelihood with separate nonnegative-matter and nonbouncing-big-bang domain\n  restrictions, two-component acceleration bridge, named-systematic\n  assessment with unresolved evolution, and separate age and eternal-expansion\n  routes. Terminal propositions retain the paper's 15-object primary sample,\n  magnitude excess, method-specific flat-`Lambda` fits, significance ranges,\n  `q_0`, age, and eternal-expansion outputs. Its source-sensitive shared\n  explanation is derived directly from the raw observation, distance,\n  likelihood, deceleration, and robustness calculations.\n- `PhysicsLogic/Papers/PerlmutterEtAl1999.lean`: paper-local matched low- and\n  high-redshift samples, cross-filter and stretch standardization, Fit A/B/C\n  progression, the printed selected-Fit-C double integral that marginalizes\n  the joint four-parameter probability density over `cal M_B` and `alpha`,\n  primary acceleration interpretation, identified error budget with grey-dust\n  and evolution loopholes, and qualified comparison with the partially\n  overlapping Riess analysis. Terminal propositions retain the 54-object Fit\n  C result, the nuisance-marginalized cosmology probability, joint and flat\n  density estimates, 99-percent positive-`Lambda` confidence, zero-`Lambda`\n  dimming requirement, and both dimensionless age estimates. Its\n  source-sensitive shared explanation is derived directly from the raw\n  standardization, Fit A/B/C, interpretation, and systematic-refit\n  calculations.\n- `PhysicsLogic/Papers/FixsenEtAl1996.lean`: paper-local full-mission FIRAS\n  reduction, calibrated monopole detection, Planck residual fit, original\n  `2-21 cm^-1` band and `320`-sample external-blackbody calibration,\n  systematics-qualified temperature, dipole, spectral-distortion, imported\n  energy-release, and deferred-calibrator routes. Section 4 separately\n  retains thermometry `2.730 +/- 0.001 K`, color `2.7255 +/- 0.0009 K`,\n  and dipole `2.717 +/- 0.007 K`, including the shared color/dipole\n  frequency calibration. The dipole retains `3.369 + 0.003 = 3.372 mK`,\n  `0.004 mK` statistical and `0.006 mK` Galactic-systematic contributions,\n  the rounded `0.007 mK` uncertainty, distinct one-sigma and 95-percent\n  directional intervals, and a separately imported `371 km/s` Doppler\n  interpretation. Section 6 retains the\n  printed equation-(3) linear fit and equations (4)-(7) Bose-Einstein,\n  chemical-potential derivative, optical-depth `y`, and Compton-shape\n  formulas as selected value-level packages tied to the FIRAS spectra,\n  temperature, Galactic contaminants, and distortion objects. A source-valued\n  Table 4 witness retains the `2.27 cm^-1` bin, `5 kJy/sr` residual,\n  `14 kJy/sr` uncertainty, and nonzero `4 kJy/sr` Galactic foreground;\n  the `2.728 +/- 0.004 K` temperature retains its systematics-dominated\n  95-percent confidence qualification. The `mu` and `y` fits retain their\n  separate redshift epochs and are not jointly fitted. Eighteen independent\n  physical countermodels separate the reported calibration, method,\n  dipole, and distortion claims from stronger unsupported interpretations,\n  including the independently imported Wright energy-release conversions.\n- `PhysicsLogic/Papers/Kibble1976.lean`: paper-local finite-temperature\n  symmetry breaking, including the original one-loop scalar-plus-gauge\n  effective potential, gauge-dependent critical temperature, and strictly\n  nonzero below-critical order parameter from equations (3)-(5); random\n  nonequilibrium protodomain formation explicitly consumes those formulas,\n  correlation-scale input, separate wall, string, and monopole topology\n  routes, distinct `S¹` string and `S²` monopole shortest-path production\n  estimates with separate illustrative domain families and actual normalized\n  orientation-configuration sums: two favorable three-domain chambers out\n  of eight give `1/4`, while two favorable four-domain chambers out of\n  sixteen give `1/8`. Rational unit-circle and unit-sphere vacuum vectors\n  retain their actual signed triangle/tetrahedron coefficients, origin\n  enclosure, and enclosing-versus-semicircle/hemisphere distinctions.\n  Independent unbiased orientation weights and the continuum shortest-path\n  reduction remain separate explicit assumptions; bias, correlations,\n  missing obstruction geometry, raw-versus-normalized weights, and the\n  distinct simplex arities have inhabited physical countermodels. The paper\n  also retains wall and string evolution assessments and explicitly unresolved\n  present-density, string-mechanism, and `pi_3` obligations. Its shared\n  adapter exports only\n  the selected domain-to-vacuum-value assignment and the causal-domain\n  assembly, obstruction, and monopole-formation route, with an exact\n  paper-context retention certificate for the shared model. Its local\n  grounding input is a valid selected transition plus independent\n  protodomains, not a shared-framework implementation detail.\n- `PhysicsLogic/Papers/Guth1981.lean`: paper-local cosmological models,\n  initial conditions, phase transitions, conserved quantities, monopoles,\n  bubbles, Higgs orientations, bubble and monopole counts, rates, an explicit\n  structural definition of the horizon problem from causal disconnection and\n  thermal uniformity, a separate structural flatness diagnosis from Hubble\n  tuning and conserved curvature, a source-anchored bridge to generic problem\n  targets, a phase-attached real-valued readout for equations (3.5) and\n  (3.8)-(3.13) that retains the shifted false-vacuum density, temperature-form\n  Friedmann equation, halted and unchecked curvature branches, bounded-relative\n  cooling approximation, exponential scale factor, and Hubble relation without\n  promoting those formulas into a generic cosmology framework, an explicit\n  distinction between slow nucleation and the presumed subcritical\n  percolation regime, converted volume fraction and connected phase\n  completion, and cosmological consequences; checked routes expose the\n  family-level topology-and-coalescence logic of Kibble monopole production,\n  the causal bubble-radius bound in equation (4.1), the explicitly\n  order-qualified inverse-volume monopole estimate in (4.2), Preskill's\n  independent observational abundance bound in (4.3), the resulting\n  coalescence-temperature bound and four-order supercooling estimate in\n  (4.4), and the separate weaker strong-transition revision in (4.5);\n  inhabited countermodels prevent a named horizon bound, causal radius\n  inequality, Kibble density estimate, or revised temperature estimate from\n  supplying the missing source formulas, independent Preskill observation,\n  or superseded stronger coarse limit,\n  including the selected bubble-to-Higgs-orientation assignment, pairwise\n  causal independence, and uncorrelated assigned orientations,\n  with an exact paper-context retention certificate for the shared\n  defect-formation model,\n  uses a paper-local GUT-transition and independent-bubble setup for\n  grounding,\n  and distinguish successful horizon/flatness and monopole mechanisms from\n  the original scenario's graceful-exit\n  nonviability and the open status of proposed repairs. The sharp-nucleation\n  assessment supplies only its conditional physical outputs; separate\n  source-mapped establishment requirements derive why the proposed repair\n  remains unestablished. Its local-patch source relation separately retains\n  the preprint's locally prepared sub-horizon region, accelerated expansion,\n  observed-region coverage, and distinct horizon/flatness transfer before any\n  established shared patch or graceful-exit result is used.\n- `deprecated/paper-formalizations/`: retired paper-first formalizations and\n  their source maps, coverage proofs, and target documents. They remain\n  available for comparison but are outside the active package.\n- `PhysicsLogic/Logic/Formula.lean`, `Argument.lean`, and `Route.lean`: auxiliary\n  source-map syntax and structural validation, including transitive route\n  dependency inheritance, topological-order checks, and premise-sensitive\n  propagation of epistemic justification statuses to route outputs.\n- `PhysicsLogic/Logic/Semantics.lean`: reusable propositions stating that a\n  source claim, each inference step, and every output of a named route holds\n  under a paper-local Lean interpretation. Its checked step-lookup interface\n  lets coverage proofs certify the exact premise-to-conclusion rule declared\n  by a source-map step without copying the paper's semantic vocabulary into\n  the shared library. Conclusion-only certification is restricted by its Lean\n  type to steps whose declared premise list is literally empty; the policy\n  audit checks the same invariant for every active paper. For ordinary\n  non-reductio routes, ordered step soundness computes output truth\n  compositionally.\n  Witten 1982 now follows the same discipline across its full graph:\n  ordinary and twisted calculations inherit the finite-volume index logic,\n  while the chiral interpretation inherits both index multiplicity and the\n  computed zero-mode charge sequence. The ordinary calculation distinguishes\n  the true-invariant `U`-tower candidate from the pseudo-invariant `V`\n  multiplet and now retains the preceding gauge logic: periodic gauge shifts\n  plus Gauss law make the Cartan variables periodic, while identity-connected\n  Weyl transformations plus Gauss law make physical states Weyl invariant.\n  Both source calculations now have direct paper-local endpoints: the\n  periodic endpoint retains pure-theory scope, weak-coupling reduction,\n  Cartan gauge constraints, Cartan/Weyl data, and the signed branch result\n  together, while the twisted endpoint retains pure-theory scope,\n  sector-classification data, and `I=N` together. A separate electric-flux\n  refinement keeps ordinary zero flux on the unresolved periodic branch,\n  gives zero index to nonzero ordinary and transverse twisted sectors, and\n  gives unit index to each parallel twisted sector. The twisted calculation\n  now exposes its complete nonzero-index,\n  zero-state, finite-volume, and large-volume chain before applying the\n  separately qualified boundary-condition expectation. Its true-invariant\n  branch selection remains a separate author-qualified proposition. The\n  deformation argument also realizes the shared protected-prediction\n  paradigm: admissible connection, index protection, and value transfer are\n  distinct propositions, and the periodic-volume theorem consumes that\n  adapter. Bell 1964 distinguishes unrestricted bipartite outcomes from\n  Bell-local response functions: the EPR-predetermined outcomes are connected\n  to the candidate completion by an explicit realization bridge, locality is\n  an explicit factorization equation, the shared applicability result retains\n  the exact selected response pair, and the established result stores the\n  nontrivial response domain and physical outputs while reconstructing the\n  route separately. Remote influence is\n  witnessed by changed outcomes under changed\n  distant settings, equation (15) is checked from explicit normalized\n  positive-average laws, and downstream routes inherit their EPR and no-go\n  inputs from certified predecessors. Its final physical route separates the\n  Lorentz causal-direction principle from the checked boosted-frame order\n  reversal. Maldacena 1997 likewise represents its\n  original v1 complex\n  coupling dictionary by explicit real-component equations for `g`,\n  `gYM`, `theta`, and the RR scalar `chi`, rather than an opaque correspondence\n  predicate; its symmetry evidence records `SO(2,4)`, `SO(6)`, `N=4`, and\n  the doubled superconformal supersymmetry rather than comparing arbitrary\n  symmetry labels. Its sector argument now identifies the worldvolume and\n  near-horizon theories through two explicit decompositions of the same D3\n  low-energy system with the same asymptotic closed-string spectator sector,\n  rather than inferring identity from bare survival in a common limit. Its\n  supergravity calculation now realizes the shared regime-and-accuracy\n  approximation semantics: admissible boundary data, reliability, and an\n  explicit calculation-correctness bridge are all required before exact bulk\n  predictions are transferred to the supergravity description. Its\n  paper-local reliability condition preserves both the direct `gN >> 1`\n  branch for `g \u003C= 1` and the original footnote's S-dual `N/g >> 1` branch\n  for `g > 1`.\n- `PhysicsLogic/Papers/*/SourceMap.lean`: primary-source provenance and paper\n  ordering; these files do not substitute for the formal logic.\n- `PhysicsLogic/Papers/*/Coverage.lean`: exhaustive interpretations from every\n  source-map atom to a proposition in the primary semantics or an explicit\n  paper-local context, plus checked output theorems for every named route.\n  `RouteSemanticallyCertified` strengthens this with soundness of every\n  individual source-mapped step. Every active benchmark now uses the stronger\n  certificate for every route: Witten 1981, Witten 1982, Bell 1964,\n  Maldacena 1997, AMPS 2012, Jarzynski 1997, Noether 1918,\n  Hohenberg-Kohn 1964, Kaplan-Savage-Wise 1998,\n  Epelbaum-Gloeckle-Meissner 1998, Einstein 1916, Guth 1981, and\n  Gubser-Klebanov-Polyakov 1998, Knox 1995,\n  Scott-Srednicki-White 1993,\n  Goldstone-Salam-Weinberg 1962, Anderson 1963, Landau 1941, and\n  Bogoliubov 1947. A source step classified as a\n  reductio hypothesis introduces a temporary assumption; it is not asserted\n  globally, while all uses and the discharged conclusion remain ordinary\n  checked semantic obligations.\n  Adding an unmapped atom or omitting a required certificate fails the build\n  or policy audit.\n- `docs/targets/witten-index-1982.md`: benchmark scope and acceptance criteria.\n- `docs/targets/witten-dynamical-breaking-1981.md`: original vacuum-energy,\n  perturbative-protection, lower-dimensional model, four-dimensional\n  obstruction, qualified proposal, and open-question routes.\n- `docs/targets/bell-1964.md`: original-paper scope and logical cautions.\n- `docs/targets/maldacena-1997.md`: original-v1 D3-brane scope and epistemic\n  distinctions.\n- `docs/targets/amps-2012.md`: original-v1 contradiction routes, extensions,\n  scope limits, and acceptance criteria.\n- `docs/targets/jarzynski-1997.md`: original-v1 isolated, reservoir, limit,\n  ensemble-consequence, thermostat, and practical-scope routes.\n- `docs/targets/riess-et-al-1998.md`: original-v1 sample, calibrated-distance,\n  FRW-fit, acceleration-interpretation, systematic, age, and fate routes.\n- `docs/targets/perlmutter-et-al-1999.md`: original-v1 standardization, Fit\n  A/B/C, systematic-budget, residual-loophole, age, ontology, and qualified\n  cross-check routes.\n- `docs/targets/noether-1918.md`: original finite-group, arbitrary-function,\n  converse, on-shell, mixed-group, and Hilbert-energy routes.\n- `docs/targets/hohenberg-kohn-1964.md`: original exact density theorems,\n  nearly uniform response, gradient limitation, slowly varying expansion,\n  and partial-summation scope.\n- `docs/targets/landau-superfluidity-1941.md`: original quantum-liquid,\n  phonon-roton, zero-temperature threshold, two-motion, hydrodynamic, and\n  qualification routes.\n- `docs/targets/bogoliubov-superfluidity-1947.md`: original weak-gas\n  diagonalization, quasiparticle, equilibrium-threshold, frictionless-motion,\n  approximation-scope, and proposed-extension routes.\n- `docs/targets/kaplan-savage-wise-1998.md`: original pionless PDS,\n  large-length power counting, explicit-pion completion, scale cancellation,\n  fit warning, and coupled-channel scope.\n- `docs/targets/mayer-1949.md` and\n  `docs/targets/haxel-jensen-suess-1949.md`: independent original\n  nuclear-shell routes, their exact relation-retaining shared models, and the\n  distinction between Mayer's square-well ordering and the\n  Haxel-Jensen-Suess isotropic-baseline/anharmonic/Yukawa construction; Mayer's\n  qualified Table I order, thallium crossing, and pair-filling caveat remain\n  paper-local.\n- `docs/targets/epelbaum-gloeckle-meissner-1998.md`: original chiral\n  projection formalism, unitary decoupling, recursive construction,\n  two- and three-nucleon calculations, and open-program scope.\n- `docs/targets/gubser-klebanov-polyakov-1998.md`: original boundary\n  generating-functional proposal, conformal-symmetry, correlator, spectrum,\n  controlled-regime, and open-program routes.\n- `docs/targets/ryu-takayanagi-2006.md`: original static minimal-area\n  proposal, exact and qualitative checks, finite-temperature interpretation,\n  and open-extension scope.\n- `docs/targets/lewkowycz-maldacena-2013.md`: original density-matrix,\n  replica, Einstein, cone, AdS/CFT, reflection, and extension-scope routes.\n- `docs/targets/knox-1995.md`: original single-sky estimator,\n  instrument-design, likelihood-forecast, consistency-test,\n  cosmological-correction, and cosmic-confusion routes.\n- `docs/targets/goldstone-salam-weinberg-1962.md`: original perturbative,\n  current-spectral, charge, composite, and outlook routes.\n- `docs/targets/anderson-1963.md`: original plasma response, gauge\n  invariance, bare-response spectrum criterion, superconducting mode\n  conversion, analogy, and scope routes.\n- `docs/targets/thooft-1974.md`: original double-line color counting,\n  topological large-rank expansion, planar dominance, light-cone surface,\n  Hamiltonian reconstruction, and conditional binding routes.\n- `docs/targets/stanley-1968.md`: original vector-spin definitions,\n  normalized-partition derivation, supporting checks, heuristic comparison,\n  proposed uses, and critical-index order-of-limits scope.\n- `docs/targets/einstein-1916.md`: original motivation, covariance, metric,\n  motion, field-equation, conservation, fluid, electromagnetic,\n  Newtonian-limit, and prediction routes.\n- `docs/targets/nyquist-1928.md`: original frequency-balance,\n  transmission-line, circuit-noise, carrier-scope, and Planck-replacement\n  routes.\n- `docs/targets/callen-welton-1951.md`: original perturbative-dissipation,\n  equilibrium-fluctuation, generalized-relation, Brownian, vacuum,\n  acoustic, and interpretation-scope routes.\n- `docs/targets/kubo-1957.md`: original weak-response, operational-scope,\n  canonical-relaxation, separate static-limit, correlation, magnetic and\n  conduction, reciprocity,\n  fluctuation-dissipation, sum-rule, and Einstein-relation routes.\n- `docs/targets/epr-1935.md`: original reality-criterion, completeness,\n  noncommuting-pair, separated-system, remote-prediction, incompleteness,\n  objection, and open-theory routes.\n- `docs/targets/wetterich-1993.md`: original exact effective-action flow,\n  endpoint, exact-potential, qualified-truncation, and grounding routes.\n- `docs/targets/wegner-houghton-1973.md`: original infinitesimal shell,\n  exact-generator, fixed-point, invariant-projection, epsilon-expansion,\n  large-`n`, and qualified finite-integration routes.\n- `docs/targets/bond-cole-efstathiou-kaiser-1991.md`: original Gaussian\n  hierarchy, sharp-`k` first crossing, correlated-filter numerics, N-body\n  assessment, merger/bias, shared abundance, and qualified-scope routes.\n- `docs/targets/tknn-1982.md`: original magnetic Bloch, bulk Kubo,\n  curvature-integrality, Harper/Diophantine equations (9) and (11),\n  tight-binding, conditional deformation, and flux-limit routes.\n- `docs/targets/niu-thouless-wu-1985.md`: original many-body twist,\n  thermodynamic averaging, integer Chern, conditional fractional,\n  nonrigorous parent-state, and bulk-scope routes.\n- `docs/targets/fu-kane-2009.md`: original QSHI junction spectrum, local and\n  bulk parity accounting, fractional Josephson response, switching-rate,\n  telegraph-noise, and experimental-scope routes.\n- `docs/targets/chandrasekhar-1931.md`: original nonrelativistic comparison,\n  relativistic equation-of-state, index-three-polytrope mass, ideal maximum-\n  mass interpretation, and scoped synthesis routes.\n- `docs/targets/oppenheimer-volkoff-1939.md`: original relativistic\n  hydrostatics, equations (11)-(19) cold-neutron formula package, numerical\n  family, turning-point mass curve, free-energy stability, Tolman comparison,\n  and qualified stellar-scope routes.\n- `docs/targets/evans-cohen-morriss-1993.md`: original proposed segment\n  measure, thermostatted reversal, finite probability-ratio, molecular-\n  dynamics, second-law, and qualified-scope routes.\n- `docs/targets/gallavotti-cohen-1995.md`: original dissipative-reversible,\n  chaotic-hypothesis, SRB construction, long-time fluctuation-ratio,\n  numerical-comparison, and qualified-scope routes.\n\nThe two Hall papers independently earn\n`PhysicsLogic/Framework/TopologicalTransverseResponse.lean`. The shared\ncomponent contains only the gapped closed two-parameter family,\nresponse-curvature identity, integrality calculation, integer-unit\nnormalization, and explicitly conditional gap-preserving stability. Magnetic\nBloch momentum and many-body boundary twist remain distinct paper-local\nrealizations. Its proof-free model retains all nine selected indices and all\neleven route-used relation families. Each context owns one exact selected\nmodel, and route applicability consumes equality to it. Both paper adapters\nprove exact semantic retention and construct the direct established response\nfrom their paper-local setup and three outputs before recovering the generic\nroute. Theory/model/world grounding requires the actual selected gapped-family\nsetup but does not assume curvature identity, integrality, normalization, or\nthe quantized-response route. A positive countermodel grounds\nthe exact model while the technical route is false; exhaustive mutation\ntheorems reject all nine index and eleven relation changes. The established\nresult is definitionally the direct nonvacuous proposition containing the full\ngapped-family setup and all three calculation outputs at one model. A finite\nwitness makes every retained index and relation directly active, while a\nvacuity countermodel proves that implication-valued calculations without setup\ncannot be grounded or counted as an inhabited response route.\nThe five directional shared countermodels now retain a positive gap and\nparameter-cycle area, response unit, curvature integral, integer invariant,\nselected and comparison responses, curvature/integrality/normalization\nresiduals, and the minimum deformation gap. A checked positive witness has\nunit gap, unit cycle, curvature and invariant one, and response one; separate\nwitnesses falsify the curvature identity, integrality, normalization, other\nresponse, or actual gap openness. TKNN's eight paper-local witnesses retain\nmagnetic flux `3/1`, a gapped family, Kubo and phase-patching residuals,\ngap index three, Diophantine coefficients `(s,t)=(0,1)`, and Landau level one,\nsubband responses `(0,1,0)` with integer total one, distinct linear and\nstrong electric fields, a nonzero tunneling rate, and interacting/disordered\ncomparison strengths. NTW's seven witnesses retain a finite twist gap and\nsize/correlation scales, fixed-twist responses `0,2` with average one,\nnondegenerate versus degree-three sectors, Chern-sum and parent-derivation\nresiduals, bulk response and edge residual, and a gapless interacting,\ndisordered comparison. No proposition-pair or `Unit` truth table replaces\nthese distinctions.\nThe optional deformation stage is also output-led. Its applicability route\nrequires the established integer response, a selected connecting deformation,\nactual gap preservation, and a paper-local conditional stability calculation;\nits established endpoint stores only the direct response, open-gap setup, and\nstability output. That endpoint now realizes the mature protected-prediction\ncontract between typed source and target ends of the selected deformation,\npreserving the response, integer witness, and response unit. TKNN's shared\nadapter still needs an independent open-gap premise because the original paper\nexplicitly says gap nonclosure was unproved, while Niu-Thouless-Wu includes the\nopen-gap condition in its selected deformation setup. Countermodels prevent a\nvacuous conditional calculation, a missing open gap, or a bare stability label\nwithout the source quantization from establishing the transfer.\n\nThe shared component now also records derivational provenance without\ncollapsing the two constructions. A proof-free\n`TopologicalTransverseResponseSourceConstraint` stores the exact selected\nmodel, a typed paper-local derivation token, and its proposition-valued\ninterpretation. TKNN realizes its token only from the magnetic-Bloch,\nbulk-Kubo, state-derivative, Stokes, boundary-phase-winding, integrality, and\nnormalization stages. Niu-Thouless-Wu realizes a different token only from the\nmany-body fixed-twist Kubo calculation, short-range/thermodynamic boundary\ninsensitivity, twist averaging, first-Chern identification, integrality, and\nnormalization. Both raw routes realize\n`SourceStructuralTopologicalTransverseResponseExplanationAt`; neither may\nconsume the established or nonvacuous shared response.\n\nThe source-sensitive result extends through deformation only by also consuming\nthe raw gap-preserving setup and conditional stability calculation. TKNN still\nrequires an independent proof that the gaps remain open; NTW uses its explicit\nopen-gap deformation setup. A finite converse model retains the completed\nresponse, ordinary structural explanation, open-gap stability, and protected\ntransfer while making the source relation false. Thus common topological\noutput and protection do not manufacture common derivational provenance.\n\nTKNN 1982 and Haldane 1988 independently earn the coarser\n`PhysicsLogic/Framework/GappedBandHallQuantization.lean`. Its ordinary shared\nroute retains the selected periodic noninteracting gapped-band setup, a\npaper-local integer-index calculation, and a paper-local transport\nnormalization rooted in the same setup. The shared contract does not order\nthose outputs: TKNN locally reaches\nintegrality before normalization, while Haldane's Streda calculation supplies\nthe signed index and response relation together. A separate value-bearing\n`PhysicalSourceGappedHallReadout` now retains TKNN's nonzero magnetic field,\nmagnetic Bloch boundary winding, original `r = s_r q + t_r p` and\n`2 |s_r| \u003C p` branch, and\n`sigma_xy = (e^2/h)(t_v + N - 1)` formula without identifying them with\nHaldane's zero-net-flux honeycomb model. Haldane's paper-local source atoms\nretain all four coefficients of the printed honeycomb Bloch Hamiltonian,\nthe opposite valley momentum commutators, the original relativistic Landau\nladder, and its valley-signed, field-odd unpaired zero mode. The shared\nsource readout retains the exact `M ± 3 sqrt(3) t2 sin(phi)` masses and\ndistinguishes the number-density shift `Delta n = e B/h` from the printed\nelectric charge-density shift `Delta rho = e^2 B/h`; the original Streda\nrelation is `sigma_xy = d rho/dB`, not an additional multiplication by `e`.\nIts `e = 2` witness also keeps the continuum and lattice half-indices\ndimensionless until their sum is multiplied by the conductance quantum. It\nseparates trivial, anomalous, critical, spin-doubled, and Zeeman-metal\nrealizations. The proof-free ordinary model\nretains all seven selected physical indices and all ten route-used relation\nfamilies. Both adapters construct one named model, prove exact retention,\nexhaustively realize all nine shared claims, and derive grounding from the\nselected pre-output gapped-band setup plus paper-local interpretation inputs.\nGrounding assumes neither calculation nor response output. Converse models\nseparate grounding from calculation, and a seventeen-component mutation audit\ndetects every retained index and relation family. The established result is\nthe direct nonvacuous proposition containing the complete setup, integer index,\nHall conductance, and normalization relation at one actual model; both\ncalculations and the route are reconstructed from it. A finite witness realizes\nit, while a countermodel blocks vacuous\nimplication-valued calculations from masquerading as a completed physical\nroute. A separate countermodel shows that a response plus an index-unit\nnormalization relation does not itself supply the integer-index predicate.\nNamed adapter theorems expose the seven indices directly and project\nthe direct proposition from both papers. Haldane's occupied-band predicate is\nrestricted to the anomalous description, and its Fermi-gap predicate is\nrestricted to both that description and the selected honeycomb system rather\nthan silently ranging over foreign models. Haldane's separate same-sign branch\nstill selects one paper-local deformation object and requires both continuity\nand preserved gap along that object before transporting the zero-Hall index;\nthe shared source readout independently distinguishes its zero-index phase.\n\nHaldane's directional paper-local countermodels are now value-bearing.\nThey retain canceling local fluxes `(1,-1)` with nonzero chiral hopping phase,\nanomalous corner masses `(-1,1)` and index one versus equally gapped trivial\nmasses `(2,2)` and index zero, the continuum and lattice half-contributions,\nindependently falsifiable Bloch coefficients, valley Landau terms,\nnon-unit-charge number/charge density and direct Streda response,\nindependent continuous-gap-closing and\ngapped-discontinuous deformations, and spin multiplicity two with Zeeman\nshift two against gap one. The named Streda setup itself now requires\nopposite masses and positive probe/Planck values. A checked positive witness\nrealizes the source boundaries. No proposition-pair or status-enum truth\ntable replaces these Haldane distinctions.\n\nThe complete shared route now also realizes the route-bounded\n`RouteStructuralGappedBandHallQuantizationExplanationAt`. Its constraint and\nphenomenon are distinct proof-free types. Satisfaction requires exact model\nselection, the inhabited gapped-band setup, and both calculations; necessity\nis proved by applying those calculations rather than by unpacking the\nestablished endpoint. TKNN reaches this theorem from magnetic-Bloch, Kubo,\nand phase-patching inputs. Haldane reaches it independently from opposite-mass\nweak-field spectral flow, filled-level counting, and the Streda relation. A\nmodel with all terminal response relations but no physical gapped-band setup\nshows that the phenomenon does not explain itself. The claim is limited to\nthe selected integer-normalized response and does not add disorder,\ninteraction, plateau, bulk-boundary, or universal-topology conclusions.\n\nA second, source-sensitive projection keeps the two derivations distinct.\n`GappedBandHallSourceConstraint` retains the selected model, a typed\npaper-local derivation token, and its proposition-valued interpretation.\nTKNN realizes its token from magnetic-Bloch, Kubo-curvature, Stokes, and\nboundary-phase inputs; Haldane realizes a different token from opposite-mass\nweak-field Landau levels, spectral-flow counting, and the Streda relation.\nThe generic source theorem requires both the realized token and the raw\nshared route. A finite countermodel retains the completed quantization, the\nroute, and the response while making the source relation false, proving that\nshared output cannot manufacture derivational provenance.\n\n## Transfer-Complete Shared Components\n\nThe following reused framework contracts now have named paper-level theorems\nthat transfer every retained shared claim to both a selected theory and a\nrepresented physical world through explicit grounding:\n\n- partition-zero/phase-boundary correspondence: Lee-Yang 1952 and BBCKK 2004;\n  its output-led endpoint stores the actual finite-family, boundary,\n  accumulation, and singularity outputs, its two-stage finite audit model\n  realizes them, and direct activity theorems show that every selected index\n  and relation family changes a route-used proposition;\n- tripartite sharing constraints: Coffman-Kundu-Wootters 2000 and AMPS 2012,\n  with a context-owned exact selected model, retention of all tangle or\n  entropy functions, an output-led conditional result, and grounding bounded\n  by the actual three-party setup but independent of the monogamy or\n  entropy-inequality output; the conditional exclusion now projects, only with\n  an actual dominant demand, to a direct nonvacuous endpoint. CKW exposes that\n  endpoint under explicit selected-pair saturation, while AMPS exposes it\n  before thermal outgoing-mode entropy supplies the contradiction. Its\n  composed bipartite-entanglement handoff distinguishes CKW's actually\n  entangled dominant `AB` pair from AMPS's actually entangled competing `BC`\n  pair: the first realizes an inhabited composed sharing endpoint, while the\n  second contradicts the completed sharing exclusion through its positive\n  entropy witness. Exact ordered subsystem placement, witness/demand equality,\n  and paper-local tangle or strong-subadditivity calculations remain separate;\n  finite models exclude missing calculation handoffs, missing sharing bounds,\n  and relabeling one pair as the other. The source-sensitive composition also\n  retains separate entanglement, sharing, and pair-to-demand derivations; an\n  inhabited countermodel has both child source explanations and ordinary\n  composition but lacks the independent handoff derivation. Its\n  complete bound-plus-dominance route also realizes a typed structural\n  explanation of the excluded positive competing demand. A distinct-setup\n  countermodel retains that exclusion while removing the sharing bound, so\n  the output does not explain itself. Its\n  saturated finite audit model has positive demand and capacity, an\n  implication-without-dominance countermodel blocks vacuous completion, and\n  all ten retained fields directly change the nonvacuous endpoint;\n- anomaly-selected vacuum multiplicity: Witten 1982 and Seiberg-Witten 1994;\n- finite-symmetry vacuum counting: Witten 1982 and Seiberg-Witten 1994;\n- linear-response transport: Nakano 1956 and Kubo 1957;\n- accelerated-frame gravity: Einstein 1911 and Einstein 1916;\n- ground-density variational semantics: Hohenberg-Kohn 1964 and Kohn-Sham\n  1965, with selected-density admissibility and direct nonvacuous\n  attainment/minimization retained;\n- broken-symmetry mode conversion: Nambu 1960 and Anderson 1963, with\n  source-sensitive mode-conversion explanations checked to entail the shared\n  ordinary mechanism while preserving their distinct derivations;\n- macroscopic coherence suppression: Zeh 1970 and GRW 1986, with exact\n  retention of five selected physical indices and five relation families,\n  branch-pair-setup-bounded grounding, eight-claim transfer, directional\n  setup/output countermodels, a direct seven-fact nonvacuous stopping point,\n  exhaustive direct mutation of all five selected indices and five relation\n  families, and a typed mechanistic-explanation projection in which the\n  environmental or localization process produces coherence suppression while\n  the separate interpretation predicts unavailable interference. A converse\n  model retains both outputs without mechanism action. A second,\n  source-sensitive mechanistic projection retains the derivation of that\n  process rather than only its selected mechanism token. Zeh's source requires\n  dense-spectrum environmental correlation, equation (9)'s branch-dependent\n  environment states, matrix-element suppression, autonomy, and\n  noncommunication. GRW's source requires randomly timed localization,\n  universal constituent-wise application, a macroscopically distinct pointer\n  pair, amplified decorrelation, and an interference bridge. Neither source\n  theorem accepts an established endpoint or ordinary explanation. A checked\n  forgetful theorem strips only source provenance and recovers the ordinary\n  mechanism from the same physical witnesses. A finite converse model\n  completes both while falsifying source realization, so the common endpoint\n  cannot identify universal linear environmental decoupling with objective\n  stochastic collapse dynamics. Mixture, collapse, branch deletion, and\n  outcome selection remain outside the shared projection. A checked\n  value-bearing boundary readout now makes that stopping point substantive:\n  it retains distinct weighted branches, coherence magnitude and operational\n  threshold, full-state and reduced-pointer purities, a mixture-transition\n  count and residual, and a selected-branch count and residual. Zeh realizes\n  suppressed coherence and a diagonal reduced pointer with full purity one,\n  zero mixture transitions, and no selected branch; GRW realizes the same\n  suppression with full purity falling from one to one-half, one mixture\n  transition, and exactly one selected pointer branch. A separate checked\n  converse retains the produced mixture while withholding branch selection;\n- linear relative-state measurement: Everett 1957, Zeh 1970, and Rovelli 1996,\n  with exact retention of thirteen selected objects and seven relation\n  families, an output-led fifteen-fact endpoint, calibrated-setup-bounded\n  grounding independent of correlation and record outputs, eighteen-claim\n  transfer, converse models, and a twenty-field mutation audit. Each completed\n  alternative is also exposed as a calibrated, present, correlated, relatively\n  definite record branch. Everett and Rovelli independently map that branch to\n  the neutral operational-observer contract through explicit physical-system,\n  interaction, information-production, and information-availability bridges;\n  Zeh is not promoted without those semantics. A completed-measurement\n  countermodel with absent observer relations blocks name-based observerhood;\n- trapped-surface stability: Penrose 1965 and Hawking 1965, with exact\n  retention of nine selected indices and five route-used relation families,\n  route-independent grounding, seven-claim transfer, converse models, and a\n  fourteen-component mutation audit;\n- adiabatic closed-cycle phase: Berry 1984 and\n  Arovas-Schrieffer-Wilczek 1984;\n- planar exchange statistics: Wilczek 1982 and\n  Arovas-Schrieffer-Wilczek 1984;\n- finite-velocity commutator cones: Lieb-Robinson 1972,\n  Nachtergaele-Sims 2006, and Hastings-Koma 2006;\n- spectral-gap clustering: Nachtergaele-Sims 2006 and Hastings-Koma 2006,\n  with a direct model-native completed clustering route, a false-setup\n  vacuity countermodel, and fifteen selected-index plus sixteen\n  relation-family direct mutations; the cone-supported source order now has\n  its own direct endpoint and a countermodel showing generic clustering does\n  not manufacture a finite-velocity cone; the complete route also realizes a\n  typed structural explanation with a propagation-missing countermodel;\n- Bogoliubov particle production: Parker 1969 and Hawking 1975, with exact\n  context-owned six-index/seven-relation model membership and\n  incoming-vacuum-bounded, output-independent grounding; Parker's equation (52)\n  coefficient norm and Hawking's equation (2.10) beta-row sum remain local;\n  a nonvacuous route witness and direct activity audit cover all thirteen\n  retained components; both routes realize a typed structural explanation of\n  the distinct vacuum-to-outgoing-particle phenomenon, while a no-mode-\n  expansion countermodel blocks occurrence-to-explanation; distinct typed\n  Parker and Hawking source constraints additionally prevent a common\n  completed route from erasing canonical-creation-coefficient versus\n  asymptotic-beta-row provenance;\n- gravitational ray deflection: Einstein 1911 and Einstein 1916;\n- gapped incompressible fluids: Laughlin 1983 and Haldane 1983;\n- fractional Hall quasihole charge: Laughlin 1983, Haldane 1983, and\n  Arovas-Schrieffer-Wilczek 1984, with a direct ten-component realized\n  endpoint audit and three nested route-binding selections kept separate;\n- post-calibration prediction: KSW 1998, Bedaque-Hammer-van Kolck 1998, and\n  Epelbaum-Gloeckle-Meissner 1999;\n- brane worldvolume decoupling: Maldacena 1997 and Itzhaki et al. 1998. Its\n  exact proof-free model retains all five selected indices and all eight\n  route-used relations. Each paper-local context owns its five physical\n  selections and exposes one unique `selectedModel`. Model use,\n  representation, entailment, grounding, and route applicability require that\n  exact model; both papers supply their named retention certificate\n  independently of the later survival and mutual-decoupling calculation. A\n  thirteen-component mutation audit shows that every index or relation change\n  fails the original context's exact semantics. The setup requires pairwise\n  distinct parent, worldvolume, and asymptotic-bulk descriptions. The\n  established result is output-led: it combines exact selection with\n  `NonvacuousBraneWorldvolumeDecouplingAt`, which retains setup, survival, both\n  sector assignments, and both decoupling directions but no implication-valued\n  calculation. That calculation is reconstructed from the realized outputs.\n  The completed D3 and D2 routes also project to a typed derivational-\n  reduction endpoint whose parent object retains the open-string description,\n  asymptotic spectator, brane system, and limit, and whose reduced object\n  retains the surviving worldvolume description. Realization requires setup,\n  survival, and sector membership; support and exhibition require the full\n  mutual-decoupling decomposition. Survival-only and one-way-decoupling\n  countermodels block weaker routes. A separate proof-free source description\n  now retains the exact model and a typed paper derivation. Maldacena's token\n  requires the D3 setup, fixed-`U` scaling limit, superconformal\n  specialization, and open-string calculation. Itzhaki et al.'s token\n  requires the D2 setup, its field-theory scaling, and the D2 decoupling\n  calculation. That D2 scaling explicitly retains positive `alpha'` tending\n  to zero, fixed `U`, fixed field-theory energy, and\n  `gYM^2 = gs / sqrt(alpha')`. Both source routes yield the same reduced\n  description and behavior without identifying the derivations. A completed\n  route with an always-false source relation has no source-sensitive\n  reduction. The projection asserts no AdS/CFT,\n  physical equivalence, emergence, multiple realization, or unique recovery.\n  Grounding requires the selected setup and no survival or decoupling output.\n  False-setup and setup-complete/no-decoupling witnesses guard both boundaries,\n  while a distinct-role finite model makes all five selected data and eight\n  relation families directly mutation-sensitive;\n- finite-precision trajectory predictability: Miller 1964, Portegies\n  Zwart-Boekholt 2014, and Lorenz 1963, with shared setup replay at the\n  divergence and reliability stages and a direct structural explanation of\n  deterministic point-prediction failure;\n- equilibrium noise-dissipation: Nyquist 1928, Callen-Welton 1951, and Kubo\n  1957, with an inhabited frequency-resolved equality and direct activity for\n  all nineteen retained components, plus a typed structural-explanation\n  projection and an equation-only/no-readout countermodel;\n- field-free magnetic interference: Aharonov-Bohm 1959 and Berry 1984, with\n  distinct split-beam and exact transported-box source tokens, ordinary and\n  source-sensitive structural explanations, and a false-source converse;\n- forward-amplitude positivity: Adams et al. 2006 and\n  Komargodski-Schwimmer 2011, with five context-owned selected indices, a\n  unique model retaining fourteen relation families, an exact-model\n  certificate consumed by route applicability, setup-bounded output-free\n  theory/world grounding, an output-led established endpoint with\n  reconstructible audit contracts, grounding-without-result countermodels, a\n  direct nonvacuous positivity proposition with source-anchored paper\n  realizations, a false-forward-setup vacuity countermodel, nineteen direct\n  mutations, and nineteen exact-retention mutations. The complete dispersive\n  route also realizes a typed structural explanation of the identified\n  positive coefficient; a positive-coefficient/analytic-branch model with no\n  optical theorem refutes the shortcut from sign to explanation. Adams grounds its\n  regulated channel setup and maps its direct established positivity result;\n  Komargodski-Schwimmer grounds the low-energy theorem and constructs the\n  direct dispersive result before reconstructing the route;\n  its five shared countermodel theorems now retain actual regulator/cut,\n  analytic/crossing, contour, optical, cross-section, spectral-weight,\n  integral, coefficient, interpretation, and grounding residuals. Adams's\n  five paper-local scope countermodels additionally retain the stable-vacuum\n  kinetic sign, controlled constant-gradient background, negative leading\n  coefficient, Goldstone fluctuation equation and widened cone, regulated\n  cut/pole locations and power-corrected sum rule, zero-interaction\n  strictness failure, and the massless `G_N s^2/t` graviton pole;\n- body-dependent self-gravity response: Nordtvedt 1968 and Eardley 1975, with\n  exact retention of seven selected objects and nine relation families,\n  inhabited-setup-bounded and output-free grounding, twelve-claim transfer,\n  grounding-without-route models, an output-led established endpoint with\n  explicit unequal-body and unequal-response witnesses, source-anchored paper\n  realizations, a theorem excluding false-setup grounding, a separate\n  false-common-field vacuity countermodel, direct activity for all seven\n  indices and nine relation families, and a sixteen-field exact-model mutation\n  audit. The complete route also realizes a typed mechanistic explanation:\n  the body comparison, distinguished responses, common external field, and\n  paper-local effect remain separate roles. A response-collapse countermodel\n  retains both the effect calculation and attribution but refutes the\n  mechanism. A second, source-sensitive activity now keeps Nordtvedt's general-\n  metric and stationary-bound-system derivation distinct from Eardley's\n  field-dependent-mass, compact-sensitivity, and scalar-dipole derivation.\n  Both are rebuilt from raw paper-local premises rather than established\n  outputs; a checked forgetful theorem recovers the ordinary response\n  mechanism from either source-sensitive explanation, while a completed common\n  route with its ordinary mechanism but a false source relation proves that\n  neither derivation can be reconstructed from the shared result. Nordtvedt's\n  independent paper-fidelity certificate additionally checks the original\n  weak-field values `omega = 6`, coefficient `-1/8`, binding fraction\n  `1/10`, test response `1`, massive response `79/80`, external field `2`,\n  and distinct accelerations `2` and `79/40`. Separate inhabited controls\n  distinguish test-body universality from massive-body universality and\n  reject Einstein cancellation, a vanishing external field, or vanishing\n  gravitational binding as substitutes for the Brans-Dicke effect. Eardley's\n  paper-local semantics additionally retain the original seven-row\n  neutron-star table, sensitivity-dependent pair-force cross term, scalar\n  charge `(1-s)*M/(2*omega+4)`, complete eccentric-orbit dipole decay,\n  separately rounded PSR 1913+16 estimate with observed mass function kept\n  distinct from reduced mass, and the original varying-gravity/inertia/clock\n  equations. Physical witnesses establish ordinary-matter and identical-body\n  dipole cancellation, negative decay for unequal sensitivities, and a\n  black-hole companion with zero scalar charge and clock variation but\n  nonzero dipole decay. Distinct selected orbital positions and unequal\n  selected sensitivity values now force the actual nonzero scalar dipole and\n  negative decay, while result-level theorems independently derive the\n  identical-PSR and black-hole-companion alternatives;\n- spin-orbit shell closure: Mayer 1949 and Haxel-Jensen-Suess 1949, with\n  context-owned exact 18-component retention, named exact selected-setup\n  grounding, seventeen-claim transfer, Mayer's checked Table I\n  `twiceJ + 1 = capacity` formulae for the selected high-`j` rows,\n  converse models, and an\n  eighteen-component semantic mutation audit in which every change fails the\n  original exact semantics, plus a shared mechanistic-explanation projection\n  that keeps empirical prediction short of physical explanation without the\n  separate account bridge, and separate ordinary/source-sensitive structural\n  explanations so shared route logic cannot manufacture paper provenance;\n- thresholded collapse abundance: Press-Schechter 1974 and Bond et al. 1991,\n  now also realizing a scoped derivational reduction from threshold counting\n  and mass accounting to the normalized differential spectrum through direct\n  source-input routes, independently of their terminal-result compatibility\n  adapters;\n- boundary Majorana modes: Kitaev 2001, Oreg-Refael-von Oppen 2010, and\n  Fu-Kane 2009, with source-anchored direct nonvacuity adapters, a false-setup\n  vacuity countermodel, and nine selected-index plus twelve relation-family\n  activity mutations, plus a typed structural-explanation projection whose\n  converse model retains two classified gapped phases but no boundary\n  solution; governed source-valued witnesses additionally retain Kitaev's\n  paired-chain criterion and nonzero finite-wire splitting, the nanowire\n  critical surface `B^2 = Delta^2 + mu^2` and double-mode pairing wall, and\n  Fu-Kane's `2 pi` Hamiltonian versus `4 pi` fixed-parity branch;\n- parity-resolved fractional Josephson response: Kitaev 2001 and Fu-Kane\n  2009, with direct nonvacuity adapters, a false-setup vacuity countermodel,\n  six selected-index plus eleven relation-family activity mutations, and a\n  typed structural-explanation projection that rejects both branch-only and\n  uninterpreted-current routes;\n- three-body pairwise-input insufficiency: Thomas 1935 and\n  Bedaque-Hammer-van Kolck 1998, with a typed nonvacuous stable-prediction\n  determination projection, ordinary plus distinct source-sensitive\n  structural explanations, and countermodels for label independence and\n  source-provenance self-reconstruction;\n- bulk-boundary scalar mass-dimension semantics:\n  Gubser-Klebanov-Polyakov 1998 and Witten 1998.\n- scalar-correlator composition: Gubser-Klebanov-Polyakov 1998 and Witten\n  1998, consuming both shared child results plus exact paper-local links and\n  a distinct two-point scaling calculation.\n- balance-law conservation: Noether 1918 and Einstein 1916;\n- equilibrium sampling: Metropolis et al. 1953 and Creutz 1980, with balance,\n  target-space accessibility, asymptotic equilibration, and equilibrium\n  interpretation retained as distinct obligations;\n- reciprocal transport: Onsager 1931 and Casimir 1945, with a finite\n  opposite-parity, field-reversed realization and direct activity for all\n  four selected indices, three retained functions, and seven physical\n  relation families; their shared reversible setup projects to a typed\n  physical field-reversal symmetry, while a finite countermodel keeps that\n  symmetry short of macroscopic regression and coefficient reciprocity. Typed\n  source-sensitive explanations separately retain Onsager's zero-field heat\n  derivation and Casimir's parity/field-reversal/independent-regression\n  derivation, with a countermodel blocking source reconstruction from the\n  completed shared route; their value-bearing field-reversal boundary\n  separately retains nonzero `H`, `-H`, trajectory balance, parity, and\n  selected cross coefficients;\n- remote correlation prediction: EPR 1935, Bohr 1935, and Bell 1964, with\n  Bohr retaining the original separated double-slit pair, alternative\n  position/momentum values, and explicit rejection of joint measurement and\n  common reality, while Bell retains its concrete spin-singlet data and\n  separated-measurement stage; all three give direct source-sensitive\n  structural explanations of inhabited certainty without disturbance;\n- vacuum metric dynamics: Einstein 1916 and Schwarzschild 1916, with an\n  output-led direct endpoint, reconstructed equation and motion bridges, and\n  selected-physical-setup-bounded grounding;\n- random-displacement diffusion: Einstein 1905, Smoluchowski 1906, and\n  Linde-Linde-Mezhlumian 1993;\n- transverse Meissner screening: BCS 1957 and Nambu 1960;\n- protected-index transport: Witten 1982 and Strominger-Vafa 1996, with a\n  direct output-led source-to-target endpoint, pointwise transfer\n  calculation, a typed structural explanation of the situated target indexed\n  prediction, a target-occurrence-without-explanation countermodel, and seven\n  selected-object plus nine relation-family direct mutations; Strominger-Vafa\n  separately retains its Cardy logarithmic-growth and charge-substitution\n  formulas locally;\n- planar diagram expansion: 't Hooft 1974 and Witten 1979;\n- RG endpoint monotonicity: Zamolodchikov 1986 and\n  Komargodski-Schwimmer 2011, with a direct model-native endpoint, a\n  false-setup vacuity countermodel, and ten selected-index plus ten\n  relation-family direct mutations;\n- exact regulated scale flow: Wegner-Houghton 1973 and Wetterich 1993, with\n  output-led full and projected results, setup-bounded grounding, a direct\n  nonvacuous full-flow-plus-projection endpoint, and exact/direct audits of\n  six selected indices and four route relations; Wegner-Houghton now\n  separately retains the original p. 403 equation-(2.20) value-level\n  sharp-shell formula with its shell logarithm/open-line quotient, momentum\n  renumbering, volume, field, and trace contributions, plus an idempotent\n  shell-erasing retained-configuration projection and explicit angular\n  integral, Fourier-sum, positive projected-Hessian, derivative, and\n  primed-momentum\n  obligations. Wegner-Houghton also separately retains the pp. 405-406\n  controlled-epsilon coefficient package for `v4`, `v2(k)`, `eta`,\n  and `y_1s` as selected truncated values tied to the invariant\n  `n`-vector expansion; source-valued framework controls independently check\n  the selected `v4 = 1/180`, `v2 = 59/60`, `eta = 1/5400`, and `y1 = 59/30`\n  without adding them to the neutral endpoint.\n  Wetterich separately retains the original equation-(2)\n  value-level trace formula\n  `partial_t Gamma_k = 1/2 Tr[(Gamma_k^(2) + R_k)^(-1) partial_t R_k]`\n  with an explicit positive scale path satisfying `dk/dt = k`, plus\n  regulator-derivative, actual two-sided inverse, trace, and differentiability\n  obligations. The formula is derived from the connected trace calculation\n  and retained by the paper-supplied shared relation, without adding\n  Wetterich-only conventions to the neutral framework. Separate controls retain the modified Legendre\n  subtraction, independent infrared/ultraviolet endpoint conditions, distinct\n  Goldstone and radial denominators, truncation-without-error-control,\n  zero-momentum regulator caveat, and unproved constrained-action\n  equivalence;\n- homogeneous cosmic expansion: Friedmann 1922 and Lemaitre 1927, with an\n  exact eight-index/nine-relation shared model, source-ordered field-equation,\n  branch-selection, and interpretation stages, and a typed structural\n  explanation. Both papers now realize that explanation directly from their\n  original calculation inputs before a terminal paper or shared expansion\n  result exists. Friedmann executes the stationary/nonstationary split,\n  nonstationary reduction, root classification, and monotone-world calculation\n  before applying a separately reconstructed curvature-radius interpretation;\n  Lemaitre executes the variable-radius field equations and constant-mass\n  increasing solution before applying his explicit expansion interpretation.\n  Distinct typed source constraints retain those reconstructed-versus-explicit\n  derivations even though both explain the same shared phenomenon. A finite\n  false-provenance countermodel shows that a completed route does not itself\n  realize either paper derivation. Their terminal-result adapters remain\n  compatibility paths.\n- finite-parameter congruence focusing: Raychaudhuri 1955 and Penrose 1965,\n  with exact retention of eight selected indices and ten route relations.\n- qualified nebular distance-velocity calibration: Lemaitre 1927 and Hubble\n  1929. Lemaitre locally retains its exact equation-(22) period/radius/Doppler\n  chain and separate equation-(23) nearby-source `R'/R = v/(c r)` formula;\n  those source-specific redshift semantics are not exported into the shared\n  qualified-fit contract.\n- causal-domain defect formation: Kibble 1976 and Guth 1981, with output-led\n  established semantics, exact selected-model and independent-domain\n  grounding, a setup-complete countermodel with no formation output, a direct\n  nonvacuous endpoint, and an eighteen-component direct activity audit.\n- exact quantum error recovery: Calderbank-Shor 1996 and Steane 1996, with\n  a context-owned exact model retaining twelve selected indices and fifteen\n  route relations; output-led intermediate and terminal results record direct\n  recovery facts and reconstruct calculation routes, both papers provide\n  direct encoded-state and environment-action setup witnesses for grounding,\n  setup-complete grounding remains independent of every recovery output,\n  recovery outputs cannot replace the selected setup, and a finite witness\n  makes all twenty-seven model components directly active. The complete route\n  additionally realizes a typed mechanistic explanation: complementary\n  syndrome/recovery operations act on a supported environment-coupled error,\n  organized production is arbitrary-error reduction, and the separate\n  prediction is restoration plus environmental decoupling. Countermodels\n  block both prediction without recovery activity and organized reduction\n  without decoupling. Both papers now also reach this explanation directly\n  from source-stage inputs, before a terminal paper result or shared recovery\n  endpoint is available. Calderbank-Shor executes nested-code construction,\n  supported decoherence, bit recovery, phase recovery, and arbitrary-error\n  restoration in order. Steane executes the coset construction, supported\n  defection, basis-one recovery, basis-two recovery, and final restoration and\n  disentanglement in order. Steane's paper-local basis-two calculation now\n  also retains author-TeX equation Cij as the finite signed\n  `(-1)^(wt(j and l))` syndrome sum over complex state-coordinate amplitudes;\n  that normalization is not promoted into the shared route. The generic\n  route-to-mechanism theorem now obtains\n  the direct nonvacuous endpoint without passing through an established-result\n  wrapper. A stronger source-sensitive activity pairs the ordinary recovery\n  activity with a typed paper derivation and an independent realization\n  relation: Calderbank-Shor supplies nested-code Fourier decoding and\n  logical-state-independent ancilla/environment factorization, whereas Steane\n  supplies coset parity checks, the residual-entanglement intermediate, and\n  final apparatus/environment disentanglement. A checked forgetful theorem\n  recovers the ordinary recovery mechanism from either source-sensitive\n  explanation. A finite countermodel retains the complete shared route and\n  ordinary mechanism while falsifying the source relation, so common recovery\n  behavior cannot reconstruct historical derivational provenance. The older\n  terminal-result projections remain compatibility adapters. A genuinely\n  carrier-polymorphic `NoCloningExactRecoveryHandoff` now also composes the\n  actual selected recovery model with an independently selected no-cloning\n  model through proposition-valued unknown-state identification,\n  distributed-encoding, syndrome-privacy, and independent-copy relations.\n  Its stronger sourced result retains exact selection of both child contexts,\n  their independent recovery and no-cloning explanations, and a third\n  physically specific encoding-compatibility derivation. Calderbank-Shor's\n  version retains both nested-code expansions and the separate syndrome\n  ancillas; Steane's retains the selected coset, equation Cij, and both\n  parity-check apparatus records. Independently typechecked downstream\n  clients supply the no-cloning arguments from Wootters-Zurek and Dieks,\n  respectively, while countermodels reject an actual independent copy and a\n  missing compatibility derivation even when both child explanations hold.\n  The independent\n  paper-local coding results now also retain their actual binary-entropy\n  formulas: Calderbank-Shor distinguishes the weakly self-dual classical\n  dimension from the encoded quantum dimension, retains\n  `R = (n - 2k) / n >= 1 - 2 H_2(d / n)`, and separately retains the\n  abstract's `1 - 2 H_2(2t / n)` achievable rate. Steane retains the distinct\n  code dimensions `k_1 + k_2 = n + K`, the proved two-distance Hamming upper\n  bound, the general Gilbert-Varshamov lower bound only under its explicitly\n  unproved simultaneous-code conjecture, the separately proved equal-distance\n  case, and the printed inverse-entropy window and numerical estimates.\n  Independent countermodels prevent a named rate from replacing either paper's\n  formulas, prevent a counting bound from replacing its abstract error-rate\n  formula, and prevent a conjectural numerical window from establishing\n  general code existence or noisy-channel capacity. A separate finite\n  source-grounded witness now also computes Calderbank-Shor's exact printed\n  sixteen-word Hamming table and signed `1/4` logical amplitudes, Steane's\n  printed simplex generator and parity-check matrix, their distinct\n  coordinate conventions, eight-word logical cosets, GF(2) syndrome\n  equations, and actual syndrome-directed single-qubit recovery. Every\n  syndrome identifies the physical error without revealing the logical\n  coset; equal same-qubit amplitude/phase syndrome values retain distinct\n  basis-tagged apparatus records. A first-plus-second-qubit error aliases a\n  single-qubit syndrome and flips the recovered logical coset in both source\n  conventions. Nine new independent physical fidelity boundaries reject\n  Boolean-only parity certificates, invented syndrome records, collapsed\n  correction bases, erased Calderbank-Shor relative phases, mixed Steane\n  cosets, and unsupported two-error recovery. No collapse, threshold, or\n  fault-tolerance claim is imported into the shared recovery framework.\n  The general coherent refinement additionally binds both paper routes to\n  actual local recovery matrices and binary X/Z component equations. Their\n  certified exact-recovery results expose restored reduced density and a\n  normalized common environment factor. Four further fidelity boundaries\n  use actual isometric basis-recording and relative-phase interactions to\n  distinguish coherent recovery from basis-only recovery and private\n  apparatus probabilities.\n- subthreshold excitation stability: Landau 1941 and Bogoliubov 1947, with\n  exact retention of seven selected indices and fifteen route relations; both\n  source-facing paper chains directly realize distinct typed derivations of\n  the shared structural explanation before any terminal paper or shared\n  endpoint is available; a provenance countermodel prevents the shared route\n  and ordinary explanation from identifying those derivations.\n- momentum-resolved variational bounds: Feynman 1954 and GMP 1986, with\n  exact retention of eleven selected indices and seventeen route relations;\n  an inhabited route and exhaustive direct activity for every component;\n  both source-facing calculation chains directly realize the typed structural\n  explanation before any terminal paper or shared endpoint is available;\n  Feynman's terminal established spectrum supplies the shared adapter without\n  replaying its variational contract, and its false-setup countermodel blocks\n  seven vacuous local calculations; GMP's terminal established projected bound\n  likewise supplies its adapter without replaying the unprojected, projection,\n  or energy contracts, and its staged countermodel blocks all nine vacuous\n  paper calculations; Feynman-Cohen 1956 is a dependent reuse client whose full\n  local route reaches the shared component only after independently established\n  trial, norm, numerator, quotient, and upper-bound outputs. The two\n  terminal routes remain compatibility adapters. A countermodel shows that a\n  declared inequality without the quotient route does not explain itself.\n- one-parameter localization scaling: Abrahams et al. 1979 and\n  MacKinnon-Kramer 1981, with context-owned exact retention of eight physical\n  indices and fourteen relation families; both project to one direct\n  nonvacuous scoped-scaling proposition, while their analytic and finite-\n  numerical methods remain paper-local; both realize the ordinary shared\n  structural explanation from the applicable route and separately realize\n  source-sensitive refinements from their source-local derivations, while a\n  converse model keeps the endpoint, route, ordinary explanation, and\n  phenomenon but refutes source-provenance self-reconstruction.\n- resolvent-decay localization: Anderson 1958 and MacKinnon-Kramer 1981, with\n  distinct selected kernels and descriptors; each context owns five selected\n  indices, and both papers project to one direct nonvacuous scoped-localization\n  proposition that stores no implication-valued route contract; the complete\n  route is reconstructed from direct descriptor, decay, localization, and\n  scope outputs. Grounding requires each paper's physical propagation setup\n  but no decay or localization result. A countermodel realizes every direct\n  output at a non-selected model and proves that those outputs cannot ground\n  it. Mutations of every index and all eight predicate families destroy that\n  proposition as well as failing exact selected semantics.\n- operational error-disturbance: Heisenberg 1927, Bohr 1935, and Ozawa 2003,\n  with the corrected microscope, fixed-diaphragm slit and local recoil, and\n  operator-universal calculations kept distinct by their selected measurement\n  data and paper-local predicates; all remain distinct from prepared-state\n  dispersion uncertainty, and Bohr's local recoil does not become remote EPR\n  mechanical disturbance.\n- magnetic mass-deformation consistency: Seiberg 1994 and\n  Kutasov-Schwimmer 1995, with fundamental one-color and\n  nilpotent-adjoint-chain k-color Higgsing kept distinct through their selected\n  condensates and rank data; F-term response, condensate, Higgsing, reduced\n  parameters, and rank matching are separate calculations with exact retained\n  outputs, while countermodels separate every missing stage, outputs from\n  setup, consistency evidence, and duality proof. The output-led established\n  result is exact selection plus a direct nonvacuous proposition requiring setup, all five\n  calculations, all five outputs, evidence, and explicit nonproof at one\n  model; a positive finite witness and direct mutations of all ten indices and\n  eleven relation families audit that endpoint itself. Complete direct outputs\n  under the wrong selected description cannot establish or ground themselves.\n- exact exterior vacuum-metric solutions: Schwarzschild 1916 and Kerr 1963,\n  with static point-mass integration and algebraically special rotating-mass\n  construction kept distinct; vacuum verification, exact expression,\n  asymptotic matching, and scoped regularity are sibling paper-local\n  certificates rather than a shared chronology. Schwarzschild keeps\n  asymptotic behavior as a problem condition and continuity in the integration;\n  Kerr keeps vacuum/expression and flatness/ring-scope pairs in their local\n  routes. Checked countermodels reject all three artificial predecessor\n  arrows. Grounding now requires `SelectedExteriorVacuumSetupAt`: exact model\n  selection plus an actual physical metric, governing field equation,\n  exterior-vacuum situation, and paper-local construction, with none of the\n  four outputs. Schwarzschild's construction setup stops at the\n  determinant-preserving polar construction rather than importing the reduced\n  field-equation calculation; Kerr's stops at the selected null tetrad rather\n  than importing the already-calculated branch equations. Kerr's exact-\n  expression adapter additionally consumes its value-level displayed\n  stationary line-element formula; the Euclidean-radius quartic remains\n  paper-local and is not promoted into the shared interface. Each context\n  owns its four selected indices, and mutations of every index and all eight\n  relation families directly fail exact selected semantics. Kerr's eleven\n  paper-local countermodels are now value-bearing: zero time/azimuthal\n  derivatives coexist with vacuum residual one; a nonzero imaginary rotation\n  component can accompany an exact Type-D vacuum metric; `r=1, theta=0,\n  m=a=0, du=dt=k=1` yields line elements `-1`; `r=2` with `R=x=1` violates the\n  radial quartic by twelve; the ring `R=a=1, z=0` remains exceptional; and\n  EIH orders `(2,1)`, zero approximate higher multipole, no exact invariant\n  definition, and a desired but unsampled interior preserve the original\n  scope. No status enum or proposition wrapper replaces these Kerr\n  distinctions. The established\n  route also projects definitionally to selected semantics plus a model-native\n  nonvacuous proposition requiring the physical setup and all four realized outputs;\n  the implication-valued calculation contracts and complete technical route\n  are reconstructed from those outputs. A false physical setup cannot ground,\n  while setup-complete grounding with false outputs does not manufacture the\n  route. The complete route also realizes a typed structural explanation:\n  its constraint retains the exact selected metric, exterior situation,\n  boundary, construction, and applicable route, while its distinct phenomenon\n  is the direct nonvacuous exact exterior solution. Schwarzschild and Kerr\n  expose separate paper theorems for this projection. Completed outputs with\n  the physical setup removed fail the explanation, so this adds no generic GR,\n  uniqueness, horizon, interior, or global-causal claim. The applicable route\n  now yields that direct phenomenon without an established-result detour. A\n  stronger source-sensitive constraint keeps Schwarzschild's determinant-\n  preserving spherical reduction, exact integration, continuity, and point-\n  source scope distinct from Kerr's algebraically special null congruence,\n  degenerate stationary branch, asymptotically flat transformation, and ring\n  scope. A finite countermodel retains the common route, established endpoint,\n  and ordinary explanation while denying source derivation, so shared exact\n  metric behavior cannot certify historical provenance. The same twelve\n  mutations falsify the direct solution proposition itself. A construction\n  mutation also directly breaks construction selection and the indexed vacuum\n  output. The distinct\n  paper-local constructions carry the route difference without an inert enum.\n  Uniqueness, free motion, EIH parameter identification, multipoles, horizons,\n  and global causal structure remain paper-local or outside the source scope.\n- self-gravitating equilibrium mass limits: Chandrasekhar 1931 and\n  Oppenheimer-Volkoff 1939, with their ultrarelativistic index-three-polytrope\n  and relativistic numerical turning-point constructions kept paper-local;\n  each supplies an explicit bridge from its calculation, finite mass, and\n  retained scope to its distinct maximum-equilibrium interpretation. Each\n  context owns seven selected components, and mutations of every component\n  and all eleven predicate families directly fail exact selected semantics.\n  Every selected value also changes a predicate used by the route, independently\n  of whole-model equality. The established endpoint is output-led: selected\n  semantics plus the direct setup, equation-of-state, equilibrium-mass,\n  finite-limit, scope, and maximum-interpretation facts. Its contracts and\n  applicability route are reconstructed. Chandrasekhar and\n  Oppenheimer-Volkoff separately expose source-native physical setups for\n  grounding, before the `n = 3` selection or relativistic hydrostatic reduction\n  is calculated. A setup-complete grounded model can still have every\n  downstream output false. Chandrasekhar's paper-local setup also retains\n  positive electron and mass densities, molecular weight, hydrogen-atom mass,\n  Planck constant, and light speed, together with a nonnegative ion/electron\n  ratio. Its exact `n = rho/(mu H (1+f))` equation stays distinct from the\n  qualitative usually-negligible-`f` approximation: positive `f` strictly\n  changes the density, while exact agreement with the dropped-`f` formula\n  would force `f = 0`. The shared framework's source-shaped validation model\n  likewise uses a positive ratio and keeps its exact correction and\n  approximation premise independently mutable. Oppenheimer--Volkoff's\n  original pp. 378-380 now also distinguish the selected equilibrium's\n  `0.71 M_sun` gravitational mass from its greater fixed-particle-number\n  proper rest mass: `M_rest = N m_n` and\n  `M_binding = M_rest - M_gravity > 0`. Their approximately ten-percent\n  excess is represented by an explicit nonzero approximation tolerance, not\n  an invented exact `M_rest = 1.1 M_gravity`; both exact and genuinely\n  nonexact source-valued witnesses satisfy the same physical contract.\n  This neutron-star accounting is absent from Chandrasekhar's neutral shared\n  route. Stability, realistic\n  high-density matter, nonstatic\n  evolution, horizons, and black holes remain paper-local or unresolved. The\n  complete applicable route also projects to a typed structural explanation.\n  Its proof-free constraint and phenomenon both retain the body, matter,\n  gravity, equation of state, equilibrium construction, mass, and regime,\n  while satisfaction requires the full calculation and separate\n  maximum-equilibrium interpretation bridge. Chandrasekhar and\n  Oppenheimer-Volkoff expose direct and granular paper adapters. The former\n  reconstructs the equation-of-state, polytropic-mass, and interpretation\n  stages; the latter reconstructs relativistic equilibrium, the cold-neutron\n  family, mass curve, and qualified scope. A finite scoped mass\n  without interpretation fails the phenomenon, and a declared maximum-mass\n  output with invalid equilibrium setup fails the explanation. Thus the\n  projection explains only the selected model's equilibrium limit, not a\n  universal mass bound or dynamical stellar fate.\n  A source-sensitive projection now keeps the two derivations distinct.\n  Chandrasekhar's token requires the relativistic electron equation of state,\n  imported index-three polytrope calculation, and separate ideal-limit\n  interpretation. Oppenheimer--Volkoff's different token requires the GR\n  hydrostatic reduction, cold-neutron numerical family, turning-point mass\n  curve, stability and Tolman branches, and qualified high-density scope.\n  The generic source theorem consumes the realized token plus the raw shared\n  route. A countermodel retains the complete result, route, and phenomenon\n  with a false source relation, proving that a common maximum-mass shape does\n  not identify the calculation that produced it.\n  The stellar paper countermodels now also retain their source-shaped values\n  instead of enum truth tables. Chandrasekhar keeps the relativistic density\n  threshold, pressure/composition and four-thirds relations, polytropic index,\n  gram and solar reports, density-profile mismatch, and model/world values.\n  Oppenheimer--Volkoff keeps regular hydrostatics, the cold-Fermi pressure and\n  density formulas, sampled rise/turn/drop masses, free-energy curvature and\n  a possible continuity jump, repulsive-pressure correction, compactness,\n  contraction-time bound, and central-density grounding mismatch. These\n  witnesses block setup-to-calculation, turning-point-to-stability,\n  exact-equation-to-physical-domain, vanishing-denominator,\n  nonzero-ratio-to-zero-ratio, exact-to-dropped-composition,\n  formal-pressure-to-positive-pressure, ideal-to-actual-matter, and\n  static-limit-to-horizon shortcuts without\n  identifying the two stellar constructions.\n- critical-collapse scaling: Choptuik 1993 and Evans-Coleman 1994, with\n  separate threshold-outcome, mass-scaling, and vanishing-mass calculations;\n  Choptuik additionally retains its paper-local printed\n  `M_BH = 2 r_BH` horizon readout, separately formalizes the preceding\n  apparent-horizon threshold `2 M_BH = r_BH`, proves the two formulas\n  incompatible at positive radius, and retains the tolerance-bounded\n  equation-(12) fit\n  `c_f |p - p*|^gamma`, and Table II interval `0.366 \u003C= gamma \u003C= 0.380`\n  through its calculation and complete conclusion without promoting those\n  one-paper formulas into the shared layer; typed countermodels showing that\n  threshold outcomes do not imply a mass\n  fit, a positive fit does not supply its limiting bridge, completed outputs\n  do not reconstruct their setup, and technical completion and physical\n  grounding are independent in both directions. The established result is\n  output-led: it retains exact selected semantics and a direct nonvacuous\n  model-native scaling proposition requiring an actual threshold setup and\n  all six completed outputs at one model, while reconstructing the three\n  route contracts only when needed. Grounding requires the threshold setup\n  but no outcome, mass-fit, limiting, route, or terminal result. A\n  false-setup witness blocks vacuous implication-only success, and a\n  route-shaped finite model makes all nine selected indices and twelve\n  relation families directly mutation-sensitive. A source-sensitive\n  structural projection additionally distinguishes Choptuik's adaptive\n  Einstein-scalar threshold search and mass fit from Evans--Coleman's\n  Gaussian radiation-fluid numerical route. Their independent self-similar\n  ODE construction is not used to obtain that shared token. A false source\n  relation can coexist with the complete route and all outputs, so numerical\n  and conjectural status and local/global similarity scope remain paper-local.\n  Source-sized scalar countermodels retain the `3.44` echo period,\n  family-indexed residuals and fitted exponents, the Table II interval,\n  actual one-sided vanishing mass, and a nonzero visibility residual.\n  Radiation-fluid countermodels retain local and exterior metric data,\n  transient near-critical similarity, the `0.129` redshift exponent,\n  distinct `0.36` and `0.37` numerical matter exponents, and the absence\n  of a proved visible singularity or universal matter exponent.\n- linear state-replication obstruction: Wootters-Zurek 1982 and Dieks 1982,\n  with basis-state copying, deterministic output uniqueness, the calculated\n  linear superposition output, and comparison with the required clone output\n  retained as separate obligations; twelve shared claims transfer through\n  exact paper-local interpretations whose contexts own all nine selected\n  indices, typed countermodels block each missing stage and output-to-setup\n  reconstruction, and a finite three-state/four-output model realizes the\n  output-led direct obstruction. Grounding requires exact selection, the\n  inhabited two-state setup, and deterministic output uniqueness, but no\n  calculated output, mismatch, route, or obstruction. All nine selected indices, the clone-output\n  function, and all eight relation families are active in that physical route,\n  independently of the older exact-semantics mutation audit. Both papers\n  derive the direct nonvacuous proposition from their source-local\n  calculations;\n  polarization, spin, EPR protocols, statistics, and causal mechanisms remain\n  local. Dieks's repeated-trial and one-run conclusions additionally realize\n  the narrow nonvacuous operational signal-exclusion interface, independently\n  of Minkowski's stronger light-cone propagation realization. His p. 272\n  multiplier calculation separately retains signed `sqrt(2)/2` coherent\n  branch amplitudes, the orthogonal `(N/2,N/2)` occupation sector, and exact\n  probabilities `(1/2,1/2,0)`; source-level countermodels prevent either\n  named branches or matching classical probabilities from replacing that\n  actual quantum calculation. The direct\n  obstruction now also realizes a typed structural explanation: the\n  constraint retains the exact selected states, device, ready state, linear\n  output, required clone output, deterministic uniqueness, and output\n  mismatch; it necessitates the distinct arbitrary-replication exclusion\n  phenomenon. The necessity proof rederives exclusion rather than consuming\n  the endpoint's stored conclusion. A model with the exclusion and terminal\n  outputs but no valid replication setup blocks the converse. A typed source\n  constraint now distinguishes Wootters-Zurek's six-input polarization and\n  apparatus-record derivation from Dieks's five-input spin-multiplier\n  derivation. Both raw routes invoke the same substantive contradiction\n  without consuming their completed obstruction paths. A further model has\n  the completed obstruction, valid route, and exclusion phenomenon but no\n  source-sensitive explanation when the derivation relation is false.\n  Separate original-source physical controls now retain Wootters-Zurek's\n  normalized polarization and `sqrt(2)/2` example, actual complex\n  apparatus-record overlap and two-by-two reduced photon density matrix,\n  `Tr(rho^2)` purity, physically distinct record rays versus phase-equivalent\n  unequal vectors, and partially coherent nonorthogonal records. Independent\n  witnesses retain overlap `-1` with purity `1`, overlap `0` with purity\n  `337/625`, and overlap `3/5` with purity `11017/15625`. The common actual\n  record-state construction now comes from `FiniteQuantumState.TwoBranchRecordState`,\n  shared with Zeh. Wootters-Zurek retains the symmetric `VV/HH` embedding\n  into a full two-photon density and a separate apparatus trace. The main\n  route derives pair mixedness for physically distinguishable records and\n  pure-clone exclusion from explicit density identifications, not free\n  mixed-output or mismatch conclusions. It no longer excludes unequal\n  phase-equivalent records: their actual pair is pure but the general\n  density comparison still forbids the tensor-square clone.\n  A pure correlated pair can have mixed single-photon marginals and is not\n  the tensor-square clone. The source also\n  retains nonzero ordered `alpha beta` tensor-square\n  cross terms, equal stimulated/spontaneous emission, random companion\n  polarization, and explicitly unfinished experiment. Dieks now has a\n  genuine electron-spin multiplier with orthogonal `x+`/`x-` states and a\n  `z+` superposition rather than an abstract nonorthogonal-photon surrogate.\n  His coherent burst retains exact `(1/2, 1/2, 0)` Born probabilities; an\n  illustrative `N = 4` independent-copy hypothesis gives half-split\n  probability `3/8` while actual linear evolution gives zero. Thirty-two\n  mutations separately reject apparatus, tensor, emission, singlet,\n  orthogonality, occupation, signalling, and epistemic-scope collapses.\n  Dieks's joint burst now has actual machine-record/occupation basis states,\n  signed real sector amplitudes, and an off-diagonal coherence of 1/2 or\n  -1/2. Different source phases give identical observable occupations, equal\n  machine records do not destroy occupation-sector orthogonality, and false\n  coherence or orthogonality reports cannot replace the physical equations.\n  The independent Born-rule countermodel remains normalized without silently\n  deriving probabilities from the branch state.\n- entropy-production fluctuation structural explanation: Evans-Cohen-Morriss\n  1993 and Gallavotti-Cohen 1995, with a typed qualified-ratio constraint\n  retaining the selected dissipative setup, source-specific reversal pair,\n  represented probabilities, implication-valued probability-weight\n  calculation, and qualified scope, but no calculated ratio. The calculation\n  necessitates the distinct leading probability-ratio phenomenon. Reversal\n  and represented probabilities alone do not calculate the ratio, while a\n  finite converse model declares the ratio in an invalid setup and hence has\n  no structural explanation. ECM's adapter consumes its equation-(8)\n  calculation without an established ratio or second-law result; GC's adapter\n  consumes its SRB weight calculation without an established fluctuation-\n  symmetry result. No output-led endpoint is converted into an explanation.\n  A stronger source-sensitive projection retains two noninterchangeable typed\n  derivations: ECM's proposed finite-segment natural weight plus fixed-shear\n  aggregation, and GC's SRB/Markov-partition time-reversal Jacobian ratio.\n  Each is extracted from direct paper inputs before invoking the generic\n  source theorem. A completed qualified route and ordinary explanation with\n  an unrealized source relation has no source-sensitive explanation, so the\n  common leading ratio cannot manufacture derivational provenance.\n- complete-integral structural reconstruction: Hamilton 1834 and Jacobi 1837,\n  with a typed constraint retaining the selected first-order equation,\n  complete parameter family, endpoint evolution, and separate momentum,\n  parameter-selection, dynamics-recovery, and completeness calculations, but\n  no solved-motion or complete-integrals output. Applying those contracts in\n  source order necessitates the distinct complete-motion phenomenon. A finite\n  output-without-valid-setup model blocks the converse, while another model\n  realizes the explanation together with forward branching and therefore\n  refutes any explanation-to-determinism shortcut. Both adapters consume\n  source-local calculations rather than established recovery or shared\n  terminal bundles.\n- holographic region-entropy structural explanation: Ryu-Takayanagi 2006 and\n  Lewkowycz-Maldacena 2013, with a typed constraint retaining the selected\n  boundary/bulk descriptions, region and anchored surface, area and entropy\n  values, native observables, physical duality, dictionary, surface-selection\n  and area-entropy bridges, area calculation, and normalization, but no final\n  entropy agreement. The route necessitates the selected boundary entropy\n  value and matching native boundary/bulk predictions. RT consumes its static\n  proposal directly; LM consumes replica fixed-point, continuation, Einstein,\n  cone, and AdS/CFT calculations rather than established intermediate or\n  shared terminal bundles. Direct entropy outputs on an unselected region do\n  not explain themselves, and no full prediction-relation equivalence follows.\n  RT's Brown-Henneaux, large/small regime, cutoff, global-AdS3, and BTZ\n  interval formulas remain explicit paper-local route outputs rather than\n  being folded into this shared explanation contract.\n- adiabatic-cycle transport quantization: Laughlin 1981 and Thouless 1983,\n  with setup, adiabatic following, integrated transport, selected integer\n  index, and index-to-unit correspondence retained as separate calculation\n  stages. The output-led established result stores exact selected setup and\n  the five direct outputs, then reconstructs the implication-valued route;\n  fourteen shared claims transfer through paper-local interpretations, typed\n  countermodels block every\n  missing stage and output-to-setup reconstruction, and a direct nonvacuous\n  transport proposition makes all ten selected indices plus twelve relation\n  families active in the completed physical route. Grounding requires exact\n  selected setup but no following, transport, index, correspondence, or\n  quantization output; flux, Hall conductance, Bloch bands, Chern classes, and\n  finite-torus physics stay local. A proof-free typed source constraint now\n  gives the route a source-sensitive structural explanation. Laughlin's token\n  retains current/phase rigidity, the ideal Landau-gauge flux calculation,\n  and the dirty mobility-gap extension. Its ideal branch now also retains\n  equations (7)-(9) as a selected scalar state-center/energy readout:\n  `y_0`, the `-Delta A/H_0` center shift, and both\n  equation-(9) energy values are proposition-valued source formulas, and Lean\n  checks their linear-energy consequence before the existing equation-(11)\n  current/conductance chain is used. Its qualified-error route also retains\n  the actual printed equation `(abs (Delta R_H / R_H)) = (R_H / R)^2`,\n  derives the negative Hall-resistance deficit `-R_H^3 / R^2`, and preserves\n  thermal-error dominance as speculation. Independent countermodels separate\n  mobility gaps from density-of-states gaps, ideal from dirty transfer\n  integers, reversible edge thermalization from Hall error, and the signed\n  correction from an arbitrary resistance label. Thouless's token instead retains the\n  adiabatic current calculation, Bloch derivative substitution, two-parameter\n  integral, and first-Chern interpretation. Both execute the raw shared route\n  and invoke the same checked integer-unit necessity theorem without using a\n  completed transport endpoint. A finite model with completed quantization\n  and a valid route but a false derivation relation blocks the provenance\n  converse.\n- calibrated residual-background detection: Penzias-Wilson 1965 and Fixsen et\n  al. 1996, with exact retention of ten selected indices and fourteen relation\n  families. Each paper-local context owns the ten indices and constructs one\n  `selectedModel`, so a candidate cannot select itself by supplying different\n  observational data. Separate calibration, component-separation, uncertainty,\n  robustness, interpretation, and detection bridges; the established result\n  is exactly selected semantics plus a direct nonvacuous model-native\n  detection proposition retaining setup and all eight outputs at one model.\n  The six calculations or bridges are reconstructed afterward. Countermodels\n  block every missing stage and output-to-setup reconstruction. A\n  false-setup witness blocks vacuous implication-only success, while a\n  route-shaped finite model makes all ten selected indices and fourteen\n  relation families directly mutation-sensitive. Both paper adapters replay\n  the shared selected setup at calibration, separation, uncertainty, and\n  robustness stages, rebuild their horn or FIRAS local setup before each\n  paper-local calculation, and use a named exact selected-setup witness for\n  theory/world grounding. Exact selection and outputs without setup cannot\n  ground, while setup can ground without detection outputs. The framework now\n  also owns the common observation-procedure, instrument implementation,\n  performed raw-record, and operational-value assembly independently repeated\n  by both papers. Their temperature representations remain parameters:\n  completed detection plus an assigned represented value yields a recorded\n  measurement, and only faithfulness yields an operational physical value.\n  Countermodels block both detection-to-assignment and recorded-but-unfaithful\n  value promotion; cosmological interpretations remain paper-local.\n  Penzias-Wilson additionally checks both a source-valued positive accounting\n  witness and a negative witness retaining the calibrated `4080 Mc/s`\n  foreground budget while withholding the `3.5 K` residual. The actual paper\n  argument now separately retains the central `0.8 K` ohmic loss, a nonnegative actual\n  ground back-lobe strictly below `0.1 K`, and the distinct calibration,\n  atmospheric, and ohmic uncertainties `0.3, 0.3, 0.4 K`. Thus the rounded\n  `0.9 K` antenna allowance strictly exceeds the central-ohmic-plus-back-lobe\n  contribution; central-component subtraction lies above `3.5 K` and at most\n  `3.6 K`. The arithmetic `0.3 + 0.3 + 0.4 = 1.0 K` checks compatibility\n  with the reported residual budget without inventing a confidence level or\n  statistical error-propagation rule. Six independent physical countermodels\n  separate rounded allowances, central estimates, strict bounds, uncertainty\n  components, and rounded versus central residual subtraction. A separate\n  explicit component-error model now computes candidate actual temperatures;\n  three additional countermodels prevent treating central estimates or their\n  arithmetic bounds as exact physical values. Its proof-note\n  countermodel preserves the `404 Mc/s`, `16 K` and `4080 Mc/s`, `3.5 K`\n  measurements without supplying the `lambda^0.7` spectral conclusion.\n  FIRAS retains its actual Section 6 equations (3)-(7), Table 4 Galactic\n  foreground and confidence-qualified temperature. Its external blackbody\n  calibration, three unequal and partly correlated temperature methods,\n  finite-beam-corrected dipole, rounded systematic uncertainty, and\n  separate distortion epochs remain paper-local. Its approximate\n  `400 MJy/sr` figure-caption peak is used only as a scale witness; values\n  inside the `mu` and `y` bounds are logical counterexamples, not claimed\n  experimental central estimates.\n  Separate source-valued controls now retain the complete\n  `6.7 - 2.3 - 0.9 = 3.5 K` horn budget, its independent atmospheric and\n  ohmic uncertainties, ten-month observation scope, and the separate\n  `404 MHz` proof-note comparison. FIRAS retains `6068` sky pixels, four\n  components, two Galactic templates, a strictly nonzero Table 4 residual\n  below `50 ppm`, `2.728 +/- 0.004 K` at `95%` confidence,\n  `3.372 +/- 0.007 mK` dipole amplitude, and the distinct\n  `|mu| \u003C 9e-5` and `|y| \u003C 15e-6` bounds. Nineteen mutations reject exact\n  blackbody claims, zero residual, pure detector-noise uncertainty,\n  exhaustive foreground exclusion, and derivation of cosmology from one\n  horn frequency.\n- Schwarzschild master-equation reduction: Regge-Wheeler 1957 and Zerilli 1970\n  independently retain odd/even parity, coupled radial equations, calculated\n  master-variable transformations, tortoise coordinates, effective potentials,\n  homogeneous master equations, and explicit no-stability scope. The\n  established route projects to\n  `NonvacuousSchwarzschildMasterEquationReductionAt` and from there to a\n  typed, nonvacuous derivational-reduction result. The latter retains the\n  parity-resolved coupled problem, master description, effective potential,\n  homogeneous equation, and explicit no-stability scope. A false-setup\n  countermodel blocks vacuous implication contracts, and all thirteen selected\n  indices plus thirteen relation families directly change the completed\n  reduction. The compatibility adapters retain their output-led paths from\n  completed odd/even results. Separate source adapters now execute Regge-\n  Wheeler's parity-resolved odd calculation and Zerilli's corrected-system,\n  transformation, potential, equation, and scope calculations in source order,\n  realizing the derivational interface before a completed shared endpoint\n  exists. A source-sensitive refinement pairs the exact selected model with a\n  typed paper-local derivation token: Regge-Wheeler must discharge its\n  harmonic/canonical-gauge/odd-radial relation, while Zerilli must discharge\n  its corrected-even-system/nonunique-transformation relation. The common\n  master-equation shape therefore cannot erase derivational provenance. A\n  completed route with an everywhere-false derivation relation still realizes\n  the ordinary reduction but not the source-sensitive one. Neither path\n  imports a stability analysis. Vishveshwara 1970 is a\n  downstream odd-parity consumer only, so its later Kruskal boundary argument\n  remains outside this shared reduction. Its paper-local setup nevertheless\n  retains value-level equations (4.6a), (4.7a-c), and (4.8a-b): the tortoise\n  logarithm, `Q`/`V_eff` definitions, odd wave equation,\n  `h_0` reconstruction, and positive-imaginary-frequency specialization.\n  A checked master/stability boundary now retains the selected objects,\n  positive exterior potential and formula residual, nonzero master amplitude,\n  homogeneous residual, boundary-calculation count, outer-decay and\n  inner-regularity residuals, and admissible growing-mode count. Its exact\n  bridge ties those values to the selected master model and its explicit\n  no-stability scope. Regge-Wheeler and Zerilli independently realize valid\n  odd/even homogeneous equations while withholding boundary exclusion;\n  Vishveshwara realizes a positive odd potential while an even growing mode\n  remains. A separate positive witness supplies the missing boundary mismatch\n  and excludes the growing mode.\n- scoped Schwarzschild linear mode stability: Regge-Wheeler 1957 and\n  Vishveshwara 1970, with wormhole matching and Kruskal regularity kept as\n  distinct selected inner boundaries. The output-led established result is\n  exact selected semantics plus one direct nonvacuous proposition retaining\n  the small linear setup, odd/even\n  exclusions, real-frequency behavior, completeness scope, linear conclusion,\n  and explicit nonlinear exclusion; the complete implication-shaped route is\n  reconstructed from these facts. Theory/model/world grounding requires the\n  exact selected perturbation, parity, frequency, and boundary setup but no\n  boundary calculation, exclusion, completeness assessment, or stability\n  output. Regge-Wheeler and Vishveshwara prove this setup from different named\n  source-local inputs. A false-setup countermodel blocks vacuous\n  implication contracts, and all eleven selected indices plus fifteen relation\n  families directly change the direct endpoint. Converse countermodels ground\n  setup without stability output and reject output-only grounding.\n  Regge-Wheeler's stability adapter accepts\n  only its output-led scoped conclusion and extracts all earlier physical\n  results from that certificate; no arbitrary-data or nonlinear stability\n  theorem is imported. A narrower\n  `GrowingModeExclusionRouteApplicableAt` now projects both papers to a typed\n  structural explanation: their distinct inner/outer boundary calculations\n  necessitate only the selected odd/even growing-mode exclusions. The\n  projection does not consume completeness or the terminal stability result,\n  and a checked output-without-boundary-calculation model blocks the converse.\n  The checked stability-scope boundary separately retains odd/even analyzed,\n  growing, and total mode counts, regular-packet count and amplitude bound,\n  and nonlinear deviation and bound. Its exact bridge ties the growing-mode\n  and real-frequency counts to the selected stability model. Regge-Wheeler\n  realizes a complete non-growing linear family with an excessive nonlinear\n  deviation; Vishveshwara retains one non-growing analyzed even mode out of\n  two total modes and a regular packet while withholding both completeness\n  and nonlinear control. A positive witness retains complete odd/even\n  expansions and a nonlinear bound, so these absence-of-entailment checks do\n  not assert instability. The stronger master/stability composition now\n  formally distinguishes an independently derived odd master equation from\n  an adopted prior result. Regge-Wheeler must supply its original\n  harmonic/canonical-gauge/radial derivation before the wormhole mismatch;\n  Vishveshwara explicitly adopts the earlier tensor/master machinery and\n  retains corrected radial equations, Kruskal divergence, odd-dipole gauge\n  removal, even divergence, missing even completeness, and its absent\n  rigorous arbitrary-data proof. Inhabited countermodels reject both\n  reclassifying adoption as independent derivation and manufacturing a\n  missing joining argument from otherwise complete child calculations.\n- gauge-field mass generation: Englert-Brout 1964 and Higgs 1964, with broken\n  and residual generators, their massive and massless gauge fields, nonzero\n  vacuum order, longitudinal-mode response, and approximation scope kept\n  explicit. Exact context-owned retention covers eleven selected values and\n  fourteen relation families, while a separate model-native nonvacuous\n  endpoint drops equality and retains the actual setup and six realized\n  outputs, including distinct direction roles, without storing any\n  implication-valued calculation or bridge contract. The established result\n  is exactly selected semantics plus that direct endpoint, while the complete\n  route is reconstructed from its outputs. Theory-model grounding requires\n  the selected setup but no mass, residual, longitudinal, or scope conclusion.\n  False-setup and setup-complete/no-mass countermodels keep those boundaries\n  active, and typed eleven-index plus fourteen-relation mutations all destroy\n  the direct endpoint; lowest-order and linearized paper-local calculations\n  remain distinct. The adapters also keep\n  Englert-Brout's Abelian mass separate from its selected compact-group mass,\n  and Higgs's U(1) bare mass separate from its selected semisimple component\n  mass; each group calculation is replayed from the shared setup before its\n  mass-to-broken-direction bridge is used. Englert-Brout's p. 322 Abelian\n  tensor, `mu^2 = e^2 \u003Cphi_1>^2`, compact tensor, and\n  `mu_a^2 = -\u003Cphi|T_a T_a|phi>` are now literal proposition-valued\n  formulae with four-component momentum, metric, complex polarization,\n  coupling, vacuum-order, mass-square, and generator-expectation readouts.\n  Their established routes retain them, while a reduced countermodel\n  prevents a named gauge-mass calculation from supplying the printed mass\n  equations. The direct endpoint now also\n  realizes a typed mechanistic explanation: the broken-direction gauge field\n  is the component, the broken-vacuum longitudinal response is the activity,\n  the nonzero locally gauge-invariant broken vacuum with distinct residual\n  roles is the organization, and selective massive/massless gauge response is\n  the phenomenon. The separate mass calculation supplies prediction. An\n  output-complete model with an invalid\n  broken-vacuum organization blocks the converse. This explains mass\n  generation conditional on the selected vacuum; it does not explain why the\n  vacuum broke or promote either calculation to an all-orders quantum result.\n  A proof-free source constraint now also retains a typed derivation token and\n  its proposition-valued realization. Raw source inputs establish the route\n  before either paper obtains a source-sensitive structural explanation:\n  Englert-Brout uses lowest-order polarization, compact-generator selection,\n  rotated vacua, and qualified scope, whereas Higgs uses linearized U(1)\n  equations, zero-coupling mode conversion, semisimple selection, and\n  conjectural quantum scope. Both explanations entail the same selective\n  mass phenomenon, while a completed shared route with an unrealized source\n  token has no source-sensitive explanation. Source-sized QFT countermodels\n  now distinguish Englert-Brout's order-zero transverse polarization and\n  positive pole from an independent higher-order zero pole, and realize\n  rotating and stabilizing generator masses from their actual vacuum-square\n  expectations. Higgs's solved classical equation has field-strength\n  divergence `-1`, while an independently selected quantum inverse\n  propagator is nonzero at the candidate massive pole; its positive broken\n  mass and zero residual mass are physical values. The equation-(4),\n  perturbative, quantum, and residual-direction caveats are not represented by\n  Boolean, evidence-status, mass-status, or generator-role truth tables.\n- entropy-production fluctuation symmetry: Evans-Cohen-Morriss 1993 and\n  Gallavotti-Cohen 1995, with conjectured finite-segment-measure and chaotic-\n  SRB modes kept distinct. Each paper-local context owns thirteen selected\n  indices and constructs one exact model carrying eighteen relation families;\n  every index or relation mutation fails that model equality. The established\n  endpoint is exactly selected semantics plus one direct nonvacuous proposition\n  containing the dissipative reversible setup, paired windows, represented\n  probabilities, scoped leading ratio, finite negative production, and\n  long-time suppression. Calculation contracts and route applicability are\n  reconstructed from those outputs. Each paper derives a source-native complete\n  setup and bridges it to the shared setup before grounding; a setup-complete\n  grounded countermodel still makes every output false. A false-setup\n  countermodel blocks vacuous implication contracts, and every selected index\n  or retained relation mutation breaks the direct endpoint. Both papers derive\n  that endpoint from their own source-local routes without strengthening their\n  qualifiers. The shared result records\n  negative entropy production neutrally: ECM's explicit\n  finite-time \"second-law violation\" interpretation remains paper-local and\n  is not projected onto GC. Finite-time versus leading-long-time scope\n  remains preserved. Source-sized statistical countermodels distinguish\n  ECM's normalized `1 / 2` segment weight from an independently observed\n  `1 / 3` weight despite exact slope agreement. GC retains its two positive\n  contraction samples, separate negative invariant-mean witness,\n  zero-weight negative tile, and reversible dynamics with missing\n  hyperbolic directions; source caveats are not represented by status\n  truth tables.\n- exact memory-kernel reduction: Mori 1965 and Zwanzig 1973, with orthogonal\n  projection and shifted-quadratic bath elimination retained as distinct\n  source derivations. Both routes calculate an exact history-dependent\n  reduced equation, eliminated-sector memory, a residual force, and the\n  force-correlation/noise-memory relation. A typed proof-free source\n  constraint now feeds two independent projections of the raw paper\n  calculations: a source-sensitive derivational reduction and a structural\n  explanation of the exact-memory phenomenon. Neither consumes completed\n  force-correlation, canonical-noise, or shared endpoint bundles. A converse\n  model has every exact output, a reconstructed route, and the ordinary\n  derivational reduction, but neither source-sensitive result when the\n  source-derivation relation is false. Mori's short-memory plateau argument\n  and Zwanzig's Debye/Markov limit remain paper-local and are not promoted\n  into the exact shared phenomenon.\n- unitary similarity decoupling: Głazek-Wilson 1993 and\n  Bogner-Furnstahl-Perry 2007, with finite-similarity and continuous-flow\n  modes kept distinct. The output-led result is exact selection plus the\n  direct qualified transformation, suppression, band, and preservation facts;\n  calculation contracts and the route are reconstructed. Grounding requires\n  the source-local qualified setup but no decoupling output. Exact retention\n  covers seven selected indices and thirteen relation families. A separate\n  `Representation.InterpretationContext` distinguishes the actual unitary\n  mathematical isomorphism from scoped physical equivalence based on an\n  independent selected-content preservation calculation and output.\n  Countermodels block both inference from unitarity to preservation and the\n  converse. Głazek-Wilson select spectrum preservation; Bogner-Furnstahl-Perry\n  select two-body observable preservation without extending it to omitted\n  induced many-body content. The same complete route now satisfies a distinct\n  proof-free structural constraint and necessitates a qualified\n  band-decoupling phenomenon. Terminal outputs with invalid unitary setup do\n  not explain themselves, and an explanation for the selected sector and\n  content does not extend to omitted sectors or content. A stronger typed\n  source constraint now distinguishes the two original derivations: the 1993\n  divergence diagnosis and finite-similarity calculation versus the 2007\n  hard-interaction diagnosis, continuous flow, momentum suppression, and\n  two-body preservation calculation. Both raw routes establish the shared\n  explanation without consuming completed paper or framework endpoints. A\n  checked model with every terminal output and a reconstructed route but a\n  false source-derivation relation still has no source-sensitive explanation.\n  Głazek-Wilson's opening diagnosis now also retains its actual journal\n  pp. 5863-5864 three-level Hamiltonian: diagonal `(Lambda,m,m)`, four\n  cutoff-sized high/low entries `g Lambda`, and two degenerate low/low entries\n  `g m`, all tied to the selected bare, free, and interaction Hamiltonians\n  and cutoff. The source map exports that exact matrix as its own certified\n  claim; inhabited countermodels independently separate degenerate mixing\n  from ultraviolet jumps and reject named obstacle sectors with incorrect\n  cutoff scaling. Its solvable-model branch retains journal p. 5870\n  equations (4.2)-(4.3) as a selected real-valued readout, including positive\n  cutoff and nonzero-denominator assumptions, representation links to the\n  selected cutoff, observable, interaction, counterterm, and transformed\n  interaction, plus an explicit relation from that interaction to the\n  transformed Hamiltonian, and the checked reference-cutoff values\n  `u(Lambda_0) = f` and `\u003Cz|V'|z'> = -g-f` for every nonnegative\n  model-label pair. A named running\n  counterterm no longer stands in for those equations. Bogner-Furnstahl-Perry's\n  explicit continuity in\n  its selected flow parameter and its counterterm, momentum-space,\n  numerical-convergence, and omitted-three-body claims stay paper-local. Its\n  nuclear momentum branch now retains author-TeX equation (6) as a selected\n  real-valued derivative/integral formula with the `-(k^2-k'^2)^2 V_s` term,\n  `2/pi` radial kernel, and dominance-qualified\n  `exp(-s (k^2-k'^2)^2)` leading-term relation; a named suppression label no\n  longer stands in for that source equation, and the source map exposes the\n  conjunction as a checked formula-package output.\n  Its flow route now also retains actual finite Hamiltonian matrices,\n  two-sided unitary similarity, `H_s = U H U† = T_rel + V_s`, the\n  anti-Hermitian generator `eta = (dU/ds)U† = [T_rel,H_s]`, both actual\n  matrix commutators in `dH_s/ds = [[T_rel,H_s],H_s]`, and the distinct\n  inverse-fourth-root resolution law `lambda^4 s = 1`. Its numerical\n  convergence route now consumes the actual ordered free-resolvent kernel\n  `(E-T_rel)^(-1)V_s`, a nonzero eigenvector, a nonpositive source energy,\n  and the exact geometric Born-series criterion `|eta| \u003C 1`. The initial\n  repulsive eigenvalue `-2` gives divergent partial sums; the evolved\n  `-1/2` gives a genuinely convergent series. Nineteen inhabited\n  source-specific boundaries reject arbitrary anti-Hermitian generators,\n  missing double commutators, an incorrect inverse-square scale, nonunitary\n  congruence, insufficient eigenvalue reduction, the divergent `|eta|=1`\n  boundary, finite truncation, reversed resolvent order, positive source\n  energies, and zero eigenvectors.\n  Its five directional paper-local countermodels are now value-bearing: the\n  selected witness retains `s=1`, off-diagonal momenta `(0,1)`, equal initial\n  and evolved matrix elements, and zero derivative/integral contribution, so\n  equation (6) and actual suppression fail despite the named sector. It also\n  retains zero unitary defect with a `(0,1,1)` continuity jump, equal two-body\n  observables within numerical tolerance, a size-four basis with errors\n  `2 -> 1` and Weinberg magnitude `2 -> 1/2`, and two-body-only triton\n  energies `(-7,-8)` at `lambda=(2,1)` with omitted contribution one. No\n  proposition wrapper or dependency-status truth table replaces these nuclear\n  distinctions, and all five source-valued countermodels are independently\n  required by the compiled nuclear fidelity certificate.\n- thin viscous boundary-layer reduction: Prandtl 1904 and Blasius 1908, with\n  the full viscous equation governing the selected full flow, seven further\n  setup relations, separate momentum and continuity reductions, and their\n  coupling. The established result is selected semantics plus all eleven\n  relations stated directly; its implication-valued calculation route is\n  reconstructible but is not stored in the endpoint. Grounding requires each\n  paper's checked eight-relation source setup and no reduction output. A finite\n  role-typed projection additionally realizes a scoped derivational relation:\n  the physical setup realizes the full/reduced descriptions, both equation\n  reductions supply micro support, and equation coupling supplies macro\n  exhibition. Each paper now also constructs that result directly from its\n  source setup and calculation, before any output-led established reduction\n  is packaged. A stronger source-sensitive derivational projection requires a\n  typed paper-local derivation plus that applicable route: Prandtl retains the\n  original thin-wall-layer scaling and omission argument, while Blasius\n  retains the explicitly imported program and his own order counting. A\n  separate ordinary structural projection entails the coupled reduction\n  phenomenon without source provenance; its source-sensitive refinement adds\n  the typed derivation, exposes it, and entails the ordinary explanation.\n  A complete output-led reduction, ordinary derivational bridge, and ordinary\n  explanation with the derivation relation made false realizes neither\n  source-sensitive result.\n  Prandtl's route retains its short-wall-path and negligible-\n  curvature inputs locally; Blasius's route retains streamwise-diffusion\n  omission, curvature contribution, and explicit boundary conditions locally.\n  `BoundaryLayerVelocityMatchingReadout` now gives those boundary conditions\n  physical content: matching both tangential and normal fluid velocities to\n  the selected wall, and recovering the outer tangential velocity as the wall\n  distance grows. Prandtl's wall may move. Blasius's original p. 4 instead\n  requires `u(x,0)=0`, `v(x,0)=0`, and `u(x,infinity)=U(x)` before any\n  flat-plate specialization. Both papers realize stronger shared\n  velocity-matched reductions, and independent witnesses distinguish wall\n  slip, wall penetration, failed outer-flow recovery, and moving walls.\n  Prandtl also retains its original p. 487 steady planar momentum and\n  continuity equations as real-valued derivative formulas with explicit\n  density, viscosity coefficient, regularity, selected fields, and the\n  selected wall/free-fluid velocity boundary data. The displayed PDE and its\n  coefficients remain paper-local, while its velocity-matching semantics\n  project to the reusable shared refinement.\n  These are separate formal realizations, not independent discoveries:\n  Blasius explicitly imports Prandtl's small-friction program and adds his own\n  order-counting calculation.\n  The shared friction boundary is now value-bearing:\n  `BoundaryLayerFrictionContrastReadout` retains friction, layer thickness,\n  wall-velocity jump, outer second derivative, outer and wall viscous effects,\n  negligibility tolerance, and global-flow difference. It checks\n  `delta^2 = friction`, the two viscous scaling equations, outer\n  negligibility, and wall significance. Prandtl's original pp. 486-488 and\n  Blasius's original pp. 4-5 independently realize this contrast with distinct\n  witnesses; small friction therefore cannot be read as global\n  irrelevance. Their remaining scope witnesses are also value-bearing:\n  Prandtl retains inviscid residual versus wall slip and limiting-flow\n  difference, abstract outputs versus the displayed equation pair,\n  surface-path length versus its admitted maximum, pattern agreement versus\n  drag/vorticity agreement, and cylinder suction versus outer-wall\n  separation. Blasius retains potential adherence/vorticity failures versus\n  the independent Helmholtz pressure-boundary objection and distinguishes an\n  instantaneous velocity jump from finite-duration uniform acceleration. No\n  fluid region, flow-description, reduction, path, boundary, introduction, or\n  start-protocol enum truth table substitutes for these distinctions.\n  A separate source-valued framework audit now checks Prandtl's displayed\n  momentum and continuity equations, short-wall-path scope, neglected\n  streamline curvature, boundary-generated vorticity, necessary-but-not-\n  sufficient adverse pressure, nonvanishing global effect at zero limiting\n  thickness, and actually performed local cylinder suction with separation\n  retained at the outer wall. Blasius's distinct branches retain his imported\n  Prandtl program, independent order counting, nonzero normal-curvature term,\n  original far-field profile derivative `2`, matched coefficient `1.3266`\n  bounded by `1.326` and `1.327`, local wall stress, one-face integral,\n  exact two-face drag, and the strictly larger rounded `1.327` report. They\n  also retain the explicitly truncated `0.65` separation root, qualified\n  `11%-12%` offset, impulsive versus uniformly accelerated starts, and\n  viscosity-dependent thickness and drag at equal reduced onset. Independent\n  controls reject each erased assumption and forbid universal drag,\n  sufficient adverse pressure, global suction suppression, exact wake\n  prediction, universal series convergence, or an already proved uniform\n  zero-viscosity limit.\n  Countermodels separate setup from reduction and reduction from coupling.\n  This adds no Navier-Stokes limit or error-bound claim. A finite\n  model realizes all eleven physical relations, and direct activity theorems\n  cover all fifteen selected data and eleven relation families; separation,\n  curvature choices, profile calculations, and unsteady-flow applications\n  remain paper-local.\n\n- Broken-symmetry spectra now distinguish Goldstone's nonzero Hessian null\n  direction and separately bridged current pole; Nambu's gapped\n  quasiparticles, zero-energy collective pair, and Ward cancellation;\n  Anderson's `4 pi n e^2/M` Coulomb plasma; and the Maxwell photon as a\n  Goldstone of an electric one-form global symmetry. Wilson/'t Hooft charges,\n  the mixed anomaly, and intact local gauge redundancy are separately\n  governed.\n- Gauge-field mass generation now distinguishes Englert-Brout's transverse\n  lowest-order Abelian polarization, different compact-group broken/residual\n  masses, and chiral pseudovector Ward pole from Higgs's classical\n  `B = A - (ev)^(-1) dphi`, massive field equation, independent radial\n  scalar mass, zero-coupling limit, and semisimple residual direction.\n  Neither argument silently becomes an all-orders quantum proof.\n- Cosmological defect formation now retains Kibble's actual scalar-plus-gauge\n  thermal potential, critical temperature, unequal correlation and\n  penetration lengths, and distinct wall/string/monopole homotopy classes\n  with conditional `1/4` and `1/8` initial fractions. Guth's independent\n  bubble junction, conditional entropy dilution, and exponentially failed\n  old-inflation percolation remain separate; no graceful exit is invented.\n- Exact gravitational exteriors now retain Schwarzschild's determinant gauge,\n  original radial cube substitution, four metric coefficients, and\n  relativistic orbit correction alongside Kerr's twisting Type-D stationary\n  metric, exact implicit Cartesian quartic, Kerr-Schild one-form, mass/spin\n  assignment, excluded ring, and zero-spin reduction. Original papers are\n  not retroactively credited with interior solutions, global event horizons,\n  maximal extensions, or an exact invariant no-hair theorem.\n\nThe milestone list above is not the complete inventory. Every active shared\nframework component has policy-enforced required-theorem and retained-route\ncontracts, and every registered component-to-paper realization exposes a\nchecked transfer of each retained claim to both a selected theory and\nrepresented physical world.\n\nThese certificates preserve the narrow shared vocabulary. They do not import\npaper-local mechanisms or stronger interpretations into the framework layer.\n\n## Build\n\n```bash\npython3 scripts/check_all.py\n```\n\nLiteral complete-line audit registrations are counted through a bounded,\ncontent-keyed index rather than repeated full-file regex scans. Differential\ntests preserve exact names, leading whitespace, duplicate counts, LF boundary\nsemantics, and changed-source behavior. This is a text-check optimization,\nnot a Lean parser or a replacement for the source, axiom, fidelity, and\nelaborated dependency audits. Its focused tests run with\n`python3 -B scripts/test_policy_line_index.py` and in the standard suite.\n\nThe standard verification includes duplicate-key integrity for its Python\ngovernance policies, primary-source JSON portfolio, and versioned physical-\ncountermodel governance manifest. The manifest independently retains named\nphysical controls, declaration-local source fragments, and forbidden\ncollapsed-witness regressions across the shared technical frameworks. It is\nvalidated by schema, duplicate-key, deletion, and mutation checks alongside\nindependently checked\nequivalence of indexed forbidden-pattern matching with direct regex searches,\nsingle-read exhaustive retired-foundation identifier audits, source\nprovenance, an\nexplicit declaration-scoped proof-trust boundary, the\nformalization policy, direct independent physics clients for every philosophy\nand paradigm module, an explicit ten-family classification of every\nsource-certified primary paper, actual cross-family elaborated declaration\ndependencies for every domain-neutral foundation, physically justified and\naudited scopes for narrowly specialized paradigms, independently reviewed\nthree-family grounding for every active philosophy module and every\ndomain-neutral paradigm, two independent\nprimary-paper clients for every shared\ntechnical framework, explicit proposition-valued nonvacuity contracts for all\nshared frameworks, two independent primary-paper clients actually using each\nnonvacuous physical result, source and elaborated Lean audits that every\nframework-composition edge actually consumes its child's nonvacuous physical\nresult, an elaborated Lean audit that clients use their directly imported\nfoundational and technical semantics, exhaustive independent review of every\npublic paper conclusion and source route, inhabited countermodel boundaries\nwhose actual retained and rejected propositions cannot unfold to `True` or\n`False`, complete and synchronized paper editions with independently checked\nsource-derived per-paper and aggregate theorem, claim, step, route, and\nfidelity-boundary inventories, the Lean library build, and a kernel-checked\nfoundational-axiom audit of the\nindependent fidelity certificates and representative results from quantum\nfoundations, gravitation, cosmology, statistical mechanics, condensed matter,\nnuclear physics, fluid dynamics, plasma physics, holography, and supersymmetric\nfield theory. The named audit resolves declarations from a Lean-parsed block,\nso inline entries, multiline entries, and intervening documentation all receive\nthe same dependency check. Core-only regression fixtures reject direct and\nindirect untrusted axioms and distinguish documentation from executable entries.\nEvery standard run also exhaustively audits the reviewed\nproduction declaration inventory through a shared proof-dependency traversal\nthat independently covers every elaborated production declaration, including\ngenerated theorems, proof-valued definitions, and unused axioms.\nSource-authored `theorem` and `lemma`\ndeclarations are separately cross-checked, including inline and multiline\nattributes, rather than relying only on the manually reviewed declaration list,\nrejecting unexpected axioms while first verifying that every non-auxiliary\nproduction declaration depends only on Lean's foundational axioms. Remaining\ncompiler-assisted decisions are permitted exclusively inside named theorems in\npaper `SourceMap.lean` and `Coverage.lean` modules, counted separately for\nfinite provenance and semantic route coverage, and checked against their\nactual elaborated source modules and source-authored theorem owners.\nThe source audit excludes nested comments,\nquoted strings, non-theorem declarations and metaprogramming commands,\nnested lookalike paths, and every\nframework, foundation, main paper, and fidelity module. Use `--skip-build` to\nreuse an existing verified\nLean build, or `--legacy-axiom-trace` when the much slower verbose\ndeclaration-by-declaration trace is specifically required. An\nexternal-client-style Lean check exercises quantum-foundation,\nelectronic-structure, condensed-matter, cosmology, plasma, nuclear-EFT,\nholography, supersymmetry, and statistical-physics public APIs without adding\nassumptions or strengthening the original conclusions. It additionally\ncompares independent Everett/Rovelli operational-observer realizations,\nWu/Bohm calibration-versus-faithfulness semantics, and\nPenzias-Wilson/FIRAS operational temperature assignments without identifying\ntheir distinct physical systems or source-specific premises.\n\nCasimir's main heat-current route now derives the antisymmetric column condition\nfrom reciprocal bulk operators tested on arbitrary regular functions. It derives\nnonuniqueness from distinct actual currents and keeps the original tensor separate\nfrom the convention-selected symmetric representative. Kernel reciprocity,\nmacroscopic-equivalence interpretation and vacuum/shape selection remain explicit\ninputs; one temperature profile cannot replace the arbitrary-test condition.\n\nThe independent `CasimirHeatRouteClient` now constructs all five main-route\npremises together, with positive conductivity, an actual energy-density rate\nof 6, and a normal-current difference of 4. Its exact theorem-type checks\nexclude hidden assumptions about the setup or result. A second choice preserves\nbare vacuum/shape agreement and local reciprocity but fails selection, with a\nnonzero skew jump at the sample boundary. This identifies the missing global\ninterface condition; it is not a counterexample to the original paper. The\nfixture does not assert the paper's unrelated statistics or electrical routes.\n\nCasimir's heat-current fidelity boundary now uses actual differentiable\ntensor-generated currents, rather than assigned derivative readouts.\nThe paper-local refinement retains both conditions in the original equation\n(18): antisymmetry and vanishing column divergences. Its positive-temperature\ncube witnesses have equal bulk divergence but distinct currents; a spatially\nvarying antisymmetric tensor fails the missing column condition. An independent\nclient preserves a nonzero bulk operator. Boundary exchange, vacuum extension,\nand sample-shape conventions are not inferred from these local results.\n\nThe separate `tests/consumer` Lake package now adds an actual external\ndependency test. It reconstructs finite Gibbs-quench work logic, a\ndeterministic finite-resolution prediction limit, Bell's three-setting\ninequality, full-sky cosmic-variance logic, local geodesic focusing, nuclear\namplitude expansions, signed and spectral Hall response, coherent molecular\nspectroscopy, supported quantum-error recovery, self-consistent plasma phase\nmixing, and Brownian joint-law and coordinate distinctions using only public\ntechnical and foundational APIs. Its own\nelaborated audit checks real theorem dependencies, rejects paper imports and\ncanned countermodels, and permits only the three foundational proof axioms.\n`python3 -B scripts/check_external_consumer.py` stages this source-only\nconsumer in a temporary directory against the exact locked Mathlib revision;\nno consumer build artifacts enter the source fixture.\nAdd `--compare-reference` to compare indexed public-API dependencies, including\nabsent ones, against fresh Lean collector traversals.\n\nThe in-repository downstream audit uses an immediate-dependency fast path for\npublic-API queries, with Lean's fresh transitive collector as the fallback.\nIts mandatory differential examples compare 304 queries against the original\ncollector, including type-only, opaque, inductive, quotient, missing-name,\nand unrelated-client cases. Complete axiom traversals, forbidden-dependency\nchecks, namespace scans, and individual `#print axioms` remain unchanged.\n\nExpensive verification can also be split into independently reproducible\nstages without changing the default complete audit. Run\n`python3 -B scripts/check_all.py --skip-build --list-checks` to inspect the\nstable identifiers. `--check trusted-axioms` isolates the long foundational\nproof audit; repeated `--check` options preserve canonical stage order.\n`--from-check trusted-axioms --through-check axiom-inventory` runs an\ninclusive named window, and `--from-check downstream-reuse` resumes at the\nremaining client, graph, and integrity gates after an externally interrupted run. Use\n`--check external-consumer` for the isolated package check. Governance regression\ntests verify the default full inventory, canonical numbering, inclusive\nwindows, optional build/legacy stages, and rejection of invalid selections.\n\nThe standard sequence begins with a lightweight `policy-keys` preflight and\nends with exhaustive `policy-integrity` regressions. All sixteen previously\nrequired checks remain mandatory; the preflight is an additional seventeenth\ncheck, not a substitute. This lets a bad source, physical contract, or client\nfail before the expensive regression suite. `--check policy-keys` scans only\ngovernance keys and explicitly reports that semantic regressions were not run.\nIt cannot produce a complete-suite result. The standalone integrity command\nstill runs its full suite by default. Successful full runs retain the same\nsemantic checks; this ordering improves failed-run latency, not physical assurance.\n\nWithin policy integrity, source/governance regressions run before the compiled\nmeaning-inspection suite. A source failure returns a failing status and reports\nthat the compiled suite was not run; successful runs still execute every check.\nFailure-injection regressions exercise every scheduling boundary in both normal\nand full-source-reference modes. This reduces failed-run latency, not the amount\nof semantic scrutiny required or the cost of a successful complete audit.\n\nAdd `--report /absolute/existing/cache/directory/new-run.json` to retain a\nmachine-readable result. The parent directory must already exist outside\nboth the project and the selected reference archive. Reports are published\natomically and never replace an existing file, including one created during\nthe checks. Keep them outside the repository; they are verification artifacts,\nnot production sources.\n\nSchema version 2 records the exact source-snapshot file hashes and aggregate\ndigest, Python runtime, selected and completed stage identifiers, each actual\ncommand and return code, per-stage elapsed times, and final result. Only a\nsuccessful run of every standard stage, including the build and unchanged\ninput boundaries, sets `complete_standard_suite` to true. A successful\nselected window or `--skip-build` run is explicitly narrower. Optional legacy\ntracing does not substitute for any standard stage.\n\nThe schema's `assurance` record explicitly states that these are automated\ncheck results: they do not establish physical fidelity, human semantic review,\nor completion of the project. These limits apply even when\n`complete_standard_suite` is true. A recorded review of a particular semantic\nscope is separate evidence, not global approval. Historical schema-1 reports\nlack this explicit record and must not be interpreted as stronger evidence.\nLikewise, fidelity-ledger coverage and registered source-family counts are\nnot counts of human-reviewed or physically certified papers. The runner and\nstandalone audits now state these limits in their terminal output.\n\nOrdinary check failures, source invalidation, unreadable inputs, and command\nlaunch errors produce non-success reports when publication is possible.\nChild signal return codes remain signed in their stage records; the runner\nreturns the conventional `128 + signal` exit status. Invalid destinations or\nreport-publication errors return status 2 without printing a successful final\nsummary. Cleanup failure after successful publication instead produces a\nwarning naming the leftover temporary file; it does not change the recorded\nverification result. An interrupted or killed runner need not produce a report; absence\nof a report is not evidence of success. These local records are not signed\nattestations, clean-checkout builds, runtime dependency-cache hashes, or a\ncertificate of physics fidelity beyond the checks actually executed. The\nsnapshot guarantee concerns the observed stage boundaries, not undetected\ntransient edits made and restored inside a running check.\n\nAfter extending a paper formalization, update its readable edition and\nstructured source-derived catalog inventory with\n`python3 scripts/sync_html_papers.py --write`. The synchronizer also repairs\nexisting displayed theorem, route, claim, and fidelity-countermodel counts;\nthe independent HTML audit verifies those numbers against actual Lean\ndeclarations, including theorem names written on the next line and multiple\nsource-map constructors on one line. The separate elaborated Lean fidelity\naudit additionally checks every paper's catalogued claim, route, and physical\ncountermodel counts against the actual compiled argument.\n\nThe original Witten 1982 and Seiberg-Witten 1994 vacuum calculations now\nprovide a source-sensitive composition benchmark: the shared anomaly and\ndiscrete-vacuum frameworks retain three independent source explanations and a\nseparate physically meaningful joining derivation. Witten's finite-volume\nindex, hypothesized gluino condensate, and additional infinite-volume\nidentification remain distinct. Seiberg-Witten's mass-deformed route instead\nretains the `Z_8 -> Z_4 -> Z_2` sequence, exact local monopole equations,\ndistinct mutually nonlocal monopole/dyon charges, and independently realized\ntwo-vacuum agreement.\n\nBell 1966 now has twenty physically inhabited Bell boundaries and an actual\nspin-half source model. The binary threshold `lambda=-1/2` still selects the\nallowed eigenvalue `+1`; the formerly used ternary `Real.sign 0=0` would\ninstead make the construction impossible. The certified routes retain\nthree incompatible Stern-Gerlach outcomes `1,1,sqrt(2)`, noncommuting\nzero-meet projectors, and cumulative Born intervals `[0,1/2)` and\n`[1/2,1)` with equal quantum probability and distinct deterministic values.\n\nKnox 1995 now has twenty physically inhabited Knox boundaries. Its actual\nfive-mode full-sky calculation retains quadrupole variances `8/5` and\n`2/5`, fixed detector weight with distinct pixel noise, the original\nchi-square degrees `5` and variable `V=5`, foreground cross-pixel covariance\n`1/2`, distinct squared scalar/tensor correction factors, and baryon\nnuisance shifts exceeding both conditional forecast errors.\n\nThe original D-brane regime calculation now has twenty-one inhabited D-brane\nboundaries. Its source witness retains `N=3`, `g_eff^2=16`, and `N^4=81`,\nseparate curvature and local-dilaton control, a genuinely inhabited\nlarge-rank D2 window, an infinite NS5 throat, and D6 ALE orbifold geometry\nwith a nonextremal horizon and actual asymptotic Hawking flux.\n\nNakano's electrical-conductivity paper now has twenty-six inhabited Nakano\ntransport boundaries. Its certified approximation route retains the original\nfrequency selection, the double-commutator memory kernel\n`f(t)=(2+cos(t))/2`, an independently assumed exponential tail, and\nzero-frequency conductivity `2/pi`; doubling the static scattering weight\nchanges the result to `1/pi`.\n\nEvans and Coleman's radiation-fluid collapse now has forty-six inhabited\nEvans-Coleman boundaries. Its similarity route uses actual reduced equations,\nprofile fields, and calibrated exterior limits. The report labels\n`n=1.1485` and `beta=0.36` remain distinct estimates. Setup does not assume a\nsolution or exact reported index; the mass ratio is calculated from the metric.\nIndex admissibility follows conditionally from the boundary-value calculation,\nwithout uniqueness or an exact printed decimal. Actual center,\nsimilarity-boundary, and sonic regularity now replace the scalar regularity\nproxies and are retained in the complete result. C2 metric and C1 fluid\nextensions must match the selected profile's fields. A center-regular model\ncan still have divergent boundary density and fail the Einstein equations.\nThe acoustic principal matrix now comes from derivatives of the actual\nprinted fluid fluxes. Its two nondegenerate characteristics have nonzero\nfluid amplitudes and lie inside the metric light cone. A separate main claim\nidentifies the selected sonic surface with the incoming branch, without\nassuming local-attractor correspondence. Independent moving-fluid tests\ncheck the matrix coefficients and distinguish fluid-frame direction from\ncoordinate motion; vacuum degeneracy is not interpreted as sound propagation.\nThe local-asymptotic representation is explicitly an author expectation.\nIt now means convergence of the actual critical evolution's four rescaled\nfields to the same constructed profile, not a freely assigned relation.\nThe pointwise limit shares its physical fields with the separate only-critical\nexpectation; it implies neither exact spacetime equality nor a flat radial tail.\nFinite numerical comparison no longer assumes that interpretation or a solved\nprofile; exact sampled metric agreement can coexist with failed field equations.\nThe mass route retains the\nreported `eta_c=1.018828234` and `K=3.27`, both numerical grids, and the finite\nobserved scaling range. The central density and boundary lapse now use actual\nprofile traces. A lapse-defined inverse proper-time clock transfers the\ncoordinate density scaling to its proper-time limit, retaining the clock and\nfield bindings in the result. Three countermodels reject a wrong clock and\nunbound density or boundary-lapse readouts. Curvature still uses a separately\nsupplied identity for curvature computed from the actual metric derivatives.\nIts central readout is bound to a radial limit through the proper clock.\nA regular flat-metric countermodel rejects even a divergent scalar readout\nwith the radiation formula and correct density if that geometric binding is absent.\nObserved redshift is a separate\nconditional deduction using normalized observers and actual photon trajectories.\nThe continued metric matches the selected precritical profile; position derivatives\nand both covector geodesic equations constrain the photons. Endpoints are derived,\nwith emission at t=0 and reception at one fixed positive radius. Lean proves\nreception requires t>0, and derives boundary-lapse matching by continuity. Three\nnew controls reject non-affine momentum, a different selected metric, and\nprecritical-only reception. Continuation and the required photon family remain\nexplicit hypotheses, not constructed solutions for the critical spacetime;\nthe required transport calculation, outgoing visibility, and a measure-zero\nproof are not supplied. Full paper fidelity is not claimed.\nThe intermediate route now selects the actual radial-metric observable in\nFigure 4, without inferring unplotted fluid agreement, and retains an approximate\ndeparture scale tied to the actual later mismatch radius. A remote exterior\ndiscrepancy cannot stand in for breakdown at that inner scale.\nOnly-critical persistence is a separate\nneighborhood-wide expectation, and eventual nonpersistence needs that\nexpectation: a smooth field can depart at a later finite time and still return\nto the profile near the critical point.\nThree additional mass-route boundaries distinguish finite fits from a zero\nmass limit, calibrated report values from exact physical thresholds, and\nfinite polar-slice estimates from exact horizons. Common relative-error\ncontrol and physical-family realization are separate explicit inputs to the\nshared mass-limit deduction, not consequences of the finite report.\n\nHannay's classical adiabatic-holonomy paper now has twenty-four inhabited\nHannay holonomy boundaries. One witness realizes all nine source equations\nwith dynamical angle `1`, geometric angle `1`, and total angle `2`. Its\nnoncircular `(A,L)=(1,4)` hoop has angle `-pi^2/2`, while a provably\ndifferent circular hoop has angle `-2 pi`; a nonspinning driven top still\nretains geometric rotation `1/2`.\n\nTwo-dimensional melting now has twenty-four inhabited Halperin-Nelson\nmelting boundaries. Its actual triangular Burgers charges sum to zero,\nnonzero fugacity realizes all three source RG equations with genuine\nangular-integral Bessel functions, and positive `I_1(2)` makes the bulk flow\nstrictly greater than the shear flow.\n`eta_6=18 k_B T/(pi K_A)` distinguishes hexatic orientation from\ntranslation, and floating stability requires both `lambda_M\u003C0` and\n`K_R>16 pi`. The quoted exponent near `0.44817` remains approximate.\n\nThe four-dimensional a-theorem now has twenty-eight inhabited\nKomargodski-Schwimmer a-theorem boundaries. Its source-valued routes retain\n`ghat=exp(-2 tau)g`, separate Euler and Weyl anomalies, an independently\ncontrolled spectator and tuned vacuum, the exact positive optical dispersion\nintegral, nested running tails, and the original scalar-loop value\n`a_UV-a_IR=1/(5760 pi^2)` without claiming gradient flow.\n\nThe original Gurney-Condon nuclear letter now has twenty-eight inhabited\nGurney-Condon nuclear-decay boundaries. Its certified scattering calculation\nretains the `4 million volt` emitted alpha, uranium range `2.7 cm`, faster\nincident alpha `5`, exterior turning radius `2`, and inverse-square force\n`5/2`. Independent countermodels reject missing wave tails, unconditional\nenergy-rate ordering, invented quantitative tunneling formulas, and\nmisidentification of the field-emission analogy as a nuclear derivation.\n\nThe original Vishveshwara Schwarzschild analysis now has twenty-five inhabited\nVishveshwara Schwarzschild-stability boundaries. Its nonzero master mode has\n`m=1`, `r=3`, `l=2`, `V_eff=4/27`, and `Q''=31/27`; the infinity-decaying\nbranch grows to `exp(2)` at the horizon. A removable nonstationary dipole\ncoexists with stationary source rotation, and the `k=2-i` damped resonance\nretains independent radiation boundaries, complete odd modes, incomplete\neven modes, and uncontrolled nonlinear deviation.\n\nThe original stochastic-inflation paper now has twenty-three inhabited\nLinde-Linde-Mezhlumian inflation boundaries. Its certified routes retain\n`delta_phi=H/(2 pi)`, `\u003Cphi^2>=H^3t/(4 pi^2)`, `D=H^3/(8 pi^2)`, and\n`e^3/2` rising daughter domains. Most importantly, raw physical volume is\n`P_p(t)=15 exp(2t)` while only `tilde P_p(t)=15` is stationary; the spectral\ngap, both absorbing Planck boundaries, unequal clock densities, and\nnonstationary comoving density remain independent.\n\nMinkowski's original spacetime lecture now has twenty-nine inhabited\nMinkowski spacetime boundaries. Its certified route realizes\n`beta=3/5`, `gamma=5/4`, upper-hyperboloid coordinates\n`(3/4,5/4)->(0,1)`, proper time `4` from separation `(5,3)`, orthogonal\nfour-acceleration, a unique retarded null separation `(5,3,4)`, and\npotential `e/r=2/5`. Charge product `6` does not become the proposed mass\nproduct `10`, and a checked approximation does not prove universal gravity.\n\nEverett's original relative-state paper now has thirty-two inhabited\nEverett relative-state boundaries. Unequal amplitudes `3/5` and `4/5`\ngive weights `9/25` and `16/25`; the four two-observation histories have\nweights `81/625`, `144/625`, `144/625`, and `256/625`. Their mixed-branch\nmeasure `288/625` is not the counting fraction `1/2`, and the positive\nfinite exceptional measure `81/625` is not erased by its genuine Born-product\nhistory tail `(9/25)^(n+2)`. Decay of that one history does not imply decay\nof the entire exceptional set. Local noncommuting disturbance remains\ndistinct from remote noninteraction.\n\nLandau's 1941 helium paper now has forty-six inhabited Landau\nsuperfluidity boundaries. Its original zero-momentum quadratic roton has\n`Delta=8`, `mu=4`, energy minimum at `p=0`, and wall-speed minimum `2`\nat `p=8`. Simultaneous motions `rho_n=1`, `rho_s=3`, `s=1/2`, `T=2`,\n`v_n=3`, and `v_s=-1` give zero mass current, entropy current `6`, and\nthermal current `12`. These integer response coefficients admit an\narithmetic four-atom partition; the separate actual phonon response `3/2`\nexcludes every exact subset partition of one hundred unit-mass atoms.\nThe author's nonliteral microscopic interpretation remains a separate\ninput. Actual thermal functions distinguish a three-dimensional population\nfrom its activation factor, heat from energy, and a weak gap inequality\nfrom one-percent response accuracy. Sound readouts now come from one\nthermodynamic potential and actual propagating-wave families. The four\nlinearized balances yield a coupled characteristic and explicit errors in\nequation (9)'s approximate sound formulas. The same phonon-roton thermal\nand normal-response functions derive the low-temperature estimate; actual\nmode limits also require the pressure limit and vanishing coupling errors.\nAmplitude rescaling makes the actual fields arbitrarily small without\nchanging their speeds or mixing corrections.\nThe lambda limit has separate thermal-prefactor control. A leading-phonon\ndiagnostic has `u_1=2`, `u_2=1` at `T=2` and a genuine second-sound limit\n`2/sqrt(3)` at zero temperature; a different response family agrees at `T=2`\nbut has limit zero. Other potential-based controls distinguish held-variable\nconventions and show why vanishing superfluid density alone is insufficient.\nRestoring positive normal viscosity produces an actual nonzero wave residual,\nnot merely a different assigned scalar. These are ideal-model diagnostics,\nnot numerical predictions for physical helium or nonlinear vessel solutions.\n\nCallen and Welton's original generalized-noise paper now has forty-five\ninhabited Callen-Welton noise boundaries. At `hbar=k=T=1` and\n`omega=log(2)`, the upward/downward ratio is `1/2`, the dissipative\ndifference is `1`, and the fluctuation sum is `3`. The zero-point energy\n`log(2)/2` and Planck term `log(2)` remain distinct; resistance `pi` gives\nquantum noise `3log(2)` and classical noise `2`. Brownian spectra\n`9log(2)/pi` and `10log(2)/pi` are not white, dipole resistance is `4/3`,\nand wall pressure `3/pi^2` doubles volume pressure `3/(2pi^2)`. The source\nenergy balance `10=2+8` does not complete the proposed future theory.\nThe strengthened classical controls compute their oscillator energy and\nactual Dirac-measure integrals. A two-bin quantum spectrum has a controlled\nlow-frequency bin but violates the integrated classical tolerance; a\npositive-frequency continuum satisfies the pointwise quantum formula while\nits total noise integral diverges. Zero-probe, reactive-response, peak/RMS,\nand angular-measure controls separately guard the response comparison.\n\nAnderson's original plasma paper now has thirty-four inhabited Anderson\nconductor boundaries. Carrier data `n=1`, `e=2`, and `M=1` give response\n`K=4`, plasma gap `omega_p^2=16pi`, screened field ratio `1/5`, and\n`1+2=3` polarizations. Crucially, the normal plasma retains gapless matter\ndespite its gapped gauge sector; only the distinct superconductor is fully\ngapped. Conducting spectral weight `1` gives `Z=0`, ordinary weight `1/2`\ngives `Z=1/2`, and charge moves from the dressed particle to the surface\nwithout particle loss. The gravitational mode has signed frequency square\n`-4pi G rho`, so `3+2=5` polarization counting does not establish a stable\nmassive graviton or complete the non-Abelian and baryon-gauge programs.\n\nRegge and Wheeler's original Schwarzschild paper now has twenty-six\ninhabited Regge-Wheeler boundaries. At `M=1`, `r=3`, and `l=2`, the lapse\nis `1/3`, the tortoise derivative is `3`, and the gravitational potential is\n`4/27`; frequency `1` gives effective wave number squared `23/27`. The\nnegative-frequency mode decays at both ends but fails smooth continuation\nthrough the two-ended wormhole; equal and unequal incoming/outgoing strengths\nare both allowed. The independent even constraint is not implied by its\nequation-(29) first-integral transport or a later Zerilli potential. Static\nsources occur on both wormhole sides, and a nonzero quadratic residual blocks\nany nonlinear-stability claim.\n\nZeh's original measurement paper now has twenty-eight inhabited Zeh\nmeasurement boundaries. The actual complex x- and y-spin projectors both\naverage to `I/2` without determining preparation or selecting an outcome;\nthe trace formula presupposes rather than derives the measurement postulate.\nThe printed energies `10^-42 eV` and `10^-7 eV` give microscopic ratio\n`10^35`, while the dipole coupling weakens as `R^-3`. Unequal retained branch\nweights `9/25` and `16/25` now come from an actual finite composite ket;\nglobal and reduced purities are computed from its density and partial trace.\nReduced purity depends on environmental-record overlap: orthogonal records\ngive `337/625`, while overlap `3/5` gives `11017/15625` with nonzero\ncoherence `36/125`. Two populated branches or unequal record vectors alone\ndo not imply reduced mixedness. These numbers are diagnostics, not values\nprinted in Zeh; dynamical coupling estimates remain separate. The source\nalso retains distinct sugar/ammonia tunneling scales, two anticorrelated EPR\nrecords, and a globally symmetric sum of individually asymmetric components.\n\nYoung's original two-dimensional melting paper now has twenty-one inhabited\nYoung melting boundaries. Genuine angular-integral Bessel functions support\nthe nonzero-fugacity recursion, and triangular Burgers fusion\n`(1,0)+(0,-1)=(1,-1)` produces the quadratic channel absent for square\nvectors with composite squared length `2`. The equal-force exponent is\n`0.3696`, dislocations erase shear without erasing orientational correlations,\nand vacancy/interstitial contributions distinguish the true bulk modulus from\nthe dislocation-only result without determining the correction sign. The\nlater disclination transition and competing first-order melting remain\nunproved.\n\nWhen the large primary-paper archive is kept outside the published checkout,\nset `PHYSICSLOGIC_REFERENCE_ROOT` to the local `references/` directory before\nrunning `check_all.py`. Both the complete artifact/checksum audit and the\npolicy check's original-source passage comparisons then read that external\narchive. Without the variable, both continue to use the repository-local\n`references/` directory.\n\nThe active lane intentionally avoids technical mathematical proofs and\ncalculations. Those may later be imported from specialist libraries; until\nthen, they appear as explicit hypotheses of checked Lean theorems.\n\n## Recorded Estimates And Exact Values\n\nThe Penzias-Wilson 1965 and FIRAS 1996 adapters now distinguish a performed,\nrepresented temperature estimate from exact possession of its central value.\nTheir actual-temperature relations are independent of the calculations, and\nLean checks that changing those relations leaves each complete source result\nunchanged. Reported uncertainties, detection bridges, and FIRAS's Planck fit\nand systematic qualifications remain part of the source routes. Exact-value\nstrengthening requires a separate faithfulness premise, not an inferred one.\n\nSixteen source contracts and twelve mutations guard this distinction. An\nindependent consumer realizes a 300 K recorded estimate with a 299 K actual\ntemperature and bounded bias, then uses the public interface to reject exact\nphysical equality to the recorded center. This is an adapter correction, not\na claim that every measurement formalization has already passed this audit.\n\nRabi 1939 now makes the same estimate/exact-value distinction while keeping\nits physical moment parameter separate in the resonance and molecular\ndynamics. The source retains nominal 0.5% absolute and 0.1% relative accuracy,\nseparate from the tentative 0.2-0.3% line-minimum shift assessment. The source\nroute and independent epistemic ledger preserve that author expectation.\nA symmetric diagnostic dip with 1% half-width and a 0.4% displacement shows\nwhy width and symmetry alone cannot establish the proposed shift bound.\nA calibration-only model derives the field-scale factor in moment extraction\nand its cancellation from ratios only when common. Three additional inhabited\nfidelity boundaries and an independent common-standard consumer test why\nrelative moment information need not fix an absolute moment. The quoted\naccuracies are not silently promoted to hard bounds or confidence coverage.\n\nRamsey 1950 now calibrates its quoted pulse-area prescription to the actual\ncoupling, interaction length and beam-speed scale used by the source dynamics.\nThe on-resonance integral is derived exactly for double resonance and with\nthe retained error bound in the more general near-resonance regime. Two\ninhabited countermodels and an independent coherent-evolution consumer show\nwhy a quoted area needs physical calibration and why equal areas do not fix\nthe frequency response or width scale. The numerical optimizer remains an\nexplicit source input.\n\nIts calculated-profile comparison also retains the two numerical FWHM error\nbounds. A resolved nominal gap gives actual profile narrowing; ratio control\nrequires a positive lower bound for the reference width. Four inhabited\ncontrols and an independent eight-theorem profile client reject dropping an\nerror or treating positive actual width as resolution of the error-bound\ndenominator. The comparison concerns\nthe near and conventional calculated profiles, not the exact coherent or\nobserved response. The original numerical roots and validation budgets remain\nexplicit inputs.\n\nRamsey's weak-excitation argument also distinguishes the incident beam from\nthe transition-selected speed law. Lean derives the quadratic signal limit,\nthe normalized selected density `2 y exp(-y^2)`, and its inverse-square\nenhancement relative to the incident density. A finite-field theorem retains\nthe phase regime under which halving the coupling relatively favors slower\nmolecules. Three inhabited boundaries exclude a uniform small-phase claim,\nunqualified coherent speed ordering, and conditioning at zero drive. A fresh\nsix-theorem physical-beam client audits these APIs independently; no linewidth\nis deduced from selection alone.\n\nThat selected-speed law now enters the normalized cosine-squared interference\naverage explicitly, including its weak-field limit. Positive peak\nnormalization preserves a separately computed FWHM. Mean-speed substitution\nand unqualified relative accuracy near a weak peak are rejected by inhabited\ncounterexamples; the controlled near-frequency sweep retains the actual\npeak-referenced error bound. A separate seven-theorem client tests these APIs\nwithout production diagnostic witnesses. Fixed nonzero detuning can leave\nthe near regime as the field weakens, so the near-model limit is not silently\nidentified with an exact-experiment limit.\n\nFigure 2's width labels and equation (22)'s nominal coefficients are now\nseparate dimensionful evaluations, including the distinct near and broad\nfrequency scales. The empirical route retains their nonzero Table I\nresiduals. The former displayed-precision check is correctly identified as\ncoarse consistency, not decimal rounding. Three inhabited boundaries and an\nindependent five-theorem client protect these distinctions.\n\nKSW's pionless RG output now retains a real subtraction-scale coupling family.\nLean differentiates the imported equation-(11) solution on its non-pole domain,\nderives the printed beta equations, and recovers the zero-scale boundary data.\nThe source beta-function atom includes actual derivative semantics, and sampled\ncouplings are identified with the real family. Three inhabited controls reject\none-point sampling, vacuous zero-scale weighting, and inclusion of the pole.\nA separate six-theorem client uses three public APIs with independent physical\nparameters. No claim is made to derive the solution from scale independence\nalone.\n\nThe pion-inclusive route now has separate actual retained-model derivatives,\nliteral pion corrections, and the inhomogeneous D2 running term. Its computed-\norder scope is expressed with formal amplitude coefficients at powers n - 1:\nfull invariance, coefficient completion, and no omitted p^-1 or p^0 terms\nderive retained agreement through p^0 and explicit higher-order compensation.\nFive new fidelity boundaries and a seven-theorem independent client prevent\npromotion to all-order equality, confusion with pionless flow, or unqualified\nzero-scale continuation. These are local derivative and formal-coefficient\ntests, not a global RG solution, convergent expansion, or nuclear fit.\n\nHohenberg-Kohn's response route now derives actual nonanalyticity from its\npunctured-neighborhood derivative divergences. Finite isotropic gradient\nkernels are polynomials in q^2, and their analyticity is proved. They cannot\nagree with the exact singular kernel on any neighborhood of 2 k_F; this\ndirect obstruction does not assume a Fourier-tail calculation. The Friedel\ntail has an explicit additive inverse-cube envelope limit with positive\nfrequency and nonzero amplitude, retaining cosine nodes and allowing smaller\ncorrections without claiming exact equality. Five new fidelity boundaries\nand an eight-theorem independent client verify these distinctions. The\nFourier calculation, nearly-uniform approximation, and separate slowly-\nvarying expansion remain explicit obligations.\n\nThe slow-gradient expansion now distinguishes order and scale limits using\nactual coefficient sums, replacing the former shared Boolean status wrapper.\nThe paper-local source calculation identifies the same scaled density shape,\nenergy-density readout, fourth-order sum, absent fifth order, and sixth-order\nremainder. The explicitly assumed asymptotics then give orderwise eventual\nerror budgets and the sixth-order coefficient limit. Three further fidelity\nboundaries and nine independent client theorems separate asymptotic behavior,\nfixed-scale convergence, and summation to the physical target. None proves\nthe author's expectation or supplies a uniform numerical error estimate.\nThe actual fourth-order error also realizes an inhabited controlled\ntruncation in the existing shared framework, without inferring empirical\nadequacy or extracting the one-paper series vocabulary prematurely.\n\n## Finite Work Sampling\n\nThe Jarzynski 1997 parsing now separates exact ensemble validity, failure\nwithin a declared sampling budget, convergence of the actual finite\nexponential-work estimator, and accuracy of a selected observed dataset.\nThe original pp. 7 and 9 do not turn rare-event difficulty into a prohibition\nof every finite experiment. Ten source routes and eight additional fidelity\nboundaries retain this distinction. The Gaussian variance label is also\nidentified with the actual normalized work-law variance.\n\nConstructed canonical Hamiltonian quenches realize an exact identity and\nrare-tail dominance while a ten-trial budget is insufficient, yet prove\neventual convergence and reliable larger counts. Correlated repetitions can\nretain all canonical marginals without converging. A selected 100-trial\ndataset can be exact without its experiment meeting the confidence target.\nThe IID moment calculation is a sufficient semantic diagnostic, not a proof\nof the general paper or an author's necessary hypothesis.\n\nThe independent three-state consumer derives a different canonical law,\none-trial error probability `1/5`, and a five-trial exact estimate. It uses\nthe shared canonical integration and probability-role selection APIs without\nimporting paper files or canned production witnesses. The new general\nsampling vocabulary stays paper-local until a second independent source\njustifies extraction.\n\n## Cosmological Posterior Logic\n\nThe Riess 1998 and Perlmutter 1999 routes now require actual normalized\nposterior evidence for acceleration, separately from positive-Lambda\npreference. Shared semantics retain the two-component threshold\n`Lambda > M/2`, nuisance marginalization, proper normalization, the coasting\nboundary, and the distinct flat-prior threshold. Riess's method-specific\nGaussian likelihoods and Perlmutter's supplied correlated-error joint\ndensity remain different constructions. Numerical probability bounds are\nexplicit imported calculations, not new fits or proofs of physical truth.\nFive additional paper-fidelity boundaries and an independent sixteen-theorem\nfinite posterior client test these distinctions. The main results and shared\nadapters retain the evidence, so an interpretation flag cannot bypass it.\n",1794686183076]