PhysicsLogic

PhysicsLogic is a Lean 4 project for parsing the formal logic of theoretical physics papers.

The present objective is faithful logical reconstruction, not technical proof completion. A paper formalization must expose:

typed physical vocabulary;
proposition-valued definitions of the paper's claims and principles;
explicit hypotheses for imported mathematics, physical principles, approximations, and calculations;
Lean theorems deriving the paper's conclusions from those hypotheses;
primary-source anchors for claims and transitions;
unresolved assumptions, approximations, deformations, and interpretations.

A citation graph or an enumeration of opaque claim names is not the formalization. Source maps are auxiliary provenance. The formal content lives in Lean data, predicates, definitions, and checked deductions.

A source statement does not become true by being cited. Unproved physics and mathematics enter theorem signatures as explicit propositions. Lean then checks the logical consequences without pretending to prove those inputs.

Development Strategy

The light-cone review separates the Minkowski interval, future orientation, and an explicit signal-speed bound. It repairs the selected Minkowski boost readout so both time readings describe the same event under an admissible boost. Three duplicate signalling predicates now delegate to the existing signalling context with unchanged meanings. The independent coordinate test does not replace the paper's explicit geometric hypotheses or constitute human semantic approval.

The paper's signal route now requires an actual global time/Euclidean-three-space chart, tied to its own first-frame coordinate values for every worldpoint. Strictly timelike interior points and null light-signal endpoints have separate roles. Signal exclusion and the distance/time value c follow from this explicit interpretation, not from an arbitrarily named causal relation. The same review exposes every calibration clause and concrete stationary-signal and transverse- separation counterexamples. This realizes the flat causal-coordinate sector, not all worldline derivatives, force laws, or frame transformations in the paper.

Human semantic review is a separate requirement from compilation and automated audits. The repository is currently a research corpus with substantial automated verification, not a human-validated, production-mature physics specification. The review obligation covers all meaning-bearing declarations, including structure constraints, inductive alternatives, implicit instances, and theorem hypotheses, not only declarations introduced with def. Calling a concept central or peripheral does not change that obligation. Development now prioritizes complete reviewable argument slices and demonstrated semantic consolidation over further breadth. New papers and frameworks are frozen during the semantic-consolidation stage. No reviewed production subset is claimed until actual human approvals cover its meaning-bearing dependencies; the wider corpus remains experimental. The first reviewability pilot exposes Guth's eight causal definitions in RadiationHorizon/Definitions.lean. Its implementation proves both the fixed-emission distance characterization and the particle-horizon characterization; neither is an assigned access flag. Thermal and flatness obligations remain separate paper-local modules. This is a candidate for human review, not a completed semantic approval.

The same core now distinguishes a signal between comoving worldlines from one shared past event for a whole nonempty region. A closed radial interval has a regular common past exactly when its physical width is below four times the age; the particle-horizon radius remains twice the age. An explicit interval shares one past event while its extreme worldlines cannot have signalled each other by that epoch. Guth's entropy-rescaled closed region also has one shared event under the existing subhorizon inequality. None of these geometric results establishes thermal equilibration or an inflationary history.

The radiation review also derives the expansion rate from the scale factor, and shows why its inverse equals the particle horizon specifically in this model. An explicit incoming null ray has local radial speed -1 but proper distance rate H D - 1. A constructed ray starts at distance 6 at time 1, outside the Hubble radius 2, with proper-distance rate +2, yet arrives at the origin at time 16. The same trajectory obeys the causal speed bound throughout. This tests the distinction between local light speed, recession, and future reception without adding a physical definition or assuming an event horizon. The radiation approximation is retained throughout the example, not asserted across a full inflationary history; the numbers are not observations.

The interactive semantic-review pilot starts at the radiation-horizon characterization and exposes its actual meaning dependencies separately from proof references. Nodes show elaborated types, predicate bodies, parameters, joint hypotheses, and external mathematical boundaries. Review records are scoped to content versions; no human review has yet been recorded. This is one complete causal argument, not validation of the whole Guth paper or the full library. Regeneration and review rules are in CONTRIBUTING.md.

A second prediction review slice connects the dynamics paradigm to a metric forecast obstruction and an explicit linear flow. Its checked examples distinguish failure of the nominal forecast from failure of every forecast compatible with the same initial information, retain the strict factor-two error bound, and reject vacuous success on empty input. This is information-limited accuracy feasibility, not a claim of computational predictability. It now also separates existence and uniqueness from continuous dependence, and fixed-time continuity from one error bound for every future time. The paradigm contract is named TotalDeterministicEvolution; its earlier WellPosedForwardEvolution name is deprecated because it did not assert stability. Existing consumers remain compatible. Human review remains pending.

The density-functional review slice adds a checked expansion into explicit quantum-state constraints. Its three-site counterexamples separate fixed-number minima, density-dependent constrained energies, and local-potential eigenstate representability. All model fields remain inspectable; this finite diagnostic does not settle the continuum representability problem or constitute human semantic approval. It now distinguishes nondegeneracy from literal wavefunction uniqueness: the ground eigenspace is one complex line, and its normalized vectors form exactly one global-phase orbit. A sign-change control preserves density and energy but changes the vector. The HK quotient review now exposes a conditional construction of the complete framework on classes, preserving its readouts and representable-density domain. The original determination and variational arguments are reused there; global phase is an explicit unit-modulus relation, not an arbitrary label. Concrete continuum domain and invariance inputs, and human semantic approval, remain open.

The chemical-force review connects Onsager's ideal-solution free-energy formula to its actual derivative. The variation contract now explicitly conserves total amount, as do the selected and reference populations. This removes the common RT term from the derivative; the resulting variations determine only force differences, not three absolute forces. A positive reference state separates this derivative from an amount-adding direction and separates the logarithmic force convention from its common-shift freedom. The former arbitrary approximation-comparison field is replaced by the actual first-order derivative at the reference state. The linearized forces and a stationary reference reproduce mass-action rates. A positive nearby-state family retains detailed balance at the reference and first-order agreement, but substituting exact logarithmic forces into the same coefficient map gives a nonzero rate error at arbitrarily small positive displacement. A separate quantitative scalar-force estimate gives, on |x/n|<=1/2, an error of at most 2 RT (x/n)^2. The positive cutoff min(1/2,tolerance/2) controls the error relative to the linearized force for every positive reference amount. Absolute smallness alone fails uniformly as that reference varies: x=n can be arbitrarily small while the RT=1 force error stays 1-log(2)>0. These are consequences of the ideal logarithm, not error bars stated by Onsager or bounds on kinetic-rate error. Fifteen literal definition contracts and twenty-eight statement contracts expose these distinctions. The bounds required no additional physics definitions. This is the paper's chemical analogy, not a general transport theorem or a human semantic approval.

The self-consistent energy review distinguishes a stationary state, a total-energy minimum and convergence of frozen-Hamiltonian ground-state updates. In the existing two-site Hartree model, the premature eigenvalue subtraction misses exactly the quadratic energy of the output-minus-input density. At fixed particle number this is five times the squared site-density residual. The actual alternating ground updates have identical successive energies but a nonzero density jump and no density limit. These are finite diagnostics of the self-consistency condition before Kohn-Sham equation (2.10), not a general XC error bound or an algorithmic failure attributed to the paper. Human review remains pending.

The exact HK determination review now starts from ten physical fields, instead of requiring the full 51-field paper record. The existing paper proofs invoke this core, with the original energy, fixed-number domain and source premises preserved by checked equalities and equivalences. The full-model bridge remains inspectable; response expansions and atomic predictions have not been erased or filled with defaults. This reduces review scope, not the need for physical judgment.

The Bell common-probability review exposes one probability measure and two local dichotomic responses. It derives almost-everywhere opposition, the single-response integral, and Bell's original three-setting bound, then excludes agreement with the actual singlet density matrix on unit directions. Explicit controls separate a null set for each setting from one null set for all settings, and a common law from separately normalized setting-dependent laws. EPR predetermination and angular-averaged nonapproximability are separate routes; human semantic review remains pending. The real spin values are defined directly as +1 and -1. A checked equality preserves the original generic encoding, which remains inspectable through its own review statement. The complete exclusion specification no longer depends on that generic arithmetic-record interface; no dependency is hidden by the viewer. The real-valued bound is also stated directly, with a checked equivalence and consumer compatibility readback for the old interface.

The locality and averaging review characterizes deterministic locality directly by remote-setting independence. Three checked equivalences remove the need to mentally unpack auxiliary possibility relations; they add no physical definitions. A finite diagnostic then averages actual response pairs with one fair hidden law. Both observed marginals are uniform despite remote-setting dependence at every hidden value. A different local realization gives the same complete joint distributions. The distinction is locality of a specified response model versus existence of some local model of its statistics, not a Bell-inequality violation or a singlet reconstruction. All four diagnostic definitions and both response structures remain inspectable; human review is pending.

The nuclear-expansion review separates the source's leading-contact resummation from one derivative insertion, exact elastic unitarity, and numerical remainder control. In the declared reference-scale window, checked amplitude bounds give a relative insertion of at most 1/32 and a range-resummation difference of at most 1/1024. A bound on unknown higher terms of k cot(delta) is still a separate input. An explicit polynomial has the same first two low-energy coefficients and exact elastic unitarity, yet differs substantially from the truncated amplitude. It does not realize a finite-range nuclear potential or refute controlled EFT power counting. Seven original source fields and all diagnostic data remain visible; no new physical definitions were introduced. Human review is pending.

The nuclear review also distinguishes forward stability from inverse recovery. The exact amplitude-to-phase distance identity divides by both amplitude magnitudes. A uniform positive amplitude floor therefore gives a checked reconstruction bound on the actual selected predictions. On 1<=p<=2, bounding both real phase functions by one gives phase error at most nine times the amplitude error in the fixed normalization. By contrast, K=L and K=2L have exactly unitary amplitudes with arbitrarily small difference on that same band while retaining a phase difference at least one. This changes scattering length across models, outside the large-length regime; it is not a potential realization, an experimental fit, or a regulator change. No definitions are added, and human review remains pending.

The nuclear review's finite-chart exercise separates a choice from its consequences. NonvacuousElasticSWaveAt now contains only positive momentum and the real-K formula f=(K-ip)^(-1). A checked equivalence preserves the previous contract, which also listed elastic unitarity. Both scalar S-matrix unitarity and the optical theorem follow from the formula. The zero-contact amplitude satisfies both laws but is outside the finite-K chart. One redundant clause was removed; no physical definition was added or removed. Reality, domain, normalization and interpretation still require human validation. This is not a reduction of the whole nuclear framework to two physical choices.

The default nuclear review statement now exposes one complete conditional argument: the source bubble formula with real contact implies unit norm of 1 + i p M A/(2 pi). Its five quantities and five premises are written with ordinary real and complex arithmetic, without project-defined predicates. The existing seven-field source API calls this theorem and retains its stronger global assumptions. The PDS integration and resummation are an explicit formula input; this does not prove their correctness or the model's physical accuracy. Positive mass and nonnegative momentum delimit the physical interpretation, even though they are not required by the algebra. The nonpole restriction is retained to exclude a totalized quotient at a physical pole. An independent consumer keeps the amplitude fixed and changes the normalization denominator from 2 pi to 4 pi, changing the S-matrix norm square from one to one half. No physics definitions have been deleted or added, and neither the source interpretation nor practical human manageability has yet been approved.

The ordered-limit review exposes both iterated limits as checked epsilon/delta equivalences. These show exactly which size cutoff may depend on a fixed field and which field cutoff may depend on a fixed size. One normalized two-orientation diagnostic realizes different limiting magnetizations and rejects a cutoff uniform near zero field. Other controls distinguish the value at zero from its positive-field limit, exclude empty approaches, and separate source certification from mathematical existence. This is not a short-range Heisenberg model or a counterexample to Mermin-Wagner; human semantic review remains pending.

The same review now exposes a repaired Mermin-Wagner spectral assumption. The earlier Gibbs contract required every field-dependent Hamiltonian to be diagonal in one fixed basis, unintentionally forcing them to commute. The original p. 1134 instead uses a complete energy basis of the selected Hamiltonian. An explicit channel- and field-dependent matrix now supplies those coordinates, with completeness and diagonalization stated as conditions. Thermal averages and the spectral inner product use the same transformed operator entries. Two checked readbacks reconstruct the Hamiltonian and the fixed-coordinate thermal trace. A finite two-field diagnostic has noncommuting Hamiltonians, valid Gibbs states, and an expectation changed by ignoring the eigenvectors. It is not a Heisenberg lattice or a new no-order calculation.

The spin-observable audit makes Cartesian Hermiticity explicit in the same fixed Hilbert inner product. Commutators and the Casimir alone did not imply it. Three checked consequences give mutual adjoints for the ladder operators, real Gibbs averages for Hermitian observables, and real Cartesian spin averages. Ordinary spin-half matrices satisfy the repaired contract. A nonunitary rescaling retains the algebra and a selected zero-Hamiltonian Gibbs state but fails that contract; the normalized vector (3/5,4i/5) gives its x matrix the nonreal expectation 9i/25. The graph exposes the full condition, explicit matrices and local state. These are finite diagnostics, not a Fourier-lattice realization or a complete no-order proof. Human review is pending.

The measurement review separates basis calibration, linearity, record agreement, and a definite outcome. Checked equivalences expose transport of every complex amplitude and exactly when a pointer or match-only record determines a value. A normalized two-component input retains both sectors after communication. A deliberately nonlinear rule calibrates the unit basis and preserves normalization while selecting a sector, but fails superposition. This is a diagnostic outside linear quantum mechanics, not a model attributed to Everett or a resolution of the measurement problem. Human semantic review is pending.

The typicality review exposes the single selected state before the quantifier over all licensed properties. A finite canonical diagnostic has 100 tests, each passing with probability 99/100, but no common passing state. Dropping one test leaves a sound, nonempty common set of probability only 1/100. Individual high probability, nonempty selection, sound selection, and high joint probability are distinct. The existing two-level Gibbs example also separates typical agreement from universal truth and exact finite-frequency equality. These are diagnostics, not a derivation of Bohmian typicality or completed human semantic review.

The DGZ finite-time review exposes the paper's common-law inference as explicit empirical sums and reference-law integrals. Agreement at every selected time uses a summed failure budget; agreement at most times uses an average divided by the tolerated bad-time fraction. Controls distinguish a strict joint budget, the closed tail, time-dependent measures, rare conditioning environments, and empty selections. A separate complete scope retains the actual paper's Born-law specialization. Conditioned bounds and disintegration remain inputs, not proved physics or claims about every configuration. Human semantic review remains pending.

The Witten spectral-index review follows a convergent graded trace to an actual normalized charge-kernel state. Two checked equivalences expose the complete basis/operator representation and the vacuum predicate's positive normalization, symmetric charges, and normalized common kernel. Controls separate pair cancellation from trace convergence, the index from a normalized thermal expectation, and zero infimum from an attained ground state. The larger four-charge physical specialization retains all of the paper model's fields and its momentum, rotation, and trace bridges. This does not compute the SU(N) index or establish its infinite-volume limit; the diagnostic spectra are not Yang-Mills spectra. Human review remains pending.

The Bethe triplet-range review separates squared parahydrogen data from a signed coherent amplitude, making the selected sign explicit before a scattering-length decoder can be calibrated. Equal-record alternatives test the lost information. The paper join retains equation (19)'s bound-energy range and the separate replacement-error budget. A further check preserves the printed plus sign in (25) while exposing its conditional conflict with the fixed-mass binding-energy response. These are central-value and conditional inference checks, not exact empirical knowledge or an approved erratum. Human semantic review remains pending.

The actual Bethe intensity context now uses the shared mapRecords operation on the signed-record context, removing duplicate domain and value assignments. A checked equality retains the original squared formula and full physical description. All squared-record value constraints already follow from signed records. With the additional coherent-sign restriction on both domains, their constraints are equivalent for every property, not just for one chosen decoder. The existing opposite-sign ambiguity remains. No physical definition or diagnostic model is added by this consolidation; human review is still pending.

The physical-observer review separates an occupied physical role from an interaction that produces an accessible record. The physical-role predicates share one definition family and are unchanged by arbitrary consciousness reclassification. Everett's model no longer requires an unused consciousness relation; its operational specialization still exposes calibration, branch correlation, and record-interpretation inputs. An explicit realization premise now connects that role to the same calibrated coefficient model and supported first-record amplitude. Every operational record determines a value in a nonempty pointer fiber; zero-output measurement dynamics cannot realize a role, even when the primitive role and correlation labels are retained. Both the direct route and shared-framework bridge require this realization; neither derives it from a label or assumes a global outcome. Finite role assignments are interface diagnostics, not physical machine models or a theory of consciousness. Human semantic review remains pending.

The same review now checks Rovelli's observer adapter against the actual coefficient model in P's description. Three separate premises require calibrated dynamics, equality with the stored post-measurement coefficients, and nonzero first-record support. Every operational record determines its correlated value in that description; zero dynamics or zero input cannot supply it. Changes to other coefficient descriptions leave the selected role unchanged. This does not identify P's coherent description with O's conditioned account or a later comparison reference. The repair adds no physical definition; independent readbacks and mutations check the existing adapter's reference and record data.

The cosmological-inference review separates the variance of a chosen estimator from impossibility for every alternative decoder. It connects the explicit Gaussian moment calculation to the full-sky estimator law and noise-free sampling result. A finite diagnostic has unbiased readings with variance one yet allows exact decoding of either unknown target. The shared paradigm states the different, cross-model obstruction from a common accessible realization with unequal targets. A scalar Gaussian contrast excludes a common almost-surely exact decoder by transferring null sets, not by projecting an estimator-variance assumption. This is not a full-sky optimality theorem. The degenerate zero-power boundary demonstrates why both Gaussian variances must be positive. All eleven statements and their definitions remain pending human semantic review.

The impermeable-layer review tests the thin-layer operators with an actual periodic viscous flow. Unlike the separate suction diagnostic, it keeps normal wall velocity zero and the same oscillating wall forcing for every parameter. Its full and retained balances are exact, and the far-field condition is a checked limit of the profile. Nevertheless, pointwise outer recovery and uniform recovery away from the wall do not give uniform convergence on the whole open half-line. Wall shear vanishes while interior viscous acceleration remains nonzero; deleting the time acceleration breaks the equation. This is neither Prandtl's steady flat plate nor a fixed-initial-data limit theorem. All thirteen statements remain pending review.

The Onsager variational review exposes the fixed-temperature argument through actual linear entropy supply, quadratic dissipation, spatial integral representations, and boundary fluxes. A checked characterization retains the source's force normalization X = -grad(T)/T, distinct from grad(1/T) and from an unnormalized temperature gradient. The constitutive entropy identity cannot be substituted before varying the flow. Explicit matrix controls distinguish nonnegative dissipation from uniqueness and strict dissipation from reciprocity. Isolation, the stationary power constraint, and prescribed normal-flux profiles restrict the trial as well as the physical flow. This is not a universal maximum-entropy-production principle or a derivation of microscopic reversibility. All sixteen selected statements remain pending human review.

The coarse-graining review exposes an independent finite Ising test of prediction preservation, generated interactions, and model closure. Its exact marginal retains an outer-spin pair mean but is not any pairwise Gibbs law, even allowing additive energy constants. Two positive-mass states with the same retained configuration also obstruct almost-sure recovery of the hidden spin. A separate null-state control distinguishes that obstruction from merely pointwise disagreement. The readable normalization equivalence adds no new physical assumptions. Rescaling requires reexpressing observables; successive decimation requires the transformed domain. The chain's Boltzmann weights and probability bounds are shown separately from its algebraic composition identities. These eighteen statements are diagnostics of RG distinctions, not Kadanoff's critical lattice or an interacting fluid, and remain pending human semantic review.

The Hubble calibration review joins the finite radial-fit argument without replacing the solar correction by a label. Positive distance rescaling preserves every radial readout and fixed-weight loss while changing the coefficient. An exact distance anchor removes this scale freedom; a sufficiently small anchor error only bounds it. An independent positive-distance diagnostic shows unbounded coefficients when the error budget reaches the anchor distance, despite unchanged residuals. The full paper adapter and its tentative cosmological interpretation remain separate inspectable scopes. These are conditional calibration statements, not a historical refit, quoted probable errors, or proof of cosmic expansion. The joint-fit extension now varies the solar solution at fixed distances. Opposite sky directions cancel its projection in a sum; a common direction at different distances uses a difference. Both decoders retain peculiar residuals. The bounded-residual result supplies an interval, with an explicit nonzero-error control attaining the bound and a second compatible coefficient with zero residuals for the same observations. A separate two-direction sample keeps its distinct, exact distances and every residual while K changes from 500 to 600. Thus removing the distance-scale freedom need not resolve the joint fit. These nine additional theorems use the existing physical vocabulary; all local example data remain visible in their statements. All twenty-five selected statements remain pending human semantic review.

The local-invariance review repairs an actual quantifier error in the equivalence-principle paradigm: position invariance previously compared arbitrary frames and therefore implied Lorentz invariance by definition. It now holds a repeatable laboratory configuration fixed across places; the Lorentz clause independently changes configuration at one place. A checked transfer theorem exposes the intermediate frame's availability. Numeric diagnostics separate both clauses and show why inhabited but disconnected comparison scopes do not imply global agreement. The five context fields remain unchanged. Matching conventions and local calibration remain interpretation obligations, not a canonical identification of tangent frames. This is not a complete dynamical theory or a proof of EEP; all eleven statements remain pending human semantic review.

The frequency-reference review repairs a missing Atomichron input in Hughes's nuclear scan, independently of the atomic route. Positive numerical configurations show that even an exact null ratio can hide unbounded common frequency variation. Independent reference access recovers the frequency; finite ratio and reference allowances instead give the bound d + e + d*e, attained by a checked example. These use the philosophy layer's actual record-determination and record-constraint definitions. The expanded fifteen statements also expose the diagonal rank-two spin spectrum: an unchanged spin-half gap, three spin-three-halves gaps, their positivity domain, and the separate need for field stabilization. Two arbitrary reference predicates have been replaced by one frequency-response map and an explicit zero-response condition. The proton control follows only after identifying that physical response with the model calculation. Cesium dynamics, nuclear matrix elements, line-width conversion, and human semantic review remain open.

The work-sampling review tests a tempting converse of Jarzynski's practical warning. An independent canonical two-state quench has work variance below 1/1000 in thermal units and satisfies the exact work identity. Nevertheless, at every positive sample count up to 1000, the specified estimator has probability at least 999/1000 of both exceeding its 25-percent relative exponential error and misestimating free energy by more than log(2). The actual rare-event probability, product sampling law, and logarithmic readout are exposed. Ten statements also retain the source interface's independent-repetition and exponential-moment premises. This is not an obstruction to every estimator or every finite count. No production definition is added; human semantic review remains pending.

The state-positivity review repairs an insufficient shared state predicate. A normalized complex-linear functional can have a nonnegative real part on every a* a while assigning 1/2+i to a yes/no projection. The repaired predicate requires reality as well as nonnegativity, yields real projection probabilities in [0,1], and is retained by vector states, finite ground averages, and nontrivial-filter weak limits. An independent two-outcome algebra checks both rejection and an ordinary equal-mixture control. Ground-sector realization and human review remain separate obligations.

The local-operation review connects a commutator estimate to the actual expectation change under a unitary preparation. A normalized vector supplies both full positivity and the contracting-functional bound. An independent two-qubit Hamiltonian changes a remote Y expectation from zero to -sin(t) after a first-site bit flip, while retaining exact equal-time exclusion. For every tolerance and candidate finite front velocity, a positive earlier time has a nonzero but smaller-than-tolerance readout change and commutator norm. Unit separation and interaction-energy time units are explicit. This is a finite diagnostic, not an infinite-lattice Lieb-Robinson proof or a relativistic signalling claim; human review is pending.

The phase-mixing review connects vanishing number-density contrast to retained velocity information. An ideal velocity reversal of the existing positive, neutral two-species solution preserves the instantaneous density; subsequent forward streaming recovers the complete initial modulation. For every tolerance, the initial contrast can be uniformly smaller while later contrast is exactly 1/2. Actual kinetic equations and Poisson closure remain checked. This is an externally controlled recovery, not autonomous recurrence, entropy production, a nonlinear plasma echo, or Landau's fixed-ion field damping. The separate source argument exposes its contour asymptotics and nonzero residue. Human review remains pending.

The thermal-calibration review distinguishes common from relative gain uncertainty. Actual matrix traces give detector-squared noise and detector-times-drive response. Matched nonzero gains cancel in a ratio that identifies the four-level Gibbs state under explicit normalization and commutation assumptions. Independently uncertain positive gains instead allow two different stationary states to give identical complete records in all three nonzero channels. The measurement layer consequently excludes exact recovery and certification at the declared temperature. These are finite inverse-inference diagnostics, not additional Callen-Welton source claims, empirical estimates, or human semantic approval.

The thermal-probe review tests the converse of fluctuation-dissipation inference. Two strictly positive stationary states of the same four-level Hamiltonian have identical full correlations, noise, and response for one Hermitian probe. The alternative is not Gibbs at any real inverse temperature, yet its selected spectral line obeys the same FDT. The measurement layer excludes thermal certification from that record. Three separately resolved adjacent-transition balances and normalization instead determine the Gibbs populations within the diagonal family. These probes still miss a positive state's off-diagonal coherence even when all their individual noise and response records agree with Gibbs. A cross correlation detects that coherence, and actual free evolution changes the state. Commutation with this nondegenerate Hamiltonian removes the ambiguity; normalization and the adjacent balances then identify the full density matrix. The direct record route now decodes each pair from its noise at zero and response at pi/(2 log 2). Probes 0 and 2 suffice to recover all four diagonal entries; these four calibrated entries and commutation identify Gibbs without assumed population balances. The measurement layer certifies this conditional claim, not the commutation premise. A stationary positive non-Gibbs state still matches all three equal-time records. No new physical definitions were needed. These ideal records are not finite measured samples or full state tomography. The test is independent of the original Callen-Welton forward derivation; human review remains pending.

Structure inspection now displays every field type in an ordered table under the shared constructor parameters and earlier fields. Local field names link to their exact qualified declarations; dependencies and full projection signatures remain available beside each row. All field types stay visible, including proposition-valued restrictions and instance bindings, without shrinking the text. These are Lean-derived types, with explicit links to parameter, field, instance, and declaration dependencies. Full structure and projection types remain available. Constructor-signature checks retain parameter order, dependent fields, and proposition-valued restrictions; diamond inheritance is not flattened away. Earlier schema-4 exports remain comparable, with the schema change distinguished from a change in physics. This improves readability without changing production physics definitions.

Statements with local definitions now have a separate scoped inspection view. It exposes each assigned value and its type, retains later hypotheses and shadowed or unused bindings, and links references to their actual earlier positions. Defined proofs are not labeled independent assumptions. Hubble's competing datasets are a concrete use: their values can be inspected before reading the conclusion. Reconstruction is checked against the original Lean type, which remains visible. Schema-4 and schema-5 exports remain comparable; this tooling check does not certify physical meaning or human approval.

Each review page can compare two selected statements' complete meaning scopes. Shared, current-only, and comparison-only declarations are listed separately from external mathematical boundaries, with both exact statement types and links into the correct argument context. Shared names do not mean identical instantiated premises, independent assumptions, or prior human approval. This helps avoid repeated navigation without shrinking the semantic review scope. Statement selection order no longer labels every secondary result a diagnostic; source attribution remains in the review scope and exercises.

The representation review exposes nonempty assignment soundness through all seven primitive relations. An independent bounded-bias thermometer makes the obligation concrete: every admitted temperature and bias must satisfy the decoder equation. An exact reference correction satisfies it inside that model. One correct reading does not establish global soundness, and a sound partial representation need not cover other physical states. Recorded estimates and informative bounds remain distinct from exact values. Neither the model's truth in nature nor human semantic approval follows from these checked results.

The same review exposes deterministic record processing through one shared operation that leaves admitted configurations and physical values unchanged. Fifteen exact results distinguish lossless relabeling, reflection of a selected record fiber, and lossy processing. A finite quantum pointer retains its outcome under injective relabeling. Squaring a thermometer reading above one preserves its constraints because the other preimage is outside the admitted domain. In the existing Pound-Rebka mean-response diagnostic, dropping thermometry retains signal and calibration but loses gravity identification. A constant processing function also shows why an attained output cannot certify an impossible original record. Everett's original p. 458 and Pound-Rebka's temperature companion p. 275 ground the distinctions; these constructed models do not assert collapse, experimental precision, or human approval. An exact shared criterion now characterizes preservation of every proposition about a selected value: each processed-compatible alternative must have a value already realized in the original record fiber. Full records need not survive. The quantum example merges outcomes 0 and 2 but retains whether the outcome was 1. Reversal signal, calibration, and thermal differences retain gravity in the specified mean-response model while discarding common-offset information, following the distinction in Pound-Rebka's original pp. 339-340. Both use the same theorem. Their local value selection and encodings are exposed in Lean and the review graph; this is not a claim about statistical sufficiency.

The residual-inference review slice uses Penzias-Wilson's bounded-error record model to distinguish a positive residual, an exact temperature, and an origin claim. A checked interval characterization exposes what is constrained and what remains unspecified. Its controls retain actual-model compatibility and the strict sum of an additional other-contribution bound and the error budget. Neither a confidence level nor a cosmological identification is inferred from the scalar record alone; human semantic review remains pending.

The same review now connects bounded component errors to the actual subtraction used by the record model. The sharp uniform budget includes both the component error sum and any shift of the center. The numerical control's backlobe and recentered radius are diagnostic choices, not revised historical measurements. The resulting compatible record transfers positivity to that same subtraction. The separate spectral route now derives exclusion instead of importing it: a strictly steeper candidate cannot supply the whole high-frequency residual without exceeding the low-frequency sky budget. Diagnostic controls preserve the equality boundary and possible partial contributions. The observed bound, known-source classification, and source spectra remain explicit inputs.

Each review page also offers a Complete project specification view: every meaning-bearing declaration for the selected statement, with exact Lean types, data and predicate bodies, fields, binders, and direct dependency links. Groups put dependencies first and keep mutual references together; external types remain explicitly unexpanded boundaries. This removes the neighborhood limit from inspection, not the need to review the meaning of every declaration. The Connection to selected statement disclosure gives one shortest path through actual specification references to the declaration being inspected. Every step is navigable, including inherited fields and selected instances; external boundaries terminate the path. Declarations reached only through proof exploration are explicitly outside that statement's meaning closure. This is neither a chain of logical implications nor a smaller review scope. Each statement also exposes which declarations and earlier binders occur in each parameter, hypothesis, and conclusion. These Lean-derived links separate the meaning of a premise from that of the result; they do not say whether a premise is necessary or used by the proof. Local references retain their telescope positions even when names are shadowed. For a project predicate at the head of a statement part, One-step predicate expansions substitutes its actual arguments into its definition. The extractor kernel-checks definitional equality and preserves implicit instances, proof arguments and assigned local values. Original applications and remaining references stay visible. This is one substitution, not recursive simplification, an independently written characterization or physical validation. External definitions and predicates hidden inside larger expressions are not unfolded. Structure fields retain Lean's elaborated declaration order and distinguish explicit, implicit, and instance fields. Every direct parent is separately listed in extends order, including parents reconstructed from shared fields in diamond inheritance. Parent structures and projection bodies are inspectable without misrepresenting reconstructed parents as additional stored fields.

The same pages can export their inspection as compact JSON and compare a prior export locally. The comparison covers the selected statement's complete meaning closure, shows exact before/after values, and distinguishes changed declarations from declarations entering or leaving scope. Owning-source and configuration fingerprints are compared separately. It never imports review approvals or equates unchanged displayed specifications with physical correctness; source changes can still invalidate a review. No build copies are needed.

The Inspection notebook keeps reader-authored observations, open questions, and suspected mismatches separate from the human-review ledger. Entries attach to exact declaration-meaning fingerprints; external-type notes conservatively track the entire extraction snapshot. Older notes remain visible when a version changes. Browser storage retains entries where available; compact JSON export and merge provide portable backups without replacing existing notes. A matching attachment is not an authenticated author, a semantic approval, or a completed review of any dependency. Unsubmitted text survives in-page navigation only.

Guth's radiation horizon now has actual causal semantics. From a(t) = A sqrt(t), A > 0, Lean computes the integrable conformal-time integral and derives the physical particle-horizon radius 2t. Radial causal curves from strictly positive emission times reach exactly its open interior. Entropy rescaling can place a selected region inside that horizon without making all space accessible. Continuing this radiation model into the future gives no future event horizon, despite a finite particle horizon at each age. Independent examples test a nonunit scale normalization and reject treating a divergent integral's default Lean value as a physical radius. This remains paper-local flat-radiation kinematics, not a complete inflationary history or measurement theory.

Canonical preparation now has an explicit approximation regime. For each fixed finite ensemble, coupling, observable, and positive error-per-field tolerance, Lean derives a positive field radius controlling the remainder. The same bound realizes the existing paradigm's ControlledApproximation with absolute error tolerance * radius. Kubo uses the actual isothermal coefficient; Mori's orthogonality gives a small force mean on that window. Rescaling the coupling by s transports the window to radius/|s| and its error-per-field tolerance to tolerance*|s|. The positive three-state diagnostic retains zero derivative and local control at every coupling scale, yet refutes any common field cutoff giving absolute error at most 1/14. This separates model-dependent local validity from an unsupported uniform claim. It provides no numerical radius, quadratic remainder constant, time-uniform control, or thermodynamic-limit estimate.

The Mori-Kubo preparation refinement now derives response from a normalized finite ensemble with energy E-h*A, rather than assigning its linear coefficient. Differentiating the partition sum gives the connected covariance. Mori's finite sampling bridge uses the existing projected-force geometry and equilibrium moments to derive a zero linear response; Kubo's finite diagonal bridge identifies the existing isothermal admittance with the actual derivative while retaining a different isolated response. A positive three-state model rejects exact finite-field cancellation from orthogonality alone. An independent nonuniform four-state consumer checks both zero and nonzero susceptibilities, observable-offset invariance, and a nonzero nonlinear residual mean. These are finite classical/commuting specializations, not quantum, continuum, bath, or most-probable-path proofs. The existing source-route inventories are unchanged.

The bounded-record parity inference now feeds the complete selected Wu and GLW parity routes. The paper adapters construct the earlier observation calculations from calibrated records rather than assuming a physical rate inequality. Wu still requires gamma calibration, time/directional reports, three artifact controls, and physical prediction/interpretation. GLW still requires the precession apparatus, polarization interpretation and scoped stopped-pion control. Its formerly arbitrary count-rate-distinction predicate now means actual inequality. A separated record for an unrelated system does not calibrate a symmetric angular law. Independent consumer tests quantify over every compatible analyzer coefficient: they reject all symmetric candidates while retaining two different asymmetric coefficients for the same record. Generic integration clients additionally check the full paper-route contracts and actual proof dependencies; they are not inhabited reconstructions of the historical experiments.

The parity-experiment refinement now separates finite rate records from physical mean rates. Explicit bounds on both measurement errors give an interval for the actual mean contrast. An inhabited record separated by more than the combined budget rules out equal means; Wu and GLW adapters use the selected angular observables and physical reflection to reject angular invariance without assuming the rate inequality. A reflection- symmetric finite sampling law still permits an asymmetric record, and GLW's reported null band admits both equal and unequal normalized means. The independent consumer combines these APIs with its own angular law to derive physical symmetry breaking. Error coverage, detector corrections and the paper's interpretation remain explicit inputs, not automatic consequences of a finite sample or printed error bar.

Riess and Perlmutter now share explicit population-selection semantics: detection efficiencies reweight a population, light-curve correction removes the modeled shape term, and the remaining distance bias is a residual mean shift. The relative comparison retains the difference of the two shifts. Perlmutter's main systematic assessment now bounds that numerical difference by [-0.01, 0.03] mag under the stated source estimates, replacing an opaque bound predicate. Inhabited controls distinguish brightness selection from distance bias and matching shape distributions from bias cancellation. A separate consumer reconstructs different populations through the public API. These finite realizations do not reproduce survey simulations, jointly refit the width correction, or establish the empirical error-budget assumptions.

Blatt-Jackson's empirical range route now reduces actual spin-weighted threshold equations instead of accepting an opaque extraction flag. The coherent amplitude and epithermal rate select a central triplet length only on the declared physical sign branch; the shared measurement API checks that identification. The same calibrated length and binding momentum give the central range with explicit rounding control. Under the stated central calibration, rounding and bound-state truncation errors add; this is not an experimental confidence interval. Two-method comparison bounds a method-specific error only under explicit error controls. Actual scattering models with equal measured records but different positive ranges show why agreement cannot remove an uncontrolled common offset. Independent numerical clients test the branch, calibration, information, and combined-error distinctions without importing the production countermodels.

The finite-accuracy route now propagates bounded errors in all three inputs through the nonlinear triplet decoder and inverse bound-state formula. Explicit sign and positive-denominator conditions give a conservative range interval; the separately controlled model error widens it further. This route does not require exact central calibration. Its physical error bounds remain assumptions, not consequences of recording error bars, and no statistical confidence or reproduction of the historical fit is claimed.

Observed-state determinism now connects the paradigm and stochastic prediction layers. Both endpoints must come from the same admitted history; exact future-state closure is equivalent to uniqueness of the induced observed transition. The existing Mori and cosmological-history closure tests now use this shared logic. An independent free-particle consumer checks actual derivatives, position-only branching despite unique phase evolution, closure on a fixed-velocity sector, and closed velocity evolution without full-state recovery. No statistical Markov property, objective randomness, or existence of an unrepresented state follows from this pointwise relation.

Choptuik and Evans-Coleman now share actual threshold-mass logic in Framework/CriticalCollapseScaling. A positive exponent and one common near-threshold relative-error bound derive a one-sided zero limit. Separate physical-family realization supplies evolutions, positive masses, and matching ideal horizons, giving arbitrarily small black holes in the selected family. Both primary adapters consume the same nonvacuous result. Finite numerical fits do not certify these continuum hypotheses or an exact threshold.

Evans-Coleman's printed fit labels and grid spacings are no longer combined with invented exact residuals or a stipulated out-of-range failure. Physical parameter calibration and approximation budgets are explicit; a finite polar slice is strictly outside its apparent horizon and estimates final mass only within a supplied budget. Actual two-point mass curves, not residual flags, test finite-fit overclaims. The separate Lake consumer has twelve new source theorems and five audited framework API uses, with its own nonexact mass curve and Schwarzschild mass/horizon data. It imports no paper or production diagnostic. These are algebraic readout tests, not Einstein-matter evolution proofs or held-out-paper validation.

The original onset paragraph uses both mass scaling and echoing, and the source graph now requires both routes. The finite formula package is recovered directly from the numerical calculation without requiring extrapolation. Six new inhabited boundaries include a continuous positive-mass curve fitting every point of any finite positive sample exactly while approaching nonzero mass, fixed absolute tolerance, a varying coefficient, zero exponent, threshold-location error, and zero curves without positive objects. An independent eleven-theorem paper-API client also retains its own nonexact curve and horizon readouts. The shared extraction adds no new primary paper or framework module and claims no collapse simulation or genericity theorem.

Mermin-Wagner's zero-field limit is now derived from its dimension-specific small-field estimates, rather than supplied by the infrared-calculation premise. Each estimate has a positive neighborhood and one common coefficient at the selected positive temperature. The original 1966 erratum is archived and cited for equations (2), (8), (9), and (14) and the real-space omega sum. The finite selected readouts now tie magnetization to the thermal spin mean, the mode denominator to the double commutator, and the corrected squared numerator to the same magnetization. Their scalar Bogoliubov conversion is proved. The denominator bound retains its nonstrict zero-mode boundary; the ratio formulas retain positive-omega and nonzero-field domains.

Susceptibility is an actual eventually defined field derivative with a specified limit, not an assigned predicate. A bounded odd response satisfies both corrected estimates, has zero spontaneous limit, and has divergent susceptibility. Controls distinguish zero temperature, field-dependent coefficients, the uncorrected field factor, and the zero-exchange domain. The reported exchange moment must equal the actual sum even in the finite- range branch. A fresh bounded response at temperature three independently uses both limit theorems and has finite susceptibility one-third. These are response-level diagnostics, not microscopic Heisenberg constructions. The finite spin sums, infrared integrals, physical Gibbs realization, and uniformity across a temperature family remain distinct obligations.

The FPU numerical-validation route now requires a Hamiltonian computed from the same bond forces and sampled particle states. Separate linear/nonlinear component errors bound the discrepancy with the reported energy; a small readout drift gives a physical-energy drift bound only after including the evaluation errors at both endpoints. Seven additional constructed controls separate modal energies, nonlinear energy, equations of motion, weak forces, and finite-time scope. An independent fifteen-theorem cubic-chain client checks the energy components and unequal readouts without reusing production countermodels. The original LA-1940 typescript is archived alongside the reprint: its energy equations are (5a)/(5b), while the reprint repeats (5a). The coordinate dictionary, evaluation bounds, numerical trajectory accuracy, and reconstruction of the original computation log remain distinct obligations.

Rabi's detector route now uses a full magnetic-sublevel transition matrix and an incoherent initial population at every speed. The auxiliary spin-half probability, selected higher-spin pair, any reorientation, aperture rejection, mean signal loss, and finite observed decrease are different formal objects. Actual projections, normalized rows, populated resolved channels, and controlled gain/background derive the detector inference. It concludes some populated reorientation, not a unique pair or an independently identified isotope.

The higher-spin reconstruction is checked against original Majorana 1932, Rabi 1937, and Rabi 1939 scans. Separate literal-expression diagnostics retain two factorial-printing discrepancies and distinguish a continuous polynomial endpoint from totalized tangent division. All matrix entries and row sums for J=1/2, 1, and 3/2 are proved; general-spin normalization, physical realization of the effective pulse, and exact laboratory evolution are not silently supplied. An independent mixed-population beam computes its unequal-speed detector means and explicit finite-reading bounds through the new APIs. The retained binary client remains a selected-channel diagnostic. Rabi has 47 inhabited fidelity boundaries; no new shared framework or paper benchmark is claimed.

Rabi's precision route now also requires a physically interpreted molecular spectrum, a nonempty electronic sector whose restricted first-order moment operator vanishes, and an explicit interaction-energy bound. Lean derives relative moment accuracy from adjacent multiplet gaps and the same h, spin, field, and signed moment used by the Li-7 readout. Arbitrary precision needs uniform control across a valid field family and access to sufficiently large valid fields. It is not inferred from one high-field result. A solved rotating-frame countermodel makes the moment error arbitrarily small while the unshifted and shifted pulses retain probabilities 1 and 9/25. A separate spin-3/2 client checks all nine gaps of two nonzero interactions and keeps its finite validity range. Pulse approximation, line-minimum location, and empirical calibration remain distinct obligations.

The detector route now also requires a molecular-force reduction. The same energy spectrum supplies actual spectator and interaction derivatives; adiabatic force identification, secular approximation, and spectator transport remain explicit inputs. Joint outgoing PMFs and possibly infinite discrete spectator populations retain spectator-dependent slit transmission. The nuclear-only mean signals are derived only after calculating their nuclear marginals and effective preparation weights. A separate force-slope error budget preserves aperture decisions only with an adequate margin. An actual spectator-only joint unitary produces a detector loss without nuclear reorientation, and a source-direction filter changes transmitted flux despite endpoint cancellation. A fresh spin-3/2, three-spectator client derives joint-model signals 6 and 59/16 and error-resolved nuclear reorientation. These conditional model results neither identify a microscopic molecular Hamiltonian nor establish full laboratory evolution or apparatus error bounds.

The shared nebular calibration diagnostic now distinguishes changes of reduction from changes of cosmic realization. Its weighted/unweighted and individual/grouped comparisons retain the same assigned catalogs but distinct printed coefficients; they supply neither an ensemble target nor cosmic sampling variation. The original 43-object Stromberg catalog replaces the OCR-derived 48, and Hubble's fitting method is not labeled as a precise least-squares algorithm. Relabeling without changing the numerical report, or substituting a different catalog, fails the corrected comparison.

Both nebular papers now use NebularRadialData in the existing calibration framework for actual observer-corrected radial residuals and fixed-weight distance-scale identities. The adapters retain Hubble's selected angular solar-reflex projection and Lemaitre's separate first-order correction. A prescribed coefficient is distinct from recomputing an estimator. A separate consumer constructs three new objects with residuals (2,-1,3) and weighted loss 42; seven audited public-API uses certify the positive scale comparison, retain the loss while changing K=7 to 7/2, and check paired numerical reference offsets. Counterexamples reject one-sided data changes, zero-scale residual invariance, negative distances, and empty-sample nonvacuity. These are kinematic diagnostics, not historical catalog reconstructions or new cosmic expansion measurements.

Lemaitre's calibration now computes positive photometric distances from apparent magnitudes and the assumed common absolute magnitude, applies the selected first-order solar correction, and forms weighted and unweighted means on the same finite sample. The 43-to-42 catalog exclusion acts on actual identifier sets. Explicit data-to-report controls derive coefficient bounds that retain the separate 6.25 and 3 km/s rounded-mean residuals; the printed 625 and 575 reports are not silently replaced by ratios of rounded means. A two-object diagnostic has zero weighted mean residual yet a strictly larger squared-residual sum than another positive coefficient. It distinguishes the mean estimator from least squares without recalculating historical data or certifying that the proposed weighting removes systematic error.

The same actual data now expose calibration sensitivity. Shifting the assumed common absolute magnitude rescales all assigned distances by 10^(-shift/5); the selected identifiers and corrected velocities are unchanged. The unweighted coefficient scales inversely. For the weighted coefficient, common weight transport is sufficient, not necessary. One finite control preserves every radial residual and the fixed-weight loss while its recomputed weighted mean changes differently; an exactly proportional control preserves inverse scaling despite nonuniform reweighting. Neither control changes the historical calibration or certifies new uncertainty or regime assessments.

Hubble's calibration refinement now preserves the distinction between a radial-velocity fit and its independently supplied distance scale. A common positive distance rescaling and reciprocal coefficient change preserve each selected solar-corrected readout and weighted residual sum. The individual, grouped, and adopted solutions keep separate calibrated families. An exact nonzero distance anchor removes this particular freedom; a controlled anchor and positive scale floor give a conditional coefficient-error bound. An inhabited two-object counterexample retains positive distances and nonzero residuals. It is not a historical recalibration or a claim that shared-data fits are independent validation.

Bethe's empirical branch now computes the dimensionless Coulomb function from measured phases and separates finite calibration and validation samples. The laboratory-energy convention derives the slope-to-range conversion and propagation of slope and reporting errors. Wilson's error-compatible comparison is distinct from Dearnley's unexplained upward departure. The charge readout uses the same fitted intercept, with independent zero-energy extrapolation control rather than an assumed exact threshold value.

Five empirical fidelity cases now use actual phase curves, unitary relative amplitudes, and derivatives instead of assigned curvature and energy-error flags. They distinguish finite sampling from continuum control, a fitted line from a resolved curvature sign or higher-energy agreement, and the laboratory-energy conversion from the relative-energy conversion. These are inhabited logical diagnostics, not historical measurements or claimed fixed-potential reconstructions; no new framework is extracted from one paper.

The localization limit audit now uses actual complex kernels in place of an assigned infinite-volume proof flag. Decay at every fixed width can coexist with a nonzero limit at the exact aspect ratio N/M = 100. A second, bounded kernel family has the same asymptotic decay rate at every width but a width-dependent onset. A separate uniform-tail condition suffices for fixed-aspect attenuation; these diagnostics do not construct Anderson Hamiltonians or refute the paper's qualified numerical conclusions.

The MacKinnon-Kramer resolvent normalization now separates the literal positive rate printed in equation (1) from the negative rate for actual attenuation. The former finite-bar contract implied kernel growth; it is no longer used as a physical decay premise. A separately sourced reconstruction premise, exact recursion, and full selected-kernel calibration now produce actual attenuation at fixed width. The source route also proves the literal sign discrepancy. Complex-amplitude controls distinguish decay from inverse- kernel growth and reject an independently assigned localization length. The selected length denotes a defining rate parameter, not an exact finite noisy estimate; no author-approved erratum or microscopic Anderson proof is claimed.

The localization-scaling refinement connects AALR 1979 and MacKinnon-Kramer 1981 to an actual positive logarithmic-scale trajectory. AALR's derivative readout is no longer independently assignable. Its zero-conductance limit and exclusion of a persistent conducting response are checked consequences of negative monotone beta and a separately recorded global-continuation premise. The numerical paper's two-length differential and fixed-aspect beta product are actual chain rules for calibrated scaling and transport functions. Five new fidelity boundaries test fictitious derivatives, finite continuation, finite-data ambiguity, and aspect-ratio changes. An independent consumer uses four public API deductions on conductance curves with or without a small positive floor. These are conditional flow diagnostics, not microscopic Anderson-model or universal localization proofs.

The DGZ typicality refinement now derives conditioned agreement-set bounds before applying them to a selected configuration. Actual finite empirical means, normalized probability laws, bounded probes, and the sum of per-test failure budgets replace the former direct weak-law-to-selected-state step. Conditional-to-global disintegration remains explicit, and Born-reference identification derives the property bridge. Six new fidelity boundaries include positive-probability exceptions and a rare environment with certain failure despite a small averaged error. An independent Gibbs consumer uses the shared typicality API with computed excitation probabilities and a nonzero exceptional sample. These finite diagnostics do not construct a complete Bohmian universe or prove the general large-sample limit.

The symmetry foundation now distinguishes arbitrary admissible states from law-specific selected vacuum or equilibrium families. Physical spontaneous breaking requires a functional transformation preserving that family; missing images and conflicting images no longer qualify. The chiral-vacuum adapters prove these action properties for their actual modular phase maps. Neutral vacuum-orbit statements now use UnclassifiedSymmetryContext, which has no physical, descriptive, observable, or variational classification fields. Unspecified interpretation is not encoded as a false proposition. SymmetryActionContext supplies the common law and state action. PhysicalSymmetryContext adds physical classification and readouts without requiring vacuum selection; SelectedPhysicalSymmetryContext adds the selected family. VariationalSymmetryContext independently records variational invariance and conservation, while the full SymmetryContext combines explicitly supplied roles. Noether's adapter needs only the variational interface. Microscopic reversal and parity tests need only the physical interface; omitted conservation claims are not encoded as false. An independent quantum consumer realizes the same neutral orbit both by global phase and by exchange of orthogonal states; their actual density matrices distinguish the two interpretations. A separate continuous free-energy consumer distinguishes an excited asymmetric configuration from asymmetric selected minima. An independent mechanics consumer computes translation-covariant damped motion whose mechanical momentum decreases while the canonical momentum of a time-weighted variational description is conserved. Its actual derivatives distinguish equation covariance, variational realization, and the identity of the conserved quantity. See docs/paradigm/symmetry-breaking-and-anomaly.md for scope and API changes.

The current Blasius refinement derives the original similarity ODE and its boundary conditions from selected physical velocity fields. The stream-function identities, continuity, and exact residual are checked deductions, while selection of the ansatz, reduced momentum balance, and numerical profile matching keep distinct logical roles. Actual trial profiles reject replacing momentum balance by wall matching and incompressibility; a local shear control separates equation covariance from invariance of a selected solution. The independent fluid consumer adds a dynamically valid suction layer that fails impermeability. See docs/targets/blasius-1908.md for the precise scope.

Development is paper-first:

reconstruct one paper locally;
reconstruct a second paper with different logical structure;
extract only the infrastructure independently required by both.

The emerging semantic architecture is layered: interpretive foundations and paradigm commitments constrain a technical physical framework, which in turn states its mathematical realization obligations. Paper provenance and route order remain orthogonal to these layers. See docs/architecture/semantic-layers.md and the comprehensive docs/architecture/philosophy-paradigm-roadmap.md.

The active foundation contains 17 philosophy modules, 24 domain-neutral paradigms, and 12 explicitly scoped specialist paradigms. Every philosophy module and every domain-neutral paradigm has formalized original-paper clients from at least three registered physics families, with both source-import and elaborated-declaration reuse audited. The 135 active technical frameworks each have a nonvacuous physical result consumed by at least two independent original papers. All 191 active primary-paper formalizations now directly use at least one shared technical framework, with 302 independently checked paper-to-framework integrations. Their 32 source-audited composition edges preserve actual physical child results and paper-specific dependency orders. These are registration and checked-reuse counts, not completed human reviews of the physical interpretations.

The Hawking-Penrose geometry refinement now derives cosmological past trapping from actual metric-normal area variations and the expanding Friedmann branch. The exact threshold is mu*(R*r)^2 > 3; the printed convergence scalar is kept separate from the normalized screen calculation, which gives half its value. Whole-surface, both-family error bounds derive the reduced positive margin delta-epsilon. Hawking's 24 fidelity cases include actual area models rejecting saturated bounds, one-point or one-family control, and mixed normalizations. A point-dependent positive example stays trapped. Penrose's future and Hawking's past geometries independently use one shared oriented normal-area component. A separate framework-only consumer computes flat-space Jacobi area densities and rejects trapping despite actual ingoing focusing. Ambient representation, physical perturbation estimates, and global incompleteness remain explicit obligations; local readouts are not global Einstein solutions. No new framework module, foundation, or paper is added.

The Kubo section-2 refinement derives classical and quantum first-order mean responses from retarded density solutions, actual integral domains, phase-volume conservation, and admitted trace operations. Probability normalization and real response are checked. The time-domain result has its own route, independent of finite periodic calibration; two real probe quadratures then derive a finite Abel gain and fixed-time harmonic readout. Nine added boundaries tested preparation, resonance, finite-amplitude error, positivity, and measurement disturbance using actual matrix dynamics. The subsequent operator-spectrum refinement added four independent fidelity cases. One faithful energy-coefficient representation now ties the selected Hamiltonian, Gibbs density, propagator, and observable pair to the same spectral response. Density tests and separating evolution probes have distinct trace domains. The canonical time-derivative identity follows from an explicit interchange input, which is proved for finite matrix systems. An infinite diagonal control shows why density normalization does not make the propagator trace class. The independent thermal consumer computes its own three-level matrix correlation and exercises three public spectral APIs, in addition to its earlier two causality results. General unbounded-operator and continuum-basis realizations and empirical observation remain separate obligations. No new shared framework, foundation, or paper is added.

The section-3 force-removal refinement replaces five schematic predicates with actual force profiles, density readouts, and analytic conditions. The main route derives Phi(t)=C_full(t)-beta*I_AB, both regulated admittance identities, and the isolated static gain. A finite transform of Phi is derived at nonzero frequency and is not required at zero frequency. Generic finite matrix systems prove the cutoff density integral, remote-past preparation, post-cutoff weak equation, and fixed-time readout limit. Five additional controls bring Kubo to 44 fidelity cases: finite nonzero- frequency gain need not give an Abel tail; Abel relaxation need not settle; a derivative does not fix invariant normalization; isolated preparation is not perturbed-Gibbs equilibration; and a zero removal probe cannot identify a relaxation curve. These are paper-local deductions, not a new shared response API or a proof of macroscopic irreversible relaxation.

The subsequent Kubo-Nakano source test earns a narrower shared canonical operator-correlation core. Actual Hamiltonian exponentials, Gibbs traces, current matrix elements, and integral domains now derive Nakano's equations (2)-(4); the equal-energy coefficient follows from the same imaginary-time integral. Kubo uses that core for his full canonical time correlation and its negative response derivative, without equating it to the invariant-subtracted relaxation. Five additional Nakano boundaries bring its fidelity matrix to 26 cases. A current computed as a polarization's Heisenberg derivative has a nonzero canonical kernel but neither an ordinary DC integral nor late-time settling. A separate degenerate observable exposes lost zero-gap weight and is proved not to be such a finite polarization current. The independent three-level consumer computes its own thermal trace through eight additional audited public calls. The common correlation is one new reviewed component; no new framework module, foundation, paper, or client file is added.

The Callen-Welton refinement now derives the quantum force-noise relation from canonical absorption and the independently represented velocity fluctuations. Actual sinusoidal cycle averaging fixes the peak-amplitude factor; the Heisenberg derivative and energy-gap Jacobian fix the noise normalization. The comparison input no longer contains the final formula. The pointwise theorem needs no finite-frequency-integral premise; the separate finite readout retains its physical domain and angular measure. Classical behavior is a quantitative approximation, with whole-response-band control required for an integrated error estimate. Seven new boundaries and two strengthened controls bring the paper to 45 cases, including actual finite spectra and a nonintegrable continuum. A separate three-level thermal consumer uses the public canonical-response API with non-unit hbar and a complex impedance. Dense-spectrum power correspondence, canonical spectral reconstruction, and measured readout identification remain explicit inputs. No new framework, foundation, or paper is added.

The Nyquist refinement now derives the classical thermal-noise coefficient from actual finite standing-mode counts, quadratic energy moments, a controlled long-line limit, source correspondence, and Joule heating. The filter argument distinguishes equal total power from equal band power; local spectral representation is explicit before using a pointwise density. Complex impedance and modulus-squared transfer derive the network and finite current-noise equations with their frequency Jacobian. Twelve new fidelity boundaries include a computed family with noncommuting length and bandwidth limits, which genuinely uses the shared OrderedLimits paradigm. Literal printed equation (8) is kept separate from its equation-(7) energy substitution. Thermalization, physical representation, the Planck-energy evaluation, and experimental qualifications remain explicit inputs. This adds no new shared circuit framework or independent consumer fixture.

The Pound-Rebka refinement now computes the measured contrast from actual counts and live exposures, calibrates it against opposite Doppler records, and retains line, gain-transfer, counting, and thermal residuals. Reversal derives twice the gravitational shift plus offset drift and those residuals; inversion stability removes only the drift. The reported uncertainty is an actual sampling RMS, not a deterministic error bound. Fourteen new fidelity boundaries test these distinctions, covariance, inverse-gain bias, partial absorber sampling, and the separately printed table and ratio. The original temperature paper and Josephson's separate mass-change explanation are archived and distinctly attributed. An independent affine mean-response consumer uses two public measurement API results to recover gravity with thermometry and reject determination from the same counts without it. No unpublished raw counts, microscopic lattice solution, or confidence coverage has been manufactured.

The Kohn-Sham ground-state refinement now uses actual complex spin orbitals, Coulomb integrals, weak kinetic domains, and fixed-number density variations. Lower analytic and noninteracting-reference inputs derive the potential gauge, local orbital equations, normalization, and energy double-counting identities. Exact functional differentiation remains distinct from a known explicit formula, and the nonlocal Fock alternative retains approximate correlation and its selected-orbital identification. Actual local energy integrals must exist at the selected density and along admitted variations; scalar differentiability and the Fock integral domain are explicit, so totalized Lean values cannot replace these physical domain requirements. Twenty-seven fidelity cases include an actual repulsive Hartree iteration with no density limit despite a self-consistent global minimum. An independent three-site quantum consumer proves its constrained density minimum and exercises four shared API results. The thermal extension now computes fermionic Gibbs occupations, mean-number fluctuations, complex weighted orbital densities, and grand-potential variations. It separates the exact Mermin minimum from local stationarity, internal free energy from grand potential, and fixed-number entropy from a path derivative with chemical work. The literal signs in (3.13) and (3.15) are tested separately from thermodynamic reconstruction; no author-approved correction is asserted. Actual entropy and heat derivatives retain controlled component remainders and their slope bounds. An independent three-mode consumer computes its own Gibbs probabilities, fluctuations, conditioning, and unequal ensemble entropies through seven audited public API uses. This deepens paper logic, not continuum existence, universal SCF convergence, an unconditional bulk Sommerfeld limit, or full spin-response realization.

The BCS finite-temperature refinement now derives branch minima, actual gap closure, normal Fermi occupations, and the finite heat-jump transition from explicit integral and derivative inputs. The original variational free energy retains the pair-amplitude derivative and a controlled finite-cutoff correction. Physical state and temperature representations, a complete variational reduction, and independent error budgets for the printed numerical estimates remain visible. Fifty-nine new source theorems replace two obsolete assigned-readout controls; six additional fidelity boundaries and fourteen independent internal client theorems test actual functions and admissible states. This thermal core remains paper-local, not a newly claimed shared framework or a microscopic BCS solution.

The shared effective-range error component now connects Bethe's actual radial comparison and Blatt-Jackson's stationary functional to the same uniform fourth-order remainder and actual low-energy coefficient limits. The derivations stay paper-local: Bethe fixes one potential and zero-energy reference across momenta; Blatt-Jackson uses normalized trial-wave error. The shared API proves coefficient uniqueness and composes independent errors. Thirteen new independent consumer theorems retain a nonzero shape remainder, distinguish equal coefficients from equal amplitudes, and reject unchanged phase-to-amplitude error tolerances. These are dimensionless diagnostics, not empirical fits or fixed-potential reconstructions. No new framework or philosophy module is added.

The Bethe radial-comparison refinement derives the infinite comparison from actual one-sided radial dynamics, finite Wronskian identities, and an explicit boundary limit. Actual overlap integrals and an interior error integral derive a quantitative phase-error bound; the two-parameter prediction is no longer equated to the physical phase shift. Uniform quadratic range control, not mere continuity, gives quartic phase accuracy. Three new fidelity boundaries and nine independent client theorems test boundary matching, nonzero remainders, elastic unitarity, and composition of a separate readout error. These are paper-local semantics, not a fixed-potential scattering solution or an added shared framework.

The charged Bethe refinement binds the phase shift to actual regular and irregular Coulomb waves. The dimensionless source function, common origin logarithm, and two-proton normalization remain explicit. Separate routes derive the exact comparison, charged range error, same-potential neutralization error, and a conditional nuclear threshold. Six new fidelity boundaries reject omitted Coulomb terms, normalization changes, exactness upgrades, and suppression inferred from penetration alone. An independent consumer uses the public scattering API to transfer a plotted-function error through the Coulomb conversion scale and amplitude denominators. Special-function realization, boundary integration, empirical fits, and threshold regularity remain explicit inputs; no new shared framework or fixed-potential solution is claimed.

The weighted Bethe charge comparison now derives the neutral reciprocal length from actual weighted Wronskian identities and a positive-cutoff boundary argument. Its estimate keeps radius, fit, wave, and truncation errors separate. A strict calibrated gap implies unequal potentials only with normalized-scattering uniqueness; pointwise closeness additionally requires the cited depth calculation and common range and shape. The uncorrected exponential/Gaussian bracket remains an author expectation. Actual potential profiles and eight new quantitative boundaries replace two scalar mismatch controls. A public-API consumer transfers parameter errors to amplitude errors and demonstrates distinct amplitudes with equal cross sections. No new shared framework or original paper is claimed.

The HTML source-name audit now separates plain Lean references from notation and checks actual code tokens and qualified declarations. Stale API labels and non-theorem ledger entries have been corrected, and long inline source identifiers wrap within the shared edition layout.

The Penrose surface refinement replaces independent expansion and convergence scalars with the printed reference metric, its computed sphere area, and actual normal-area derivatives on a compact two-surface. The reference condition r<2m no longer constrains a general nonspherical target. A strict relative bound on both expansions derives target trapping; matching the same local optical area curve derives initial convergence, and the optical equalities derive concavity. The 23 fidelity boundaries include actual marginal spheres, one-point versus whole-surface contraction, reversed area-curve parameters, and equal initial areas with different derivatives. Every point and both normal families now have their own optical profile. Transverse continuity on the compact surface derives a positive uniform convergence margin, and the all-normal optical calculation derives area zeros within one common affine bound. Discontinuous pointwise trapping, unbounded inverse-convergence estimates, and a positive-tail companion profile reject shortcuts from pointwise or selected-generator results. An independent internal metric client computes both convergence margins and both area zeros. Ambient geometry, source estimates, every-normal continuation, caustic interpretation, and global causal topology remain explicit obligations; no new shared framework or global collapse solution is claimed.

The Landau operational-transform refinement uses actual time and velocity integrals, explicit coordinate coverage and integrability, and positive-time limits of finite inverse contours. Integration by parts and the integrated kinetic/Poisson equations now derive the distribution and potential quotients. Four additional boundaries distinguish future support, genuine integration, analytic continuation, endpoint reconstruction, and absolute integrability. A six-theorem independent damped-signal client tests a larger convergence domain, changed prehistory, and clock calibration. These are paper-local refinements, not a full plasma solution or a new framework.

The initial-value refinement now derives uniqueness of an actual selected Fourier-mode state from the same initial datum, equilibrium, physical constants, and common zero-free inverse contour. Its velocity distribution, Poisson potential, and electric field are computed from the readout; existence uses an admissible readout with defined initial and evolved charge-density moments. No independent global-determinism premise remains. Three new boundaries bring Landau to 35 cases: one Laplace sample does not determine a history, one Fourier mode does not determine the whole field, and zero-wave Poisson data leave a constant-potential gauge freedom. The independent signal client also tests rationalized contour data with a removable exceptional point. Inversion and analytic domains remain explicit; neither arbitrary-data PDE well-posedness nor nonlinear evolution is claimed.

The Anderson dynamics refinement binds equation (1) to actual future-time amplitude derivatives and a defined summable hopping action. Explicit Hermitian compatibility derives opposite bond currents and finite-site probability conservation from the single-site initial state. Constructed controls reject fabricated derivatives, non-Hermitian conservation, and accidental diagonal hopping; an actual unbounded coherent lattice realizes the new evolution interface. A separate complex-hopping client tests current signs and conservation. Infinite-site operator domains and probability-sum interchange remain separate obligations, not consequences of finite algebra.

The Anderson spectral-return refinement replaces a false all-late-times return-amplitude requirement with an actual energy-resolved pole calculation. Finite normalized locator limits derive positive pole weights; an explicit uniform bound and tracked-weight limit derive infinite-volume persistence. The transport endpoint applies a separate conditional dynamical bridge. Normalized coherent evolution on an unbounded lattice has positive pole weights and positive mean return but arbitrarily late return zeros. Further controls distinguish finite positivity from positive limits, energy-grouped weights from degenerate mode squares, and the printed Laplace sign from the resolvent energy convention. An independent spectral client uses its own three-mode data and isolated level. These are paper-local fidelity checks, not a general spectral-to-dynamical localization theorem or a new framework.

The Hubble observer refinement distinguishes measured velocity, the actual angular solar reflex, corrected velocity, and peculiar residual. The main validation route derives a conditional relative-motion bound after solar subtraction, replacing an incorrect raw-velocity inference. The individual, grouped, and adopted solutions retain distinct solar parameters; their printed Cartesian and polar reports are not asserted jointly exact. Seven new countermodel boundaries and a thirteen-theorem independent client test correction signs, fit ownership, chosen-distance dependence, and consistent observer changes. Group construction, numerical fitting, and the quantitative interpretation of relative smallness remain explicit inputs. This is paper-local refinement, not an expansion theorem or a new shared framework.

The scalar zero-mode refinement replaces Witten's assigned deformation flags with an actual one-dimensional differential family, square-integrable complex solution spaces, and dimensions computed from those spaces. The printed potential (m*x-g*x^2)^2 has minima escaping every fixed field bound as g approaches zero. Its diagnostic graded kernel index changes from one to zero despite pointwise continuity and formal charge grading. Witten 1981 now uses the same shared first-order/L2 interface: actual primitive-tail bounds exclude nonzero normalizable solutions, rather than defining normalizability by two assigned signs. Thirteen independent consumer theorems use different wells and hbar=2. Self-adjoint closure, trace identification, and four-dimensional physics remain separate realization obligations.

The molecular-beam refinement replaces Rabi's opaque refocusing and detector predicates with actual ray maps, geometry-weighted gradients, finite-aperture acceptance, and one common beam measure. Lean derives the mean signal loss from populated, resolved transitions with explicit gain and background control. Observed readings have separate accuracy bounds: a decrease must exceed the combined errors to establish a mean loss and infer transitions. Ideal point refocusing, normalized baseline velocity statistics, approximate experimental recovery, and field-scan resonance location remain distinct. A twenty-theorem client joins actual coherent pulses at two flight times to different beam weights and a calibrated detector and a resolved observed decrease. Paraxial validity, physical preparation, and readout accuracy remain scoped inputs; the work is paper-local and adds no unearned shared framework.

The latest Landau refinement replaces bare microscopic commutation and conservation predicates with actual particle operators, a zero-curl joint kernel, Hamiltonian limits, and Schrodinger evolution. Sector ground states have normalized eigenvectors and energy lower bounds; their existence, the state domain of vorticity separation, the additional energy-gap inference, and physical level ordering remain explicit. A separate three-state client checks actual reuse. The liquid's joint microscopic representation remains open, and this paper-local work does not add an unearned shared framework.

The weighted-reversal refinement computes probabilities from actual finite segment or tile weights. ECM's paired-weight aggregation is distinguished from its additional printed mean-exponential claim. GC's transverse-volume correction and its finite-weight/SRB-probability comparison remain separate; their bounds derive the actual event ratio. Uniform bounds across a whole observation family, not merely positive bounds at each time, give the time-normalized logarithmic limit. An independent driven-ring consumer tests normalization, reversal from the actual endpoint, unequal preparations, and long-time bias. These finite models do not establish a chaotic fluid, an SRB construction, or a universal arrow of time.

Finite-resolution inference now keeps actual observation intervals distinct from exact-value representatives. The same weights derive a nonvacuous log-ratio error bound and realize the approximation paradigm with the computed log ratio as target. ECM uses the maximum actual contraction spread; GC retains both reflected interval endpoints and both correction sources. Growing observation durations, shrinking bin resolution, and sublinear logarithmic errors are explicit conditions, not consequences of finite-time control. Inhabited probability models and the independent walk consumer reject both fixed-width-to-central-rate inference and the converse claim that every leading rate requires uniformly bounded multiplicative correction.

The shared decay-time refinement computes survival and conditional escape from actual measurable lifetime events under one probability law. Gamow's finite interior probability admits an exponential record-law representation; identifying measured lifetimes with that curve remains a separate bridge. Gurney-Condon's observed exponential law supplies the selected record inputs, from which Lean derives residual-life memorylessness. Independent consumers reject memorylessness for an equal two-rate mixture and a lifetime reading of recurrent quantum occupation. These are statistical and interpretation checks, not new nuclear tunneling calculations or quantum monitoring rules.

The Gamow refinement uses actual analytic wave branches, derivative matching, probability current, and finite-region probability. The complex time phase derives damping and normalized survival; outgoing flux and an imported leading normalization derive the equation-(5) rate. The radial equation contains the actual centrifugal term, and actual Coulomb-action derivatives yield the log-base-corrected slope, its decrease with energy, and a finite comparison bound assembled from separate model and Taylor errors. Concrete wave and barrier controls distinguish standing amplitude from transmitted current, leading exponentials from exact transmission, finite probability from global normalization, and suppression from zero escape. Printed derivative and radial-exponent discrepancies remain explicit diagnostics. Unknown-potential calculations and the approximation regimes remain inputs.

The Kennard refinement uses actual complex amplitudes, positive-sign Fourier transformation, mean and variance integrals, and the paper's precision-squared equals twice variance convention. The reference Gaussian is matched to the same selected width and means. Fourier moment identities and integrated factorization identities remain analytic inputs; Lean derives the phase-current cancellation, the nonnegative derivative-remainder balance, and the uncertainty bound. Normalized continuum Gaussian tests distinguish density from phase, derivative energy, and the effect of a mismatched reference mean. Gaussian saturation requires zero quadratic phase. The apparent inconsistency between the original printed nonzero-phase parameter formulas is recorded, not silently corrected or assumed. This remains a finite-moment, explicit-calculus-domain reconstruction, not a general unbounded-operator proof.

The Robertson refinement retains the original doubled Schwarz construction, its twice-variance norms, and its antisymmetric commutator overlap. Lean now derives the half-absolute-commutator uncertainty bound from those inputs; the remaining calculation contract only calibrates commutator readouts. Finite Pauli-state tests distinguish the doubled overlap from covariance, the doubled norm from a single variance, and source-pair saturation from single-vector Schwarz saturation. Operator domains, surface terms, and analytic integration remain explicit obligations.

The BCS-Nambu response refinement uses complex spatial amplitudes and actual current-response matrices. Tensor contraction derives pure-gauge cancellation; finite-wavevector opposition is distinct from a positive London limit. BCS uses the finite-temperature gap and its actual inverse-temperature derivative. Nambu retains the contact-plus-vertex contraction, separate c-number and static-polarization conditions, and qualified transverse corrections rather than exact equality. An independent anisotropic consumer distinguishes selected-probe response from isotropy and a limit from the assigned zero-momentum value. Regulated calculation outputs, approximation estimates, and bulk-field interpretation remain explicit inputs; the controls are not microscopic superconductors.

The cosmological-history refinement ties radius, velocity, acceleration, density, and pressure to actual functions. Both Friedmann and Lemaitre use the shared differential compatibility result. Constraint and conservation alone do not determine the pressure equation at a zero-rate point; actual history controls retain this limitation. Friedmann's nonstationarity and selected growth now require actual motion and numerical ordering. Lemaitre's matter mass and radiation energy have different scaling, and his asymptotic past radius is distinct from finite-time emission. Radius growth and energy conservation are derived from the selected history obligations. An independent coasting-fluid client checks pressure work and distinguishes expansion from acceleration. Metric reduction, integration, and the chosen asymptotic dust solution remain explicit inputs.

The nuclear-spectrum refinement derives both partner energies from one effective central-field spin-orbit coefficient. Its sign, the level gap, degeneracy-weighted centroid, and chemical-potential filling are checked; an s orbital has no fictitious lower partner. Actual finite spectra separate splitting from shell isolation. Mayer's measured spins, moment-derived orbital assignments, and doubtful molybdenum report are distinct data. Haxel-Jensen-Suess's deferred detailed account is not an asserted exact many-body result. The effective angular model and numerical controls are reconstructions, not microscopic nuclear-force calculations attributed to either original.

The Mayer source-boundary correction removes six predicates and their conclusions that had been attributed to Mayer from a neighboring letter on the same scanned journal page. Her own isotope exceptions, limited data, within-shell ordering, pair-filling caveat, and isomerism interpretation remain. The adjacent original is archived for attribution only. This is a source-fidelity repair, not new physics coverage, and illustrates why a successful Lean build does not by itself establish faithful source parsing.

The Prandtl-Blasius refinement computes wall traction from the same velocity fields and integrates it over a finite plate face. It keeps dynamic viscosity, one-sided wall derivatives, leading-edge integrability, and identical-face doubling explicit. Blasius's coefficient is calibrated to the actual second profile derivative; its printed bracket remains an unproved numerical input, not a certified exact constant. Prandtl's incomplete 1,1... report is not assigned an invented precision. Actual controls distinguish velocity accuracy from force accuracy and wall matching from solving the profile equation. An independent exact channel flow computes unequal wall forces and pressure balance through the public interface. General profile existence, the original numerical accuracy, and a boundary-layer solution limit are not claimed.

The Bohm-Durr-Goldstein-Zanghi refinement uses actual squared-wave Born measures and a common configuration pushforward. Later agreement and probability normalization are derived; wave measurability and construction of the transport from the differential equations remain explicit inputs. Computed oscillator controls distinguish equivariance from stationarity, phase information from Born density, and nontrivial coarse records from full configuration laws. Bohm's stationary balance no longer requires a positive energy origin. An independently constructed translating-trap consumer checks the public transport and detector-statistics interface. Neither a global flow through nodes nor a general relaxation theorem is claimed.

The Onsager-Casimir refinement defines correlations as integrals over an actual normalized stationary ensemble. Microscopic evolution, time reversal, field reversal, and observable parity derive the correlation relation; a separate finite-lag moment obligation then yields coefficient reciprocity. Controlled moment errors instead bound the reciprocity defect. Both papers retain an explicit relative lag window, and an independent three-coordinate thermal consumer uses the same public interface. Actual Gaussian oscillator controls distinguish zero initial slope, finite-time change, mixed parity, field-paired symmetry, and global exponential relaxation. These do not prove regression applicability or construct a microscopic heat or Hall conductor. Onsager's dissipation route also uses actual linear entropy and quadratic resistance functionals. Reciprocity and the constitutive equation derive the variation gap; nonnegativity yields a maximum and strict positivity yields uniqueness. Isolation derives zero boundary exchange, and stationary comparisons retain power and full normal-flux constraints at fixed temperature. Concrete matrices and an independently constructed client test the physical versus trial-flow distinction. Continuum integral/Green identities remain explicit inputs; this variational interface stays paper-local pending reuse.

Ordered-limit realization now uses one observable family, two nontrivial approach filters, and actual inner and outer limits. Mermin-Wagner retains finite-volume convergence before the small-field limit; source certification of that order is distinct from mathematical commutation. Wetterich's original exponential profiles have checked limits for the full positive shape-parameter ranges, with explicit wavefunction conditions before transferring inverse- propagator results to the regulator. Normalized magnetic controls and an independent relaxation-model consumer test the distinctions. These controls do not construct a complete Heisenberg model or interacting quantum field theory.

Wetterich's exact-flow formula now uses actual kernel-ring operations and Ring.inverse, not an independently supplied operation named inverse. The connected-propagator trace and two-sided inverse identities are separate inputs; Lean derives their inverse-Hessian flow and retains it in the paper's shared result. Coherent quadratic and independent two-mode matrix controls test derivatives, Hessians, and trace substitution. False connected propagators and totalized singular inverses do not certify an exact flow. Functional integration and analytic realization remain explicit obligations.

Feynman's two-fluid audit now separates the original equation (42)'s literal n^2 integral from the n(1+n) weight obtained by differentiating the moving Bose occupation. The same spectrum, measure, and momentum data underlie both quantities. Integrability, differentiation under the integral, and full tensor isotropy are explicit inputs; the checked difference is a positive occupied momentum moment when that sector is populated. Six-direction controls and an independent finite-gas client test both directions of the distinction. This does not assert an author-approved erratum or construct microscopic helium.

Landau's two-motion transport now computes mass, entropy, and reversible thermal currents from the same state, retaining the temperature factor and the distinction between aperture-frame thermal transport and heat relative to mass flow. Rotation supplies calculated angular momentum and inertia, not a separate capillary experiment. Source-observable correspondences retain the selected density/current families and distinct endpoint normalizations. An actual finite phonon response tests every exact atom partition; a contrasting integer response admits an arithmetic partition without proving a microscopic interpretation. Small constitutive counterflows are derived without claiming a solution of the hydrodynamic boundary-value problem.

Landau and Feynman now independently use the shared equilibrium-excitation response component. It differentiates the actual moving occupation, retains the statistics-dependent weight and full tensor isotropy, and keeps mass and number normalizations distinct. Landau's original zero-momentum roton has a three-dimensional thermal population with its prefactor; heat is derived from the same energy functions. Radial moment inputs derive the per-unit-mass normal-fraction formula, and a gap-dependent bound controls the quantum-statistics correction. The printed quartic heat statement is kept separate from the cubic derivative of quartic phonon energy. An independent different-energy finite gas consumes the public response API. These results do not establish microscopic helium, moving-wall equilibration, or dilute-gas validity at the lambda point. See docs/framework/equilibrium-excitation-response.md.

Stanley's critical-index appendix now uses the same represented free-energy functions as the noncritical calculation. Applying a response functional to the limiting free energy is separated from taking the limit of finite-model responses. A specific transport premise is needed to identify those operations. Actual stable free-energy controls have uniform convergence but unequal critical indices; another has uniform free-energy and entropy convergence without specific-heat convergence. These replace two scalar-only controls. The constructed exponents are not attributed to Stanley's spin models, whose critical-index comparison remains open in the original argument.

Blatt-Jackson's variational route now constructs Schwinger's actual integral quotient. The standing-wave equation derives directional stationarity and the quadratic trial-error identity. The zero-energy radial equation uses a regular integral form, avoiding an overly strong smoothness requirement at potential steps and rejecting discontinuous origin assignments. A fixed zero-energy trial is compared with a consistently normalized exact wave, and uniform interaction/overlap bounds transfer its expansion to actual physical phase limits. This uses the shared approximation-composition paradigm. Computed operator controls retain both error signs, the possibility of bounds with extra positivity, and a nonzero phase error despite vanishing unnormalized wave error. The original trial-integral calculation remains an explicit input; the controls are not microscopic nuclear fits, and no new one-paper framework is extracted.

Its bound-state route now derives the two corrections in equation (5.5) from the continued quartic phase remainder and a quantitative small-range branch, instead of receiving the expansion as an input. Relative binding accuracy, a common uniform remainder bound, and inverse range-extraction error remain distinct. Two entire phase families have the same first two effective-range coefficients and unitary on-shell S matrices with genuine continued zeros, yet different next binding coefficients. An independent dimensional client computes nonzero forward and inverse errors through the paper and shared APIs. These are controlled scattering-function diagnostics, not microscopic nuclear Hamiltonians or new experimental fits.

The shared stochastic-prediction framework now applies those semantics to actual cosmological Gaussian histories. Arbitrary finite sharp-k bands derive Markov prediction from whole-history independence. A two-band Gaussian-window control has exact Gaussian one-point laws but is not Markov. Independent thermal consumers test conditional Gaussian kernels and separate exact static coarse-grained predictions from temporal predictive sufficiency. The first-passage refinement now connects actual crossing events, killed survival measures, law-preserving first-hit reflection, and derivative-bound density families to the selected source formulas. Two actual Gaussian Markov histories with identical one-point laws have different absorbed probabilities. Continuous field construction, reflection, and halo identification remain explicit inputs; corpus size is not a completeness claim.

The sharp-k density now has actual field and variance derivatives, a checked heat equation, its Gaussian survival integral, and a one-sided boundary flux. Actual mass calibration separates the negative cumulative derivative from positive differential abundance. The literal printed boundary and Gaussian expressions are retained separately. Nonunit controls use a genuinely varying variance curve, and four scalar-only tests no longer certify physical fidelity. The Gaussian-tail derivative and path-to-halo identification remain explicit inputs; no cosmological Fourier process or halo catalog is thereby constructed.

Crossing counts now come from actual sampled transitions, while smooth continuous crossings are separate root-and-derivative counting measures. Their ensemble intensities give the first-crossing rate bound almost everywhere and, with continuity, at the selected variance. A normalized shifted-cubic control computes repeated crossings and their three rates. Seven new boundaries retain sampling, point-mass, endpoint, density-version, and singular-limit distinctions. These are paper-local semantics, not a construction of the cosmological Gaussian field or a new shared framework.

The Gaussian-rate refinement binds continuous finite counts, field-gradient laws, and source formulas to the same ensemble. It retains explicit crossing-window and Gaussian-integration inputs, the printed coherence-sign convention, and the distinction between conditioning on the past and on the current field. Actual Gaussian controls reject invalid density-version and regulator identifications. A separate law-preserving reflection route derives the first-passage normalization without equating it to a sampled net-rate limit.

Actual survivor-history laws now retain every preceding barrier test in equation (3.10), distinguish propagation from killing at the new endpoint, and require an actual joint-density realization for the integral form. In the two-band Gaussian-window control, two positive-probability cohorts survive the entire earlier interval and have identical current-field laws, but opposite endpoint and first-passage outcomes. Their selection is measurable from the observed past. A bounded current-averaged forecast still exists and has the same ensemble mean as the full-history forecast; it does not reproduce that forecast almost surely. Earlier assigned-number history tests are now explicitly scalar tests, not conditional-law guarantees. The cosmological Fourier path construction and general-filter classification remain separate work.

The state-sufficiency refinement defines Markov prediction using conditional expectations of all integrable observable queries given the entire observed past. It separates this property from deterministic closure, microscopic reconstruction, local-looking equations, and independent noise samples. Mori and Zwanzig supply actual Gaussian oscillator realizations and counterexamples; an independent consumer additionally retains an unobserved coordinate and tests a genuinely stochastic three-time random walk. No continuum, white-noise, or universal reduced-particle Markov limit is inferred from these finite examples.

The initial-ensemble refinement connects deterministic force evolution to actual probability laws of all finite collections of observation times. Mori retains complementary observable evolution and its classical scalar product; Zwanzig retains a fixed initial system state and the shifted bath preparation. Counterexamples separate zero mean from absent fluctuations, orthogonality from independence, and stationary covariance from stationary joint laws. Gaussian integration is an explicit mathematical input, not an axiom or an automatically proved consequence of a named canonical ensemble.

The memory-kernel refinement computes actual finite-history errors rather than encoding locality as a name. Mori retains the rotating carrier and positive Abel regulator; Zwanzig retains both coupling gradients, the printed Debye normalization, and separate continuum-replacement and localization budgets. Primitive bounds preserve oscillatory cancellation. An independent public-API consumer checks a changing history, a quantitative nonzero readout, rectangular cancellation, and matrix order. These are equation-residual results, not global trajectory approximation or a derivation of white noise.

The response interface now computes past-time convolution, real-amplitude probe derivatives, measure-valued impulses, and positive-time Fourier readouts. Nakano's current and static-conductivity formulas and the FNS bare velocity response independently use these operations. FNS does not thereby acquire the full equilibrium-to-conductivity transport contract. A Gaussian fluid witness derives spectral scaling from both force and velocity maps; Model-A fluctuation-dissipation normalization stays paper-local.

The two-dimensional viscosity refinement retains the higher-order term in the source's differential equation. Only an explicit zero-remainder truncation, positive viscosity, and the cutoff boundary give the leading-log square root. A supplied uniform weighted-remainder budget instead controls the squared-viscosity error. An isolated regular-response consumer computes continuous-force, impulse, static, and finite-frequency readouts, with no paper or production-countermodel imports.

The response refinement computes the complex viscosity denominator and its real spectral coefficient. Full-response scaling identifies viscosity only with explicit nonzero-wave-number and finite-response hypotheses; equal real spectra do not supply that reconstruction. A source-qualified two-dimensional, zero-frequency one-loop ansatz now couples the actual running bare-coupling coordinate, viscosity, time exponent, and nonzero spectrum. This is not a finite-frequency or all-order fluid solution. A separate public-API consumer composes readouts with viscosities 4, 2, and 2/3 and detects an incorrect reset of the intermediate viscosity.

For the optional finite exponential correlation-length convention, subexponential multiplicative corrections preserve the decay rate. Uniform relative error strictly below one is sufficient on the connected channel; algebraic prefactors are also allowed. Even one-percent relative agreement of raw correlations can conceal different connected lengths. None of these conditional results supplies the original paper's missing numerical error bounds or extends the above-critical formula to the critical isotherm.

The observable-scale refinement composes actual argument maps and scalar prefactors only on an inhabited transformed-domain intersection. Kadanoff's cell correlations and Forster-Nelson-Stephen's velocity spectra independently use this interface. Supplied absolute residuals compose as e1 + |a1| e2; no numerical truncation estimate is inferred from scale matching. Independent Gaussian-spectrum and normalized Ising-transition consumers test error amplification, successive decimation, and loss of microscopic information.

Kadanoff's correlations retain both critical parameter windows. A separately declared finite exponential-length convention now connects the length readout to actual connected-correlation decay and derives length covariance from exact tail and mean-square reexpression. Critical-isotherm continuation remains an additional input; the literal printed equation (30) is not silently repaired. The fluid client composes two shell steps at the updated coupling. Its two-dimensional one-loop flow demonstrates why resetting the bare coupling changes the accumulated time exponent, without asserting an exact interacting fluid solution or quantitative control of generated couplings.

Controlled approximation now composes through explicit accuracy rules and actual observable readouts, retaining a common regime and an active target sector. Blasius's reported separation coefficients remain comparisons of truncations, not certified error bounds against the exact flow. KSW and BHvK use quantitative phase-to-amplitude bounds only with supplied remainders and a positive lower momentum. A sixteenth independent consumer computes effective-range and shape-term budgets and proves that no uniform phase-to-amplitude error factor follows from positive momentum and unitarity alone. This strengthens error propagation without asserting EFT convergence.

The statistical coarse-graining refinement computes reduced probability laws from actual measurable projections. Kadanoff's two-valued cell configurations and Forster-Nelson-Stephen's regulated, transverse Fourier fields independently use this interface. It separates retained observable laws, invertible reexpression, and exact closure in an effective-model family. A fifteenth independent consumer computes a five-spin Ising marginal: the pair mean is 1/9, but a nonzero generated four-spin coupling rules out every pairwise Gibbs description of the exact reduced law. This finite diagnostic neither supplies critical scaling nor refutes controlled neglect of generated interactions.

The supersymmetry refinement computes Hamiltonians and energy expectations from actual supercharges. Witten 1981 retains normalized states, four-charge normalization, and ground-state attainment; Witten 1982 connects a complete spectral basis to actual positive-energy pairs and convergent, unnormalized index traces. Constructed counterexamples distinguish zero infimum from an attained vacuum and finite spectral sublevels from heat-trace convergence. A separate finite-operator consumer tests pairing, energy shifts, and two systems with the same zero index but different supersymmetry-breaking status. Witten 1982 now also derives the actual zero-momentum restriction from a joint spectral bound and identifies physical fermion grading with four finite quarter turns. A proper-sector operator witness preserves zero modes and their parity while changing the full thermal trace. The four-charge rest algebra now has an explicit Clifford multiplet, common vacuum kernels, and a checked normalization comparison. The nonzero-index existence theorem needs no rotation-covariance premise; the separate vacuum-orbit theorem uses Hamiltonian-rotation invariance without asserting that each degenerate vacuum vector is fixed. Physical domains, trace convergence in Yang-Mills theory, admissible deformation, and infinite-volume transport remain explicit obligations.

The Majorana refinement now computes adjoints, canonical anticommutators, occupation parity, and effective energy blocks from actual finite fermionic operators. Kitaev, Fu-Kane, and Oreg-Refael-von Oppen retain their distinct normalizations, phase conventions, and physical representation assumptions. An independent two-site wire checks finite end splitting and distinguishes total parity from subsystem parity and electron-number conservation. This algebra does not supply localization, a bulk phase, or a Josephson current.

The shared ordered-limit paradigm distinguishes a candidate iterated value, an actually established source order, a separately established reverse order, and a justified commutation principle. Stanley's unresolved critical limit, Mermin-Wagner's thermodynamic-then-zero-field magnetization, and Witten's circle-decompactification-then-strong-coupling argument realize that contract without inventing a reversed calculation. Wetterich supplies a fourth independent source: its actual regulator profile has commuting limits at the preferred exponent one and a divergent versus finite noncommuting pair at exponent two. Physical observerhood and nuclear-outcome possibility likewise remain separate from consciousness or ontic completeness when an original source supplies no such classification.

The finite driven-work refinement now composes computed canonical weights, actual stochastic updates, trajectory work and heat, and normalized path expectations. Jarzynski and Crooks consume this common construction while retaining their different source routes. Physical reversal, actual final equilibration, and canonical reference entropy are separate checked claims. An independent three-event process has a nontrivial heat update, an exact exponential work average of 9/8, and a final distribution that is not canonical.

The constrained-dynamics refinement now uses evaluated canonical functions and actual coordinate derivatives. Local first-order constraint completeness and the Poisson identity derive Dirac's first-class bracket closure; Anderson-Bergmann's invariant action commutator yields generator closure and quadratic-primary ambiguity on the same surface. Computed examples separate weak value, first-order action, global equality, and physical identification. An independent p=2 system derives its completeness condition, nonzero generator commutator, and Hamiltonian translation.

The boundary-layer refinement now computes the full and retained momentum operators from actual time and space derivatives. Prandtl's steady equations hold on a selected inhabited physical patch; Blasius's general reduction retains the time derivative, continuity, and separate outer Euler input. Discarded streamwise diffusion and pressure-gradient mismatch give a finite residual budget, not an exact equation or convergence of solutions. Separate mixed-derivative control is needed to pass from small transverse pressure variation to streamwise pressure matching. Curvature can leave first-order pressure variation where the planar estimate is second order. An independent decaying shear flow checks the shared operators, calibration error, and nonzero viscous acceleration without importing paper witnesses.

The entanglement framework now also has a finite complex density-matrix realization. Separability is an actual convex product decomposition, partial traces and spectral entropy are computed operations, and a calibrated partial-transpose witness proves nonseparability. CKW's singlet and GHZ reductions, AMPS's distinct Page-purification and pure-interior-pair controls, and Bell's original isotropic product-mixture comparison independently test this infrastructure. The source-specific tangle, entropy, Bell-locality, and black-hole assumptions are not identified with one another.

The Brownian refinement now uses actual probability measures and displacement observables. Einstein's Gaussian route binds the printed densities and scalar readouts to normalized integrated moments. Smoluchowski's route constructs fixed-angle three-dimensional paths from independent uniform azimuths and derives the finite-path moment from an explicit angular-average input. Raw moments, central variance, collision independence, persistence, and the distinct large-count and small-angle approximations remain separate. An independent Gaussian consumer has identical first observations but different accumulated spreading, testing the need for joint-law information. Einstein's finite-step density, reduced continuum density, and displacement count density are now distinct. Actual derivatives and exact residuals separate the finite-step balance from the retained diffusion equation; extra bounds give a nonempty rate comparison, not an exact PDE. Individual origins give zero initial displacements without physical co-location. The Gaussian count density is tied to a selected finite population and actual expected bin counts, not an exact finite observed histogram. The independent consumer also checks origin-invariant displacement statistics.

The predictive Brownian route now uses disjoint nonempty displacement intervals and actual trajectory-event probabilities. Their positivity is derived from the Gaussian law; it is no longer a supplied density label. Finite arithmetic mean-square readouts are distinguished from their ensemble expectation. The molecular-count proposal derives an inverse-moment interval under separate instrument-calibration and sampling-accuracy conditions, and does not assert that a finite observation exactly recovers the ensemble value. An independent two-particle consumer represents the empirical record through the public observation API and proves positive-probability sampling error even with noiseless readouts.

Einstein's mesoscopic clock now binds selected time roles to actual readings. Jointly independent stationary increments of the same histories derive the displacement-law convolution. Finite-step and retained continuum histories use the same selected population and aligned initial laboratory positions, but their later laws need not agree. Integrable density-error bounds transfer to actual expected bin counts; Gaussian bin positivity transfers only under a sufficiently small actual probability error. The exact finite-step second moment at mesh times separately supports the molecular-count readout method without an exact Gaussian finite-step law. The independent consumer has a process with Gaussian laws and diffusive moments at every prefix time but dependent increments, testing why marginal fits do not identify dynamics.

Guth's converted-volume and percolation predicates now come from one actual three-dimensional region history. Spatial density is a normalized Lebesgue volume limit over expanding finite windows; percolation requires an unbounded connected component. A growing geometric control has arbitrarily large converted fraction but only bounded components, even though the whole region is unbounded. Additional controls distinguish infinite point cardinality from spatial extent and percolation from connectedness of the entire phase. These paper-local controls do not prove the unknown critical threshold, collision mechanism, or qualified exit assessment.

Guth's nucleation refinement now uses actual Euclidean light fronts, birth configurations, and normalized Poisson laws. The same geometry derives the conformal spherical volume and keeps interior fictitious births inside real bubbles. Survival is the actual zero-engulfing-count event, with the physical volume factor retained. The late constant-rate approximation computes its time constant and a convergent exponent correction, not an exact finite-time pure exponential. Imported tunneling gives double-exponential parameter dependence, but enormous expansion remains a qualified plausibility assessment.

Actual and retained ensembles remain distinct. Convergent integrated error transfers the late decay law; separate spatial averaging relates it to the selected realized universe. A countable-time theorem also gives an almost-sure version without selecting an arbitrary history as typical. Large converted fraction is now derived on this route, not supplied by the percolation input. Seven inhabited controls test local finiteness, fictitious containment, the volume factor, expansion plausibility, the late correction, spatial averaging, and null-exception histories. Exact integration, approximation control, and spatial correspondence remain explicit inputs, not calculations claimed solved.

Kolmogorov's moving coordinates, velocity differences, and conditional finite-point laws now come from an actual random field and its joint measure. The retained increment ensemble is distinct from the absolute-velocity field; its exact local isotropy does not assert exact conditional independence for the actual field. Probability accuracy and squared-moment accuracy are separate inputs. Computed moment profiles, spatial partial derivatives, and strain dissipation feed the radial source calculation and the shared fluid adapter. A selected coordinate match and the separate moment bound give an actual conditional longitudinal-moment prediction interval.

The named increments use the same sample-dependent moving points as the conditional joint law. A fixed source-point identity requires the selected base-velocity condition. An incompressible rigid-rotation control agrees at the selected conditioning sample but has positive-probability disagreement when that condition is dropped.

The turbulence fidelity matrix now has 25 boundaries. Actual drift and shear fields distinguish local increment laws from whole-velocity isotropy and unconditioned homogeneity from conditional homogeneity. Further controls reject exact two-endpoint independence at nonzero variance, transfer of unbounded squared moments from probability error alone, and independently assigned derivative values. The archived equation (18) has no visible equality sign between 1/a and its square root. Literal-product and possible equality-chain readings are separate Lean propositions; the unit-normalization equations independently determine the positive time scale used by the main route. The printed outer ratio U/L remains distinct from the crossing time L/U. Local and Taylor isotropy also differ in both temporal stationarity and velocity scope, not by a blanket stronger/weaker ordering.

This refinement does not complete the fluid interfaces. Numerical Reynolds and geometric scale-window bindings, similarity-law transformations, asymptotic paths, and independent fluid-consumer reuse remain depth work.

The nonequilibrium-work framework now uses actual realization measures. Jarzynski's switching ensemble and Crooks's path ensemble expose normalization and the exponential work moment separately from existence of the ordinary mean. Mathlib's integral Jensen theorem derives the work bound. An empty realization space is rejected, and an inhabited mass-two counterexample shows why matching scalar equations cannot replace a probability ensemble. The two original Hamiltonian and forward/reverse derivations remain distinct. Crooks's joint path weights, reversed preparations, entropy pushforwards, and scaled-work pushforwards are now tied to those same measures. The measure route derives the integrated identity without a density-version assumption; source density formulas and the original v1 work-coefficient discrepancy remain separately visible.

The cosmological sampling-variance framework now also has an actual-measure realization. Normalized first and second estimator moments determine its variance; positive variance and physical support derive distinct possible sky estimates. Scott-Srednicki-White's finite-patch integral and Knox's noise-free harmonic calculation use this bridge without identifying their Gaussian, survey, or likelihood assumptions. A separate consumer derives the full-sky estimator formula from explicit Gaussian moment inputs and keeps its full probability law distinct from matching moments.

The geodesic-focusing framework now derives finite collapse from actual positive-region evolution and explicit continuous extension. Penrose's area transport fixes the first derivative, so positive convergence yields actual contraction; his optical route no longer supplies this as an independent label implication. Raychaudhuri uses the same calculus for the past-directed G-profile while retaining G^3 as volume. An independent Minkowski null-ray client computes the transverse Jacobi area and exhibits a caustic with complete geodesic continuations and an expanding outgoing family.

The quantum-locality framework now has an actual C*-algebra realization. Local observables belong to star subalgebras, disjoint supports commute, finite-volume Hamiltonians sum local self-adjoint interaction terms, and Heisenberg evolution is exponential conjugation. Lieb-Robinson's original asymptotic estimate and Nachtergaele-Sims's metric estimate now constrain actual operator norms. The latter's extended weighted interaction norm is computed from the metric, full one-site matrix dimensions, and interaction operators, with finiteness stated separately. A two-spin Ising model realizes the printed separated-support bound but has a nonzero commutator at arbitrarily early positive times. It therefore tests approximate locality without pretending to realize the 1972 infinite-lattice asymptotic theorem. The 1972 source now also uses actual integer lattice coordinates, Euclidean displacement lengths, full finite-region matrix algebras, and a faithful support-covariant translation action. Translation invariance transports the finite interaction neighborhood at the origin to every site and derives spacetime covariance from the finite-volume limit. Explicit infinite-lattice interaction controls distinguish exponential decay from finite range and origin-local finiteness from uniform finiteness. Both spin papers require disjoint local algebras to generate their joint algebra.

The collisionless-plasma framework also retains actual phase-space distributions, derivatives, signed charges, and velocity integrals. Landau's linear equation is checked as the first variation of Vlasov dynamics, while BGK's stationary energy profiles are checked locally on their own orbit branches. Both certified paper routes retain the resulting kinetic and Poisson equations. Positive integrable controls distinguish a first-order solution from a nonlinear solution, and stationary species populations from self-consistent charge balance.

Landau's late-time route now uses the actual transverse marginal, its half-line Laplace transform, and the residue of its printed resolvent. An explicit contour estimate derives field decay; a vanishing marginal remainder and nonzero residue derive microscopic nondecay. A canceled candidate pole establishes neither a genuine residue nor persistence, and zero frequency gives a constant leading term, not an oscillation. The nonsmooth-data assertion remains a separate unproved source calculation.

The entire-data premise now requires an everywhere analytic extension of the actual initial marginal. Plasma frequency and Debye length are computed from the same Maxwellian density, charge, mass, and thermal energy, including in the independent half-space branch. The wavelength formulas determine an estimated damped mode; an exact bound for the target field requires separate error control. Smooth mode counterexamples show that arbitrarily close decay rates need not give an eventual bound at the estimated rate. The source's small-parameter qualifications are not replaced by a numerical accuracy claim for every ka < 1 or ka > 1.

The wavelength routes now use actual real-wave-number families at fixed Maxwellian parameters. Explicit auxiliary mathematical limits yield the observable long- and short-wave limits; decrement dominance is eventual as k tends to infinity, not an unconditional finite-ka inequality. The phase equation admits higher odd branches, so the principal-root selection remains separate. Equation (20) is derived from that selection and equation (19). A nonempty comparison of leading and corrected frequency estimates uses the shared controlled-approximation paradigm, without claiming accuracy for the exact plasma solution. Physical controls reject the converse from small extrapolated relative damping to long-wave validity.

A tenth independent consumer constructs a positive Gaussian cosine disturbance in a neutral two-species Vlasov-Poisson plasma. Its actual number-density integral approaches equilibrium while each Fourier velocity mode keeps nonzero amplitude, and reversing the streaming recovers the initial mode. A single-species zero-potential probe instead fails Poisson. The test establishes phase mixing, not Landau's fixed-ion damping decrement, a BGK trapped wave, collisional relaxation, or microscopic irreversibility.

The low-energy nuclear-resummation framework now also has an actual complex elastic S-matrix. KSW's real-contact bubble amplitude implies unit norm and the optical theorem. BHvK's regulated square-root propagator has a checked lower-side on-shell limit; attaching external lines removes the auxiliary field normalization and recovers the leading scattering-length amplitude. The certified paper routes retain these formulas, while concrete controls reject a complex absorptive contact, the wrong square-root boundary value, and an unnormalized auxiliary propagator.

KSW's mixed expansion now retains the actual resummed C0 amplitude and a single C2 insertion with its squared bubble denominator. The shared complex amplitude API derives the first-order optical theorem and the quadratic unitarity defect of a finite truncation. An independent nuclear client reconstructs scale-independent leading and correction terms from running contacts, then distinguishes that truncation from an exactly unitary resummation that adds higher-order terms. Neither scale hierarchy nor exact unitarity alone is treated as proof of EFT accuracy. Two resummations can be exactly unitary yet disagree between subtraction scales even while their retained leading and correction terms agree.

The band-Hall framework now also has actual differential response semantics. Haldane's signed weak-field density slope and separate fixed-chemical-potential Streda principle derive both Hall signs, rather than silently excluding the negative-index phase. TKNN's Kubo coefficient is an actual electric-field current derivative; its within-level gap invariant is distinct from the total occupied-sector index including filled lower Landau levels. A seventh independent consumer connects honeycomb corner masses and cone spectra to signed density response, and tests why zero-field quantization does not determine a finite-field current ratio.

TKNN and Niu-Thouless-Wu now also share actual spectral Kubo data: domain-aware Hamiltonians and operators, complete orthonormal eigenstates, occupied and empty sectors, energies, and convergent transition sums. Unitary basis identification and hbar rescaling derive the transformed response. NTW's curvature bracket uses actual ground-state derivatives; its torus average uses actual integrals and retains the reversal of derivative order in the original equation (2.9). The independent two-level client tests real response, rephasing invariance, and opposite Hall signs at the same gap, while rejecting integer quantization from local spectral data alone.

The resonance-spectroscopy framework now also has actual complex two-state vectors and unitary pulse matrices. Ramsey's three source amplitude relations derive the interference probability, with the energy-valued laboratory Hamiltonian and solved rotating-frame generator retained. Rabi's printed weak-field probability has a separate coherent realization; concrete controls prevent it from becoming an exact laboratory solution or silently changing the historical frequency-ratio convention. Both certified paper routes use this shared dynamics.

Ramsey's drive-free region now retains a spatial list of actual energy-valued Hamiltonians in a common basis. Chronological phase multiplication and constant positive molecular speed derive the source's time-to-space mean reduction. Equal mean splittings preserve the complete coherent response and its positive-speed beam average, even when both energies shift together. Concrete controls reject variable-speed weighting, an unaligned static energy basis, and unconditional transverse mean-field averaging; the precision route derives these qualifications instead of receiving them as an assumed conclusion.

An eighth independent consumer now tests this spectroscopy API without importing either paper. It derives the resonant pulse response, uses the original normalized continuous beam weight, and proves a strict distinction: the selected-speed molecule can invert completely while the coherent beam's average transition probability remains between zero and one. A drive-free interval preserves populations but changes the recombined fringe. Separate tests reject amplitude averaging across independent trials and automatic dephasing from a large single-molecule phase. The chosen pulse strength is not claimed to optimize the beam or determine its linewidth.

Quantum error recovery now also has actual complex code amplitudes, local recovery matrices, binary supported-noise components, and reduced densities. Calderbank-Shor's final result uses the two preceding correction equations; Steane's uses the printed Cij identity through an explicit normalization bridge. Both derive restoration of every coherent superposition and a logical-state-independent residual environment instead of receiving those outcomes as final calculation inputs. Source coding identities and physical model identifications remain explicit obligations.

A ninth independent client constructs a three-qubit known-support code and an actual dephasing dilation. The first correction preserves normalization but fails to restore a codeword's off-diagonal coherence; the complete operation restores it. Separate shared controls show that successful basis density recovery and state-independent apparatus probabilities do not by themselves establish quantum recovery. No unknown-error-location or noisy fault-tolerance claim is made for this three-qubit example.

The same independent code now carries an entangled reference qubit through the complete recovery. Actual joint density restoration preserves every joint observable and a calibrated nonseparability witness. A separate isometric logical-basis recorder restores all basis densities and both local marginals but destroys their entanglement. The shared recovery framework therefore composes with actual bipartite entanglement, while noise-environment decoupling remains distinct from reference-code separability.

For example, Bethe's and Blatt-Jackson's original 1949 nuclear-scattering arguments share effective-range reduction and a qualified deuteron-range extraction without being collapsed into the same derivation. Their composed Lean results require independent reduction and extraction source proofs plus a third historical handoff: Bethe retains radial comparison, ground-state specialization, and binding/free-proton/parahydrogen evidence, while Blatt-Jackson retains the stationary variational functional, analytic continuation, its printed scattering-matrix pole formulas, and binding/epithermal/coherent evidence. A physical countermodel keeps distinct scattering and bound-state energies, both component source explanations, and the extracted result while rejecting a missing paper-specific handoff.

Wilson's original 1974 confinement argument and Creutz's original 1980 SU(2) Monte Carlo study likewise share finite-regulator gauge invariance and regulated loop-area confinement without conflating their physics. Wilson's joined proof retains compact angular-link equations, analytic minimal-surface tiling, normalized-loop formulas, and the small-hopping vacuum-loop restriction; Creutz's retains pure SU(2), detailed-balance equilibration, independent-start and finite-size checks, statistical uncertainty, and the printed constant/perimeter/area square-loop fit. The shared result does not claim continuum confinement, and its physical countermodel distinguishes the gauge groups and mechanisms while rejecting a missing joining derivation.

Two modern rigorous condensed-matter arguments, Hastings-Koma 2006 and Nachtergaele-Sims 2006, share finite-propagation and spectral-gap clustering frameworks while retaining different physical logic. Hastings-Koma's joined proof requires an independently selected exponential support-chain branch, Gaussian ground-sector subtraction, finite-volume uniform transfer, and its corrected bosonic correlation formula. Nachtergaele-Sims instead retains weighted arbitrary-metric commutator bounds, target ground-projection conditions, analytic-contour optimization, and its explicitly restricted imaginary-time estimate. The shared composition neither accepts power-law propagation as exponential nor identifies corrected decay with unsubtracted correlation decay.

Five historically broad shared frameworks additionally retain independently governed, source-valued physics without widening their neutral contracts. Heisenberg/Ozawa distinguish corrected microscope recoil, prepared-state dispersion, the full noise-disturbance commutator, and conditional product bounds. Everett/Zeh/Rovelli distinguish squared branch weights, memory trees, reduced versus global coherence, and physical observer comparison. Guth/Albrecht-Steinhardt distinguish subcritical percolation, wall thermalization, a radiative finite-temperature potential, and fluctuation replacement. KSW/BHvK distinguish complex PDS loops, running contact beta functions, bound-state poles, pion counterterms, and a one-datum three-body limit cycle, with both derivative-contact and sine-ratio running enforced at two distinct scales. TKNN/NTW distinguish magnetic Diophantine gaps, twist-torus averaging, and a degree-three fractional ground-space response that explicitly does not satisfy the integer-only shared endpoint. Each family has checked formula mutations, explicit unproved-claim boundaries, independent-client reuse, and a trusted-axiom audit.

The dimensional-analysis paradigm distinguishes a nonempty selection of relevant physical inputs from the stronger assumption that this selection covers every relevant input. Its finite countermodel selects length and time while leaving a genuinely relevant mass scale unselected, so dimensional admissibility and a scoped result cannot silently establish exhaustive physical input coverage.

The thermodynamic-limit paradigm distinguishes small and large finite systems, critical versus off-critical control parameters and neighborhoods, large-volume exceptional points, and bounded-correlation versus spontaneous- magnetization properties. Its countermodels keep actual finite-volume data while separating singular limiting behavior, empty accumulation scopes, uniform finite control, and the additional property-preservation bridge.

The renormalization-group paradigm distinguishes infrared and ultraviolet effective descriptions and running couplings while retaining a protected physical amplitude with a definite scale-independent prediction. Separate finite models distinguish an out-of-regime prediction from a selected prediction and a genuine one-scale prediction from a two-scale comparison; running parameters and formal agreement cannot substitute for physical nonvacuity.

The mathematics-and-nature philosophy keeps mathematical models, physical states, coordinate quantities, physical observables, and mathematical versus physical values distinct. Its finite witnesses separate charge from temperature, selected from control states, and an actual physical value from a mathematically assigned but spuriously represented one; representation faithfulness therefore cannot be inferred from matching labels.

The observability philosophy likewise keeps weak system-scoped observable availability, operational access, performed measurement, and physical existence separate using distinct spectroscopy and radiometry procedures, resonance-frequency and background-temperature quantities, matching apparatuses, and observer-dependent availability. A nonvacuous availability sector must contain an actual available quantity; bare availability supplies neither a procedure nor an ontology. Its independence results therefore remain physically discriminating after names or labels are changed.

The observer philosophy separately distinguishes physical targets, nonconscious instruments, conscious persons, actual versus unproduced information records, and reference frames. Its frame countermodels retain different entities, position versus energy, invariant versus alternative physical values, and frame-dependent coordinates without identifying a frame representation with an observer's physical agency.

The probability philosophy distinguishes numerical predictions, objective physical chances, population assignments, observed sample frequencies, and measure-relative typicality. Explicit bridges are required before one role can justify another, while typicality becomes nonvacuous only when an actual selected state exists. Finite models retain different events, models, physical states, populations, samples, measures, and exceptional properties.

The measurement philosophy separately models selected and control systems, reference preparations, active versus idle interventions, calibrated and control detectors, actual versus reported values, recorded outcomes, and physical state changes. A real control run cannot silently stand in for the missing selected measurement or reference calibration.

The active benchmarks include:

Witten's 1981 analysis of dynamical supersymmetry breaking, including the global vacuum-energy criterion, Goldstino consequence, perturbative protection, lower-dimensional nonperturbative mechanisms, four-dimensional zero-mode obstruction, qualified proposals, and unresolved conclusion;
Witten's supersymmetric-index argument for four-dimensional N = 1 supersymmetric Yang-Mills theory;
Einstein, Podolsky, and Rosen's original 1935 completeness argument, separating the sufficient reality criterion, the single-system noncommuting joint-representation obstruction, the Lean-derived completeness-or-no-simultaneous-reality alternative, separated conditional-state assignments, the concrete position-momentum route, the incompleteness reductio, the distant-choice objection, and the open status of a complete alternative theory;
Heisenberg 1927, Kennard 1927, Robertson 1929, and Ozawa 2003 as a deliberately nonflattened uncertainty benchmark. Heisenberg now retains the complete article's operational kinematics, microscope and energy-time procedures, independent selected-Gaussian calculation, experiment-relative value partitions, coherent versus measured transitions, high-excitation and repeated-observation classical-limit routes, free-packet and grating cases, jump timing, causality, resonance, weak quantization, coupled-system energy, and proof-stage corrections. Kennard retains transformation probabilities with pointwise square-modulus density formulas, doubled-variance precision, Gaussian saturation, the general positivity inequality, measurement interpretations, and simple-motion scope. Robertson retains normalized complex wavefunctions, centered rms deviations and doubled Schwarz overlaps, actual noncommuting observable matrices with state-dependent positive and zero bounds, integer-spin angular generators with their zero-magnetic and extremal branches, and the stated but unproved operator extension. Ozawa separates all three uncertainty formulations, derives the correlation-term and generalized error-disturbance relations, recovers the product law under independent intervention, and supplies a dependent-intervention violation plus a qualified optical proposal. Kennard and Robertson alone earn the prepared-state dispersion framework; Heisenberg and Ozawa independently earn the operational error-disturbance framework without identifying their epistemically different calculations;
Born's full 1926 collision paper, separating periodic-state frequencies, the continuum limit, one-dimensional flux balance, directional scattering, elastic and inelastic channel calculations, thresholds, the qualified dipole approximation, limited diffraction evidence, practical rather than ontic indeterminism, and the unresolved radiation extension. Born and Kennard independently earn only the neutral shared amplitude-to-outcome- probability route; Born's selected collision state and scattering amplitude are not promoted to Kennard-style preparation and representation, and their scattering and exact-observation meanings remain local. Both paper adapters now retain their own Complex.normSq value formulas, but Born's discrete coefficient weight and Kennard's continuous probability density are not collapsed into one shared mathematical carrier;
Wu et al. 1957 and Garwin-Lederman-Weinrich 1957 as independent controlled parity-falsification benchmarks. Their shared technical framework imports the mature experimental-symmetry paradigm and retains an admissible experiment, physical reflection between two admissible configurations, controlled detection, invariant-law equality prediction, measured count- rate distinction, and explicit breaking. Its finite countermodels retain positive forward/reflected count rates 3 and 5, calibration signal 1, and field-reversal residual 0; those numbers are logical witnesses, not historical measurements. They separately reject detection without the invariant prediction, a physical test without detection, and distinctions under nonphysical maps, while an independently considered detector-drift hypothesis remains open after the selected remanence control. No Unit-alternative truth table replaces the physical experimental data. The shared route now gives an ordinary structural explanation without paper provenance. A stricter source-sensitive wrapper keeps the two granular derivations distinct: Wu starts from gamma calibration, beta asymmetry, and three control families; Garwin-Lederman-Weinrich starts from delayed stopped-muon detection, precession, and the scoped stopped-pion null control. Each source theorem exposes its derivation and entails the ordinary explanation without consuming a terminal parity result. A converse model retains the full falsification and ordinary explanation but has no source-sensitive explanation when its source derivation is false. Cobalt orientation, pion-muon transport, artifact-control mechanisms, decay dynamics, charge conjugation, and time reversal remain paper-local. Wu's original Fig. 2 gamma-count quotient, opposite cold beta-count branches, common warm-rate baseline, and two independent zero-asymmetry control specimens are actual real-valued propositions with separate source-route dependencies and inhabited counterexamples. Separate source-valued controls additionally retain the reflection-odd spin * momentum pseudoscalar, approximate cobalt coefficients, the unperformed time-reversal test, Garwin's 0.75-2.0 microsecond delayed gate, partial-polarization angular curve, 0.989 +/- 0.028 stopped-pion null control, finite g = 2.00 +/- 0.10, and distinct 1.92 +/- 0.19 versus 2.5 high-energy model comparison. Twenty inhabited mutations prevent these source facts from being promoted to exact asymmetry, exact magnetic moment, a completed future experiment, or a uniquely established neutrino theory;
Wilson's original 1974 lattice-gauge confinement argument, separating exact finite-spacing gauge invariance, transfer-matrix qualifications, strong-coupling surface expansion, area-law binding, string-like loop-surface structure, weak-coupling expectations, and the unresolved continuum limit;
Witten's original 1979 large-rank baryon argument, separating reviewed planar meson counting and the independent confinement premise from N-quark combinatorics, Hartree control, scattering, exponentially suppressed production, distinct transfer limits, and the final monopole analogy. Its eleven directional paper-local countermodels are now value-bearing: the rank-four witness retains g^2 N=1, relative corrections (1/16,1/4), six exact pairs with pair force 1/4 and total interaction 3/2, order-rank mass eight with a nonzero Hartree residual, and pair-production weight (1/2)^3=1/8. Fixed momentum gives velocity change 1/8, whereas fixed velocity gives momentum transfer eight; inverse-coupling baryon and monopole mass scalings do not imply identity, and qualitative success does not bound finite-rank error 1/3 by 1/10. No proposition-pair or named-calculation truth table replaces these Witten baryon distinctions;
Bell's original 1964 EPR no-go argument, including its exact inequality, robustness argument, scope examples, and conditional physical conclusion.
Bell's original 1966 hidden-variable analysis, separating the explicit spin-one-half dispersion-free construction with its value-level Pauli observable, two eigenvalues, hidden-sign rule, and uniform average, the rejected von Neumann and Jauch-Piron premises, the dimension-scoped Gleason obstruction, context-dependent projector values, and Bohm's qualified nonlocality lesson with its two-particle density, Schrödinger equation, and guidance-velocity formulas. Its proof-free apparatus readout retains a nonfactorizable two-by-two spin amplitude, positive density, distinct remote analyzing fields, local currents, and density-divided velocities; nonfactorability without remote current coupling has no trajectory effect, while the explicit current bridge proves distant apparatus dependence.
Kochen and Specker's original 1967 hidden-variable analysis, separating statistical reproduction from functional preservation, the finite 117-direction coloring obstruction, its spin-one and rhombic-field realization, the homomorphic-relation objection, the positive two-dimensional sphere-and-disk model, the von Neumann critique, and the quantum-logic consequence. The source readout retains 117 distinct normalized real rays, actual complex spin-one matrices and commutators, complementary zero/nonzero squared-spin projectors, the metastable orthohelium sector n = 2, l = 0, s = 1, the distinct-coefficient rhombic Hamiltonian, all three equation-(8) reconstruction polynomials, and the three measured energy branches. The paper's printed nonzero-spin proposition is explicitly complemented into the shared exactly-one zero-spin coloring convention; its inconsistent printed J_z prefactor is isolated rather than assumed. The proposed adjustable external field is not confused with fixed nickel-crystal evidence or a performed direct test.
Berry's original 1984 geometrical-phase argument, separating slow closed eigenstate transport, dynamical and geometrical phases, interference observability, gauge-dependent connection from gauge-invariant spectral curvature, the two-level monopole and real sign rule, arbitrary-spin predictions, the transported-box Aharonov-Bohm construction, and the paper's isospectral and wider wave-physics qualifications.
Hannay's original 1985 classical angle-holonomy argument, separating the physically assumed adiabatic angle-averaging principle from exact Liouville conservation, action invariance from angle anholonomy, connection convention dependence from invariant curvature, three independent physical illustrations, the integrable many-freedom extension, and the explicit failure of a generic mixed-system generalization.
Maldacena's original 1997 D3-brane route to AdS/CFT, separating the large-N supergravity sector, the full quantum duality conjecture, evidence, calculational regimes, and interpretive consequences. The original equation-(2.2) full D3 metric now remains a proposition-valued source formula before the fixed-U harmonic limit is used.
Townsend's original 1995 compactified-supermembrane argument and Witten's original 1995 string-dynamics paper as an independent Kaluza-Klein tower benchmark. Their common extraction separates the tower and charge/mass matching calculations from a paper-local state-identification bridge and a further compactified-origin interpretation. It stops at qualified evidence for a higher-dimensional origin. The output-led established result is the selected compactification setup together with a model-native nonvacuous endpoint requiring the actual setup data, calculations, identified tower, and origin support at one model. It does not store the implication-valued bridges; a checked theorem reconstructs the complete route from the direct outputs. Theory/world grounding requires the selected setup while remaining independent of the tower calculations and conclusions. The full raw route now also realizes an ordinary structural explanation of supported compactified origin. Its source-sensitive form retains distinct origin tokens that extend Townsend's black-hole/KK identification and Witten's RR-BPS/sparse-spectrum/KK identification by their respective origin-interpretation bridges. These explanation tokens are intentionally stronger than the reduction tokens below, and Witten's separate radius/decompactification calculation remains excluded. A second checked projection maps the actual compactified higher-dimensional description, calculated and matched KK tower, protected lower-dimensional tower, and physical state identity into a nonvacuous ReductionAndEmergence.RealizationContext. It stops at the selected tower reduction: the stronger compactified-origin interpretation is deliberately absent. Countermodels show that compactification without higher-tower support and matched tower data without state identity are both insufficient. Both papers now also realize that reduction directly from source inputs, before any terminal origin result or shared endpoint exists. Townsend executes the charged black-hole tower and KK matching calculations before applying his conjectural state-identification bridge. Witten executes RR charge provenance, protected-tower, sparse-spectrum, and KK matching stages before state identification. Neither source reduction consumes the further origin-interpretation bridge. A stronger source-sensitive projection now retains typed, noninterchangeable paper-local derivations: Townsend's charged-black-hole/KK identification and Witten's RR-BPS/sparse-spectrum/KK identification. The realization relations contain the corresponding raw paper inputs, not established shared outputs. A checked countermodel shows that a completed tower-origin result, complete technical route, and ordinary reduction still do not determine which source derivation obtained them; a parallel countermodel keeps ordinary structural explanation but still has no source-sensitive origin explanation when the source relation is false. Witten's separate radius/decompactification calculation is excluded from his tower token. Their compatibility adapters still consume only the terminal origin result and reconstruct the complete stronger route. Staged paper countermodels show that implication-shaped contracts can all hold vacuously while direct origin evidence fails. Townsend's membrane and p-brane claims remain local, while Witten's r = lambda^(2/3) calculation, strong-coupling decompactification, lower-dimensional U-duality, heterotic/Type II consequences, enhanced-symmetry assessment, and speculative Type I proposal remain separate paper-local routes.
Strominger-Vafa 1996, Callan-Maldacena 1996, and Horowitz-Strominger 1996 as a three-paper black-hole microstate-entropy benchmark. Their extremal, near-extremal, protected-index, same-sector, weak/strong comparison, radiation, and information-scope routes remain distinct. Horowitz-Strominger's author-TeX formulas P = 2 pi n/L, n_R = L(delta E + P)/(4 pi), and n_L = L(delta E - P)/(4 pi) are now literal proposition-valued inputs tied to total energy, momentum, and density readouts; checked arithmetic recovers n_L + n = n_R, and a countermodel prevents a named chiral-momentum definition from supplying the printed formulas. Strominger-Vafa's microscopic branch now retains the displayed Cardy 2 pi sqrt(n c / 6) logarithmic-growth formula and selected c/n charge substitution before the protected indexed-growth endpoint. They jointly earn only the narrow shared inference from two valid same-sector entropy calculations plus an explicit paper-local comparison bridge to a scoped entropy agreement. The same raw route now directly realizes an ordinary structural explanation of that scoped agreement, and a stricter explanation retains four noninterchangeable typed microscopic derivations without consuming an established match or reduction wrapper. That complete route also realizes a direct scoped derivational reduction: a typed microscopic state-counting description supports the selected entropy behavior, a typed macroscopic black-hole description exhibits the independently calculated entropy and agreement, and the same-sector comparison supplies realization. This is entropy-level reduction only, not reduction of the complete theories or dynamics. Invalid descriptions with matching outputs and a microstate count without a macroscopic entropy calculation are checked countermodels. A stronger source-sensitive reduction now preserves four distinct microscopic derivations: Strominger-Vafa's BPS bound-state/index-growth route, Callan-Maldacena's extremal one-five-string count, their separate balanced near-extremal excitation and T-duality count, and Horowitz-Strominger's left/right-moving effective-string thermodynamic count. Each adapter starts from raw paper-local setup and calculation predicates before invoking the generic source theorem. A completed entropy match and ordinary reduction with an unrealized derivation token has no source-sensitive reduction, so a common entropy output cannot manufacture derivational provenance. A parallel countermodel keeps the completed match, route, and ordinary structural explanation but still has no source-sensitive explanation. The shared proof-free model retains the two descriptions, conserved sector, two regimes, two entropy values, and all nine route-used physical relation families. Each paper constructs a named exact model, proves a semantic-retention certificate, consumes it before route applicability, and exposes a source-native physical setup with a checked bridge to the shared grounding boundary. Grounding requires that setup but consumes no entropy or comparison output. Every established paper match is now output-led: exact selected semantics plus the direct same-sector setup and four realized outputs, with all implication-valued contracts reconstructed. An independent finite model realizes that proposition, and exhaustive proofs show that changing any one of its seven indices or nine relation families destroys the completed comparison. Its six shared and eighteen paper-local directional countermodels are now value-bearing. The shared witnesses retain area 4, Newton constant 1, nonempty degeneracy/log-count data, charge and excitation sectors, validity, comparison, leading-coefficient, finite-correction, and information residuals. Strominger-Vafa retain Q_H=1, Q_F^2/2=100, c=606, n=1, statistical and black-hole squared entropies 101,100, distinct actual degeneracies at fixed weighted index, and nonoverlapping weak/strong bounds. Callan-Maldacena retain the Q_1 Q_5 N extremal value, three balanced ratios 1/4, contributions 1/2+1/2+1/2=3/2, temperature agreement with unequal radiation coefficients, and selected horizon-state scope. Horowitz-Strominger retain Q_-=1, four bosonic species, low-density n_L=2,n_R=8 contributions 2,4, matched leading entropy 6, separate transition/evidence residuals, comparison charge two, perturbative versus nonperturbative unitarity, and unequal decay rates. Checked positive witnesses realize every source boundary. No proposition-pair or status-enum truth table replaces these entropy distinctions.
Gubser, Klebanov, and Polyakov's original 1998 correlator prescription, separating the proposed boundary generating-functional dictionary, controlled supergravity regime, asymptotic conformal symmetry, massless and massive wave calculations, stress-tensor normalization, protected partial-wave dimensions, and explicit higher-point and leg-factor obligations.
Ryu and Takayanagi's original 2006 boundary-region entropy proposal, separating the selected anchored minimal surface, exact AdS3/CFT2 check, thermal and massive checks, higher-dimensional structure, qualitative strong/free comparison, horizon interpretation, and open covariant extension.
Lewkowycz and Maldacena's original 2013 generalized-gravitational-entropy argument, separating Euclidean density-matrix preparation, integer replicas, continuation assumptions, the scalar check, replica-fixed-surface Einstein calculation, cone area term, AdS/CFT subregion translation, reflection entanglement, and open extensions.
Knox's original 1995 CMB forecast, separating ensemble spectra from one realized sky, retaining equations (4)-(5)'s estimator-variance and relative-uncertainty formulas with their positive noise-free limit, fixed-weight beam comparison, conditional likelihood precision, the signed inflationary consistency relation and cosmological-constant correction, foreground scope, and nuisance-parameter confusion.
Scott, Srednicki, and White's original 1993 small-scale CMB sample-variance calculation, separating one-sky realization logic, Gaussian moment calculation, beam-convolved equation (7), the exact circular-cap Bessel integral and distinct equation-(9) limits, both lines of the linear-scan equation (10), actual MAX/SP91 angular inputs, their linearized 25/30 percent amplitude uncertainties, the COBE galactic cut, idealized patch counting, and qualified phenomenological interpretation.
the original 2012 AMPS firewall argument, separating the strong-subadditivity and explicit Bogoliubov number-defect contradictions from the mining-dependent and scrambling-time extensions. Its entropy route now uses only S_B >= 0, treats strict thermality as a strengthening, and makes pure-pair identification depend jointly on semiclassical exterior physics and no drama. Its mode route separately represents the appendix-A early projection, the observer's prediction, number-state selection, and the fact that the early measurement need not actually be performed.
Gaiotto, Kapustin, Seiberg, and Willett's original 2014 generalized-global- symmetry paper, including higher-form defect kinematics, the checked Abelianity argument from explicit continuous defect-exchange witnesses at positive form degree, the compact-spacetime selection rule, Maxwell electric and magnetic one-form currents, their mixed anomaly, Coulomb-phase symmetry breaking, and the photon Goldstone interpretation. A second typed entropy source now reconstructs semiclassical validity, collapse mode mixing, horizon ray tracing, late-packet thermality, the surface-gravity temperature, quarter-area entropy, and compensation before realizing a source-sensitive structural explanation of generalized nondecrease. The heuristic pair picture is not a premise of that source.
Jarzynski's original 1997 nonequilibrium work identity, separating the isolated Hamiltonian calculation, weakly coupled physical reservoir, equilibrium limits, ensemble consequences, numerical thermostat extensions, and finite-sampling limitation.
Crooks's original 1999 fluctuation theorem, separating protocol-indexed directed paths, microscopic reversal, the exact entropy-production relation, the integrated exponential identity from its later Jensen mean-second-law consequence, ensemble mean nonnegativity from pathwise nonnegativity, equilibrium-work and steady-state specializations, and qualified long-time heat and Gaussian approximations. Its distinction between reversed-protocol microscopic path probabilities and same-protocol state detailed balance now uses a genuinely stochastic three-state model: all forward and reverse transition probabilities are positive, both kernels are normalized, uniform stationary state populations are normalized, and clockwise/counterclockwise probabilities 1/2 and 1/6 give a nonzero probability current 1/9. A separate balanced model proves that microscopic reversibility permits detailed balance as well; it neither requires nor forbids that stronger condition.
Metropolis et al.'s original 1953 modified Monte Carlo method, separating the canonical target, symmetric proposal and acceptance rule, pairwise balance, accessibility, asymptotic equilibration, rigid-sphere specialization, virial pressure calculation, finite numerical evidence, and unresolved convergence-rate and finite-size limitations.
Onsager's original 1931 reciprocal-relations analysis, separating thermodynamic positivity from coefficient reciprocity, equilibrium from detailed balance, the chemical triangle analogy from the fluctuation proof, ensemble-average regression from pathwise dynamics, and now retaining the printed simple-crystal equations (4.3)-(4.10): energy-displacement moments, transverse fluctuation moments, force and flux laws, regression drifts, opposite-sign delayed correlations, and reversal symmetry. Their checked comparison forces equation (4.11), omega_3 = 0, before the abstract reciprocal-coefficient result is used. The module also keeps the macroscopic time-and-length regime, dissipation and stationary-flow variational principles, magnetic and Coriolis exceptions, and the general transport theorem deferred beyond Part I.
Nyquist's original 1928 thermal-noise argument, separating total equilibrium exchange from frequency-local balance, the nondissipative filter argument, matched transmission-line mode counting, the classical voltage-noise law, general impedance and current-noise propagation, microscopic-carrier scope, and the qualified Planck-energy replacement. Its equation-(7) thermal factor h*nu/(exp(h*nu/(k*T))-1) and equation-(8) one-sided voltage spectrum are represented as an alternative to the classical 4*R*k*T law, with an explicit zero-point-free energy; countermodels separate a named quantum replacement from the printed formula and exclude Callen-Welton's later positive half-quantum term.
Callen and Welton's original 1951 generalized-noise argument, separating quantum transition dissipation, zero-force equilibrium fluctuations, the generalized quantum noise-dissipation relation and classical limit, Brownian, vacuum-radiation, and acoustic applications, and the concluding coherence interpretation from the broader theory left for future work.
Kubo's original 1957 linear-response argument, separating weak Hamiltonian response, the value-level phase-space response, after-effect function, and past-time pulse convolution of equations (2.8)-(2.10), the ensemble-to-observation qualification, canonical relaxation and static limits, equilibrium correlations, exact magnetic and conduction formulas, field-reversed reciprocity, fluctuation-dissipation, sum rules, Einstein relations, and the paper's deferred applications.
Nakano's original 1956 conductivity argument, separating arbitrary-time causal current response, the equilibrium thermal current-correlation kernel, value-level equations (1)-(4) for the convolution, thermal integral, normalized trace, and spectral kernel, equation (5)'s explicit positive-time integral and Boltzmann-weighted energy-delta sum, present non-evaluability, and the distinct perturbative one-relaxation-time approximation for a typical subsystem model.
Ramsey's original 1950 separated-oscillating-fields argument as the first dedicated atomic, molecular, and optical benchmark. It separates matched pulse interactions from fixed-field phase evolution, single-velocity probability from beam averaging, near and far approximations from the interpolated middle interval, calculated line shape from Kusch's reported potassium comparison, and general method advantages from proposed or experiment-specific applications.
Noether's original 1918 invariant-variational-problem analysis, separating finite-parameter divergence relations from arbitrary-function Euler-Lagrange identities, retaining equation (13)'s finite-generator sum_i psi_i delta u_i^(lambda) = Div B^(lambda) relation and both converses, retaining equations (15)-(16)'s arbitrary-function-weighted alternating derivative sum and vanishing identities, and separating on-shell Div B = 0, multidimensional conservation, one-dimensional first integrals, and Hilbert-energy consequences.
Hohenberg and Kohn's original 1964 inhomogeneous-electron-gas argument, separating exact nondegenerate density determination and the representable-density variational principle, including exact attainment of the physical ground energy and a quantified minimum, from nearly uniform response, the strictly nonconvergent but author-expected asymptotic status of the slowly varying gradient series, and untested partial-summation routes.
Kaplan, Savage, and Wise's original 1998 nucleon-nucleon expansion, separating pionless PDS and RG matching, large-scattering-length mixed power counting, explicit-pion subleading completion, scale accounting, numerical fit evidence from its validity interpretation, empirical fit limitations formalized as an empirically adequate but uncontrolled truncation, and mixed-order coupled-channel predictions.
Blatt and Jackson's original 1949 neutron-proton analysis, separating Schwinger's stationary functional, controlled zero-energy reduction, a shared controlled order-k^2 truncation with explicit remainder, intrinsic-range underdetermination, deuteron continuation, triplet and singlet data status, higher-order shape sensitivity, and the conditional Section VIII extraction of well parameters and interpolation formulas from any assumed conventional well shape, with formula-validity and exact-solvability qualifications retained. The distinct square and Yukawa realizers also establish, in the selected low-energy context only, derivational reduction together with autonomous multiple realization.
Einstein's original 1905 special-relativity paper and Minkowski's original 1908 space-time lecture, retaining their operational, kinematic, causal, dynamical, electromagnetic, and qualified interpretive routes separately. They jointly earn only the narrow inertial-frame inference from a finite invariant light structure, two explicitly distinct selected frames, admissible frame reexpression, law covariance, and an explicit physical no-preferred-frame bridge; synchronization, coordinate calculations, rods and clocks, causal cones, proper time, force laws, point-charge fields, and Minkowski's gravity proposal remain paper-local. Minkowski's local section-I route now retains the printed positive-c upper hyperboloid c^2 t^2 - x^2 - y^2 - z^2 = 1, the selected (x,y,z,t) -> (x',y,z,t') preservation relation, and a checked derivation of the transformed upper-sheet equation; this coordinate formula is deliberately not promoted into the neutral shared inference. Their paper-local countermodels are now value-bearing. Einstein's original pp. 892-893 clock readings retain emission, reflection, and return times: equal outbound and return durations fix the reflection reading to the midpoint, while the same two local endpoint readings admit an asymmetric distant assignment. Section 3 retains a finite-light rescaling counterexample; Section 4 keeps squared length contraction distinct from intrinsic deformation; Sections 5 and 10 retain parallel velocity composition, the stated longitudinal and transverse mass conventions, and an independently falsifiable force law. Minkowski's separate-print pp. 3-14 countermodels retain a preserved quadratic value off the unit hyperboloid, a null orientation signal with a superluminal material counterexample, covariant law residuals on distinct situations, a timelike worldline without the point-mass force equation, distinct electric/magnetic transverse components with the same field invariant, and bounded Kepler/tested-observation residuals with an uncontrolled untested residual. No enum truth table substitutes for these physical distinctions. Typed shared countermodels keep light preservation, law covariance, and physical no-preference independent, while a collapsed one-frame model shows why mere reflexive covariance is insufficient. A nonvacuous source-shaped model realizes the complete two-frame route. The established result is output-led: exact selected semantics and NonvacuousInertialFrameKinematicsAt are retained, while the derivation route is reconstructible rather than stored. In that direct result, distinct inertial frames, common-situation representation, finite light, one actual preserving reexpression, law covariance, and no-preference all hold together. Both papers derive that direct proposition. Semantic grounding requires the paper's inhabited two-frame and finite-light setup but no transformation, covariance, no-preference bridge, route, or terminal result. An empty-setup countermodel blocks vacuous implication-shaped bridges from faking it, and direct mutation theorems make every selected object and relation family falsify it when changed. Independent source-valued framework witnesses now also retain Einstein's 0,2,4 synchronization, c=5, v=3, and gamma=5/4 Lorentz boost, relative simultaneity, undeformed intrinsic rod, oriented clock dilation, and 25/7 velocity composition. Minkowski's separate witness retains the upper hyperboloid, distinct null/timelike quadratic values, an independently supplied world postulate, and qualified gravity/universality boundaries. These are concrete historical countermodels, not additional assumptions of the neutral shared route;
Einstein's original 1916 general-relativity synthesis, separating the physical motivation for extended relativity, operational covariance, metric meaning, geodesic extension, vacuum and sourced field equations, the independent limitation on source selection from relativity alone, conservation, the Newtonian limit, and static-field predictions.
Schwarzschild's original 1916 exact exterior point-mass solution, separating the determinant-preserving coordinate construction, reduced vacuum equations, exact integration and uniqueness, finite-approximation limitation, orbital and Mercury calculation, practical radial comparison, circular-orbit law, and conditional molecular analogy.
Kerr's original 1963 algebraically special spinning-mass solution, separating the imported Goldberg-Sachs characterization, diverging nonorthogonal null-congruence ansatz, massless and massive integrability branches, degenerate stationary specialization, exact Type-D vacuum metric with its displayed stationary line element, asymptotic coordinates with the Euclidean-radius quartic relation and ring-exception scope, third-order EIH identification of mass and angular momentum, and unresolved exact multipoles and interior solution.
Penrose's original 1965 gravitational-collapse theorem, separating the symmetry limitation of earlier exact models, nonspherical trapped-surface construction, null-energy focusing, compact causal boundary, noncompact Cauchy topology obstruction, future null incompleteness, physical alternatives, and the absence of a curvature-divergence or black-hole theorem.
Hawking's original 1965 open-universe argument, separating the expanding flat/open cosmological model, large-sphere past-null convergence, past-trapped-surface construction, imported global incompleteness route, finite-margin perturbation robustness, weaker matter-flow conditions, and the open closed-universe extension.
Guth's original 1981 inflationary-universe proposal, separating the horizon and flatness diagnosis, entropy criterion, false-vacuum mechanism, local-patch argument, conserved-charge and monopole consequences, the graceful-exit failure, including near-complete converted volume without percolation, and the unresolved modification outlook.
Goldstone, Salam, and Weinberg's original 1962 broken-symmetry analysis, separating the perturbative inverse-propagator argument, the general conserved-current spectral proof, the charge-and-Lorentz argument, approximate composite-order-parameter extension, and unresolved alternatives.
Anderson's original 1963 plasmon analysis, separating the uncoupled superconducting matter spectrum from the interacting physical spectrum, gauge-invariant finite-frequency plasma response, Coulomb conversion of the Goldstone mode, the nonrelativistic massive-vector analogy, and unresolved non-Abelian extension.
Bardeen, Cooper, and Schrieffer's original 1957 superconductivity theory, separating effective attraction, the coherent variational ground state, the qualified common-pair-momentum persistent-current argument, zero- and finite-temperature gap calculations, thermodynamics, case-I/case-II coherence factors, Meissner/Pippard response, empirical comparisons, and the explicitly unfinished model, transport, and strong-coupling extensions. Its zero-temperature route now retains the paper-local equation-(2.40) gap value, equation-(2.50) quasiparticle dispersion, and equation-(2.49) pair-breaking threshold value rather than only named gap predicates.
Feynman 1954, Feynman-Cohen 1956, and Girvin-MacDonald-Platzman 1986 as a cross-system variational-excitation benchmark. The helium and fractional Hall vocabularies remain paper-local; only the density-mode trial-state construction, energy calculation, and fixed-momentum upper-bound inference are shared. Feynman 1954 and GMP 1986 independently earn the component, while Feynman-Cohen is retained as a dependent refinement. Feynman's seven calculation-dependent stages are output-led, its shared adapter consumes only the terminal established spectrum, and a staged countermodel separates all seven vacuous calculation contracts from the paper's physics. Its paper-local later chain now also retains Eq. (25)'s free-energy integral, Eq. (26)'s Bose occupation, and Eqs. (39)-(43)'s moving-energy, distribution, normal-density, and current formulas, including Eq. (41)'s selected position, local v_s(r), and checked substitution into the same constrained occupation as Eq. (40), without widening the shared variational component. GMP's nine stages are likewise output-led, including explicit certified unprojected-diagnosis and projected-trial intermediates. Its paper-local source model now evaluates actual noncommuting complex density matrices, equation (4.18)'s Gaussian cyclotron subtraction, a three-state positive density-response measure, its exact zeroth and first moments, and the unsaturated 98% oscillator-strength fraction. A quartic visible response with a density-dark excitation below every proposed gap demonstrates why the source's finite first moment cannot prove an exact many-body gap. Its shared adapter consumes only the terminal projected bound, while 20 inhabited countermodels retain both the nine vacuous-contract distinction and these physical nonimplications. Both independent terminal routes now also realize a typed structural explanation of the selected sector-energy upper bound, without asserting exactness, saturation, or accuracy. The later Feynman-Cohen paper now follows the complete article through eighteen routes: inherited spectrum, packet continuity, return flow, exact symmetrization and linearization, diffraction data, zero-temperature identities, corrected Kirkwood input, separate norm and numerator calculations, optimization, momentum scope, error budget, thermodynamic qualifications, and vortex interpretation. Its paper-local scalar spine now retains Eq. (9)'s E_1(k) = hbar^2 k^2 / (2 m S(k)), Eq. (61)'s printed backflow quotient with the source coefficients and denominator condition, and Eq. (63)'s 1.85 inverse Angstrom optimized momentum and 11.5 K gap. These packages remain staged in the simple benchmark, improved spectrum, and optimized gap rather than widening the shared variational component.
Anderson 1958 as the locator-expansion, probabilistic-localization, isolated-system no-diffusion, and inverse-cube-boundary benchmark. Its Green-function-decay route now supplies one independent realization of the shared resolvent-decay-localization component while the locator expansion and transport conclusions remain paper-local. The first-order lane now also retains pp. 1495 and 1498 equations (9), (11), and (28) as a typed paper-local readout: the off-diagonal squared-coupling locator sum and Im V_0(s) = -s X(s). Lean checks denominator positivity and the nonpositive imaginary-self-energy consequence at positive Laplace scale; a countermodel prevents a named locator-distribution calculation from supplying those equations by itself. The same lane now retains pp. 1498-1499 equations (29)-(33): the Fourier representation of P(X), the characteristic-function exponent, the radial-energy integral with explicit integrability hypotheses, equation (32)'s small-x approximation, and equation (33)'s large-X heavy-tail density. Lean checks positivity and the inverse-three-halves envelope of that density; a second countermodel prevents a named heavy-tail output from supplying equation (33).
Abrahams et al. 1979 as the analytic one-parameter localization-scaling hypothesis benchmark.
MacKinnon-Kramer 1981 as the finite numerical localization-length collapse and reconstructed-conductance scaling benchmark.

The active expansion is deliberately balanced across classical mechanics, statistical mechanics, plasma physics, atomic, molecular, and optical physics, quantum mechanics, quantum field theory, general relativity, cosmology, condensed matter, nuclear physics, and string theory. All eleven listed initial rows are now active. See docs/architecture/balanced-paper-benchmarks.md. The cross-paper extraction decision is recorded in docs/architecture/technical-framework-reuse-audit.md.

These reconstructions independently require named argument routes for provenance, so route grouping and route-dependency validation are shared source-mapping infrastructure. Their semantic vocabularies and theorem hypotheses remain paper-local.

Route dependencies are declared as immediate edges. The shared validator computes their transitive closure, makes every ancestor route's declared outputs available to descendants, and separately checks topological order. Internal intermediate claims do not leak across route boundaries. A later route that needs one must require the producing route to export it explicitly. Paper source maps therefore record both the actual argument graph and honest route interfaces rather than flattening every ancestor into each dependsOn list.

Justification statuses also propagate through the actual claim-premise graph. The basis retains both each status and the exact source-mapped step that introduced it. This keeps distinctions that matter to the papers: a conclusion may remain conjectural, approximate, deferred, expected, interpretive, or unresolved, while an independent calculation in the same route does not inherit those statuses merely by route membership. Exact step origins lead back to primary-source anchors; logical conditionality encoded inside a claim's formula remains separate from this provenance analysis.

Auditable source maps give every claim node exactly one producing step. When two routes establish the same physical proposition, they use distinct claim identifiers whose formulas may coincide. This preserves each route's exact premises and epistemic history instead of merging alternative derivations.

Paper-local structures represent quantitative physical outputs as data, constrained by proposition-valued definitions and checked equalities rather than used as proof registries.

Temporary reductio assumptions have explicit discharge steps. Their epistemic origin propagates through internal intermediate claims, is removed only by the named discharge, and is excluded from route outputs and inherited dependency claims. The route validator also rejects a discharge placed in a different route from its temporary assumption.

Ordinary routes are semantically executable. Certified predecessor routes supply their declared outputs, and sound local steps propagate truth in route order to derive the descendant route's outputs from the graph itself. Coverage proofs therefore need not establish the same outputs independently. Routes containing temporary reductio introductions remain explicit paper-local proofs because those assumptions are valid only inside their discharged subarguments.

The previous broad-library, global-assumption, and metadata-heavy experiments are preserved under deprecated/. They remain available as historical source material but sit outside the Lean package tree and cannot be imported by the active root. Reuse requires a fresh primary-source comparison and must satisfy the current paper-first rules.

Framework-to-framework imports are also exact audited interfaces. Every child dependency must enter a declared semantic context, model, or compatibility bridge and must be used by a checked parent deduction or refinement theorem. The policy derives all such edges from the Lean imports and rejects missing, stale, or merely decorative dependencies. The current 31-edge audit is recorded in docs/architecture/technical-framework-reuse-audit.md.

Active Layout

PhysicsLogic/Framework/ActionPhaseComposition.lean: the narrow action-phase, intermediate-composition, and stationary-action route independently realized by Dirac 1933 and Feynman 1948. Their transformation function and path contribution remain distinct paper-local amplitude data; Dirac's adapter now retains value-level equations (7)-(9), the selected binary intermediate-coordinate integral from equation (11), and the derivative-zero stationary-action condition as explicit propositions rather than only named phase, composition, and stationarity predicates. no duplicate route-mode enum is retained. The context owns ten selected indices and exposes their unique exact model; changing any selected index or any of fifteen relation families fails the original context's exact semantics. The established result is output-led: exact selected semantics is conjoined directly with NonvacuousActionPhaseCompositionAt, where the complete setup, phase, composition, zero-parameter-limit, cancellation, and stationary-action chain holds at one model. It stores no implication-valued calculation or route proof; those contracts are reconstructed from the direct relations. A false-setup countermodel blocks both vacuous contracts and grounding, and exhaustive direct mutations make every selected index and relation family destroy that proposition. Both paper adapters derive the direct result from their source-anchored routes. The ordinary structural explanation executes the shared route without requiring paper provenance. A stricter source-sensitive explanation begins from ten granular Dirac premises or fifteen granular Feynman premises, retains a typed paper-local derivation, exposes it, and entails the ordinary explanation when provenance is forgotten. Neither explanation accepts a terminal paper or framework result. The ordinary constraint, source wrapper, stationary-action phenomenon, and paper-local derivation types remain distinct. A converse model retains the complete endpoint, route, and ordinary explanation but has no source-sensitive explanation when its source derivation is false. The same endpoint realizes the mature controlled-classical-recovery contract at the explicit zero limit: phase/composition supplies the valid quantum description, cancellation and stationary selection supply the recovery calculation, and stationary action supplies the classical behavior. A finite-small/no-zero- limit countermodel blocks conflation with approximate recovery, and no exact-replacement judgment is inferred. Theory/model/world grounding separately requires exact selection, the real endpoint/history/partition setup, and the explicit zero-parameter limit, but no phase, composition, cancellation, or stationary-action output. A setup-complete model can be grounded while composition still fails. It defines no path measure, probability rule, wave function, Schroedinger equation, operator algebra, or field-boundary functional. A checked limit boundary now retains all ten selected phase/composition indices together with positive finite Planck and action scales, nonstationary action variation, cancellation residual, finite stationarity residual and tolerance, and the separate limiting Planck and stationarity residuals. Its exact model bridge retains the inhabited setup, phase, composition, endpoint, and cancellation facts. Dirac and Feynman each realize finite-small stationary-phase dominance while the zero-limit and exact stationary-action endpoint fail; a positive shared witness supplies both zero residuals. No constant small-parameter predicate substitutes for these scales, residuals, or the limiting condition. A second checked boundary now makes the earlier logical separation value-level as well: ActionPhaseCompositionBoundaryReadout retains a positive Planck scale, action, nonzero complex normalization, local amplitude, endpoint amplitude, and independently calculated intermediate composition. Its local-phase predicate is the explicit normalized exp(i S / hbar) equality, while its composition predicate is a separate endpoint equality. The shared, Dirac, and Feynman countermodels all realize the former and fail the latter. The remaining paper-local countermodels no longer use enum truth tables: Dirac retains ordered momentum derivatives, endpoint/time-step phase, boundary geometry, and probability/grounding residuals; Feynman retains measured and coherent sums, short-time errors, temporal-memory/additivity defects, Gaussian and two-history values, final-state sums, formal-equation residuals, and measurement/prediction scope. These are checked physical non-implications, not renamed status labels. Feynman's paper-local path endpoint now nevertheless retains the original finite-time formulas before any shared extraction: equation (9)'s time-slicing limit of the regional path integral, the explicit exp(i S[path] / hbar) contribution with partition-dependent common normalization, equation (10)'s segmented action sum, and equation (11)'s minimum classical segment action. Equation (12)'s normalized exponential regional path integral is now a separate value-level endpoint supplied by an explicit calculation contract that combines equation (9), the action-phase formula, and equation (10), while equation (11) remains the separate definition of segment action. The limit, integral, minimization, and normalization remain imported mathematics. The same paper-local adapter now also retains journal equation (18)'s first-order one-step recursion and equations (22)-(30)'s selected one-dimensional scalar-potential derivation. The readout owns represented mass, Planck constant, time step, potential, wave function, derivatives, action, normalization, and real-line integral data. Equation (18) carries its bounded second-order residual, equations (22) and (23) use a positive-side little-o-of-epsilon witness for the source's smaller-than-first-order error, and equation (24) records its exact change of variables while reusing equation (23)'s residual. Equations (25), (27), and (29) keep controlled Taylor residuals, while equations (26), (28), and (30) retain the Gaussian moments, normalization square, and resulting Schroedinger equation. A countermodel prevents a named wave-equation output from replacing these source formulas.
PhysicsLogic/Framework/CompleteIntegralDynamics.lean: the narrow complete-integral trajectory-reconstruction route independently realized by Hamilton 1834 and Jacobi 1837. Its exact model retains twelve selected physical indices and nine relation families: a represented evolution, one selected first-order equation, a separately complete parameter family, separate momentum and parameter derivative calculations, motion recovery, and a separate completeness calculation. CompleteIntegralAt is the conjunction of first-order equation satisfaction and parameter-family completeness; finite countermodels show that neither conjunct supplies the other. Jacobi's adapter now keeps the endpoint-defined principal function separate from the arbitrary complete integral used for reconstruction, and selects the latter for the shared model; a countermodel blocks promotion of endpoint-principal data into arbitrary-complete-integral data. Jacobi's paper-local route now also retains p. 104's value-level Hamilton-Jacobi equation and pp. 107-109's parameter, velocity, momentum, and Newton recovery formulas at a selected configuration and time; those one-paper formulas are not exported into the shared component. The selected evolution is exposed through Paradigm.Dynamics.Dynamics, and each completed paper route now supplies an inhabited HasForwardEvolutionAt witness. A route-complete finite model nevertheless has two distinct continuations from the same initial configuration and time, blocking promotion of reconstruction to ForwardDeterministicAt or UniqueForwardEvolutionAt. This is a limit of the shared contract, not a claim that either source theory branches. The complete route also realizes a typed structural explanation of the selected solved motion and complete family of motion integrals. Its constraint contains the complete-integral setup and four implication-valued calculations but no reconstruction output. A finite model declares both outputs while invalidating the setup and therefore has no explanation; a separate branching model has the explanation without determinism or uniqueness. Hamilton and Jacobi rebuild the explanatory route from their original granular calculations rather than established recovery bundles. A separate proof-free source constraint now retains their derivational difference. Hamilton's typed token requires varying action, opposite-signed endpoint derivatives, parameter recovery, and characteristic-equation verification; Jacobi's requires the endpoint-derived PDE and the theorem for a separately selected arbitrary complete integral. A converse model keeps the complete route and reconstructed outputs while making the source relation false, so common output cannot manufacture paper provenance. Technical completion and theory/model/world grounding remain independent. It defines no action, Hamiltonian, energy law, canonical geometry, Kepler problem, general characteristic system, or Pfaff theory.
PhysicsLogic/Framework/ParentActionDualReduction.lean: the narrow local parent-action route independently realized by Rocek-Verlinde 1991 and de la Ossa-Quevedo 1992. An exactly selected symmetry is gauged with an auxiliary field and flatness constraint; separate paper-local eliminations recover the original action and produce a dual action. The established result projects the complete setup, both elimination calculations, and both action outputs. Typed countermodels keep the eliminations independent, prevent the two outputs from reconstructing a missing setup, and exhibit a completed local reduction whose actions are not physically equivalent. Technical completion and theory/model/world grounding are independent in both directions. Its nine selected indices, eight route-used relation families, exact model retention, exhaustive transfer, and seventeen-component mutation audit are checked. The established result projects to NonvacuousParentActionDualReductionAt, where validity, description, symmetry action, gauging, flatness, gauge fixing, and both elimination outputs hold directly at one model instead of only behind implication-valued calculations. It also projects to two separately typed DerivationBridge results: constraint-field elimination realizes recovery of the original action, while auxiliary-field elimination realizes production of the dual action. Their combined result is only a conjunction of those two derivations, not an equivalence relation between the actions. A proof-free source description now retains the exact selected model and a typed paper-local derivation. Rocek-Verlinde realize it from the raw first-order bosonic setup and calculation; de la Ossa-Quevedo realize it from the nonabelian setup, parent path-integral construction, and elimination calculation. The generic source theorem executes both branches without an established or nonvacuous endpoint. A converse model retains both completed outputs and output-led reductions while falsifying the independent source relation, so the source-sensitive reductions do not follow. One-sided countermodels show that either derivation can hold without the other. A false-setup model shows why the implication-shaped calculations alone are insufficient. The retained sensitivity model realizes that direct proposition, and changing any of its nine selected indices or eight relation families destroys it. Both paper adapters expose both derivational results while scoping every relation to their exact selected actions, fields, symmetries, and regimes. It deliberately asserts no global equivalence, conformality, determinant correction, transformation rule, or surviving dual symmetry.
PhysicsLogic/Framework/AmplitudeOutcomeProbability.lean: the narrow route independently realized by Born 1926 and Kennard 1927 from an exactly selected valid state and an admissible amplitude associated with that state in a selected representation, through a paper-local outcome-weight calculation, to a separate paper-local probability interpretation. Its proof-free model retains eight selected indices and eight route-used relation families. Its output-led established result contains exact selected semantics and NonvacuousAmplitudeOutcomeProbabilityAt, where all eight route-used physical relations hold together at one selected situation rather than behind implication-valued calculation wrappers. Complete setup, calculation contracts, the interpretation bridge, and the route are reconstructed from those direct facts. Grounding requires the complete selected setup but no calculated weight or assigned probability. Typed countermodels separate setup from calculation, calculation from interpretation, the assigned probability from its derivation, and technical completion from theory/model/world grounding in both directions; a false setup can keep the implication contracts true without satisfying the direct proposition. Exact selected setup and raw route now give an ordinary structural explanation of the calculated-and-interpreted probability phenomenon. A stronger source-sensitive explanation adds a typed paper-local derivation: Born's token requires elastic scattering asymptotics; Kennard's distinct token requires transformation and alternative exact-observation inputs. Neither source theorem consumes the completed endpoint or ordinary explanation, and a countermodel proves that completed outputs plus ordinary explanation cannot reconstruct missing source provenance. Exact model retention, exhaustive claim transfer, and a sixteen-component mutation audit are checked. The retained finite model realizes the direct complete route, and exhaustive direct mutations make every selected index and relation family destroy that proposition itself. The neutral shared route stops at the paper-local calculation relation, while governed source-valued witnesses separately retain Born's normalized squared channel frequencies, directional solid-angle weight, inelastic energy jump and pi^2 k^2 factor, plus Kennard's density-versus-interval distinction, Gaussian hbar/2 saturation, and regulated transformation kernel. Deterministic wave evolution does not establish deterministic outcomes or ontic indeterminism.
PhysicsLogic/Framework/Entanglement.lean: the bipartite nonseparability route independently realized by Coffman-Kundu-Wootters 2000 and AMPS 2012, with a further finite-density-matrix client in Bell 1964. FiniteQuantumState supplies positive unit-trace operators, actual partial traces, convex product-mixture separability, spectral entropy, and a proved partial-transpose witness bound. Its model retains a prepared parent state, selected reduced joint state, two distinct subsystem roles, separability, classical correlation, purity, an independent witness calibration, witness value, and marginal entropy. A positive witness is insufficient: the checked route also requires calibration plus the selected separable-state upper bound before deriving nonseparability. The output-led established result retains exact selected semantics, the direct nonvacuous prepared-pair endpoint, and calibration without storing a route object. CKW supply squared-concurrence tangle plus a zero-tangle bridge; AMPS supply thermal late-mode entropy plus pure-pair separable-entropy bridge. The shared layer identifies neither tangle with entropy nor entanglement with correlation, Bell violation, signalling, or a sharing inequality. It projects only inhabited nonseparability to Paradigm/QuantumNonseparability.lean and composes with tripartite sharing through an explicit pair-to-demand handoff. A finite countermodel keeps a positive nonseparable state while deleting witness calibration, so endpoint truth cannot reconstruct the source route. Its ordinary structural explanation retains only the common calibrated-witness route; source-sensitive explanations keep distinct CKW tangle and AMPS pure-pair entropy derivation tokens, with a false-provenance countermodel blocking reconstruction from ordinary explanation. Source-sensitive tripartite composition additionally requires independent bipartite, sharing-exclusion, and pair-to-demand derivations; CKW's dominant AB channel yields the constructive endpoint, while AMPS's competing BC channel yields the checked contradiction. A finite countermodel retains both sourced child explanations and ordinary composition while withholding the source derivation for their handoff. CKW's paper-local residual keeps all eight complex state amplitudes and the original four diagonal, six planar, and two tetrahedral monomials. Lean derives tau_ABC = 4 * abs(d1 - 2*d2 + 4*d3) from the explicitly imported determinant calculation on the two-dimensional range, not the vanishing full four-dimensional determinant. The individual polynomials are invariant under generating qubit swaps; the normalized GHZ state has unit residual, every single-excitation state has zero residual and saturates its pairwise bound, and actual planar and phase-reversed tetrahedral states require the printed -2, 4, and absolute-value factors. Residual permutation invariance is itself a derived equality of the same physical tangle with the original and both permuted polynomial values, not an independently asserted proposition or paper-framework field.
PhysicsLogic/Framework/StateDispersionUncertainty.lean: the narrow prepared-state dispersion route independently realized by Kennard 1927 and Robertson 1929. A valid selected state and two observables receive paper-local dispersion readouts, a paper-local lower-bound value, and an explicit product-bound calculation. Its proof-free model retains all nine selected indices and exactly the six relation families used by the route. Each paper-local context owns those nine values and constructs one exact selectedModel; all nine index mutations and all six relation mutations fail selected semantics. Kennard and Robertson supply that certificate before applicability can be established. The retained finite model itself realizes the complete route with distinct observables and role-matched distinct dispersions. The output-led established result is exact selected semantics together with NonvacuousStateDispersionUncertaintyAt, where validity, preparation, both observable selections, both represented dispersions, the selected lower bound, and the product relation hold together at one model instead of hiding behind implication-valued calculation contracts. A false-setup countermodel cannot exhibit that proposition, and exhaustive direct mutations make every selected index and retained relation destroy it. The older direct activity theorems independently show that every selected index and retained relation changes a route-used proposition. The complete route now also realizes a typed structural explanation of the selected state-dispersion lower-bound phenomenon. Its constraint contains the nine selected values but no dispersion representation, bound identification, or product inequality. Kennard and Robertson derive the explanation from their direct route adapters without consuming the established or nonvacuous endpoint. A false-validity model has all terminal outputs but no explanation, while a route-complete zero-bound model shows that structural explanation does not imply strict positivity. A stronger source-sensitive constraint retains one typed paper-local derivation and an independent proposition that it obtains. Kennard's token is realized by his general amplitude factorization and nonnegative remainder on pp. 338-339; Robertson's distinct token is realized by his one-particle Hermitian-rms, integration-by-parts, Schwarz, and commutator route on pp. 163-164. Both adapters construct this explanation directly from raw source contracts. A countermodel preserves the complete route, established shared result, and ordinary explanation while falsifying the derivation relation, so common outputs cannot reconstruct source provenance. It stores no implication-valued calculation contracts; a checked theorem reconstructs the complete route from the inhabited outputs. Separate interpretations ground the exact named model and its valid prepared-state and observable setup in each paper's theory and represented system. They do not consume dispersion readouts, lower-bound calculations, product inequalities, route applicability, or established results. Converse models separate technical completion from grounding and grounding from technical completion. A false prepared-state setup cannot be grounded even when every declared theory and world claim is made true. Both adapters expose named exhaustive certificates transferring every retained claim through the explicit theory/model/world bridges. The framework defines no measurement disturbance, Gaussian packet, Fourier transform, commutator, operator domain, or universally positive bound. Strict positivity remains outside the exact model because Robertson's state-dependent bound may vanish. Heisenberg's operational microscope argument therefore remains outside this component; the new structural result is not an apparatus error-disturbance explanation. Separate source-valued witnesses retain Kennard's pointwise amplitude probabilities, doubled-variance precision and h/(2*pi) product bound, Gaussian saturation, distinct arbitrary-amplitude factorization and nonnegative remainder, mutually exclusive exact observations, and classical packet-center motion with unavoidable initial spread. Robertson's independent witnesses retain rms normalization and h/(4*pi), Hermitian observables, vanishing boundary terms, the Schwarz/commutator route, its printed linear-momentum restriction, a valid zero-commutator state, and extremal angular-momentum saturation. Thirty-four controlled mutations reject swapped source formulas, missing proof hypotheses, false universal positivity, an invented polynomial-operator proof, and identification with apparatus error or disturbance.
PhysicsLogic/Framework/OperationalErrorDisturbance.lean: the narrow apparatus-level inference independently realized by Heisenberg 1927, Bohr 1935, and Ozawa 2003. Its exact model retains sixteen selected indices, including separate prepared-object and composite interaction-input states, and eleven route-used relation families, including an explicit proposition-valued bridge from preparation to interaction input. The context owns that complete measurement instance and constructs one selectedModel; changing any index therefore fails exact semantics instead of selecting a new model from the candidate's own fields. The heuristic microscope, fixed-slit diffraction/recoil, and operator-measurement universal routes remain definitionally distinct. The established result retains the selected preparation-to-input bridge, measurement run, operational error and disturbance representations, quantitative tradeoff, qualified scope, and explicit non-identification with prepared-state dispersion. Operator commutators, correlation terms, corrected inequalities, optical recoil, quadrature transducers, and experimental proposals remain paper-local. Countermodels separate preparation and performance from an interaction-input bridge, performance from quantitative representation, representation from tradeoff, and technical completion from theory/model/world grounding. The complete applicable route now also realizes a typed structural explanation: its constraint retains all sixteen apparatus data, while its distinct phenomenon retains only the observable- and apparatus-indexed quantitative tradeoff. All three papers realize it directly from their own route inputs. A second, source-sensitive projection retains a typed derivation token and its proposition-valued realization in addition to the complete ordinary route. Heisenberg supplies the microscope setup, corrected recoil, selected-Gaussian calculation, role distinction, and addendum scope as raw premises; Bohr supplies his p. 697 fixed-support slit, prepared incident plane wave, photographic record, de Broglie wavelength, local diaphragm recoil, qualitative Delta p Delta q ~ h, and apparatus/state role distinction; Ozawa supplies the system-probe setup, rms definitions, commutator/correlation calculation, generalized relation, and formulation separation. Their source theorems reach the same apparatus phenomenon without identifying those derivations or accepting a shared terminal result. Bohr's distinct p. 699 EPR preparation retains two narrowly separated slits, two short incident wavelengths, and the shared preparation diaphragm's measured before/after momentum balance. It fixes q1 - q2 and p1 + p2 while leaving q1 + q2 and p1 - p2 undetermined. His actual local slit state change independently realizes Philosophy.Measurement.StateChangeMeasurementContext.DisturbsAt; a joint theorem proves that this genuine local disturbance, the double-slit source preparation, and the nonvacuous technical route all coexist with mechanical nondisturbance of the remote particle for either later EPR arrangement. Countermodels show that a declared tradeoff without the preparation-to-input bridge and a calculated tradeoff misidentified as prepared-state dispersion realize no such explanation. A completed tradeoff and full ordinary route with a false source relation also fail the source-sensitive explanation. Sixteen index mutations and eleven relation mutations fail exact semantics, while a direct audit proves that every selected physical value affects a route-used predicate.
PhysicsLogic/Framework/OneParameterLocalizationScaling.lean: the narrow localization-flow structure independently realized by Abrahams et al. 1979 and MacKinnon-Kramer 1981. Its proof-free context owns eight selected physical indices and all fourteen route-used relation families, including the three predicates negated by the qualified scope assessment. The analytic block-composition and finite-size numerical-reconstruction methods remain in distinct paper-local calculation and scope predicates rather than a duplicate shared route tag. Each context constructs one named exact model, supplies a retention certificate before applicability, and requires that model in its theory/world interpretation. Shared projection and exhaustive claim theorems preserve the complete route, while direct data-sensitivity and mutation countermodels show that changing any retained index or relation changes the formal semantics. Both clients now also project to a direct output-led endpoint requiring the finite-scale setup, direct closure, flow, regularity, asymptotic and dimensional outputs, and the complete qualified scope, but no implication-valued calculation contract. Grounding separately requires exact selected semantics and the finite-system setup while supplying no scaling output or route. The ordinary structural explanation executes the shared qualified scaling route without treating provenance as physics. A source-sensitive refinement keeps the two derivations distinct: the 1979 client supplies analytic finite-hypercube block composition, while the 1981 client supplies recursive finite-bar collapse and reconstructed conductance flow. Each source-facing adapter constructs applicability directly from its component results rather than consuming the terminal paper result, and the generic necessity theorem executes the scaling route rather than consuming an established endpoint. A converse model retains the endpoint, reconstructed route, ordinary explanation, and dimensional-flow phenomenon but has no source derivation, so it has no source-sensitive explanation. Countermodels enforce both directions of the grounding separation, and direct mutations of all eight indices and fourteen relation families destroy the endpoint. Thouless-number definitions, transfer matrices, numerical error control, Landauer assumptions, crossover calculations, critical data, and other mechanisms remain paper-local.
PhysicsLogic/Framework/ResolventDecayLocalization.lean: the narrower propagation-kernel-decay route independently realized by Anderson 1958 and MacKinnon-Kramer 1981. Its exact model retains five selected physical indices and eight relation families. The clients select different concrete kernels and descriptors, while analytic probabilistic convergence and controlled finite-bar numerical status remain in paper-local calculations and scope predicates rather than a duplicate route tag. Both clients supply a decay calculation, a separate localization interpretation, and an explicit exclusion of unqualified all-state localization. Anderson's locator resummation, no-diffusion result, bath scope, and inverse-cube transport remain outside the common route; source-valued audit readouts nevertheless retain the positive-Laplace locator, rare-resonance heavy tail, exact Gamma(1/2) = sqrt(pi) coefficient, physically correct exponential suppression, and equation (19)'s normalized finite-width disorder box P(E) = 1/W for |E| < W/2 and zero outside. The actual paper's high-order path calculation owns that full value-level density; shared source controls independently reject its wrong height, missing support, incorrect Gamma factor, and altered suppression coefficient. Coherent versus nonrepeating paths, isolated-system qualification, finite-bar recursion, two- and three-dimensional sampled ranges, W_c = 16 +/- 0.5, nu = s = 1.2 +/- 0.3, and explicit Landauer and dominant-channel assumptions. Countermodels separate setup, decay, interpretation, universality, and theory/model/world grounding. The established route also projects to a direct nonvacuous proposition requiring the selected setup, calculation, decay outputs, interpretation, scoped localization, and denied all-state overclaim. A false-setup model fails that endpoint, and direct mutations of all five indices and eight relation families destroy it.
PhysicsLogic/Framework/SpinOrbitShellClosure.lean: the narrow nuclear-shell inference independently realized by Mayer 1949 and Haxel-Jensen-Suess 1949. Its proof-free context owns six selected indices and the twelve proposition-valued relation families that make those selections physically meaningful, and constructs one exact selectedModel. Both papers use named exact models and named exact selected-setup adapters in their applicability theorems, exhaustively realize all seventeen shared claims, and transfer them through explicit theory/model/world grounding. Grounding independently requires SelectedSpinOrbitShellClosureSetupAt: the exact selected model and its valid independent-particle central-field setup; it is not indexed by an established closure result and does not consume the spin-orbit, filling, comparison, or interpretation routes. Converse models separate technical completion from grounding and grounding from technical completion. Mayer's square-well route and Haxel-Jensen-Suess's oscillator, anharmonicity, and Yukawa construction remain paper-local. Mayer's close-within-shell/nonfixed-table-order qualification, thallium near-degenerate crossing, and pair-only h11/2 caveat are not promoted into the shared route. The Haxel-Jensen-Suess letter also retains its seven printed oscillator-group labels, six complete multiplicities and cumulative totals, five explicit closure sums from 8 + 6 = 14 through 112 + 14 = 126, and the opposite-parity rule between oscillator quantum number and orbital angular momentum as a quantified modulo-two relation with concrete marked-orbital occurrences. Its literal printed source-coordinate equation r = r1 + r2 + r3 remains distinct from physical zero-based Cartesian occupations N = nx + ny + nz, which instead obey r = nx + ny + nz + 1. The r = 1 ground shell has the unique physical (0,0,0) state; (1,0,0), (0,1,0), and (0,0,1) belong to r = 2. The r = 4, N = 3 shell retains all ten actual occupation triples, their complete membership characterization, and their spatial cardinality. Five independent value-bearing countermodels prevent conflating source and physical coordinates, incomplete enumeration, or incorrect degeneracy. The marked d through i terms additionally retain l = 2,...,6 and doubled 2j = 5,7,9,11,13 values, with a checked deduction of their j = l + 1/2 instances. The five closed-shell counts now require an explicit assembly bridge before yielding the displayed {14, 28, 50, 82, 126} pattern; the Mayer-compatible higher subset is a checked erase-14 projection rather than a second paper-local calculation. Mayer now likewise retains the full displayed {2, 8, 20, 28, 50, 82, 126} sequence, an explicit ordered-filling assembly bridge, and a checked erase-2/erase-8/erase-20 projection to the shared higher pattern. Her selected f, g, h, and i partner pairs retain common orbital values and doubled total-angular-momentum values, and both paper adapters make the shared partner-splitting relation consume their checked j = l +/- 1/2 instances rather than trusting spectroscopic names. The repeated doubled-j arithmetic itself is now the narrow shared proposition SpinHalfOrbitalPartnerRule: it exposes both j = l - 1/2 and j = l + 1/2 branches, proves their natural-number realizations, and has a countermodel showing that a named partner does not supply the rule. The two paper-local JEqualsLPlusOrMinusHalf predicates delegate to this shared definition instead of carrying disconnected duplicate formulas. A proof-free ReducedNuclearInteraction now retains positive potential depth, radius, radial-profile exponent, spin-orbit strength, a checked f7/2 state count, and the calculated higher-closure list. Two physically different potential readouts match {28, 50, 82, 126}, so closure agreement does not determine the interaction. Their unit-scale depths, radii, and profile exponents are logical witnesses, not historical nuclear measurements. Mayer's source boundary 83, qualified h11/2-3s1/2 parity adjacency, and incomplete tail remain paper-local; the HJS r = 4 to r = 3 regrouping, 20 + 8 = 28, and extra closure 14 also remain paper-local. The common route now requires the higher-j partners to be lowered and regrouped into the preceding shell relative to the two selected schemes; a wrong-sign or merely nonzero splitting cannot satisfy it. A finite source-shaped witness realizes the complete route with distinct central/spin-orbit schemes and calculated/observed pattern values; the established route projects to NonvacuousSpinOrbitShellClosureAt, and direct activity theorems make all six indices and twelve relations destroy that direct proposition when changed. The direct endpoint also projects to a typed mechanistic explanation of the observed closure pattern, keeping empirical prediction separate from the physical-account bridge; a finite countermodel satisfies the former while denying the latter. Here prediction means model-level calculated-pattern agreement, not historical novelty. A second shared projection separates ordinary SpinOrbitShellClosureConstraint, its source-sensitive wrapper, and the distinct ObservedSpinOrbitShellClosurePhenomenon. The ordinary theorem executes the complete shared route without paper provenance; the stricter source theorem adds an independently realized derivation token, exposes it, and entails the ordinary explanation when provenance is forgotten. Haxel-Jensen-Suess supply their oscillator-table, anharmonic-classification, marked-high-j filling, and assessment route; Mayer supplies her square-well, strong-spin-orbit, ordered-filling, bounded isotope-assessment, and qualified-interpretation route. Neither theorem consumes the established or nonvacuous shared endpoint. A finite converse model retains the complete shared result and ordinary explanation while denying source derivation, so reusable route logic does not manufacture provenance. A vacuity countermodel prevents implication-valued shell calculations without setup from counting as an inhabited closure route.
PhysicsLogic/Framework/Charge.lean: the first shared technical-framework component, extracted from the independently realized chiral-charge sectors of Witten 1982 and the Seiberg-Witten 1994 electromagnetic BPS sectors, and now also realized by Maldacena's quantized D3 five-form charge, Polchinski's D-brane Ramond-Ramond charge, Laughlin, Haldane, and Arovas-Schrieffer-Wilczek fractional excitations, and charged Maxwell lines. Seiberg-Witten's seventeen independently audited paper-local boundaries retain projective singularity support, the printed monodromy matrices and their fixed (1,0) and (1,-1) charges, the exact monopole-point values a_D(1) = 0 and a(1) = 4 / pi, period and BPS mass values, candidate counts, asymptotic Higgs winding, quantized magnetic flux, distinct F-term and D-flat vacuum equations, nonzero deformation and modulus derivative, separate magnetic Higgs and electric-confinement outcomes, distinct electric/magnetic patches with nonzero Dirac pairing, and the exterior real-axis period ratio. Lean checks that real nonzero a and purely imaginary nonzero a_D force Im(a_D/a) != 0; path connection, matrices, and labels alone cannot supply the missing physics. No Unit-carrier or empty-state truth table replaces those distinctions. It formalizes charge existence, uniqueness, applicability of functional assignment to an admissible carrier, unique sector occupancy, shared sectors, sector distinction, and the equivalence relation on well-defined charged carriers. For uniquely occupied charges it proves exact equality/same-sector and inequality/distinct-sector criteria without depending on a functional implementation. Countermodels show that admissibility alone, bare assignment without admissibility, or equal charge labels do not identify physical carriers, and that unequal assigned charges do not establish distinct sectors without uniqueness. The policy audit discovers every shared framework module and requires at least two inspectable independent paper-local realizations before admitting it. Shared framework imports are also exact-manifested: a philosophy, paradigm, or lower-framework dependency is retained only when the module actually uses it. Its base semantics remains relational, while an optional ofFunction realization captures the independently repeated pattern in which a paper supplies admissibility and paper-local charge data. The context owns the paper-selected charge map, carrier, and regime together with both relation families; SelectedChargeSemanticsAt is equality with the resulting unique proof-free model, while SelectedChargeAssignmentSetupAt additionally requires selected-carrier admissibility before grounding. FunctionallyRealizedBy validates that exact paper-local map against the retained relation, and the output-led EstablishedFunctionalChargeAssignmentAt retains exact selected semantics together with direct functional realization, occupancy of the selected sector, and charge existence and uniqueness. The route is reconstructed from those outputs rather than stored in the endpoint. ChargeAssignmentClaim gives this result an exhaustive proposition-valued semantics: selected semantics, functional realization, carrier admissibility, route applicability, selected-sector occupancy, well-definedness, and the established assignment itself. A shared theorem proves that every established assignment realizes all seven claims. The module imports Philosophy/TheoryModel.lean and Philosophy/MathematicsAndNature.lean, and separates a value-producing ChargeModel, a ChargeTheory, and a represented ChargeWorld. Each paper supplies a ChargeInterpretation specifying how its mathematical map is used by the selected theory, which physical carrier it represents, and what the theory-level and world-level charge claims mean. TheoryModelGroundingAt combines grounding of the selected numerical charge with grounding of every technical assignment claim. Numerical model entailment itself now requires carrier admissibility as well as equality to the paper-local map, so a total map does not assert a physical charge outside its declared domain. The generic theory_model_inputs_establish_grounding constructor consumes exact selected semantics, selected-carrier admissibility, model-use, representation, and conditional transfer bridges; it mentions no functional-realization, applicability, occupancy, uniqueness, or established-assignment result. TheoryModelGroundedFunctionalChargeAssignmentAt retains the output-led result plus explicit theory-transfer and world-soundness bridges; all eight active paper clients delegate their output-independent grounding to the generic constructor, transfer every shared claim, and only then combine it with their established exact-map assignments. Polchinski's adapter exposes the physical RR-source statement as a separate bridge rather than embedding the boundary-state route in model representation. Countermodels show both that a completed assignment need not be grounded and that admissible setup plus grounding need not supply either a functional assignment route or the direct output; they also reject a wrong map, an inadmissible model conclusion, bare physical charge truth, and declarations of all theory/world assignment claims as route substitutes. The grounded endpoint also projects to a quantity-representation context with distinct mathematical and physical charge-quantity types. Faithfulness and an established physical charge value follow only through the paper-local world-transfer bridge. Laughlin 1983, Witten 1982, and Polchinski 1995 expose named cross-domain adapters, while a countermodel retains the exact mathematical assignment and represented value but denies physical charge possession. Thus a successful charge calculation is not definitionally a physical charge fact. The older existential FunctionallyRealized interface is preserved as a weaker abstraction, but it cannot validate an arbitrary externally supplied map; a checked countermodel separates the two strengths. Shared theorems also derive unique occupancy and same/distinct-sector tests from the relational interface. Distinct sectors require admissibility of both carriers, and another countermodel shows why transitivity requires uniqueness of the intermediate carrier's charge. The direct NonvacuousFunctionalChargeAssignmentAt proposition requires exact graph realization, actual occupancy of the selected sector, and a charge that exists uniquely. Its index-sensitive finite model is inhabited, and direct mutation theorems make the selected map, carrier, regime, admissibility predicate, and assignment relation all route-active. Every one of the eight paper clients derives this proposition from its established paper-local assignment without importing its numerical charge calculation into the shared layer. Each adapter constructs the output directly from its own admissibility premise; policy forbids using the generic route-to-result theorem as the endpoint proof. The same context now exposes proof-free selected constraint, typed derivation-constraint, and situated phenomenon records. The ordinary structural theorem starts from the raw exact-map route and explains the direct selected assignment without consuming the output-led endpoint. The stricter source theorem additionally requires an independently realized typed paper derivation, exposes that provenance, forgets to the ordinary explanation, and only then entails the established assignment. Witten, Laughlin, Arovas-Schrieffer-Wilczek, Maldacena, and Polchinski supply distinct source-sensitive adapters: Cartan-pair charge sequencing, screening or orbital counting, density/Berry/electromagnetic matching, charged-D3 five-form quantization, and boundary-state/annulus/Dirac pairing. Polchinski's pairing branch now retains author equations (14)-(15) as a typed flux readout: source-normalized linking-sphere flux, equality with the dual-field integral and small-sphere potential holonomy, the separate Dirac-string invisibility equation, and the derived electric-magnetic charge product. Lean checks the elimination of the flux variable and the n = 1 specialization; a countermodel prevents a named pairing calculation from manufacturing those source formulas. A value-bearing D-brane countermodel now retains a p=3 mixed-boundary split (4,6), one of two bulk supercharges, six transverse modes, inverse-coupling disk tension, a nonzero direct boundary source, a vanishing three-term oscillator sum, nonzero (1,-1) NSNS/RR exchange, the printed annulus normalization and one Dirac unit, and the factor-of-two two-brane normalization conflict. The constant positive top-form witness records quantization as an open question, not as a claim of nonquantization. No proposition-pair truth table replaces these D-brane distinctions. A finite false-source model keeps the route, established assignment, and ordinary explanation while denying the derivation relation, so common charge semantics cannot manufacture paper provenance.
PhysicsLogic/Framework/FractionalHallQuasiholeCharge.lean: the narrower Hall-quasihole inference independently realized by Laughlin 1983, Haldane 1983, and Arovas-Schrieffer-Wilczek 1984. Its exact proof-free model retains five selected values and five complete relation or function families: charge admissibility, relational charge assignment, the selected charge map, Hall-fluid status, and quasihole localization. Each paper constructs a named model and proves exact semantic retention before route applicability. The route adds proper filling, positive reference charge, and a paper-local calculation of q = nu e; the established result derives the selected charge sector and strict bounds 0 < q < e. The output-led established result directly retains selected physical setup, functional assignment, exact value, sector, and bounds, and reconstructs the implication-valued calculation and complete route. It projects to a direct nonvacuous endpoint with the same physical outputs. Grounding requires the selected Hall setup, proper filling, and positive reference charge but remains independent of the charge assignment and calculation. All thirteen claims transfer exhaustively, and a direct ten-way audit makes the five realized outer indices and five realized relation families endpoint-active. The three nested assignment-selection fields remain exact route-binding data rather than extra physical facts. Directional countermodels separate grounded setup from charge outputs in both directions. Laughlin supplies independent screening and orbital state-counting calculations; Haldane supplies spherical-parent filling identification and fixed-field excitation counting without consuming its assumed parent gap; Arovas-Schrieffer-Wilczek supplies adiabatic density-phase matching. All four routes independently realize a typed structural explanation of the localized occupied q = nu e sector with 0 < q < e. A finite model retains every charge output but removes the selected Hall fluid, proving that occurrence of fractional charge alone does not reconstruct this explanation. Wavefunctions, plasma screening, Berry phases, electromagnetic phase matching, statistics, Hall conductance, and topological order remain outside the neutral charge inference. Separate source-valued controls retain the odd m = 3 planar Jastrow trial state, independent screened and flux-counted e/3 charges, Haldane's 2S = m(N - 1) monopole shift and distinct 4/9 finite versus 1/3 thermodynamic filling, fixed-field creation of three e/3 holes, and Arovas's 2 pi nu winding versus pi nu exchange phase. They also retain the nontrivial statistical potential, unproven daughter Coulomb gap, variational-state qualification, and the distinction between symmetric hole coordinates and adiabatic Berry holonomy. The same Haldane coordinate symmetry is explicitly compatible with both zero and nonzero geometric phase; only Arovas's independent transport calculation selects the nonzero exchange result. The stronger SourceSensitiveFunctionalChargeSupportedFractionalHallChargeAt additionally retains the exact nested charge model, inhabited fractional endpoint, independent source-sensitive functional-charge and Hall-charge explanations, and a third source-local joining derivation. Laughlin's plasma handoff preserves his literal equations-(7)-(8), phantom insertion, complete screening, and m q = e; his distinct one-flux/one-orbital counting handoff is explicitly forbidden from assuming plasma screening. Arovas's handoff preserves normalization, the nondynamical state-inner-product phase, the inhabited density decomposition and large-loop correction, electromagnetic matching, and q = nu e, while governance excludes the later two-hole exchange argument. A physical missing-handoff model retains the distinct e/3 and e/5 charges, unit phantom, opposite quasiparticle sign, finite-hole correction, and variational scope while rejecting composition without its joining proof.
PhysicsLogic/Framework/ParityResolvedFractionalJosephsonResponse.lean: the fixed-parity phase-response inference independently realized by Kitaev 2001 and Fu-Kane 2009. It retains two opposite-parity sectors, a paper-local branch-retention condition, local 2pi return with sector exchange, 4pi sector return, and a separate calculation of a fixed-sector current that is 4pi rather than 2pi periodic. Its exact model retains all six selected indices and eleven route-used relations. Establishment is output-led: it stores the exact inhabited junction setup and seven direct response outputs, while checked theorems reconstruct the three implication- shaped contracts and complete route. Grounding requires that selected setup but no return, exchange, current-periodicity, fractional-effect, calculation, or route output. Directional countermodels separate setup grounding from response outputs in both directions. Its direct nonvacuous endpoint is witnessed by a route-shaped model and fails under each of six selected-index and eleven relation-family mutations. The completed route additionally realizes a typed structural explanation whose constraint contains the exact junction, parity sectors, advances, regime, branch evolution, current calculation, and fractional-effect interpretation. Branch-only and current-without- interpretation countermodels block weaker explanations. Majorana chains, QSHI edges, protected crossings, parity anomalies, avoided crossings, switching noise, materials, and experimental realization remain paper-local.
PhysicsLogic/Framework/FiniteBarrierMetastableDecay.lean: the finite-barrier metastable-decay inference independently realized by Gamow 1928 and Gurney-Condon 1928. It retains a classically forbidden finite barrier, attenuated but nonzero wave coupling, a separate positive-rate calculation, spontaneous decay, and a cross-system energy-rate trend only under an explicit comparable-barrier condition. A separately earned ExponentialMetastableSurvivalReadout distinguishes a positive rate, normalized exponential survival, correctly conditioned future survival, and elapsed-time escape probability. Gamow derives the full-exponent survival curve from the actual complex-energy phase and identifies it with the finite interior probability divided by its initial value; Gurney and Condon retain their explicitly recalled observed exponential law and require a positive observation duration. Rate comparisons through escape probabilities require one common duration, and concrete models separate positive rates from survival laws and exponential survival from correct future conditioning. Both source routes construct the stronger NonvacuousMemorylessFiniteBarrierDecayAt endpoint without identifying a rate with an objective chance. Its proof-free exact model retains all sixteen selected data values and all sixteen route-used relation families. Both papers certify a named context-derived model before the technical route and prove a named selected-comparison setup bridge from their two local barrier setups, comparable profiles, and energy ordering. They independently ground that same setup without any attenuation, overlap, rate, penetration, or trend output. Both established endpoints are output-led and reconstruct their calculation contracts from realized outputs. The reusable one-decay endpoint has its own false-setup countermodel and a nineteen-component direct audit over eight selected values and eleven route relations. A separate thirty-two-component comparison audit prevents either selected physical value or relation family from becoming decorative. The complete one-decay route now directly realizes a typed mechanistic explanation before either an established one-decay endpoint or the two-system comparison exists: a metastable interior, outgoing channel, and finite barrier form the component; the attenuated nonzero wave and rate form the activity; and the organized system produces the selected spontaneous decay. Both papers expose this endpoint for both selected systems directly from source-stage inputs. Gamow executes the rectangular-barrier, damped-outgoing, and two radial-transfer calculations; Gurney and Condon execute the two wave-overlap calculations independently. Neither source theorem consumes the Geiger-Nuttall comparison or the objective-chance bridge; terminal comparison adapters remain compatibility paths. A stronger source-sensitive projection now retains a typed local derivation inside the mechanism's under-barrier activity. Gamow distinguishes lower and higher damped-outgoing radial transfers; Gurney and Condon distinguish the lower and higher interior/exterior wave overlaps. The derivation relation is proposition-valued rather than proof-carrying. A checked forgetful theorem strips only source provenance and recovers the ordinary barrier mechanism from the same physical witnesses. A countermodel completes the shared decay route and ordinary mechanism while making that relation false, so shared outputs cannot reconstruct which original calculation obtained. A second countermodel retains positive-rate production and the spontaneous-decay prediction while deleting the barrier-wave activity, so output labels do not manufacture a mechanism. An explicit ObjectiveChanceContext bridge now classifies the two selected rates as objective chances only from paper-local probability-role semantics: Gamow uses transition probability, decay constant, and spontaneous emission, while Gurney and Condon additionally require their history-independent chance premise. A complete technical decay with no objective-chance role is a checked countermodel. The mechanism does not determine an individual decay time or classify the rate as chance. Nuclear potentials, complex energies, barrier integrals, Geiger-Nuttall formulas, scattering checks, and analogies remain paper-local. Separate source-valued witnesses remain reduced scalar and source-flag diagnostics, not actual wavefunction realizations or certification that conflicting printed formulas agree. They additionally retain Gamow's doubled amplitude-to-rate tunneling exponent, complex-energy damping, radial barrier integral, higher-angular-momentum suppression, required s-wave preparation, approximate curved Geiger-Nuttall relation, and explicitly unproved gamma-ray mechanism. The earlier rectangular/radial route and later Coulomb/logarithmic comparison are separately inhabited source branches with distinct typed derivations; the comparison branch retains the complete prior radial calculation. Gurney and Condon instead retain small finite overlap, history-independent chance, conditional similar-potential ordering, an independent incoming-scattering turning point, and a field-emission analogy that does not derive nuclear decay. Forty-three mutation controls prevent these source arguments, formulas, probability roles, and scope qualifications from collapsing into one another or broadening the generic decay contract.
PhysicsLogic/Framework/SubthresholdExcitationStability.lean: the narrow selected-excitation stability inference independently realized by Landau 1941 and Bogoliubov 1947. Its proof-free model retains seven selected physical indices and all fifteen route-used relation families: a valid elementary spectrum, paper-local excitation content and positive energy-per-momentum threshold, selected subthreshold motion, positive moving-frame energy, exclusion of the selected momentum-transfer and dissipation channel, and stationary-frictionless interpretation. Both paper contexts own all seven physical selections and expose one exact selectedModel; changing any selected value or any of the fifteen relation families fails the original context's exact semantics. Both papers consume that certificate before either route applicability or grounding. Grounding also requires a direct inhabited spectrum-and-subthreshold-motion setup, plus paper-local theory/world use, representation, and conditional-transfer bridges; the positive threshold and every later stability output remain independent. The established endpoint is output-led and reconstructs its implication contracts from direct results. One checked countermodel has complete setup-bounded grounding while the threshold and route fail; another makes the calculation contracts vacuous with no setup while both output endpoints remain false. Mutation countermodels cover all twenty-two retained components. The complete selected route also instantiates Paradigm.ExplanationModes.StructuralExplanationContext: its typed energy and excitation-channel constraint structurally explains the scoped stationary-frictionless-motion phenomenon. Both paper adapters realize that explanation. A countermodel keeps every spectrum, threshold, moving-frame, and selected-dissipation calculation true while falsifying the physical interpretation, and therefore blocks the structural explanation. A source-sensitive constraint now pairs the ordinary selected excitation constraint with a typed paper-local derivation and an independent realization relation. Landau's derivation retains the quantum-liquid setup, non-derived potential-vortex ordering, phenomenological phonon-roton spectrum, and absolute-zero wall-flow threshold. Bogoliubov's derivation instead retains the microscopic weak-gas setup, interaction-stability selection, controlled linearization, canonical diagonalization, spectral asymptotics, equilibrium threshold, and relative-motion calculation. Each source theorem reaches DirectSourceStructuralFrictionlessMotionExplanationAt before its terminal paper result or any shared established endpoint is available. A finite countermodel preserves the complete common route, established endpoint, and ordinary explanation while falsifying the source relation, so the common conclusion cannot reconstruct which derivation was used. The older terminal-result and ordinary source adapters remain compatibility paths. This adds neither mechanistic explanation nor a universal no-dissipation claim. Phonons, rotons, condensates, Bose gases, walls, vortices, nucleation, hydrodynamics, universal critical velocities, and absence of every dissipation mechanism remain paper-local.
PhysicsLogic/Framework/MomentumResolvedVariationalBound.lean: the narrow density-mode variational inference independently realized by Feynman 1954 and Girvin-MacDonald-Platzman 1986. Its proof-free model retains eleven selected physical indices and all seventeen route-used relation families: setup, density-mode trial construction and admissibility, separate norm and numerator calculations, quotient identification, lowest-sector selection, and the upper-bound comparison. Feynman, GMP, and the dependent Feynman-Cohen 1956 client each assign eleven context-owned values, use the context's unique selected model, certify exact selected semantics, and consume that certificate in applicability. All three clients construct the shared route from direct established physical outputs rather than replaying stored paper-local calculation contracts. The shared established result is output-led: exact selected semantics plus the direct nonvacuous seventeen-relation endpoint. A candidate cannot select itself by supplying alternate indices. Their grounding adapters separately consume exact selected semantics, an inhabited paper-local ground-state/momentum/mode setup, explicit theory use and world representation, and conditional claim transfer. Final paper theorems combine that setup-bounded grounding with the remaining variational route; a typed countermodel has complete grounding and setup while trial construction and every later variational output are false. An inhabited finite witness realizes all seventeen relations with distinct ground/trial states and distinct trial/lowest-sector energies. Direct mutation theorems show that every one of the eleven data and seventeen relation families changes route-used semantics; all three paper adapters derive this nonvacuity from their local technical route. The complete route also realizes a typed structural explanation whose constraint retains all eleven selected data and is satisfied only by the trial, quotient, sector-minimum, and variational-comparison chain. Feynman and GMP now independently derive this explanation directly from their source-facing calculations before any terminal paper result or shared established endpoint exists. Their terminal-result projections remain compatibility adapters. A source-sensitive constraint now additionally retains a typed paper-local derivation. Feynman's unprojected structure-factor quotient, GMP's lowest-Landau-level projected oscillator-strength quotient, and Feynman-Cohen's dependent backflow/correlation refinement have distinct tokens and realization relations. Their source theorems require those relations and raw applicable routes rather than common endpoints or the ordinary explanation. A finite countermodel keeps the complete route, established bound, and ordinary explanation while falsifying provenance. A declared-upper-bound countermodel with no quotient identification blocks the shortcut from inequality to explanation. Helium, Hall liquids, structure factors, oscillator strengths, phonons, rotons, exact-spectrum equality, mode saturation, and gaps remain paper-local.
PhysicsLogic/Framework/HomogeneousCosmicExpansion.lean: the narrow homogeneous-expansion inference independently realized by Friedmann 1922 and Lemaitre 1927. Its proof-free model retains eight selected physical indices and all nine proposition-valued relation families that make those indices a homogeneous cosmology. The route requires exact selected semantics, a paper-local field-equation reduction, a separate increasing- branch calculation that places both selected radius-time points on one nonstationary solution, and an interpretation as cosmic expansion. Stationary and periodic worlds, conserved mass, redshift, observational calibration, and causal explanations remain paper-local. Friedmann's paper-local route now preserves the mixed-equation branch split, the stationary matter contrast, the density and total-mass relations, all three cosmological- parameter root regimes and forbidden radius intervals, the distinct origins of its two monotone worlds, and the periodic world's amplitude and critical- period behavior. These are ten audited routes with independent calculation contracts; only the established monotone assessment feeds the shared expansion adapter. Generic grounding now requires the context's unique selectedModel, its homogeneous relativistic setup, and explicit theory- use/world-representation bridges, but no radius evolution, branch calculation, interpretation, or established result. Both paper contexts own all eight physical selections and derive the selected shared setup from their source-local setup. A converse model has setup-complete grounding while radius evolution is false; a false-setup model cannot be grounded. A further countermodel has an evolution relation and an increasing pair but no single selected solution containing both points, so the route is inapplicable. Friedmann's expansion bridge is explicitly marked as a source-anchored reconstruction from increasing homogeneous curvature radius, whereas Lemaitre explicitly interprets expansion of space. His local constant-mass route additionally requires strict numerical radius growth; the original exact period/radius equation then proves positive spectral redshift and positive apparent recession velocity. A contracting-universe countermodel satisfies that same equation while producing blueshift, so neither conclusion is silently imported into the shared framework. Both adapters now retain that interpretation as a callable paper-local bridge and feed it the selected history and increase. Their adapters now construct the source-ordered applicable route directly; that route yields both the output-led established result and a typed structural explanation of the selected expanding history. Its proof-free constraint contains no evolution or expansion output, and neither adapter consumes the established or nonvacuous shared endpoint. A second proof-free source constraint now retains a typed paper derivation and proposition-valued realization relation. Friedmann's token includes the reconstructed interpretation bridge, whereas Lemaitre's token includes the explicit interpretation returned by his constant-mass calculation. Their source-sensitive theorems require both the raw applicable route and the corresponding realized token. A completed expansion with a false derivation relation blocks provenance from being inferred from output equivalence; a declared-output model with false setup separately blocks the physical converse. This is not a causal explanation of expansion, and Lemaitre's radiation-pressure suggestion remains local. The finite audit model has distinct ordered times and radii and realizes the complete route; NonvacuousHomogeneousCosmicExpansionAt now states that setup, radius evolution, one selected history, increase, and physical interpretation all hold directly at one model. Both paper adapters expose that proposition. The equation-backed selected history also projects to a neutral radius Dynamics, with the ordered endpoint-time pair as evolution parameter. Both papers expose the resulting actual forward-evolution witness. A no-expansion model and a branching established-expansion model prevent this projection from manufacturing either physical interpretation or determinism. The branching model also realizes the structural explanation, proving that it does not imply unique evolution. Every one of the eight index mutations and nine relation mutations destroys the direct result itself; the older seventeen mutation witnesses separately enforce exact semantics.
PhysicsLogic/Framework/NebularDistanceVelocityCalibration.lean: the qualified observational calibration independently realized by Lemaitre 1927 and Hubble 1929. Its proof-free model retains seven selected indices and all ten route-used relation families, including exact universality as a positive predicate whose negation is part of the qualified result. Applicability requires exact paper-local relation semantics plus separate fit, scope-assessment, and interpretation obligations. Both papers construct a unique model from seven context-owned values and consume semantic-retention certificates. Their selected sample and assigned data also construct a named SelectedCalibrationSetupAt witness before grounding; mutation countermodels cover all seventeen fields and refute exact semantics after any one-field change. The established result is now exactly selected semantics plus NonvacuousQualifiedDistanceVelocityCalibrationAt: valid description, selected sample, both assigned data sets, selected proportional relation, calibrated coefficient, uncertainty, restricted range, non-universality, and rough linearity all hold directly at one model. The implication-valued route is reconstructed from those outputs. Exact selection without the observational setup cannot ground a model, while a selected setup can be grounded without fit or calibration outputs. A setup-free implication model also fails the direct proposition. A separate finite witness and seven index plus ten relation mutations show that every route-used component affects the qualified result itself. Lemaitre and Hubble expose named paper adapters to this same nonvacuous stopping point. The selected sample and assigned distance/velocity datasets additionally form an explicit evidence object supporting the qualified relation and coefficient model. Both papers derive the same ModelEvidenceContext.SupportsModel proposition only after fitting and retaining uncertainty, range restriction, nonuniversality, and rough linearity. Accessible obtained data without a fit are a checked countermodel; model truth and theory support remain separate. The finite source-report diagnostic preserves assigned-catalog equality across alternative reductions while comparing their numerical reports. It does not reconstruct actual estimators or assert independent validation, cosmic sampling variation, or a cosmological ensemble target. Cosmological dynamics, numerical fit details, Hubble's downstream NGC 7619 consistency check, de Sitter explanations, and modern Hubble-constant semantics remain paper-local.
PhysicsLogic/Framework/StandardCandleAccelerationInference.lean: the qualified observational-cosmology inference independently realized by Riess et al. 1998 and Perlmutter et al. 1999. Its exact model retains ten selected indices and eighteen relation families covering calibrated magnitude-redshift evidence, a scoped model-family fit, a nonaccelerating reference, a separate acceleration interpretation, and robustness only to assessed systematics. It realizes evidence as model support rather than theory truth and keeps unquantified alternatives explicit. A finite direct model realizes the complete five-stage inference with distinct fitted-family and reference-model roles. Exhaustive activity theorems show that all ten selected data and all eighteen relations affect the realized route, rather than merely changing an exact record. Both paper adapters expose this nonvacuous proposition. Applicability retains the independent paper-local calculations, while established fit, acceleration, and terminal inference objects retain only setup and direct outputs; a vacuity countermodel guards this boundary. The complete route also realizes an ordinary structural explanation. A stronger source-sensitive explanation retains typed, noninterchangeable derivations: Riess starts from classified observations, MLCS/template/snapshot distance reduction, a scoped likelihood, a separate two-component deceleration bridge, and qualified robustness; Perlmutter starts from matched samples, cross-filter/stretch standardization, the A/B/C fit progression, acceleration interpretation, and systematic refits with grey-dust and evolution loopholes open. Neither source theorem accepts an established paper or shared endpoint. A finite converse model completes the route and ordinary explanation while its independent source relation is false. Grounding is bounded by the exact calibrated-evidence and cosmological-comparison setup, excludes every fit and interpretation output, and is independently realized by named Riess and Perlmutter adapters. The neutral route does not identify their samples, light-curve reductions, likelihoods, confidence procedures, ontological interpretations, age calculations, or cross-paper overlap. Separate source-valued controls retain Riess's 10 new/16 total distant and 34 nearby events, 15 spectroscopic confirmations, distinct Omega_Lambda = 0.68 versus 0.84 flat-prior fits, and 2.8 versus 3.9 sigma acceleration support. Perlmutter's controls retain the 42+18 sample, 60/56/54 Fit A/B/C cuts, Omega_M = 0.28 +0.09/-0.08, separate identified systematic errors, P(Lambda > 0) = 0.9979, and unresolved grey-dust/evolution alternatives. Separate searches nevertheless shared nearby Calan/Tololo observations and exactly two distant supernovae, so the teams' evidence is not statistically independent.
PhysicsLogic/Framework/GappedIncompressibleFluid.lean: the narrow shared inference independently realized by Laughlin 1983 and Haldane 1983. A selected description is valid in a regime and represents a quantum fluid; a paper-local calculation or explicit assumption establishes an excitation gap; and a separate interpretation bridge yields incompressibility and suppressed low-energy dissipation. Its proof-free model retains the three selected indices and all five route-used relation families. The context owns the description, fluid, and regime and constructs one unique selectedModel; candidate models cannot select their own indices. Applicability requires exact paper-local selected semantics plus the model-local technical route. Laughlin and Haldane each construct their named shared model from that unique selection and prove a semantic-retention certificate before using it. Model-of and representation grounding retain exact selection and the inhabited pre-gap setup, while model entailment is the shared claim itself. Grounding separately requires only that certificate, the valid selected quantum-fluid setup, and paper-local theory/world bridges; it does not consume the gap or either interpreted output. The output-led established result is exactly selected semantics plus NonvacuousGappedIncompressibleFluidAt, where the valid quantum-fluid setup, actual selected gap, incompressibility, and suppressed dissipation hold directly at one model rather than only behind implication-valued clauses; the complete route is reconstructed from those facts when needed. Laughlin and Haldane each expose a named paper-level projection to that direct result. The complete route also instantiates a typed structural explanation of the selected incompressible, low-dissipation fluid phenomenon. Satisfaction requires the gap calculation or assumption and the separate interpretation bridge; a checked gap-without-interpretation model has no such explanation. It defines no Landau level, Hall conductance, hierarchy, fractional charge, disorder, or topological order. Countermodels block setup-to-gap, gap-to-interpretation, incompressibility-to-dissipation, technical-result-to-grounding, grounding-to-technical-route, selection-without-setup grounding, and vacuous implication use. One audit shows that changing the state, fluid, regime, or any retained relation fails exact semantics; a source-shaped direct witness realizes the complete gap-to-incompressibility result, and exhaustive direct mutations make all eight retained components destroy that substantive result.
PhysicsLogic/Framework/SolitaryTravelingWave.lean: the narrow stationary solitary-wave inference independently realized by Korteweg and de Vries 1895 and Zabusky-Kruskal 1965. Its proof-free model retains eleven selected indices and all eleven route-used relation families: validity, system description, nonlinear dispersion, frame selection, asymptotic background condition, nonzero pulse-background contrast, stationary reduction, localized-profile construction, both parameter relations, and shape preservation. Each paper constructs an exact context-derived model whose context owns all eleven selected values, and constructs the established result directly from the inhabited setup, reduction, nontrivial profile, parameter relations, and shape-preserving conclusion. The generic calculation route is reconstructed from those outputs rather than stored inside the result. The same endpoint now yields a typed derivational reduction from the full nonlinear-wave description to the reduced stationary profile and its shape-preserving behavior. Separate countermodels show that a shape label without nontrivial profile support, and complete profile calculations without the physical interpretation, each fail that reduction contract. The complete route also realizes a typed structural explanation whose proof-free constraint retains the full and reduced equations, moving frame, nontrivial profile, and selected pulse parameters, while its distinct phenomenon requires nonzero contrast, both parameter relations, and shape preservation. A terminal-pulse countermodel makes that phenomenon obtain while nonlinear dispersion is absent, so the occurrence does not explain itself. Both papers expose the explanation from their own granular stationary routes. The raw routes now also realize a source-sensitive derivational reduction. Korteweg-de Vries retains the hydrodynamic long-wave setup, successive-approximation deformation-equation calculation, and stationary-profile calculation; Zabusky-Kruskal retains the selected KdV setup, stationary substitution, isolated-pulse calculation, and shape interpretation. Its physical setup now contains the literal normalized equation u_t + u u_x + delta^2 u_xxx = 0, with actual temporal and third-order spatial derivatives; its numerical protocol separately contains the period-two profile u(x,0) = cos(pi x) and delta = 0.022. Source steps make those original equations explicit dependencies, while countermodels reject inviscid steepening, linear dispersion, and a reversed-phase cosine as substitutes. A completed common pulse and ordinary reduction with a false source relation cannot recover either provenance. Theory/model/world grounding requires exact selected semantics together with the true equation, moving-frame, and background setup. Mutation countermodels show that changing any of the twenty-two model components invalidates exact semantics. A dedicated countermodel proves that profile, parameter-relation, and shape labels alone do not exclude a constant-background profile; another proves that a false setup cannot be grounded even when all implication-valued calculations are vacuously true. Korteweg-de Vries's negative and periodic branches and Zabusky-Kruskal's numerical formation, interaction, recurrence, and thermalization routes remain paper-local; the framework defines no generic soliton ontology. Korteweg-de Vries's paper-local scope countermodels now retain actual depth-wavelength and amplitude-depth scale separation, deformation and stationary residuals, cnoidal modulus and closure, third-order support, and a nonvanishing remainder sequence. They separate setup from calculation, localized from periodic stationarity, finite-order support from convergence, and one stationary profile from arbitrary waves without enum-to-Prop truth tables. Separate source-valued controls now retain the original signed coefficient sigma = l^3/3 - T l/(rho g), distinct elevation and capillary-depression pulses, the common critical depth sqrt(3 T/(rho g)), and the complete depression profile -h sech^2(x sqrt(h/(-4 sigma))). The elevation and depression witnesses keep the same fluid, gravity, and surface tension but occupy strictly different depths; the original water data give a critical depth strictly between 0.469 and 0.470 cm. Twelve inhabited source and shared-framework boundaries reject a wrong depth, missing surface tension, erased real-valued profile, wrong width, or a solitary branch exactly at zero dispersion. The normalized KdV evolution and period-two cosine protocol remain separate. The 1965 pulse relations amplitude * width^2 = 12 delta^2 and speed = background + amplitude/3, eight observed versus seven compared pulses, exact represented momentum versus nonzero five-digit energy drift, and near-profile return are independently checked. Seventeen mutations reject exact full-state recurrence, exact Euler dynamics, solved close interactions, and exclusion of eventual thermalization without widening the neutral solitary-wave contract.
PhysicsLogic/Framework/LargeComponentSphericalCorrespondence.lean: the selected infinite-component vector-to-spherical observable agreement independently realized by Stanley 1968 and Wegner-Houghton 1973. Stanley retains the original single global spherical constraint, separate local vector-spin constraint at every lattice site, nonzero finite-spin free-energy correction, equation-(24) remainder accounting, and off-critical temperature scope. Wegner-Houghton separately retains the exact infinite-component critical formulas y_m = d - 2m, nu = 1/(d-2), alpha = (d-4)/(d-2), gamma = 2/(d-2), and beta = 1/2 on 2 < d < 4. Neither derivation establishes convergence of finite-component critical indices, interchange of the large-component and critical limits, or exact finite-component perturbation theory.
PhysicsLogic/Framework/IncompressibleVelocityCorrelation.lean: the narrow nonvacuous incompressible velocity-correlation constraint independently realized by Kolmogorov 1941 and Forster-Nelson-Stephen 1977. Kolmogorov retains the original local radial equation r B_LL'(r) = 2 (B_NN(r) - B_LL(r)), positive separation, local isotropy, and a high-Reynolds interior. Its adapter now binds the tensor to actual retained-field moment integrals and the radial derivative to the same computed longitudinal profile. Forster instead retains the original Fourier projector P_ij(k) = delta_ij - k_i k_j / |k|^2, a nonzero wave vector, positive spectral amplitude, actual tensor transversality, and a long-distance, long-time infrared regime. Lean proves the Fourier tensor is nonzero and rejects a wrong projector cross-term sign. Neither source supplies a shared inertial exponent, proved cascade, whole-flow isotropy, ultraviolet turbulence control, or universality across arbitrary forcing.
PhysicsLogic/Framework/CanonicalGibbsNormalization.lean: the narrow normalized energy-weight inference independently realized by Jaynes 1957 and Metropolis et al. 1953. Jaynes retains the finite enumerated-energy sum, constrained epistemic maximum entropy, the printed exponential, logarithmic normalization, and partition equations, and the absence of inferred microscopic dynamics. Metropolis instead retains positive kT, velocity-independent momentum separation, the actual configuration-space measure integral, normalized density, and weighted observable numerator. The shared result neither requires a positive Jaynes energy multiplier nor bounds a continuous probability density by one. It does not infer detailed balance, a finite convergence rate, molecular dynamics, or an exact thermodynamic limit from the canonical target.
PhysicsLogic/Framework/DensityPotentialGaugeDetermination.lean: the narrow density-to-potential classification independently realized by Hohenberg-Kohn 1964 and Runge-Gross 1984. Its proof-free context retains the selected full description, potential, density, fixed condition, physical system, regime, source-specific gauge, inhabited domain, and separate source calculation. The static branch keeps paired nondegenerate ground states, fixed particle number, strict variational reductio, and an additive spatial constant; the dynamic branch keeps fixed initial state and interaction, time analyticity, current/continuity/boundary reasoning, printed equation (6), and a genuinely time-dependent additive gauge. Neither branch proves literal potential equality, global density representability, an unrestricted initial-state theorem, or a dynamic action minimum.
PhysicsLogic/Framework/DensityFunctional.lean: the narrow exact ground-density variational inference derived by Hohenberg-Kohn 1964 and explicitly imported by Kohn-Sham 1965. GroundDensityModel is proof-free and retains the selected state, potential, derived density, particle number, density and particle-number maps, ground-state and admissible-density predicates, and all three energy functions used by the route. The context owns the selected state, potential, and particle-number sector and exposes their unique selectedModel; a candidate cannot select itself by supplying different indices. Route applicability requires exact equality with that model. Theory use and physical representation require the stronger SelectedGroundDensitySetupAt: exact selection together with the physical ground-state, derived-density, fixed-particle-number, and selected-density admissibility setup, but no variational output. The route then requires that setup, including explicit admissibility of that selected density in the fixed-particle-number domain, and a selected implication-valued calculation yielding both physical-energy attainment and minimization over the declared fixed-particle-number density domain. A globally quantified paper result may instantiate that calculation but cannot count as an applicable route by itself. Hohenberg-Kohn derives the calculation from its energy and wavefunction-variational premises; Kohn-Sham consumes its imported Hohenberg-Kohn foundation before adding orbital machinery. A typed GroundDensityVariationalConstraint now records the selected state, potential, density, and particle-number sector, while GroundDensityEnergyMinimumPhenomenon records the selected density, its physical ground energy, and the fixed-number minimum. The complete applicable route realizes DirectStructuralGroundDensityVariationalExplanationAt: applying the selected variational calculation to its inhabited setup necessitates both exact attainment and minimization. Both papers expose that explanation directly from their source inputs. A countermodel has exact energy attainment but an admissible lower-energy competitor, so the first output alone is neither the minimum nor its structural explanation. Kohn-Sham retains the exact universal decomposition with that foundation, so the local approximation, nonlocal exact-exchange alternative, and note-added-in-proof exact formulation branch from the exact input without making either alternative inherit the local approximation. Each paper constructs a named exact model, proves a semantic-retention certificate, supplies it independently to TheoryModelGroundingAt, and transfers all eight shared claims. The established result is definitionally exact selected semantics together with NonvacuousGroundDensityVariationalAt, where selected-density admissibility, energy attainment, and scoped minimization hold together at one model instead of only behind the implication-valued calculation; the complete technical route is reconstructed from those outputs when needed. A pointwise projection to MathematicalRepresentationContext additionally proves that the selected admissible density exactly represents a physical ground state at the selected potential and particle number. Hohenberg-Kohn and Kohn-Sham both expose this result. Countermodels separately remove physical ground-state membership and density admissibility, while the framework still makes no converse representability, completeness, density uniqueness, or density-to-state determination claim. A false physical setup cannot be grounded, while a complete setup can be grounded without thereby supplying minimization or a calculation route. A route-shaped finite witness realizes that proposition, and exhaustive direct mutations make all four selected indices and seven retained semantic families destroy it. Further countermodels block vacuous implication use, automatic grounding, and reconstruction from declared theory/world claims. Orbitals, representability beyond the declared domain, exchange-correlation approximations, response kernels, thermal occupations, and spin extensions remain paper-local.
PhysicsLogic/Framework/CongruenceFocusing.lean: the narrow finite-parameter transverse-collapse route independently realized by Raychaudhuri 1955 and Penrose 1965. Its proof-free model retains eight selected indices and all ten route-used relation families: congruence and positive-profile setup, initial contraction, nonpositive evolution, finite profile collapse, and collapse-to-focusing interpretation. Both papers assign all eight paper-local values to their contexts' explicit selections, use the resulting unique selectedModel, prove retention certificates, and consume the certified semantics in applicability. Grounding separately requires only exact semantics, the valid congruence/section/positive-profile setup, and paper-local theory/world bridges. Model use, world representation, and model entailment all retain the exact eighteen-component semantics. The output-led established result is exact selected semantics together with NonvacuousFiniteParameterCongruenceFocusingAt, where the setup, contraction, nonpositive evolution, finite separation, profile vanishing, and focusing conclusion hold directly at one model rather than only behind implication-valued calculations. Raychaudhuri and Penrose each construct that direct result from their paper-local inputs, and the complete route is reconstructed afterward. The ordinary structural explanation executes collapse plus interpretation directly without requiring paper provenance. A stricter source-sensitive explanation adds a typed realized derivation, exposes it, and entails the ordinary explanation when provenance is forgotten. Raychaudhuri's zero-lambda timelike-volume derivation and Penrose's temporary-completeness null-area derivation remain distinct. A converse countermodel retains established focusing, the reconstructed route, and ordinary explanation while denying the source derivation, so no source-sensitive explanation follows. Raychaudhuri's separate nonspinning time-scale branch now also retains journal equations (13)-(16) before any interpretation: rho G^3 = C, with G^6 = -g so G^3 is the local volume factor, the zero-spin normalized-G equation, its assigned-state first integral, Q = G/G_A, the nonnegative anisotropy accumulation Theta, and the inverse-square-root proper-time integral. The readout is tied to the selected Einstein system, assigned/comparison states, G-profile, density, anisotropy, interval integral, and elapsed time. The interval inequality and isotropic-maximality reading remain separate calculation and interpretation contracts; a countermodel blocks a named comparison output from manufacturing the displayed formulas. Raychaudhuri supplies a timelike matter congruence and local spatial volume; Penrose supplies an orthogonal null congruence, cross-sectional area, and caustic. Those causal, dynamical, and singularity meanings remain outside the neutral route. Separate source-valued physical controls retain Raychaudhuri's signed G''/G equation, rotation and anisotropy branches, independent past contraction, Lambda freedom, and local static balance; Penrose's two null families, exact square-root-area optical chain, separate noncompact Cauchy hypothesis and degree obstruction, and future-null-only conclusion. Countermodels reject promoted curvature divergence, timelike incompleteness, and event-horizon claims. The Raychaudhuri client additionally retains dust stress-energy, density conservation, anisotropy and rotation equality criteria, spin identification, the nonspinning time-bound equality case, and the paper's observational distinction between anisotropy and extra freedom in the cosmological constant. Those details deliberately do not enter the shared focusing model. The grounded form transfers all thirteen shared claims. One eighteen-component audit shows that changing any retained index or relation fails the original context's exact semantics; a separate direct finite model shows that each of the same eighteen changes destroys nonvacuous focusing itself. Countermodels block setup-to-contraction, contraction-to-finite-collapse, profile-collapse-to-focusing, vacuous implication, false-setup grounding, grounding-to-technical-route, and theory/world-to-technical-route shortcuts.
PhysicsLogic/Framework/TrappedSurfaceIncompleteness.lean: the narrow global-relativity inference derived by Penrose 1965 and reused by Hawking 1965 after his independent cosmological trapped-sphere calculation. It separates global causal setup, a closed surface trapped in a selected time direction, finite focusing under temporary directional null completeness, compactness of the associated causal boundary, and the noncompact-Cauchy topology obstruction. The conclusion is directional null geodesic incompleteness. The output-led established proposition retains the exact selected global and trapped-surface setup, all three conditional reductio outputs, and directional incompleteness. A checked theorem reconstructs the complete applicable route instead of storing it. Its proof-free model retains all seven selected physical objects and all twelve relation families used by the route, for nineteen semantically observable components. The eight claims include exact model selection and a direct nonvacuous directional-incompleteness endpoint. That endpoint requires actual global setup, actual trapping, the conditional reductio laws, and rejected directional completeness at one model, without pretending that the discharged complete branch is an actual spacetime. Its structural-explanation projection uses distinct proof-free constraint and phenomenon types. The constraint retains the Cauchy surface, trapped surface, causal boundary, and full reductio scope; the phenomenon retains only the selected spacetime, time direction, and regime. Exact route applicability satisfies the constraint and directly necessitates rejected directional completeness without consuming an established-result wrapper. Penrose realizes this projection for future collapse, while Hawking realizes it for a past-trapped cosmology by applying the imported Penrose global argument. A partial route without the topology obstruction does not explain incompleteness, and incompleteness without trapping or the reductio does not explain itself. A stronger source-sensitive projection now preserves that historical and logical asymmetry. Penrose's typed token requires the granular orthogonal- congruence selection, optical-scalar evolution, finite-affine area collapse, caustic interpretation, compact-boundary calculation, and degree obstruction. Hawking's distinct token requires his flat/open large-sphere convergence calculation and explicitly imported Penrose focusing, compact-boundary, and topology contracts. A completed reductio and ordinary explanation with an unrealized source relation has no source-sensitive explanation, so the common directional conclusion cannot manufacture its derivational history. A finite direct audit makes six realized indices and nine realized relations affect that endpoint; a separate theorem records that the boundary index and three discharged-branch relations are retained but not individually direct facts after completeness is rejected. Distinct calculation, theory, and world roles make transfer explicit. Model membership and world representation require the exact selected model, actual global and trapped-surface setup, and explicit paper-local use and representation bridges. Neither relation assumes focusing, compact-boundary, topology-obstruction, or incompleteness results. theory_model_inputs_establish_grounding packages those setup-only inputs, and grounding projects back to that selected setup. A typed countermodel exhibits complete grounding while the topology step and technical route are false; another realizes every direct output on a non-selected model and proves that it cannot ground. Penrose grounds the model in his governed nonspherical-collapse and trapped-surface construction; Hawking grounds it in the expanding flat/open model and large-sphere optical calculation. Each paper has a named adapter proving that its inputs realize the selected incompleteness setup. Penrose names and certifies one collapse model. Hawking separately names and certifies its homogeneous and perturbed cosmological models, preventing the two source routes from sharing an ambiguous selection. Each paper combines that independent grounding with its separately established reductio. The component now conditionally imports TrappedSurfaceStability: an output-led established robustness result can supply the target trapped-surface setup only through a paper-local admissibility bridge. The lower component's proof-free model retains all nine selected indices and the five relation families used by that route. Its nine claims include exact semantic selection, the selected realized setup, and the direct NonvacuousTrappedSurfaceStabilityAt result. The exact-model mutation audit rejects every changed index or relation, and a separate direct fourteen-component audit shows that each change destroys the inhabited stability proposition itself. Penrose and Hawking each construct the context-derived model, prove exact retention, and ground it from the exact realized reference and controlled-target setup independently of target trapping or the stability calculation. Hawking's grounding therefore explicitly consumes the large-sphere convergence calculation that establishes the reference trapped surface. Both also project their established results to the direct nonvacuous result. Penrose composes controlled nonspherical stability into the future-directed reductio; Hawking composes finite-margin perturbative stability into the past-directed reductio. Global causality, null energy, focusing, boundary compactness, and topology remain independent inputs. The generic direct incompleteness endpoint remains stability-agnostic, while their source-order routes additionally expose NonvacuousStabilitySupportedDirectionalNullIncompletenessAt. That composite endpoint retains the direct nonvacuous stability child, exact output-led established stability result, paper-local admissibility bridge, actual upper trapped-surface setup, and direct directional-incompleteness result together. The stronger SourceSensitiveStabilitySupportedDirectionalNullIncompletenessAt additionally matches the exact description, target spacetime, trapped surface, direction, and regime across both selected models. It retains the inhabited composition, independent source-sensitive stability and global explanations, and a third paper-local joining derivation. Penrose's adapter exposes his actual optical-scalar equation and future-directed noncompact-Cauchy degree obstruction. Hawking's new perturbed-universe source cannot be replaced by the homogeneous source: its joining adapter retains the literal large-sphere/Friedmann formula, both original and perturbed past-null convergence branches, strict margin and perturbation control, broken exact local symmetry, and the imported perturbed global reductio. A physical countermodel distinguishes future collapse from past open cosmology, direct from covering-space routes, and the unequal 3/2 and 13/2 cosmological convergences while proving that completed child explanations do not manufacture their missing joining derivation. A typed countermodel establishes stability in one context while the upper context rejects target trapping. Other countermodels show that implication-valued reductio bridges can be vacuous without the global causal setup, that a completed reductio does not supply theory/world soundness, and that directional incompleteness at theory and world level does not reconstruct the trapped-surface route. A nineteen-component mutation audit rejects every changed selected object or relation. A finite composed witness realizes stability-supported incompleteness, while a converse model realizes generic incompleteness with a vacuous stability child and rejects the composite endpoint. Lorentzian geometry, Einstein equations, energy tensors, curvature divergence, black holes, cosmic censorship, collapse dynamics, and cosmological optical calculations remain paper-local.
PhysicsLogic/Framework/ValidatedNumericalPrediction.lean: the lower-level numerical inference independently realized by Fermi-Pasta-Ulam 1955, Zabusky-Kruskal 1965, and Creutz 1980. It separates regime and observable selection, protocol execution, calculated validation checks, the observable-specific reliability bridge, the paper-local numerical calculation, and the bridge identifying its reported value as a physical prediction. Its proof-free calculation model retains the system, run, regime, observable, reported value, and all nine proposition-valued relation families used by the route. The output-led established result retains exact selected setup plus the direct protocol, validation, reliability, calculation, representation, and prediction facts at the model's selected reported value. The complete implication-valued route, both calculations, and both interpretation bridges are reconstructed from those outputs. The component distinguishes the finite calculation model from a theory and represented world. Pre-calculation grounding requires exact retained semantics plus the valid regime and selected observable, but no protocol, validation, reliability, numerical calculation, selected result, or prediction. FPU grounds the finite-chain setup, Zabusky-Kruskal the physical periodic KdV setup, and Creutz the finite-cutoff measured-loop setup. The final grounded result separately combines this certificate with the complete numerical route and selected reported value; all three adapters expose complete theory/world transfers. The established result alone exposes the selected result, realizes every claim, and establishes the direct inhabited route. A countermodel proves that an existential result at a different value cannot establish the selected prediction. The thirteen-claim vocabulary exposes exact semantic selection, setup, protocol, both calculations, both interpretation bridges, validation and reliability outputs, the selected numerical result, prediction, and established route. A sensitivity theorem distinguishes every explicit-index change as a different model and rejects every retained-relation change as a failure of exact semantic retention. The same established output also yields a direct inhabited-route proposition: validity, observable scope and selection, protocol, validation, reliability, calculation, result representation, and prediction all hold at one selected five-index model. An exact finite witness realizes this proposition, while exhaustive activity theorems show that changing any of the five indices or nine relation families destroys it. FPU, Zabusky-Kruskal, and Creutz expose source-anchored adapters to this direct route; the Zabusky-Kruskal adapter preserves its existentially calculated recurrence state. The component now also exposes ordinary and source-sensitive structural explanations of that direct prediction. The ordinary explanation records the applicable selected numerical route and its situated predicted phenomenon. The source-sensitive explanation additionally requires a typed paper-local derivation relation, without consuming an established endpoint or flattening that derivation into generic numerical prose. FPU retains its finite-difference modal-energy validation and one-percent return source, Zabusky-Kruskal retains periodic-KdV validation, soliton focusing, and waveform reconstruction, and Creutz retains equilibrium checks, finite-size Wilson-loop stability, and the selected loop fit. A countermodel realizes the ordinary explanation while refuting the absent source derivation, so the two explanation levels cannot collapse. Countermodels show that a completed numerical route alone does not supply theory/world grounding, that a grounded numerical setup need not complete reliability or prediction, that numerical outputs without the selected physical setup cannot ground a model, and that declared theory and world claims do not reconstruct the numerical route. Discretization, convergence, Monte Carlo, recurrence, finite-size scaling, and continuum semantics remain paper-local.
PhysicsLogic/Framework/ValidatedNumericalNearReturn.lean: the narrower numerical-evidence inference independently realized by Fermi-Pasta-Ulam 1955 and Zabusky-Kruskal 1965. It separates run and regime selection, protocol execution, validation checks, their interpretation as reliability for an explicitly selected return observable-neighborhood criterion, and a paper-local evolution calculation yielding return to that same neighborhood at positive time. FPU selects first-mode energy within one percent; Zabusky-Kruskal selects waveform-profile reconstruction. Its explicit applicability proposition requires all of these inputs together before the established result. The return calculation is indexed by the model's selected final state, and the output-led established proposition directly retains exact selection, setup, protocol, checks, reliability, selected evolution, and selected neighborhood return. Named projections recover the setup, validation calculation, reliability interpretation, return calculation, reconstructed complete route, existential recurrence, and flattened compatibility result. Countermodels prevent implication-valued calculations from becoming applicable when the protocol is absent. NonvacuousValidatedNumericalNearReturnAt is now part of the established result itself rather than requiring a second selected-result certificate. A finite witness realizes that proposition, while six index mutations and nine relation mutations show that every route-used component matters; the protocol-free implication model fails the direct proposition. FPU and Zabusky-Kruskal expose named paper adapters to it, with Zabusky-Kruskal preserving its existentially calculated recurrence state. The component now also distinguishes the finite near-return calculation from a theory and represented physical system. Paper-local theory-use and representation bridges are grounded from the exact selected model and physical near-return setup alone. FPU uses its finite-chain setup; Zabusky-Kruskal uses its physical KdV setup and positive recurrence time. Protocol, validation, reliability, evolution, neighborhood return, and the selected final-state result remain downstream. Named paper-local setup adapters certify exactly this grounding boundary. Once separately established, those claims transfer without adding exact recurrence, ergodicity, or thermalization. Exhaustive realization follows from establishment alone. FPU names its reported return state, while Zabusky-Kruskal preserves an existentially selected state. A shared witness bridge now turns either selected near-return result into the lower-level selected numerical result and derives all thirteen numerical-prediction claims without repeating the evolution-and-neighborhood proof. Both paper adapters expose named complete theory/world transfers for all ten near-return claims. Countermodels show that a completed numerical route does not supply semantic grounding, that grounded setup does not supply the numerical route, and that declared theory/world claims do not reconstruct it. They also show that reliability for a foreign observable criterion cannot establish the selected return, and that numerical outputs without the physical setup cannot ground a model. SourceSensitivePredictionSupportedNumericalNearReturnAt additionally retains exact lower/upper model selection, their derived-model equality, the inhabited positive-time return, independently sourced prediction and return explanations, and a paper-local joining derivation. FPU's handoff retains its fixed-endpoint quadratic equation, finite chain, Fourier modal analysis, independent total-energy/linear controls, and explicitly neglected nonlinear modal-potential contribution. Zabusky-Kruskal's handoff fixes the actual recurrence state in both models and instead retains the KdV and isolated-pulse equations, period-two cosine profile, exact momentum but approximate energy conservation, unresolved soliton collisions, phase focusing, worsening second return, and open asymptotic scope. A concrete countermodel preserves all physically different FPU/KdV data and both sourced explanations while proving that neither determines a missing joining derivation. Nonlinear-chain, KdV, modal-energy, soliton, mixing, ergodicity, equipartition, and thermalization semantics remain paper-local.
PhysicsLogic/Framework/PowerSpectrumSamplingVariance.lean: the narrow one-realization estimator inference independently realized by Scott-Srednicki-White 1993 and Knox 1995. Both primary calculations now require actual measured fields: the shared quadratic readout computes the estimator, correlations, and fourth moments from one ensemble and retains a Wick-defect correction until the separate Gaussian moment identity is supplied. The finite-patch route derives its angular variance integral; the full-sky route retains the real-mode count, noise subtraction, and beam calibration while deriving residual variance. Knox's full affine estimator law requires a separate joint Gaussian law and retains negative estimates and general multipoles. Independent equal-area finite fields test variances 2 and 1 from different actual correlations. Its proof-free route model retains four selected physical indices plus all ten route-used maps and relation families, including the realization estimator and ensemble target. The context owns all four indices and constructs one selectedCalculation, so changing the model, sky, observable, or experiment fails exact semantics. Its explicit applicability proposition requires exact selected semantics, the single-realization setup, and the paper-local calculation, preventing either ambient relation substitution or vacuous use of the calculation implication. The established result is output-led: exact selected semantics plus the actual one-realization setup, estimator outputs, distinct estimates, sampling variation, and failure of exact ensemble recovery. The original implication-valued estimator calculation and complete route are reconstructed from those direct outputs. Generic grounding requires exact model identity and the observed, possible, accessible, noise-free realization setup, but no estimator law, variance calculation, or sampling conclusion. Knox remains experiment-parameterized: each theorem instance owns its selected full-sky experiment rather than imposing one global experiment. Scott-Srednicki-White retain finite coverage, the zero-lag estimator, beam/chopping treatment, the theory-distribution versus realized-value distinction, and Gaussianity in their own named exact model. A first-class exhaustive theorem realizes all seven shared claims, beginning with the selected-semantics certificate; both papers expose named grounded transfers for every claim. Countermodels separate exact selection from inhabited grounding, technical completion from grounding, grounding from the technical route and direct outputs, and declared theory/world claims from reconstruction of the route. Its retained sensitivity model has an actual observed setup and two possible skies with different estimates. A direct activity theorem makes each physical index affect a route-used predicate, while a fourteen-component sensitivity audit checks that every index, map, and relation mutation fails exact semantics. Independent sky patches remain local to Scott-Srednicki-White's later area-scaling approximation. Gaussian and chi-square laws, CMB multipoles, spherical angular kernels, sky fractions, beams, scan geometries, and experiment-specific numerical forecasts remain paper-local. A separate source-valued physical audit nevertheless retains Scott's fourth-moment contraction, 2/A^2 sample-variance integral, 1/(4 pi) convolved-window normalization, 8/A^3 skewness, distinct small- and large-area limits, qualified independent-patch estimate, correlation- dependent scan area, and variance-versus-temperature distinction. Its Knox witnesses retain 2l+1 Gaussian full-sky modes, strictly positive noise-free cosmic variance, the finite-weight beam-deconvolved noise term, improved resolution at fixed detector weight, conditional 0.016, 0.11, and 0.003 forecasts, nuisance dominance, and the cosmological-constant correction to lowest-order tensor consistency. Independent negative controls reject erased premises and formulas; unqualified area laws, complete foreground models, unconditional measurements, universal tensor relations, and resolved cosmological degeneracies are not silently established.
PhysicsLogic/Framework/Conservation.lean: shared balance-to-conservation semantics extracted from Noether 1918 and Einstein 1916. It separates a local or covariant balance equation, the physical scope in which it may be interpreted as conservation, and the explicit paper-local bridge yielding the conservation conclusion. Its proof-free model retains the selected quantity, system, and regime together with the balance, scope, and conservation relation families. The context owns those three indices and exposes their unique selectedModel; a candidate cannot select itself by changing them. Noether fixes the represented physical history, while Einstein fixes its unit-typed balance indices around one matter tensor and situation. Both construct named context-selected models and prove exact semantic-retention certificates. Applicability consumes that certificate and retains the balance, scope, and bridge without assuming the conclusion. The established result is output-led: it stores exact selected balance-and-scope setup plus the direct conservation output, while checked theorems reconstruct the implication-valued bridge and complete route. The route also realizes a typed structural explanation whose balance constraint and conserved phenomenon are distinct. Noether and Einstein now derive that explanation directly from their source inputs and the applicable route, before any terminal shared endpoint is consumed. Noether's multidimensional on-shell divergence argument and Einstein's covariant absent-exchange reduction remain different mechanisms; the adapter does not attribute Noether's symmetry derivation to Einstein. A stronger source-sensitive constraint now retains those derivations as different typed values governed by proposition-valued source relations. Its accessor recovers the selected derivation, while a countermodel retains the complete balance route, established conservation, and ordinary structural explanation with every candidate source relation false. The established-result projections remain compatibility paths. It imports Philosophy/TheoryModel.lean and Paradigm/ExplanationModes.lean and accepts paper-local theory/world interpretations. Grounded conservation requires a separate proof that the exact selected balance model has an actual balance equation and conservation scope, belongs to the selected theory, represents the selected physical case, and transfers soundly. This grounding does not require the interpretation bridge, applicability, or conservation output. Countermodels prevent missing premises or a vacuous implication-valued bridge from silently establishing the route, separate completed conservation from semantic grounding, exhibit a grounded balance-and-scope setup without a bridge or output, reject grounding from an output without that setup, and show that theory/world claims do not reconstruct the balance route. Conservation for an independent reason also fails the structural balance explanation. A complete mutation audit proves that changing any of the three indices or three relation families fails the original context's exact semantics. A separate active finite model makes the selected balance, physical scope, interpretation bridge, and conservation conclusion all true together. Direct route-content theorems show that changing any index or relation destroys this nonvacuous result. Noether's multidimensional Div B = 0 route and Einstein's absent-gravitational-exchange route each expose the same stronger proposition through named paper theorems.
PhysicsLogic/Framework/ConstraintConsistencyCompletion.lean: narrow constrained-dynamics semantics extracted from Dirac 1950 and Anderson-Bergmann 1951. Its proof-free model retains the constrained system, selected Hamiltonian dynamics, one actual primary constraint, primary family, completed family, and all six relation families that give those data their shared meaning. Exact eleven-component semantics is required before the route can establish that the selected constraint belongs to the primary family, exclude a contradictory consistency branch, and use a paper-local calculation proving primary inclusion and preservation under the same dynamics. The established result is exact selection plus the direct model-native NonvacuousConstraintConsistencyCompletionAt proposition, and derives all ten shared claims and concrete completion and preservation of that selected primary. The ordinary structural explanation retains the complete selected route without requiring paper provenance. A stricter source-sensitive explanation wraps that ordinary constraint, requires an independently realized typed paper derivation, exposes it, and entails the ordinary explanation when provenance is forgotten. Both execute the complete route to obtain primary inclusion and completed-family preservation. Dirac supplies the type-II iterative weak-constraint completion of equations (22)-(25); Anderson-Bergmann supply the canonical primary construction and invariant-generator/Hamiltonian-bracket iteration. Dirac's paper-local module separately retains equations (5)-(11) as a finite-indexed value-level Hamiltonian-construction package: the Hamiltonian definition and variation, weak canonical equality, strong primary-constraint shell equality, and the two coordinate equations. That package remains local because the shared completion component needs only constraint inclusion and preservation, not Dirac's particular variational construction. Anderson-Bergmann's electromagnetic specialization separately retains equations (6.6)-(6.9) as pointwise value-level momentum, primary/secondary surface, generator-density, and bracket-chain propositions over a nonempty field-point domain; a countermodel prevents the final count/algebra labels from standing in for those formulas. Its coordinate specialization likewise retains the structural content of equations (7.1)-(7.7): pointwise Legendre degeneracy and primary surfaces, four distinct primary and four distinct secondary constraints, primary-proportional velocity dependence in the generator, the quasi-inverse identity, velocity-bracket rule, and closing bracket pattern. A second countermodel prevents the eight-count, velocity label, and algebra flag from replacing that package. The shared boundary readout now separately retains an actual preservation transition, constraint values at its endpoints and two candidate orbit points, first-class or invariant-generator bracket closure, independent generator count, orbit dimension, and physical-identification residual. Its checked model bridge ties those values to the same selected system, primary member, completed family, state membership, evolution, and satisfaction relation as the consistency route. A completed constraint without closure, generator, orbit, or identification does not become gauge; generator closure alone does not preserve a constraint; and a positive finite witness shows that consistency and physical gauge identification are compatible when all required data are present. Dirac's first-class solution-orbit witness retains preservation and a nontrivial orbit while withholding physical identification; Anderson-Bergmann's invariant-generator witness retains bracket closure while losing the constraint under canonical evolution. Their classification, function-group, and finite-count conclusions remain outside the shared phenomenon. Dirac and Anderson-Bergmann construct named exact models and ground them through separate paper-local theory-use, world-representation, and claim-transfer predicates plus the inhabited, noncontradictory selected setup. Grounding assumes no completion calculation, inclusion, preservation, route, or result. Countermodels separate setup, inclusion, preservation, technical completion, and semantic grounding; an empty-family model blocks vacuous universal laws, and an eleven-component equality audit detects every retained datum and relation. A stronger countermodel keeps the complete endpoint, reconstructed route, and ordinary structural explanation while falsifying the paper-local derivation relation, so ordinary completion logic cannot manufacture source provenance. A separate finite initial-to-final witness makes all five selected data and six relation families directly active in the nonvacuous completion proposition. Legendre maps, constraint classes, gauge generators, electromagnetic and coordinate canonical formulas, finite counts, and quantization remain paper-local.
PhysicsLogic/Framework/CanonicalGeneratorBracketClosure.lean: narrow canonical-generator closure semantics extracted independently from Dirac 1950 and Anderson-Bergmann 1951. Each paper-local context owns the selected canonical system, admissible-generator family, and bracket relation. Its unique proof-free model retains those data and all three context selection relations. The setup evaluates those retained relations, and each paper proves equality with the exact context model before route applicability, so candidate data cannot select themselves. A separate calculation yields nonemptiness and pairwise admissible representatives. Dirac realizes admissible generators as first-class constraints; Anderson-Bergmann realizes them as generators of infinitesimal invariant canonical transformations. The bracket is relational so linear-combination or equivalent representatives need not be identified syntactically. The established result is output-led: it retains exact selected semantics and the direct nonvacuous closure output. Complete setup, calculation, and route witnesses are reconstructed from those facts, with separate theory/model/world grounding. The model-native NonvacuousCanonicalGeneratorBracketClosureAt proposition records the selected system, both selection relations, an admissible generator, and pairwise admissible bracket representatives without relying on an implication-valued calculation. Both paper adapters now expose that direct inhabited result, alongside named certificates transferring all eight retained claims to their selected theory and represented physical system. The complete route additionally realizes a typed structural explanation of the selected nonempty pairwise closure. A finite countermodel retains an inhabited closed family but removes canonical-system selection, proving that algebraic closure alone does not reconstruct the explanation. Dirac and Anderson-Bergmann independently realize the route-bounded endpoint. Grounding uses an actual canonical setup plus pre-calculation theory and world inputs, but no bracket calculation or result. A false-setup model is proved ungroundable; a separate setup-complete nonclosed model is grounded while route applicability remains false. The false-setup calculation also shows why implication-valued calculations cannot stand in for outputs. A concrete finite witness exhibits two admissible inputs and an admissible bracket result. Direct activity theorems make every selected datum and retained selection relation destroy the model-native nonvacuous result when changed, while a separate six-component sensitivity audit checks exact retention. Its three directional shared countermodels now retain canonical phase dimension, admissible-generator count, canonical-selection and left/right/ bracket-admissibility residuals, a bracket representative and its distinct constraint-combination value, a Hamiltonian bracket and its separate constraint-combination value, and theory/model/world mismatches. A false canonical selection makes the implication-valued closure calculation vacuous; pairwise closure with Hamiltonian bracket two and constraint combination one blocks compatibility; completed closure with nonzero grounding mismatches blocks physical transfer. A checked positive witness realizes all four boundaries. No proposition-pair truth table replaces these canonical-bracket distinctions. The framework now also composes the independently inhabited ConstraintConsistencyCompletion result with actual generator closure through a proof-free, source-order-aware handoff. Dirac's completed-first route retains the selected weak primary, an independently completed first-class representative, and the equation-(43) Poisson-identity calculation. Anderson-Bergmann's generator-first route retains the invariant descriptor extension, quadratic-primary generator ambiguity, equation-(5.6) function-group calculation, separate Hamiltonian-bracket compatibility, and subsequent preservation iteration. A stronger SourceSensitiveCompletedConstraintGeneratorClosureAt contract selects both child contexts exactly and independently retains their two source-sensitive structural explanations together with a third typed paper-local handoff derivation. Its projections recover each derivation separately, and its generator-first projection still requires the actual Hamiltonian-bracket calculation. Dirac's handoff explicitly has no such Hamiltonian-bracket premise. An additional inhabited countermodel keeps both completed child results, their two source-sensitive explanations, the completion-first order, and the absence of Hamiltonian-bracket compatibility while withholding the third handoff derivation; the sourced composition consequently fails. Eight finite countermodels distinguish the source orders, reject completed outputs without their paper-local handoff, separate completion from closure in both directions, withhold Hamiltonian compatibility from generator closure, reject route reclassification, and retain a nontrivial constraint-surface orbit without asserting physical gauge identification. Poisson-bracket construction, closure with the Hamiltonian, integrability, orbit dimension, gauge interpretation, and application-specific constraint algebras remain paper-local.
PhysicsLogic/Framework/ProjectorValuationObstruction.lean: narrow shared complete-projector obstruction semantics extracted from Bell 1966 and Kochen-Specker 1967. Its explicit route requires an actual available projector in a complete compatible context, complete reference contexts for every projector, and a paper-local calculation excluding every global exactly-one coloring. The established result retains those inputs, excludes a context-independent model, and realizes the generic contextuality obstruction. The model-native NonvacuousProjectorValuationObstructionAt proposition packages the inhabited complete context, complete reference coverage, no-coloring result, and context-independent-model exclusion directly. One exhaustive theorem realizes all six shared claims, and both paper adapters expose named direct, exhaustive-realization, and grounded-transfer certificates. A data-only calculation model is explicitly separated from the quantum theory using it and the physical measurement situation it represents. Grounding does not consume either no-coloring result. Bell uses only the dimension-greater-than-two condition, his selected projector in a complete reference arrangement, and both real/binary constraint translations; Kochen-Specker's finite 117-direction calculation explicitly retains an inhabited complete projector context before its no-coloring output, then separately uses the commutative-embedding, spin-one, and rhombic-field bridges. Its paper-local spin-one readout additionally retains actual normalized rays, complex angular-momentum commutators, squared-spin projectors and Casimir, all three source Hamiltonian polynomials, distinguishable energy outcomes, and separate adjustable-orthohelium versus fixed-nickel field controls. The displayed source proposition means nonzero spin; a checked complement theorem translates it to the shared zero-spin exactly-one convention. The printed longitudinal-matrix normalization typo is excluded from the physical assumptions. Its ordinary structural explanation now uses only the exact scenario and applicable no-coloring route to derive the conditional contextuality phenomenon. A separate source-sensitive refinement adds a typed paper derivation: Bell retains both real/binary translations and the Gleason obstruction, while Kochen-Specker retains the finite 117-direction calculation. The stronger explanation exposes its derivation and entails the ordinary explanation. Neither route claims indeterminism or a universal hidden-variable impossibility. Countermodels show that an empty declared complete context can satisfy a no-coloring proposition without realizing the direct obstruction, that technical completion does not automatically supply theory/world grounding, that grounding does not supply the obstruction route, and that declared contextuality in a theory and world does not reconstruct the coloring route. A finite logical witness realizes the complete obstruction route together with locally consistent contextual values; with its source derivation relation made false, the same outputs and ordinary explanation have no source-sensitive structural explanation. Direct activity theorems distinguish availability, completeness, assigned values, and reference-context choice: changing assigned values can preserve the direct no-go while breaking local exactly-one satisfaction, because neither paper claims to construct a contextual hidden-variable model. Exact model retention remains a separate four-family audit. Gleason theory, finite coloring constructions, spin realizations, apparatus dependence, and measurement bridges remain paper-local.
PhysicsLogic/Framework/DiscreteSymmetryVacua.lean: shared finite-symmetry vacuum-counting semantics extracted from Witten 1982 and Seiberg-Witten 1994 formalization. It separates exact law symmetry, spontaneous breaking, parent and residual orders, properness of the residual subgroup, the physical coset-to-vacuum bridge, applicability of the counting route, and an independent vacuum calculation. The output-led established prediction is exact selected semantics together with the direct NonvacuousSymmetryBreakingPredictionAt proposition requiring a proper residual subgroup, exact count, and more than one vacuum. Checked theorems reconstruct the complete counting route from those outputs. The agreement proposition separately retains an independent calculation. A proof-free calculation model retains system, regime, parent order, residual order, predicted count, and exactly the five route-used relation families: exact law symmetry, spontaneous breaking, both order readouts, and the vacuum-count readout. Each paper constructs a named context-induced model from five context-owned indices and proves exact ten-component retention before route applicability or grounding. A candidate with a changed system, regime, parent order, residual order, or predicted count cannot certify itself against values read back from that candidate. Paper-local bridges transfer exact symmetry, spontaneous breaking, proper residual order, arithmetic, coset realization, the derived count, and multiplicity to a theory and represented world. Model grounding itself uses only that exact-model certificate and paper-local interpretation; it does not assume any breaking, properness, arithmetic, coset, count, or multiplicity claim. The established result realizes all fourteen shared claims. Exact-retention mutations detect every changed index or relation family, and a positive finite order-four-to-order-two model passes a stronger typed audit: each of the five selected-index mutations and each of the five relation-family mutations destroys the direct nonvacuous endpoint itself. A complete direct output tested against a context selecting another system also fails establishment. A collapsed breaking label with parent order equal to residual order is a checked countermodel: it can satisfy the trivial one-vacuum arithmetic while failing both proper residual order and the direct nonvacuous endpoint. A second countermodel retains the correct count and coset arithmetic while lacking spontaneous breaking, and therefore also fails the direct endpoint. Witten's context selects rank N, a four-dimensional regime with infinite spatial volume, and counting data (2N, 2, N), then grounds that conditional count in pure N = 1 SU(N). Seiberg-Witten selects a four-dimensional, zero-matter SU(2) gauge system together with a regime recording the N = 2 parent, preserved N = 1, and preserved Z4, followed by the fixed count data (4, 2, 2). It grounds the order-four to order-two count in that distinct mass-deformed N = 1 theory, then separately checks agreement with the two vacua obtained from its monopole and dyon singularities.
PhysicsLogic/Framework/QuantumCurrentAnomaly.lean: narrow shared current-level anomaly semantics independently realized by Adler 1969, Witten 1982, and Seiberg-Witten 1994. It separates selection of the physical system and current, classical conservation, the paper-local quantum calculation, the bridge to failed quantum conservation, and the criterion identifying the obstruction as an anomaly. The output-led established proposition retains exact selected classical-current setup, the performed quantum calculation, failed conservation, and identified anomaly. The implication-valued bridge, criterion, and complete route are reconstructed from those outputs. It also projects a direct NonvacuousQuantumCurrentAnomalyAt result with the setup, calculation, actual conservation obstruction, and identified anomaly. A finite inhabited model realizes this proposition; exhaustive direct mutations show that either selected index or any of the six relation families destroys it. A proof-free calculation model records the selected system and current together with all six relation families used by the route: system selection, current selection, classical and quantum conservation, the paper-local quantum calculation, and anomaly identification. The context owns the two selected indices and constructs a unique selectedModel; exact semantics is equality with that model rather than reconstruction from a candidate's own labels. Checked mutation theorems reject both changed indices and all six changed relation families. Each paper obtains its named model from that context-owned selection. Separate theory and world wrappers and paper-local interpretations control transfer of every shared claim. Grounding consumes exact selected semantics, physical system and current selection, classical conservation, and interpretation bridges; it does not assume the quantum calculation, obstruction bridge, anomaly criterion, or anomaly result. Adler grounds the model in massless spinor electrodynamics, Witten in pure four-dimensional N = 1 SU(N) Yang-Mills at the selected rank, and Seiberg-Witten in pure four-dimensional N = 2 SU(2) Yang-Mills. Their independent original anchors are Adler p. 2434, Witten p. 269, and Seiberg-Witten author TeX §2. Witten p. 297 and Eq. (74) then calculate the residual 2N subgroup; that result and Seiberg-Witten's Z8 calculation remain in the downstream anomaly-restriction layer. Every established result realizes all nine shared claims through one exhaustive theorem, and all three paper adapters expose named realization exact-retention, and grounded-transfer certificates. Countermodels show both that vacuous implication-valued bridges cannot replace the physical setup and calculation and that an established anomaly does not automatically supply theory/world grounding. A further typed countermodel grounds the selected classical-current setup while the quantum calculation and established anomaly are false; the converse countermodel supplies all quantum outputs but cannot ground a false selected setup. It does not calculate a residual finite subgroup, spontaneous breaking, or vacuum multiplicity.
PhysicsLogic/Framework/AnomalyRestrictedSymmetry.lean: narrow shared residual-symmetry semantics extracted from Witten 1982 and Seiberg-Witten 1994. It consumes an established shared current-anomaly route, then keeps the anomaly-coefficient calculation, selected nontrivial anomaly sector, residual-order calculation, candidate-subgroup measure invariance, anomaly-phase obstruction of larger candidates, and exact finite-law bridge separate. The established proposition is output-led: it retains exact context selection together with the direct nonvacuous current anomaly, coefficient, sector, order, phase-test, and exact finite-law outputs. The embedded current result, exactness bridge, and full route are reconstructed by checked theorems rather than stored as evidence. A proof-free reduction model stores the selected system, symmetry, and residual order, the complete upstream current-anomaly model, and all six downstream relation families used by the route. The embedded current-anomaly context owns the selected system and current, while this context owns the residual order; together they construct one unique selectedModel. Each paper uses that model and proves its exact certificate before applicability. Coefficient, sector, order, phase, and exact-law claims remain proposition-valued applications of those retained relations rather than proof fields. Witten realizes coefficient and exact order 2N at one SU(N) rank; Seiberg-Witten realizes 4N_c-2N_f=8 and exact Z8 in microscopic pure N = 2, SU(2). NonvacuousAnomalyRestrictedSymmetryAt now drops exact-record equality while retaining same-system/current ties, the nonvacuous upstream current anomaly, coefficient, sector, order, positivity, both phase tests, and the exact finite-law output directly on one proof-free model. Both paper adapters project their completed calculations to that endpoint. The route now also realizes DirectStructuralAnomalyRestrictedSymmetryExplanationAt from its raw applicability proof. The stricter DirectSourceStructuralAnomalyRestrictedSymmetryExplanationAt retains a typed paper-local derivation relation in addition to the same route; forgetting provenance yields the ordinary explanation, while a finite false-source countermodel proves that a completed endpoint cannot invent provenance. Witten's full section-8 instanton-phase restriction and Seiberg-Witten's microscopic exact-Z8 restriction are represented by distinct typed source tokens and relations, separate from their narrower upstream current-anomaly source relations. The independent original anchors are Witten p. 297 and Eq. (74) and Seiberg-Witten author TeX §2. Witten's conjectural condensate breaking and Seiberg-Witten's later mass-deformation restriction remain downstream. Grounding consumes the exact-retention certificate, upstream exact current-model grounding, and paper-local theory/world interpretation; it assumes none of the anomaly-reduction calculations or conclusions. Both adapters expose exhaustive realization and grounded transfer for all fourteen claims. Exact-record mutation theorems reject all three changed indices and all seven changed model families; a separate route-active finite model shows that each of those mutations also destroys the direct nonvacuous endpoint itself. A second countermodel has all direct outputs but fails exact context selection, so it cannot establish a result for the wrong paper-selected system, current, or subgroup order. Further countermodels show that coefficient and order do not select a nontrivial sector, measure invariance does not establish maximality, and complete phase data without an exactness bridge does not establish the quantum law. The component does not identify the surviving subgroup with a spontaneously broken phase; condensates, mass deformations, and vacuum counting remain paper-local.
PhysicsLogic/Framework/AnomalySelectedVacua.lean: shared composition of anomaly reduction, paper-local selection of the exact finite symmetry used in the vacuum regime, spontaneous breaking, and coset vacuum counting. Witten's selection preserves the anomaly-surviving order 2N; the Seiberg-Witten mass deformation instead selects Z4 from Z8 before Z4 -> Z2 breaking. Each paper exposes a named complete composite route before the shared deduction. The output-led established result retains exact selection of both child models plus direct anomaly, parent-selection, and vacuum outputs. Named theorems reconstruct the anomaly route, parent-selection interpretation bridge, spontaneous-breaking data, proper residual order, subgroup arithmetic, coset bridge, and complete composite route. It exposes both the child's direct proper-subgroup, multiple-vacuum prediction and a direct composite endpoint requiring nonvacuous anomaly restriction, paper-local parent selection, and the multiple-vacuum prediction together. The implication-valued selection bridge remains a route premise rather than counting alone as physical activity. Its proof-free composite model is grounded through the two setup-only parent model groundings and permits distinct anomaly-source and vacuum-regime theories and worlds. Witten uses the same pure N = 1 theory for both roles and supplies classical chiral-current conservation; Seiberg-Witten uses microscopic pure N = 2 plus its classical current for the anomaly role and only the presence of the N = 1 mass deformation for the vacuum role. Composite grounding fixes both exact context-induced parent models, including the finite-vacuum model's five relation families, and the paper-local semantic bridges; it consumes no anomaly-reduction, parent-selection, breaking, subgroup-arithmetic, coset, or vacuum-count route. Those claims transfer only after the separately established composite result is joined to the grounding. A checked countermodel has a nonvacuous vacuum child but no active anomaly child, so the direct composite endpoint fails; another has complete grounding while the composite route is false. Complete direct outputs under a differently selected anomaly order can be neither established nor grounded. The component keeps currents, deformations, condensates, and vacua paper-local.
PhysicsLogic/Framework/BoundaryGeneratingFunctional.lean: shared source-indexed functional and correlator-transfer semantics extracted from Gubser-Klebanov-Polyakov 1998 and Witten 1998. Its explicit route-applicability proposition keeps functional equality, source generation, and the differentiation bridge separate and source-specific. The established dictionary instead stores exact model selection and the direct nonvacuous functional, derivative, and correlator outputs; a checked theorem reconstructs the complete route from those outputs. It projects to NonvacuousFullBoundaryDictionaryAt, where one actual selected source/bulk pair directly satisfies an inhabited variation scope, admissibility, extension, functional equality, both derivative equalities, and the resulting correlator equality. A finite witness and direct two-index/seven-family mutations make every retained component matter, while a vacuous derivative bridge without a dictionary is explicitly rejected. A proof-free source/bulk model is separately related to a containing theory and represented boundary sector. Grounding fixes exact selection, an inhabited variation sector, source admissibility, and boundary extension, but no functional equality or correlator calculation. GKP grounds it in the D3 near-horizon, leading-large-N strong-coupling regime using only the admissible source and selected action-minimizing bulk extension. The Witten adapter grounds its boundary CFT and classical bulk solution from the conformal boundary, regime, source, boundary value, and bulk equation. Proposals, saddle evaluations, source generation, differentiation, and correlator extraction remain in the technical routes. A further countermodel satisfies every direct functional and correlator output while withholding admissibility and extension, so outputs alone cannot supply grounding. Other countermodels separate grounding from both completed and incomplete dictionary calculations. The module does not define a generic holographic duality or import paper-local geometry and spectra. Both adapters expose named certificates transferring every retained source-indexed dictionary claim to their selected theory and boundary sector. Each also exposes the selected boundary source and bulk configuration as direct checked field equalities. GKP's direct adapter is source-anchored in author-TeX lines 484-520; Witten's is anchored in author-TeX lines 612-705 and 772-825.
PhysicsLogic/Framework/BulkBoundaryScalar.lean: shared scalar mass-dimension semantics extracted from Gubser-Klebanov-Polyakov 1998 and Witten 1998. Paper-local scalar selection and field/operator pairing make the wave-calculation route applicable. The established result is output-led: exact selected semantics plus the directly inhabited scalar/operator mass-dimension result. The complete paper-local wave route is reconstructed from those outputs. Its seven-component proof-free model records the selected field, operator, boundary dimension, both full numerical maps, and the scalar-status and field/operator-pairing predicates. The context owns its field/operator pair and induces one selectedModel; changing either object therefore fails exact semantic retention rather than producing a newly self-selected model. Exact equality with that paper-induced model is required by model use, world representation, model entailment, and grounding; grounding also requires the selected scalar/operator pair to be inhabited. It retains relation meanings without supplying the wave calculation or the mass-dimension conclusion. GKP fixes one massless scalar/operator context in its D3 strong-coupling sector before applying the flux calculation. Witten retains the source's generality by constructing a context parameterized by each selected massive field/operator pair before applying the larger-root, and source-weight calculations. Witten's two-point calculation remains a separate verification and input to the composed correlator route. Each adapter constructs a named exact model, proves its retention certificate before either the technical route or grounding, and exposes its selected field and operator directly. Countermodels separate numerical agreement and theory/world grounding from completion of the scalar route. A false pair cannot be grounded even if theory/world claims are declared universally true, and a mutation audit detects changes to every retained component. The established result is itself exact selection plus a direct nonvacuous scalar dictionary: GKP author-TeX lines 612-732 and Witten author-TeX lines 1114-1212 anchor the two adapters. A false-setup wave-bridge countermodel and a separate finite witness make both selected indices and all five retained numerical or relation families directly active. Its PhysicalBranch is the larger-root choice made in these source arguments, not a universal exclusion of later alternate quantizations.
PhysicsLogic/Framework/ScalarCorrelatorComposition.lean: narrow checked composition of the boundary generating-functional and bulk-boundary scalar contracts, independently realized by Gubser-Klebanov-Polyakov 1998 and Witten 1998. Each paper first constructs a setup-only composite certificate from exact source/field/operator and bulk-configuration/field links plus the selected setups of both child models; this step consumes no proposal, calculation, or child result. A separate paper-local bridge then identifies the complete selected boundary-correlator map with the scalar two-point power law at the established operator dimension. GKP retains its massless boundary-flux calculation; Witten retains its massive Green-function and on-shell-action calculation. The component does not define holography, functional differentiation, or either explicit correlator formula. The route now requires an inhabited variation scope. Its output-led established result retains the selected composite setup plus a model-native direct nonvacuous composition containing both direct child dictionaries, all three compatibility links, and the realized dimension-indexed two-point statement, but no route or calculation bridge. The complete route is reconstructible from those outputs. An empty-variation countermodel blocks vacuous derivative and bridge contracts, while a direct mutation audit makes both child dictionaries and every added relation physically active. Three additional inhabited composed models separate the actual child dictionaries, source compatibility, and scalar two-point bridge: mass squared one violates the zero-dimension scalar equation, source false fails a relation requiring source true, and correlator value zero fails a dimension-shifted target one. No proposition-only truth table substitutes for those physical boundaries. Grounding consumes the setup-only composite certificate but remains independent of both child results, both child routes, and the scaling calculation; direct outputs on an unselected model cannot ground it. The complete GKP and Witten routes now also independently realize a typed structural explanation of only the selected dimension- indexed boundary two-point behavior. Its proof-free constraint omits the final two-point predicate, and an inhabited output-without-functional- dictionary model blocks the occurrence-to-explanation converse. No causal mechanism, derivational reduction, or full-duality conclusion is added.
PhysicsLogic/Framework/HolographicRegionEntropy.lean: shared region/surface entropy semantics extracted from Ryu-Takayanagi 2006 and Lewkowycz-Maldacena 2013. It requires regime-scoped dual descriptions, a selected anchored codimension-two surface, explicit observable translation, a paper-local minimality bridge, and a separate normalized area-to-entropy bridge. Both papers now expose the complete shared bridge and value-calculation applicability proposition before deriving the established entropy. The established result is output-led: exact selected setup plus the direct nonvacuous entropy endpoint. Checked eliminators reconstruct both paper-local bridges and the complete calculation route. Its proof-free model retains eight selected indices and all fifteen route-used semantic families: validity, the four duality-dictionary components, both observable maps, anchoring and selection relations, and all area and entropy maps. RT and LM each construct a named exact model and prove a retention certificate before route applicability. Separate paper adapters combine that certificate with the declared RT or LM region/surface setup. Their grounding proofs use only the selected setup, theory use, boundary-region representation, and conditional transfer of all twenty-five shared claims; they do not use the proposal, replica calculation, minimality, area calculation, bridge, or established entropy result. The established result contains a model-native NonvacuousHolographicRegionEntropyAt endpoint that directly retains the exercised setup, dictionary, minimality, area, normalization, and entropy facts without counting exact context equality or implication-valued bridges. Both RT and LM prove that endpoint from their paper-local routes. Each route also projects to an inhabited singleton entropy sector in the neutral duality interface: the translated boundary and bulk observables share the selected entropy prediction. A finite countermodel preserves that common prediction while adding a bulk-only value, proving that the calculation does not establish preservation of the complete prediction relation. The calculation route now also realizes a typed structural explanation of the selected region-entropy equality and matching native boundary/bulk predictions. Its constraint contains physical duality, the exact observable dictionary, selected surface setup, both bridges, area calculation, and normalization, but no final entropy agreement. RT supplies that route from its original proposal; LM supplies it directly from fixed-surface, continuation, Einstein, cone, and AdS/CFT calculations rather than packaged minimal-surface or generalized-entropy outputs. A model with every terminal entropy output at an unselected region has no route or explanation. Countermodels separate technical completion from grounding, grounding from the technical route, declaration from derivation, and vacuous bridges from the direct endpoint. Direct outputs at an unselected region cannot be grounded. A finite model realizes the complete route with distinct boundary and bulk descriptions and observables. Direct mutation theorems make every selected index and semantic family falsify the nonvacuous endpoint, while the older route-fact audit and a twenty-three-field exact-retention audit remain independent checks. Geodesics, replicas, Einstein equations, cone actions, and all proposal or extension statuses remain paper-local. RT now also keeps its original AdS3 vacuum and BTZ interval formulas paper-local: a real-valued readout retains the Brown-Henneaux relation, explicit large/small regime controls, positive-factor cutoff matching, regulated geodesic equations, and vacuum/thermal entropy expressions, while a countermodel prevents named interval outputs from substituting for those formulas.
PhysicsLogic/Framework/SupersymmetricVacuumEnergy.lean: shared zero-energy-vacuum semantics extracted from Witten 1981 and Witten 1982. Its route separates zero-energy-state evidence, the bridge fixing ground energy, and the global-supersymmetry breaking criterion. The established result is exact selected-regime setup plus a direct nonvacuous unbroken endpoint. Its proof-free model retains the regime, ground energy, zero-energy value, and the complete zero-state, ground-energy, and breaking relation families. A selected-data certificate is one of ten exhaustive claims. Finite witnesses and six-component mutation audits show that every retained value and relation family is active in the endpoint, while direct outputs at an unselected regime do not establish it.

Witten 1981 constructs one named exact global model and grounds the shared route without a Hamiltonian, ground-state, zero-state, or completed-route premise. Its stronger absence-of-zero-state converse and positive-energy breaking theorem remain paper-local because they have no second independent client. Witten 1982 grounds the shared route from exact model identity and pure N = 1 SU(N) scope together with finite-spatial-volume representation; its supersymmetry-preserving boundary conditions, realized graded trace, nonzero index, zero-state inference, and spectral bridge remain in the technical route. Periodic and twisted routes expose exhaustive realization and transfer independently, while large-volume and boundary-condition principles remain paper-local. Countermodels establish grounding without the technical route, block converse reconstruction, and mutate all three selected values and all three relation families. The shared result is regime-scoped and does not infer infinite-volume breaking from finite-volume breaking. Supercharges, indices, Goldstini, instanton dynamics, and the local- supergravity exception remain paper-local.
PhysicsLogic/Framework/MetricConnectionCurvature.lean: independently source-qualified contracted-curvature construction shared by Einstein 1916 and Rosen 1940. Einstein's direct branch retains the original signed four-index equation (43), the separate B_mu_nu = R_mu_nu + S_mu_nu contraction, and Gamma^tau_(mu nu) = -{mu nu;tau}. Rosen's distinct Part I branch retains the formal flat auxiliary metric, the nonzero gravitational and flat determinants, the flat connection difference and derivative identity, the rewritten Ricci component, and kappa = sqrt(g / gamma). A flat metric may still have a nonzero connection in curvilinear coordinates. Neither branch supplies a vacuum or sourced field equation; Rosen's formal rewrite does not assign physical geometry to the auxiliary metric or establish background independence. Exact rational metric two-jets now compute both branches, including inverse derivatives, Christoffel symbols, full curvature, source-sign contraction, and auxiliary-covariant derivatives. A genuine Lorentzian-signature condition rejects Euclidean geometry. Kernel-checked flat spherical and Ricci-flat tidal examples distinguish coordinate connection, curvature, vacuum, and pointwise versus chart-wide volume conditions.
PhysicsLogic/Framework/VacuumMetricDynamics.lean: narrow shared metric/vacuum/free-motion semantics extracted from Einstein 1916 and Schwarzschild 1916. Its proof-free exact model retains the selected metric, situation, worldline, and all nine route-used relation families: physicality, dynamical relevance, non-fixed-background status, field-equation governance, matter absence, vacuum-equation satisfaction, free-worldline status, metric-to-motion-equation selection, and motion-equation satisfaction. Each paper constructs a named model and proves an exact semantic-retention certificate before route applicability. The paper-local context owns all three selected objects, so its modelAt is unique rather than being rebuilt from whatever indices a candidate model carries. Theory membership and world representation require SelectedVacuumMetricSetupAt: that exact certificate together with the actual physical, dynamically relevant, non-fixed metric, matter-free situation, and selected free worldline. Mutating any selected object fails exact semantics, while a false physical setup cannot be grounded. The route then requires field-equation governance and paper-local bridges separately establishing the vacuum equation and metric-selected free motion. The output-led EstablishedVacuumMetricDynamicsAt retains exact selected semantics and the direct realized setup, governance, vacuum equation, metric-selected motion, and all three outputs. It stores neither implication-valued bridge nor route; checked theorems reconstruct both from the direct facts. The ten exhaustive shared claims remain available through that reconstruction. The route also has ordinary and source-sensitive structural explanations. The ordinary explanation executes the raw applicable route into a selected dynamical-vacuum/free-motion phenomenon without first packaging the established endpoint. The source-sensitive explanation additionally requires one typed paper-local derivation relation. Einstein retains metric-as-field meaning, covariance, curvature/contraction selection, and qualified general geodesic extension; Schwarzschild retains the exterior point-mass conditions, determinant-preserving polar construction, exact integration with continuity, and metric-selected orbit calculation. A finite completed-route countermodel has the ordinary explanation but no source-sensitive explanation when the derivation relation is false. A component-wise mutation audit detects every retained index and relation family. A finite logical witness realizes a physical dynamical metric, vacuum solution, and metric-selected free motion. Direct activity theorems make all three selected objects and all nine relations affect the technical route itself, independently of the exact-retention audit. A stronger grounded result distinguishes the selected metric calculation, the gravitational theory using it, and the represented physical situation. Einstein's adapter requires the metric to describe the gravitational field and determine spacetime geometry; Schwarzschild's requires the exact exterior point-mass line element. Both papers expose a named source-local selected-setup theorem used by grounding, independently of their vacuum-equation and free-motion calculations. Curvature, Einstein equations, connections, geodesics, point masses, spherical symmetry, approximations, and observables remain paper-local.
PhysicsLogic/Framework/GravitationalFrequencyShift.lean: narrow shared local-clock frequency-comparison semantics extracted from Einstein 1911 and Einstein 1916. Its explicit route requires regime validity, stationary physically distinct locations, same-kind local clocks, signal transfer, a paper-local frequency calculation, and separate clock-rate and spectral interpretation bridges. The established result is output-led: exact selection plus the direct inhabited setup and three physical outputs. The original calculation and both interpretation bridges are reconstructed by a checked projection rather than stored as premises. Its proof-free model retains six selected physical objects and all seven relation families used by the route. The context owns those six objects, and exact semantics means equality with its unique selectedModel, not a model reconstructed from candidate-owned indices. Each paper constructs a named model and proves exact semantic retention before route applicability. Einstein 1916 does so separately at every arbitrary approximation, situation, and redshift, preserving the paper's universal scope. Named paper theorems expose all six selected indices directly in both adapters. The ten exhaustive claims include that certificate, setup, calculation and interpretation bridges, applicability, outputs, and the established result. Its stronger theory-model result distinguishes the comparison model, a paper-local theory role, and a paper-local represented world. Grounding requires the exact selected stationary-comparison setup but remains independent of the shift outputs: Einstein 1911 maps its primitive comparison setup; Einstein 1916 maps the point-mass solution, distinct locations, stationary comparison, same-kind clocks, and transferred signal. Only the combined result adds the technical outputs. The two adapters expose named certificates transferring every shared claim to theory and represented world. The frequency relation transfers to clock-rate and spectral claims only through their separate paper-local interpretation bridges. Vacuous bridges without the setup are rejected and cannot satisfy the direct NonvacuousGravitationalFrequencyShiftAt proposition. Every established route projects to that proposition, so validity, distinct locations, stationary comparison, same-kind clocks, signal transfer, frequency relation, clock-rate difference, and spectral displacement all hold at one actual selected model. A finite witness realizes it, and direct six-index and seven-relation mutations make each retained component affect the completed semantics. Its ordinary structural-explanation layer uses exact selected semantics and the pre-endpoint shared route without retaining paper provenance. A separate source-sensitive refinement adds a typed paper-local derivation: Einstein 1911 supplies an accelerated-frame Doppler-plus-equivalence derivation, while Einstein 1916 supplies a static-metric local-clock derivation. The source-sensitive explanation exposes that derivation and entails the ordinary explanation. A converse countermodel proves that the completed phenomenon, an output-reconstructed route, and the ordinary explanation cannot manufacture a missing source derivation. A same-location comparison cannot satisfy the route even when every nominal physical predicate is declared true, a completed technical result need not supply theory/world grounding, exact grounding with complete setup can hold while the route is false, exact selection without setup cannot ground, and declared theory/world claims do not reconstruct the calculation route. Separate six-index and seven-relation mutation theorems, plus their combined thirteen-component audit, detect changes to every selected object and retained relation family. A separate value-bearing shared source readout now also retains Einstein 1911's exact equations (2), (2a), and (3), its assumed extension from a homogeneous to a nonuniform field, the distinction between coordinate and locally measured light speed, its 2 / 10^6 solar shift, and explicit pressure/temperature systematics. Einstein 1916 instead retains the equation-(70) temporal metric, equation-(72) local-clock normalization, slower near-source clocks, distinct observer locations, and its explicitly inconclusive stellar-redshift test. Countermodels reject a sign-flipped potential, substituted local light speed, missing Doppler calculation, invented nonuniform-field derivation, discarded spectral systematics, incorrect metric or clock normalization, claimed confirmation, and exact strong-field extrapolation.
PhysicsLogic/Framework/GravitationalRayDeflection.lean: narrow shared gravitational light-deflection semantics extracted from Einstein 1911 and Einstein 1916. Its explicit route requires a valid description, a selected light ray in a gravitational propagation setup, a paper-local deflection calculation, and a separate assessment that the reported magnitude is nonzero. The output-led established result is exact selected semantics plus a direct nonvacuous proposition requiring validity, gravitational propagation, calculated deflection, and nonzero magnitude at one actual model. The implication-valued calculation and assessment bridges are reconstructed from those outputs. A finite witness realizes it, a countermodel blocks vacuous bridges without setup, and direct four-index/four-relation mutations show every retained component affects the completed proposition. A separate ordinary structural explanation retains the selected propagation problem without a derivation token; the applicable route realizes it. A stronger source-sensitive refinement pairs that constraint with a realized paper-local derivation, exposes the derivation, and entails the ordinary explanation. Einstein 1911 reconstructs its route from a coordinate-light-speed/Huygens token; Einstein 1916 uses a distinct static-metric/null-ray token. A finite countermodel retains the complete phenomenon, a route reconstructed from it, and ordinary explanation while making the source derivation false, so the result cannot manufacture source provenance. The grounded result separately requires exact selection plus the inhabited pre-calculation propagation setup and identifies the theory using the model and the physical world represented by it. A false setup cannot ground, while a grounded setup need not supply the calculation or direct endpoint. Einstein 1911 supplies the position-dependent coordinate-light-speed and Huygens calculation; Einstein 1916 supplies the static point-mass metric calculation and an explicit ray passing the source. A separate source readout now retains the actual original wavefront and potential-gradient formulas, equation-(70) temporal and spatial metric components, equation-(73) null propagation, Huygens' principle in both papers, and equation-(74) full bending. Independent temporal and spatial contributions make the 1916 unrounded prediction exactly twice the 1911 prediction, while the separately rounded original reports 0.83 and 1.7 arcseconds are not exactly related by a factor of two. The 1916 Jupiter prediction is 0.02 arcseconds, and neither paper is credited with a completed eclipse observation. The plus-sign coordinate-speed expansion printed in 1916 is also kept distinct from the opposite-sign expansion implied by the displayed metric and null condition; Lean proves that the two values differ. Countermodels reject omitted Huygens propagation, omitted spatial curvature, a missing null condition, the wrong coefficient, retrofitted 1911 spatial bending, swapped reported angles, and unsupported empirical confirmation. Both adapters expose the four selected model indices; their lifted deflection-calculation relations additionally require the selected description, so a paper calculation cannot silently migrate to a foreign approximation. Grounding consumes the 1911 validity, coordinate-speed, and transverse-ray facts or the 1916 static-solution, point-mass, and ray-passage facts, but no deflection calculation, nonzero result, route, or established endpoint. The direct anchors are Einstein 1911 journal pp. 906-908 and Einstein 1916 journal pp. 819-822. Einstein 1911 now separately retains its p. 907 local Huygens curvature relations, equation (4), p. 908 point-mass 2 k M / (c^2 Delta) reduction, and 4 / 10^6 = 0.83 arcseconds report as a paper-local proposition-valued readout package; the companion shared source readout additionally preserves those selected source values without claiming to prove the path integral. A separate composed optical handoff retains both the actual local-clock frequency shift and the actual nonzero ray deflection, exact shared description/regime, the selected signal/ray propagation relation, the paper-local derivation, and a positive solar angle in exact arcsecond hundredths. Einstein 1911 supplies the accelerated-frame, coordinate-speed, and Huygens chain with angle 83; Einstein 1916 supplies the static metric, radial/tangential rod effects, null condition, and its own Huygens calculation with angle 170. Inhabited countermodels separate clock shift from bending in both directions, reject incorrect reported-angle calibration, and prevent one paper's completed outputs or derivation mode from replacing the other's. The source-sensitive optical composition now also exactly selects both child contexts and independently retains the clock derivation, bending derivation, and source-local optical comparison. The 1911 token preserves accelerated-frame Doppler, coordinate-speed/Huygens propagation, and 83 hundredths; the 1916 token preserves the static metric, null ray, radial/tangential spatial effects, and 170 hundredths. A calibrated finite countermodel retains both source-sensitive child explanations and ordinary composition while withholding the optical comparison derivation.
PhysicsLogic/Framework/AcceleratedFrameGravity.lean: narrow shared accelerated-frame comparison semantics extracted from Einstein 1911 and Einstein 1916. Its proof-free exact model retains the reference frame, accelerated frame, experiment, and regime together with the four relation families used by the route: comparison setup, universal free fall, reproduced gravitational motion, and description equivalence. Each context binds one exact four-object selection, and each paper certifies its named model before applicability. The route then requires two distinct paper-local bridges: one from setup and free fall to reproduced gravitational motion, and one from that output to the paper's scoped equivalence conclusion. The established result exposes every stage plus a direct nonvacuous result as ten exhaustive claims. A source-shaped witness and direct eight-component mutation audit show that every retained index and relation family affects that nonvacuous result. Theory/model/world grounding is separately established from exact model identity and interpretation alone; it consumes no setup, free fall, bridge, output, or completed route. The framework does not identify this narrow inference with a general weak, Einstein, or strong equivalence principle, extend mechanical equivalence to all physical processes, eliminate arbitrary gravitational fields, infer the relativity postulate, or construct a gravitational field theory.
PhysicsLogic/Framework/BrokenSymmetrySpectrum.lean: shared spectrum-scoped Goldstone semantics extracted from Goldstone-Salam-Weinberg 1962, Anderson 1963, Nambu 1960, and Generalized Global Symmetries 2014. It requires a paper-local spectral bridge in addition to spontaneous breaking. The established result retains that complete route and the derived gapless mode in the declared spectrum, so the breaking claim and spectral bridge remain separately projectable. Its stronger semantics distinguish the selected spectral calculation from the theory using it and the physical system or spectrum represented by it. A generic constructor grounds the exactly selected model from explicit theory-use, world-representation, and claim-transfer bridges without assuming spontaneous breaking, the spectral calculation, route applicability, or the gapless-mode result. Goldstone-Salam-Weinberg ground the selected current and physical spectrum without importing current conservation or the spectral calculation; Anderson grounds the selected superconductor and uncoupled matter spectrum without assuming Coulomb absence; Nambu grounds the charge-vertex model with the genuinely representational premise that the quasiparticle vacuum represents the superconductor; and Generalized Global Symmetries grounds each selected current sector and physical photon spectrum without assuming current assignment or photon membership. Each final grounded theorem combines this independent grounding with its separately established technical route. The proof-free calculation model retains the selected symmetry, phase, and spectrum together with the exact continuous-symmetry, law-symmetry, phase-membership, symmetry-action, gapless-mode, and spectrum-membership relations. A finite selected model now realizes the complete route with two distinct in-phase states related by the selected symmetry and a concrete gapless mode in the selected spectrum. Direct mutation theorems show that changing any selected index or any route-used relation destroys the direct NonvacuousBrokenSymmetrySpectrumAt proposition itself, rather than merely changing whole-model equality or only a stage predicate. A vacuous spectral bridge without a broken phase also fails that direct endpoint. The complete route now realizes an ordinary typed structural explanation from a proof-free broken-phase constraint distinct from the spectrum-scoped gapless-mode phenomenon. A stricter source-sensitive wrapper adds one paper-selected derivation token and a proposition-valued relation showing that derivation obtains. Source-sensitive explanation exposes its derivation and entails the ordinary explanation, while a countermodel keeps the established spectrum result and ordinary explanation but withholds source provenance. Goldstone-Salam-Weinberg, Anderson, Nambu, and Generalized Global Symmetries each expose both ordinary and source-local adapters while retaining their current calculation, pair dynamics, uncoupled-spectrum restriction, and one-form current matrix elements locally. Each paper's named-model identity fixes its actual physical tuple, and each of the four clients exposes a source-grounded theorem exhibiting the moved state and in-spectrum mode. Only the six shared broken-phase spectral claims transfer. One exhaustive theorem realizes all six from any established result, and all four paper adapters expose named realization and grounded-transfer certificates. Mode conversion, finite-frequency generation, gauge dynamics, and gap calculations remain outside this component. Countermodels reject a vacuous spectral bridge. A nine-component extensional audit observes every selected index and retained relation family, while the direct semantic audit verifies that all nine components affect the route itself. Further countermodels exhibit theory/model/world grounding while the Goldstone route fails, and reject theory/world declarations that do not reconstruct the technical route.
PhysicsLogic/Framework/BrokenSymmetryModeConversion.lean: shared spectrum-conversion semantics extracted from Nambu 1960 and Anderson 1963. It requires a selected gapless mode in an uncoupled spectrum, interaction absence in that spectrum, interaction activity in a distinct interacting spectrum, a coupling mechanism, and a paper-local conversion calculation before deriving a finite-frequency mode in the interacting spectrum and absence of the original mode there. The generic established result is output-led: exact selected semantics plus the direct NonvacuousModeConversionAt endpoint. Its implication-valued calculation and route are reconstructed from the retained setup and outputs. The stronger established result is also output-led, retaining exact selection for the conversion model and Goldstone-spectrum child plus the direct originated endpoint. The complete spontaneous-breaking, scoped-Goldstone, and conversion routes remain reconstructible, preventing conversion alone from reconstructing a symmetry origin. Its direct NonvacuousGoldstoneOriginatedModeConversionAt endpoint now contains the nonvacuous Goldstone-spectrum child together with the generic conversion endpoint. The generic endpoint additionally projects to a typed mechanistic explanation. Its component is the original mode in the uncoupled spectrum, its activity is coupling by the selected interaction in the physical system, its organization is the before/after spectrum pair, and its phenomenon is finite-frequency replacement in the interacting spectrum. Both Nambu and Anderson realize this proposition from their distinct Coulomb-polarization and electromagnetic-coupling calculations. A source-sensitive activity now preserves that distinction formally. Nambu's source relation executes the matched Ward-vertex homogeneous zero-mode calculation before assembling the Coulomb pair-process and polarization-resummation setup. Anderson's source relation executes the self-consistent electron-plasma response, undressed-spectrum pole criterion, uncoupled Goldstone calculation, and superconducting gauge-field mixing setup. Neither source theorem consumes an established conversion or ordinary mechanism. A completed common route with an everywhere-false source relation realizes the ordinary explanation but not either source-sensitive explanation. SourceSensitiveGoldstoneSupportedModeConversionAt additionally composes exact outer and embedded selected models, the inhabited originated result, independently sourced Goldstone and conversion explanations, and a separate original-paper joining argument. Anderson's join retains printed conductor equations (4), (7), and (8), unequal finite-momentum dispersions, nonrelativistic scope, and the distinction between the normal conductor and broken superconductor without claiming non-Abelian or baryon models. Nambu's join instead retains the matrix Ward identity, the neutral acoustic equation (6.11), the Coulomb-shifted plasma equation (8.11), polarization resummation, distinct neutral/coupled spectra, and unassessed higher-order or beyond-Hartree-Fock corrections. A physical countermodel preserves both sourced children, the complete originated endpoint, different selected systems, Ward and frequency data, and normal versus broken superconducting matter while rejecting a missing source-local handoff. The projection requires actual coupling and all terminal spectrum outputs, but no spontaneous-breaking or Goldstone-origin premise. A finite countermodel retains conversion, finite frequency, final membership, and removal of the original mode while deleting coupling, and therefore refutes the mechanistic explanation. A proof-free selected calculation records both spectra, both modes, the interaction, and the physical system together with the exact six spectrum, interaction-absence, and four conversion relation families. The context owns all eight selected physical indices, so a candidate model cannot select the objects against which its own exactness is judged. Each paper proves an exact retention certificate. A generic constructor grounds the exactly selected physical conversion setup from explicit theory-use, world-representation, and conditional claim-transfer bridges without assuming a calculation, route, or final spectrum. Anderson supplies SuperconductingConversionSetup; Nambu supplies CoulombPlasmaSetup and the quasiparticle-vacuum representation. The fermion gap, self-energy-kernel equation, resummed-polarization premise, and conversion calculations remain downstream. One exhaustive theorem realizes all nineteen shared claims from an established result. A retained finite model now realizes the full composed route nonvacuously: two distinct phase states witness breaking, the original and converted modes differ, the uncoupled and interacting spectra differ, and every setup and conversion relation is active. Direct stage audits show which part of the route each changed field breaks. A generic typed audit proves that its eight indices and seven conversion relations are active while the four Goldstone-provenance mutations preserve generic conversion; a stronger typed audit proves that every one of the eight index mutations and eleven relation-family mutations destroys the full NonvacuousGoldstoneOriginatedModeConversionAt endpoint itself. Both paper adapters now expose named generic-conversion and stronger Goldstone-originated nonvacuity theorems. Countermodels reject an implication-valued bridge that holds only because its physical setup is absent and show that it cannot fake either direct endpoint; another complete generic conversion has no broken-symmetry origin. They also separate uncoupled-spectrum absence from interacting-spectrum activity, exhibit grounding while the composed route fails, reject absent setup, and reject direct Goldstone/conversion outputs under the wrong selected symmetry. They retain a separate nineteen-component extensional audit, and reject theory/world declarations that do not reconstruct the technical route. Polarization tensors, Coulomb equations, gauge fields, and superconducting dynamics remain paper-local.
PhysicsLogic/Framework/CoarseGrainedScaling.lean: narrow shared coarse-graining and rescaling semantics extracted from Kadanoff 1966 and Forster-Nelson-Stephen 1977. Its explicit route requires a controlled transformation step, an inhabited selected sector, and a paper-local prediction-scaling bridge, then establishes transformed prediction equivalence only throughout that sector. The output-led established result stores exact selected semantics plus the direct nonvacuous controlled-sector result; named projections reconstruct the route, controlled step, bridge, and sector predictions. The ordinary structural explanation retains only the exact selected scaling model and route. A separate source-sensitive refinement pairs that constraint with a typed realized derivation, exposes the derivation, and entails the ordinary explanation. Kadanoff's cell-variable/free-energy/correlation derivation and FNS's infrared momentum-shell velocity-correlation derivation reconstruct the shared route separately and remain distinct. A converse countermodel retains the established output, reconstructed route, and ordinary explanation while denying the source derivation, so no source-sensitive explanation follows. The scaling proof-free model exactly retains six selected data components and ten transformation, prediction, scope, and control families. Kadanoff and FNS prove named exact-model certificates and derive selected controlled setups from CellModelSetup and InfraredRGSetup. Their theory/model and model/world grounding uses those setups, paper-local interpretation inputs, and conditional transfer, but no scaling bridge, sector calculation, route, or output. Separate final theorems combine grounding with each paper's completed calculation. The exhaustive claim family now has nine members, including the selected setup and direct nonvacuous output. Countermodels block vacuous bridges, control without a prediction calculation, sector widening, transfer across scales, automatic grounding from technical completion, and reconstruction of the controlled route from grounding. Complementary countermodels ground controlled setup without a scaling output and reject grounding from matching output without controlled setup. A sixteen-component mutation audit observes every retained datum, map, and relation extensionally. A separate inhabited finite model realizes the actual two-step transformation, both controls, regime and sector membership, and prediction equivalence for a concrete observable. Direct route-content audits show that changing any of the six selected components or ten map and relation families destroys a transformation or sector subclaim, while a stronger typed audit proves that every mutation destroys NonvacuousControlledSectorScalingAt itself. A control-free implication-valued bridge cannot fake that direct endpoint. Kadanoff's singular free energy and FNS's velocity correlation independently witness the selected sectors in named paper theorems. The neutral route remains independent of block spins, shells, exponents, and universality classes. Separate governed source witnesses retain Kadanoff's a < L < xi, two-valued cell, L^(-d) free-energy factor, nearest-neighbor assumption, conditional exponent relation, and qualified logarithmic branch. FNS witnesses retain the transverse projector, k . v = 0, different thermal and constant forcing classes, their dimensions two and four, controlled momentum shell, thermal-only fluctuation-dissipation relation, protected advective vertex, and independently renormalized viscosity.
PhysicsLogic/Framework/ExactRegulatedScaleFlow.lean: narrow exact-flow contract extracted independently from Wegner-Houghton 1973 and Wetterich 1993. A regulated scale-dependent family at an actual selected scale, a paper-local exact full-flow calculation, a selected sector, and a paper-local exact projection calculation establish exact full and projected equations. The established projection also yields a direct NonvacuousExactProjectedScaleFlowAt endpoint where the setup, exact full equation, projection setup, and exact projected equation all hold at one model instead of only behind implication-valued calculation contracts. The second-stage adapters now consume that established shared full flow and shared projection setup before replaying only paper-local route content. Separate theory/model/world bridges ground the selected setup. Its proof-free model exactly retains six selected indices, including the actual scale, and the four proposition-valued relation families that interpret their setup, full equation, projection setup, and projected equation. Both paper adapters prove a named retention certificate before applicability and a named direct nonvacuity theorem after the projection is established. Both established results are output-led; checked eliminators reconstruct the calculation contracts and complete route. The 13 canonical claims expose the selected setup, complete route, and direct endpoint. Grounding uses the exact selected model and realized scale-dependent setup, a paper-local theory-use fact, a represented-system fact, and claim-by-claim transfer; it requires no exact flow equation, projection setup, calculation contract, or projection route. The framework does not identify sharp-shell elimination with a modified Legendre transform, and it contains no fixed-point, endpoint, derivative-expansion, epsilon-expansion, large-component, or approximation-control semantics. Countermodels separate implication-valued calculations from applicable routes, show separately that missing full-flow setup and missing projection setup cannot hide behind those implications, separate exact full flow from an exact projection, technical completion from physical grounding, and grounding from a technical route. A setup-complete grounded model with false exact-flow output proves the last separation. Exact-selection and direct ten-component audits make every retained index and relation semantically active.
PhysicsLogic/Framework/NeutralDefectConfiguration.lean: shared integer defect-charge semantics independently realized by the scalar vortex gas of Kosterlitz-Thouless and the vector dislocation gases of Halperin-Nelson and Young. It retains charge rank, actual integer components, componentwise neutrality, a nonzero opposite-charge pair, and validity scope. The active melting routes now consume rank-two Burgers configurations; rank-one scalar lifting preserves both net charge and the absent transverse component. Checked countermodels separate a lone charge from neutrality, an empty neutral gas from pair presence, and a transverse pair from rank-one admissibility. Its structural explanation retains the selected rank and integer charge list while explaining only an inhabited admissible neutral opposite pair. A source-sensitive refinement keeps KT's neutral unit-vortex premises distinct from the two Burgers-gas routes, and a false-source countermodel prevents the ordinary endpoint from inventing paper provenance.
PhysicsLogic/Framework/LogarithmicDefectThermodynamics.lean: shared value-level defect thermodynamics independently realized by the original Kosterlitz-Thouless argument and the two active melting papers. It retains two-dimensional validity, core and system scales, core energy, bare and screened logarithmic binding, positional entropy, and the actual F=E_core+(binding-T*entropy) log(L/a) competition. Checked theorems separate the cold bound regime, the large-scale hot instability, and the lowering of the bare threshold by screening; countermodels show that a positive core cost can keep a finite system bound above the bare threshold and that logarithmic binding without positional entropy does not unbind. Its structural explanation retains the finite-scale free-energy readout and screened threshold ordering while stopping short of phase interpretation. A source-sensitive refinement keeps KT's finite-area vortex estimate distinct from the two solid-side Burgers routes, and a false-source countermodel blocks provenance from the ordinary endpoint.
PhysicsLogic/Framework/DipoleScreeningResponse.lean: shared value-level linear response independently realized by the original KT scalar-vortex calculation and Young's vector-dislocation gas. A nonnegative dipole shell raises susceptibility and dielectric response, and K_eff=K_bare/epsilon weakens logarithmic binding. Checked countermodels separate density without polarizability, susceptibility without dielectric response, and dielectric response without renormalized binding. Its structural explanation retains the selected shell and binding readouts while explaining only inhabited strict weakening. A source-sensitive refinement keeps KT's finite-core dilute-pair inputs distinct from Young's solid setup, and a false-source countermodel blocks provenance from the ordinary endpoint.
PhysicsLogic/Framework/PhaseWindingCirculation.lean: shared phase-contour semantics independently realized by KT's planar-spin vortices and Feynman's original helium ring argument. Integer phase winding plus the phase-flow relation quantizes circulation; local irrotationality remains compatible with nonzero circulation in a multiply connected region. Countermodels separate phase winding from flow, circulation from phase consistency, and local irrotationality from sector selection. Its structural explanation retains the selected contour, phase increment, winding, quantum, circulation, and local vorticity while explaining only nonzero quantized locally irrotational circulation. A source-sensitive refinement keeps KT's scoped angular contour distinct from Feynman's many-body phase-gradient ring inputs, and a false-source countermodel blocks provenance from being inferred from the ordinary endpoint.
PhysicsLogic/Framework/CorrelationDecayChannel.lean: shared large-distance channel semantics independently realized by KT's spin-wave factor and Hastings-Koma's ground-sector-corrected bosonic correlation. Positive algebraic exponents or exponential rates suppress the selected channel; they do not suppress an unrelated raw or full correlator without its paper-local bridge. Countermodels separate zero exponent/rate and a finite-separation bound from genuine asymptotic decay. The explicit envelope-indexed structural constraint retains the selected norm readout, cutoff, and branch parameters, while its phenomenon is only the nonvacuously suppressed selected channel. A source-sensitive refinement keeps KT's scoped spin-wave power law distinct from Hastings-Koma's printed corrected-correlation formula; a false-source countermodel prevents the ordinary asymptotic endpoint from manufacturing paper provenance.
PhysicsLogic/Framework/DefectUnbindingTransition.lean: narrow shared transition semantics extracted from Halperin-Nelson 1978 and Young 1979. It separates the bound, rigid low-temperature phase and its suppressed defect fugacity from the high-temperature recursion calculation, then requires an explicit paper-local bridge before deriving defect unbinding and lost long-distance rigidity. Its output-led established proposition is exact selected semantics together with the direct NonvacuousDefectUnbindingTransitionAt endpoint, where the ordered phase, both flow outputs, unbinding, the unbound phase, and lost rigidity all hold at one selected model rather than merely behind an implication-valued bridge. The complete route is reconstructed from those outputs rather than stored in the result. Both paper adapters expose named route-applicability and direct nonvacuity theorems, and a countermodel prevents a vacuous interpretation implication from replacing the actual flow calculation. The complete route also realizes a typed mechanistic explanation whose component, activity, organization, and phenomenon roles retain the bound defect, selected flow, ordered-to-unbound phase data, and unbinding with rigidity loss. A model with the flow and all terminal outputs but no ordered bound-defect organization blocks the converse. A source-sensitive refinement now keeps Halperin-Nelson's smooth-substrate elastic decomposition and quadratic- fugacity recursion distinct from Young's self-consistent vector-gas screening and independent periodic-substrate consistency check. Both are reconstructed from raw paper-local premises; a checked forgetful theorem recovers the ordinary unbinding mechanism from either source-sensitive explanation, while a completed common route and ordinary mechanism with a false source relation blocks provenance recovery. Its independently audited composition now consumes the actual nonvacuous NeutralDefectConfiguration and LogarithmicDefectThermodynamics outputs before a separate original-paper screening/flow handoff and the direct unbinding result. Kosterlitz-Thouless preserves a scalar neutral vortex gas, the selected integer vortex charge, dielectric breakdown, and a distinct dissociation bridge; Halperin-Nelson retains vector Burgers charges, finite dislocation core energy, quadratic-fugacity recursion, and equations (3)-(5); Young retains the different self-consistent physical and general radial/angular vector-gas recursions and equations (25). Inhabited models distinguish screened from bare binding and cold from hot regimes, and prove that completed neutrality, thermodynamics, and unbinding do not supply the independent calculation handoff. A stronger source-sensitive composition now retains the ordinary composed endpoint, source-sensitive neutral, logarithmic, and transition explanations, and a separately typed cross-stage handoff derivation. KT supplies its original dielectric-breakdown/dissociation transition token and scalar-vortex composition token; Halperin-Nelson retains its smooth-solid quadratic-fugacity equations-(3)--(5) join; Young retains its self-consistent physical/general vector-gas equations-(25) join. A countermodel has the ordinary composition and all three child source explanations but no handoff derivation, so provenance cannot be recovered merely by composing completed stages. The module also imports Philosophy.TheoryModel: the proof-free model retains all eight selected indices and all eight relation families used by the bound-phase and recursion-flow route. Each paper constructs one named exact model and proves a definitional semantic-retention certificate before route applicability. The 17 canonical claims expose every setup premise, calculated flow output, bridge, interpreted output, direct endpoint, and final transition. Grounding consumes the exact selected, inhabited bound-defect phase plus paper-local use and representation bridges, but no high-temperature recursion flow, unbinding bridge, phase-occurrence output, or rigidity-loss result. Halperin-Nelson retain the two-dimensional triangular system and smooth substrate; Young retains the triangular lattice, continuum-elastic description, and vector-Coulomb-gas description. Their quadratic-fugacity and self-consistent triangular recursions remain in the technical routes. At the paper level, Halperin-Nelson now retains its distinct equations (3)-(5), following inverse-elastic-coupling definition, critical value, and equation (7), while Young retains equations (25a)-(29); the shared framework does not identify those different recursion systems. Typed countermodels show that exact selection without an inhabited bound phase cannot ground, while an inhabited bound phase can be grounded with the unbinding route and direct endpoint false. Further countermodels show both that a completed technical transition need not supply theory/world grounding, selected-regime validity does not become global validity, and declared theory/world transition claims do not reconstruct the missing bound-phase and flow route. One 16-field mutation audit prevents any route-used relation from becoming semantically inert in the exact selected semantics; a second direct 16-component audit shows that changing any selected index or relation destroys the nonvacuous endpoint. Dislocations, Burgers vectors, vector Coulomb gases, elastic constants, correlation laws, hexatic phases, critical exponents, and later defect transitions remain paper-local.
PhysicsLogic/Framework/InfraredOrderSuppression.lean: narrow shared no-order semantics extracted from Mermin-Wagner 1966, Kosterlitz-Thouless 1973, and generalized global symmetries 2014. A selected valid system, symmetry, charged order parameter, explicit real expectation and infrared-limit filter, actual suppression, and a separate physical no-breaking bridge yield a checked unbroken result while retaining an independent other-order value. The three adapters preserve the genuinely different limits and calculations: Mermin-Wagner uses the post-thermodynamic small-field magnetization limit; KT uses the positive-field ordinary-magnetization limit while retaining rigidity as other order; the higher-form route uses large separation, divergent Coulomb potential, and the exponential loop law. Value-bearing countermodels show that charged scope without suppression and suppression without the physical bridge do not forbid breaking. Full theory/model/world transfer is explicit for all three clients. Separate source-valued witnesses now retain the Mermin-Wagner positive-temperature isotropic scope, uniform versus staggered channels, actual finite Bogoliubov denominator, ordered thermodynamic/zero-field limits, surviving unrelated order, divergent susceptibility, and the independently calculated axial exception. Mermin-Wagner's paper-local setup additionally retains its complete matrix-valued exchange-plus-ordering-field Hamiltonian, noncommuting spin-S algebra and Casimir, both direct/inverse spin and exchange Fourier transforms, finite Gibbs partition function and Boltzmann weights, equal-energy exclusion in the spectral inner product, equations (4)-(6), and exact selected raising/lowering operators. Its physical J(0) is the dimension-correct zero lattice vector, not an empty displacement; eight independently inhabited boundaries prevent these source formulas from collapsing back into names. The KT witness separately distinguishes logarithmic energy from positional entropy, positive versus negative vortex free energy, neutral bound pairs, surviving topological order, screened stiffness, an approximate bare upper bound, and the excluded superconducting/Heisenberg cases. The higher-form witness keeps q <= d, continuous d-q < 3, discrete d-q < 2, the genuine exp(-V) Wilson-loop value at finite separation, independent surviving order, and the separate compact Ward-selection bridge. The framework now also exposes ordinary and source-sensitive structural explanations. Its ordinary constraint retains the selected system, symmetry, charged order parameter, regime, and infrared filter; typed source tokens separately preserve Mermin-Wagner's Bogoliubov/ordered-limit chain, KT's quoted ordinary-order input without its vortex route, and the higher-form dimension/Coulomb/Ward chain. A false-source countermodel shows that a completed no-order endpoint cannot manufacture provenance.
PhysicsLogic/Framework/AdiabaticCyclePhase.lean: weak shared closed-cycle phase semantics extracted from Berry 1984 and Arovas-Schrieffer-Wilczek 1984. It retains a parameter-dependent family, a closed sufficiently slow cycle, a transported sector, and a paper-local calculation of an additional non-dynamical, duration-independent phase. The proof-free context owns the five selected objects and all nine relation families used by the route. Exact semantics identifies a candidate with that one context-selected model, so the candidate cannot select its own physical indices. The output-led established result is exactly selected semantics plus NonvacuousAdiabaticCyclePhaseAt, in which all six setup relations and all three phase outputs hold at one model rather than behind an implication-valued calculation contract. A finite Bool witness realizes it, and exhaustive five-index and nine-relation mutation theorems destroy the direct proposition under every selected-value or relation-family change. The older fourteen-component exact-semantics audit remains separate. Both papers name the exact model, prove a definitional retention certificate, construct named paper-local selected-setup adapters, and expose named nonvacuity projections before using the shared inference. The selected calculation model is distinct from its containing theory and represented physical system. Exact selected semantics plus the inhabited slow closed-cycle setup is required in theory membership and world representation. The generic grounding constructor uses that selected setup, explicit theory use, explicit world representation, and conditional claim transfers. Berry and Arovas-Schrieffer-Wilczek delegate to it through separate paper-local interpretation inputs before combining grounding with their technical calculations. Exact selection without setup cannot ground, while a selected setup can have complete grounding with the phase outputs false. Further countermodels block automatic theory/world grounding and reconstruction of a missing technical route from declared final claims. The complete route also realizes a typed structural explanation whose constraint retains the selected family, parameter space, cycle, sector, and phase and whose phenomenon retains the additional nondynamical, duration-independent phase. Both papers expose named projections. A finite model with all three phase outputs but no parameter-dependent setup makes the phenomenon obtain without explaining it. Curvature, gauge representation, interference, charge, and statistics remain in stronger shared components or paper-local routes.
PhysicsLogic/Framework/PlanarExchangeStatistics.lean: narrow shared winding-to-exchange semantics extracted from Wilczek 1982 and Arovas-Schrieffer-Wilczek 1984. It retains an identical planar pair, full winding and exchange paths, both calculated phases, their two-exchange composition, and a separate fractional-statistics bridge. Wilczek grounds the model in charge-flux-composite quantum mechanics and a selected planar composite pair; Arovas-Schrieffer-Wilczek grounds it in Hall-quasihole exchange statistics and a selected separated two-quasihole configuration. Wilczek's Bose/Fermi endpoints and continuous interpolation in the charge-flux parameter remain paper-local: the shared layer keeps only the selected fractional phase classification independently supplied by both papers. Wilczek's independently sourced interpolation conclusion now requires an actual typed charge-flux composite, pair state, flux tube, potential, and winding/exchange paths for every 0 <= Delta <= 1/2. Each member retains q(Delta) Phi(Delta) = 2 pi Delta, exchange phase 2 pi Delta, full-winding phase 4 pi Delta, and its own weak-force, fixed-product approximation. Lean derives genuine continuity and proves that the Bose and Fermi composites have different charge-flux products; holding one product fixed across the entire family cannot interpolate. Independent countermodels distinguish three selected composites from the full continuum, formal phases from physical composite realization, wrong charge-flux or exchange laws, parameters outside the strict open interval, and complete two-anyon interpolation from unresolved many-anyon dynamics. The established endpoint is output-led and reconstructs both implication-valued contracts. Each paper has a named adapter from its identical planar-pair and path premises to the selected shared setup; grounding requires that setup but no phase or classification output. Countermodels separate the technical route from theory/world grounding and prevent declared final claims from reconstructing the calculation. They also show that exact selection without setup cannot ground and that the selected setup can ground while every exchange output is false. The synthetic sensitivity model makes every setup and phase relation depend on its physical arguments. NonvacuousPlanarExchangeStatisticsAt now keeps the identical planar pair, both paths, winding relation, both phases, composition, and fractional classification together at one model. Both paper adapters expose that direct result. Every one of the seven selected values and nine relation families falsifies the direct result when changed; the older sixteen-component audit still separately enforces exact model semantics. The complete route additionally realizes a typed structural explanation whose constraint retains the selected system, pair, two paths, two phases, and regime, and whose distinct phenomenon retains the fractionally classified exchange phase. Wilczek and Arovas-Schrieffer-Wilczek independently expose that projection. A finite model with declared fractional classification but no exchange-phase calculation makes the phenomenon obtain without explaining it. This adds no generic anyon, gauge, braid, Hall-charge, Chern-Simons, or topological-order ontology.
PhysicsLogic/Framework/FieldFreeMagneticInterference.lean: shared magnetic-flux interference semantics extracted from Aharonov-Bohm 1959 and Berry 1984. It retains coherent alternatives in a field-free accessible region, a closed circuit around excluded field support, the circulation-to-flux and phase calculation, coherent phase readout, and the bridge to flux-dependent interference. Its established result is output-led: it stores the exact selected model, an actual field-free setup, and the realized circulation, phase, recombination, and readout outputs, while the implication-valued proof route is reconstructed. Both clients prove setup-bounded theory/model/world grounding from their paper-local physical setups without consuming a circulation or interference calculation. Countermodels show that exact selection alone cannot ground the model, that grounding can precede all interference outputs, and that declared theory/world conclusions do not reconstruct the interference route. The established result also yields a direct nonvacuous interference model once explicit distinct-path and selected gauge-orbit witnesses are supplied. That direct route now projects the selected vector-potential orbit to SymmetryAndGauge.RepresentationContext: the closed-loop phase is a representative-independent value of one inhabited field-free flux configuration. Interferometric phase and flux readouts remain separate conjuncts. A countermodel retains the representative-independent value but has no readout, so gauge invariance is not conflated with interferometric significance or with an ontology of local potentials. This endpoint is a prediction/readout relation, not a performed-observation claim. The route also has ordinary and source-sensitive structural explanations. Aharonov and Bohm's typed source token retains the shielded-solenoid split-beam, branch-phase, recombination, and flux-interpretation route. Berry's distinct token retains the exact single-valued transported-box Dirac-phase construction, its explicit nonnecessity of adiabaticity, and reference-box readout. Neither source relation stores a shared endpoint. A finite model with complete ordinary interference but a false source relation proves that the common output cannot recover either derivation. Aharonov-Bohm pp. 486-487 and Berry pp. 52-54 anchor the two adapters; a separate twelve-index/seventeen-family direct activity audit prevents collapsed alternatives, vacuous gauge orbits, or inactive semantics from counting as physical interference.
PhysicsLogic/Framework/AdiabaticHolonomy.lean: narrow shared cycle semantics extracted from Berry 1984 and Hannay 1985. Its proof-free exact model retains eight selected indices, all three maps of the representation context, and all eleven relation families used by the route. The context owns the eight indices, and selected semantics compares candidates with that one exact model. A sensitivity theorem rejects direct mutations of every one of these twenty-two components. A separate inhabited finite witness makes those same twenty-two components directly active in NonvacuousAdiabaticHolonomyAt, rather than only visible through exact record equality. The route requires a parameter-dependent family, a slow closed cycle, local continuation data, a convention-dependent connection calculation, and a Philosophy.SymmetryAndGauge.RepresentationContext for local representatives, convention redundancy, and convention-indexed curvature values. The route requires an actual representative of the selected physical sector, curvature invariance on redundancy orbits, and the premise that all representatives of that sector lie in one orbit; the established theorem then derives a physical representative-independent curvature value. It also retains the same cycle invariant, traversal-duration independence, and a paper-specific physical-significance bridge. The established route projects to the direct nonvacuous proposition. The output-led established result is exactly that proposition plus selected semantics, and the implication-valued significance bridge and complete route are reconstructed from its facts. Berry and Hannay each expose the result from their paper-local inputs. Each paper names its exact model and proves by definitional equality that no retained component was changed in the adapter. Nine exhaustive claims include the exact selected semantics and route applicability as well as setup, calculation, significance, curvature, and the direct nonvacuous and established results. The module also imports Philosophy.TheoryModel and keeps the selected calculation, its containing theory, and its represented physical system distinct. Theory membership and world representation require exact selected semantics plus the inhabited slow closed-cycle setup. A generic grounding constructor adds explicit theory use, world representation, and conditional claim transfers; it contains no connection, curvature, duration-independence, significance, route-applicability, or established-result premise. Berry and Hannay delegate to this constructor through separately stated paper-local interpretation bridges before combining grounding with their technical routes. Berry's interference significance and Hannay's generally nonzero angle remain downstream technical conclusions. Exact selection of an open cycle cannot ground a model; a separate inhabited setup can be grounded while curvature construction, the holonomy route, and the direct endpoint remain false. Further countermodels separate existence, invariance, and orbit completeness, block a vacuous significance bridge, show that the vacuous bridge fails the direct nonvacuous proposition, show that a completed calculation does not supply theory/world grounding, and show that declared theory/world claims do not reconstruct the technical route. The framework now also separates ordinary and source-sensitive structural explanations. AdiabaticHolonomyConstraint retains only the selected proof-free shared model, while AdiabaticHolonomySourceConstraint adds a typed paper-local derivation relation. Berry and Hannay each expose an ordinary raw-input adapter and a separate source-sensitive adapter; the latter retains Berry's instantaneous-eigenstate/spectral/interference route or Hannay's action-averaging/angle-curvature route without consuming an established or nonvacuous endpoint. A countermodel realizes complete ordinary holonomy explanation while its source relation is false, so the common physics output cannot manufacture paper provenance. Quantum eigenstates, classical action-angle coordinates, spectral formulas, Liouville conservation, integrability, and concrete observables remain paper-local.
PhysicsLogic/Framework/EquilibriumNoiseDissipation.lean: narrow shared equilibrium-noise semantics independently realized by Nyquist 1928, Callen-Welton 1951, and Kubo 1957. Each paper independently constructs the direct established result from equilibrium and dissipative setup, separate dissipation, fluctuation, and relation calculations, represented physical readouts, its selected spectrum convention, and the sector-wide value equality. The setup also requires an actual member of the selected frequency sector. The output-led established proposition retains exact selected semantics plus those direct nonvacuous outputs; implication-valued readout and relation bridges are reconstructed only when a complete technical route is requested. The complete route also realizes a typed structural explanation of the represented, convention-indexed relation. Each paper now reaches that explanation directly from source-facing inputs, before an established shared relation or nonvacuity endpoint is consumed. Callen-Welton's theorem explicitly reconstructs its packaged generalized relation from the perturbative dissipation, zero-force fluctuation, and common-spectral-sum stages. The older terminal projections remain compatibility routes; a finite equation-only countermodel retains the calculation flags and numerical equality but removes both physical readouts, blocking the explanation. This adds no causal-production or observation claim and does not identify the three papers' spectrum conventions. Its proof-free source constraint now also retains a typed paper-local derivation. Nyquist's second-law/filter and transmission-line route, Callen-Welton's two quantum spectral sums, and Kubo's response/correlation conductivity theorem each realize distinct tokens before entering the same shared explanation. A complete-route countermodel with a false derivation predicate proves that matching noise/dissipation output cannot reconstruct source provenance. The separate proof-free calculation model retains the selected system, regime, temperature, force, frequency sector, validity and equilibrium predicates, force and fluctuation relations, value and prediction maps, physical readout relations, and all three calculation predicates. Each paper proves that its named model contains exactly those nineteen semantic components. Exact selected semantics and a model-native technical route are separate premises of applicability, while the direct established result realizes ten exhaustive claims, including the active frequency sector. The model is distinct from the equilibrium theory using it and the physical fluctuating system it represents. Nyquist grounds this separation through equal-temperature exchange, matched-line theory, and a pure fluctuating resistance; Callen-Welton through perturbative setup, zero applied force, equilibrium, and spontaneous fluctuations; Kubo through application setup and the selected near-equilibrium conductor. None of these grounding proofs assumes the established shared relation or its paper-local calculation package. A generic constructor requires the exact selected model and complete inhabited equilibrium linear-dissipative pre-output setup before transferring claims, so model grounding cannot be manufactured from a bare interpretation declaration. Countermodels block both automatic theory/world grounding from technical completion and reconstruction of the technical route from declared theory/world relations; a positive countermodel also constructs grounding while both the technical route and direct established endpoint are false. A separate empty-sector countermodel makes all three calculation flags true but blocks establishment. An nineteen-component sensitivity theorem shows that changing any selected index, relation, or value map changes the exact model. A finite established witness and direct activity theorems further show that every one of those changes destroys the nonvacuous sector-wide output; Nyquist, Callen-Welton, and Kubo derive that output independently. Circuits, quantum transition sums, conductivity tensors, correlation functions, oscillator factors, and application formulas remain paper-local. Callen-Welton also retains its conclusion as a separate two-system interpretation: an initially isolated coherent periodic source supplies the selected force to the dense-spectrum generalized system, later coupling lets equilibrium fluctuations act back on the source, and the resulting loss of periodic motion, coherence, and ordered energy supports only the paper's scoped macroscopic interpretation of dissipation. Separate source-valued witnesses now retain those deliberately omitted physical distinctions without widening the generic contract. Nyquist keeps frequency-local second-law filtering, matched-line mode counting, the one-sided 4 R k T voltage spectrum, current-transfer convention, indirect carrier dependence, and a zero-point-free Planck replacement. Callen-Welton keeps conjugate generalized force, separate transition and equilibrium spectral sums, the half-quantum oscillator factor, qualified classical limit, Brownian/radiation/acoustic applications, wall/volume factor two, and a future-scoped coherence-loss interpretation. Kubo keeps symmetrized rather than ordered current correlation, qualified observation, exact conductivity relation, classical recovery, conditional static/isothermal comparison, time-reversal-qualified reciprocity, full-spectrum sum-rule scope, and independent interacting Einstein relation. Thirty-three controlled mutations reject formula, convention, approximation, application, and epistemic-scope collapses among the three original papers.
PhysicsLogic/Framework/LinearResponseTransport.lean: narrow shared response-to-transport semantics extracted from Nakano 1956 and Kubo 1957. It requires explicit equilibrium and linear-response setup, separate calculations and bridges for causal response, equilibrium-correlation representation of a kernel sector, and transport extraction from the kernel family. Both papers expose a separate theorem proving the complete shared route-applicability proposition before deriving the established transport result. That result is output-led: it retains exact selected semantics, the inhabited setup, the three supplied calculations, causal response, sector-wide equilibrium-kernel representation, and the transport readout. The three paper-local bridges and complete route are reconstructed from those direct facts. The same source-ordered premises also project to a scoped Paradigm/ReductionAndEmergence derivational reduction with distinct equilibrium-response, driven-transport, and represented-behavior types. Realization requires the inhabited setup, microscopic support retains the three calculations, bridges, causal response, and equilibrium kernel, and macroscopic exhibition retains the actual transport readout. Nakano and Kubo expose direct paper adapters that do not consume the terminal shared result. A source-sensitive refinement additionally records Nakano's pulse-response/thermal-kernel/static-conductivity derivation and Kubo's canonical-response/relaxation/correlation-admittance derivation as distinct typed sources. Kubo's raw-input theorem now constructs the route directly rather than passing through its ordinary reduction wrapper. Countermodels separately block recovery of source provenance from a completed route, recovery of the derivation from a readout without an equilibrium kernel and from an equilibrium kernel without transport extraction. Kubo's shared premise stops before its paper-local zero-Planck and classical-correlation recovery, so the projection is neither a classical-limit theorem nor a reduction of complete theories. Its proof-free calculation model retains six physical indices and all fifteen route-used relation, value-map, and calculation fields. Each paper constructs a named exact model, proves a semantic-retention certificate, and consumes that certificate in the applicability theorem. Named field-equality theorems expose all six indices in each adapter; Kubo's frequency-domain kernel and admittance relations are additionally scoped to its selected force and near-equilibrium regime. The calculation model, containing response theory, and represented driven equilibrium system are separate Lean objects. All eight claims, including exact selected semantics, setup, and the three calculation claims, transfer only through explicit theory and world bridges. These calculation claims mean applicability and soundness, not literal calculation by the conductor. Generic theory/model membership and world representation now require both exact model selection and the complete equilibrium linear-response setup. A shared constructor then establishes grounding from those premises plus theory use, world representation, and conditional claim-transfer bridges. Nakano and Kubo delegate to that constructor. Kubo's paper-local operational assessment separately retains continuous observation of one particular macroscopic system, the unproved ensemble-to-observation identification, its unknown exact condition, and the unresolved optical readout bridge; none of those qualifications are promoted into shared transport semantics. Nakano uses only his arbitrary-field response setup, while Kubo adds his operational assessment, including the unproved observation bridge and unknown exact macroscopic condition. Neither proof assumes a response, kernel, or transport calculation or any established result. Countermodels block both automatic theory/world grounding from a completed calculation and reconstruction of the technical route from declared theory/world claims; a positive countermodel has exact selection and complete setup-grounding while the response calculation and route are false, while a false-setup model is explicitly ungroundable. A 21-component mutation audit shows that changing any retained field invalidates exact model selection. The causal-response bridge is now semantically grounded rather than trusted by name. Each paper constructs a paper-local Paradigm.ResponseCausality.ResponseCausalityContext; its pulse calculation exposes past kernel support, exact dependence representation, and a nonvacuous stimulus-response witness, and the shared paradigm theorem derives retarded response. This temporal result is kept distinct from interventionist influence, no-superluminal signalling, deterministic uniqueness, and Kubo's unresolved ensemble-to-observation bridge. The kernel index is neutral so that Nakano's time-domain route and Kubo's selected frequency-domain route do not get falsely identified. Hamiltonians, operators, integrals, transforms, spectral sums, relaxation models, conductivity tensors, susceptibilities, and Green functions remain outside the neutral shared inference. Separate source-valued controls retain Nakano's strictly retarded pulse convolution, beta = 1/(k T), positive normalized thermal trace, imaginary-time kernel, Boltzmann energy-gap quotient, pi hbar/(k T) conductivity factor, and explicitly assumed one-relaxation approximation. Kubo independently retains the Poisson-bracket sign, static oscillator continuation, both symmetric and antisymmetric tensor channels, and even-real/odd-imaginary frequency reflection. Seventeen mutations reject source, formula, universal-Markovianity, and strong-drive collapses while preserving the paper-independent transport route.
PhysicsLogic/Framework/RemoteCorrelationPrediction.lean: narrow shared correlation-to-remote-prediction semantics independently realized by EPR 1935, Bohr 1935, and Bell 1964. Its exact proof-free model retains twelve semantic components: experiment, local and remote subsystems, regime, the two operational observation relations, selected quantity, procedure assignment, preparation, separation, procedure availability, and correlation calculation. An exact selected setup additionally requires preparation and a witness that at least one quantity is selected. That setup, the paper-local calculation, prediction-readout bridge, and distinct non-disturbance bridge establish the direct nonvacuous output. The twelve-claim vocabulary also records model selection, inhabited setup, route applicability, and the output-led established result. EPR, Bohr, and Bell each construct a named exact model and inhabit it with, respectively, EPR's first remote quantity, Bohr's double-slit position branch, or an explicit Bell spin component. Their separate grounding theorems consume only that exact inhabited setup plus theory/world bridges, not the correlation route. The complete route also realizes a typed structural explanation. Its constraint retains the experiment, distinct subsystem roles, selected quantity sector, local procedure assignment, and regime, and requires the prepared separated setup, actual correlation calculation, both bridges, and a nonempty selected sector. Its distinct phenomenon is certainty and non-disturbance for every selected remote quantity. A correlation without the readout bridge and declared certainty/non-disturbance without a correlation calculation both fail to explain that phenomenon. Reality criteria, completeness, predetermination, hidden variables, and Bell's no-go route remain outside the common prediction model and inference. EPR separately supplies a compatible reality interpretation and an explicit sufficient-reality premise. Bohr supplies no arrangement-independent reality field, and Bell's exact model is provably unchanged under arbitrary admissibility assignments. Separate source-valued controls retain EPR's x_2 = x_1 + x_0, p_2 = -p_1, nonzero commutator, distinct incompatible local procedures, explicit common remote-reality assumption, and only sufficient reality criterion. Its ideal continuum state is distributional rather than square-normalizable, with no derived finite-resolution regularization. Bohr separately retains two distinct separated particles, measured double-slit preparation-diaphragm momentum, the source equations q2=q1-(q1-q2) and p2=(p1+p2)-p1, mutually exclusive later arrangements, and no jointly performed procedures. His source-sensitive route accepts remote certainty and mechanical nondisturbance while rejecting EPR's arrangement-independent completeness inference; a physical countermodel supplies both alternative prediction values but neither joint measurement nor a common-reality identification. Bell's controls retain same-axis singlet anticorrelation, normalized local hidden variables, the original three-setting bound with quantum values 1 > 1/2, a locally incomplete illustrative model, and an allowed nonlocal completion. They explicitly reject operational-signalling and all-hidden- variables-excluded overclaims, and distinguish a possible future fast-setting experiment from one already performed. Countermodels separate setup from output and grounding in both directions, block reconstruction of the technical route from output declarations, and prevent semantic erasure of any retained model component.
PhysicsLogic/Framework/SelfConsistentSpectralGap.lean: narrow shared inference extracted from BCS 1957 and Nambu 1960. A description must be valid in a declared regime, a paper-local self-consistency problem must receive a nontrivial calculated solution, and a separate paper-local bridge must identify a finite gap in a selected excitation spectrum. BCS and Nambu each expose a named theorem establishing the complete shared route before deriving the spectral result. Their final shared theorems establish direct output facts rather than invoking the generic route constructor. The established proposition is exact selected semantics plus the direct inhabited-gap proposition; the paper-local solution calculation and spectral interpretation contracts are reconstructed from those outputs. The proof-free model retains the selected description, gap, excitation, spectrum, and regime together with validity, self-consistency, nontrivial-solution, spectrum-membership, finite-gap, and spectrum-gap relations. BCS and Nambu each construct one named exact model and prove its semantic retention. A TheoryModel interpretation keeps that calculation distinct from the theory using it and the represented superconductor; grounding requires the exact selected, inhabited unsolved setup but not the solution calculation or spectral bridge. BCS explicitly supplies its paired-state-to-metal representation bridge, and Nambu supplies its quasiparticle-vacuum-to-superconductor bridge. Countermodels show both that implication-valued calculations can hold vacuously and that neither an established technical gap nor physical spectral truth reconstructs the missing route. The established result also yields a direct inhabited-gap proposition in which validity, the posed self-consistency problem, its nontrivial solution, excitation membership, gap finiteness, and the spectrum-gap relation all hold at the same five selected objects. An exact finite model realizes this proposition, and exhaustive activity theorems show that changing any of the five indices or six relation families destroys it. BCS anchors its adapter to pp. 1182-1183; Nambu anchors its adapter to pp. 652-653. BCS additionally retains its equation-(2.40) epsilon_0 value, equation-(2.50) square-root dispersion, and selected equation-(2.49) threshold locally. Their Lean deductions prove a strictly positive gap, exclude selected subgap quasiparticles, and show that the two-particle energy attains its minimum of 2 epsilon_0 at the Fermi surface; a positive-energy subgap countermodel separates a merely named threshold from that minimum. The shared endpoint does not collapse those formulas into Nambu's distinct source calculation. The earlier eleven-component equality audit remains as a separate exact-retention check. A source-sensitive structural projection distinguishes BCS's coherent variational paired-state derivation from Nambu's anomalous-self-energy derivation. Nambu's later Ward-identity and collective-mode routes are policy-excluded from that token. A complete ordinary route and all gap outputs can coexist with a false source relation, so result equivalence does not reconstruct derivational provenance. The gap is scoped to the selected quasiparticle excitation spectrum, not every excitation: Nambu separately has a gapless collective branch, and BCS leaves other spin sectors open. The complete direct route now also realizes the mature structural- explanation interface through distinct proof-free constraint and phenomenon types. BCS and Nambu consume their respective route-applicability theorems directly; pairing and anomalous self-energy remain paper-local. An output-only invalid-setup model blocks a gap label from explaining itself, while a second finite model proves that a structurally explained selected quasiparticle gap can coexist with an ungapped collective spectrum. Superconductors, pairing, anomalous self-energies, variational states, quasiparticles, and particular gap equations remain paper-local.
PhysicsLogic/Framework/TransverseMeissnerScreening.lean: narrow shared response-to-screening inference extracted from BCS 1957 and Nambu 1960. A description must be valid in a declared regime, a selected field must be static and transverse, and the paper-local calculation must produce an induced current whose long-wavelength response opposes that field. A separate physical bridge identifies this response with exclusion of the selected field from the bulk. Its proof-free model retains all six selected objects and all six route-used relation families. BCS and Nambu each construct a named exact model and prove a semantic-retention certificate before route applicability. The established result is output-led: exact selected semantics plus the direct setup, calculated current, sign relation, and bulk field exclusion. The calculation and bridge are reconstructed. A shared induced-current adapter must replay the model-native setup before rerunning its paper-local calculation: BCS rebuilds validity, linear response, and current decomposition with its coherence factor, while Nambu rebuilds the Ward result, longitudinal defect, collective state, and transverse response with its local Ward-vertex setup. A TheoryModel interpretation keeps the response model distinct from the electrodynamic theory and represented superconductor. Grounding requires the selected physical response setup, model use, representation, and conditional transfer, but no response calculation, bridge, or result. BCS supplies its MeissnerSetup; Nambu supplies its GaugeInvariantMeissnerSetup. All thirteen claims transfer only after that independent grounding is combined with technical establishment. The established result is exact selected semantics plus the model-native NonvacuousTransverseMeissnerScreeningAt proposition that requires an actual setup and the calculated current, screening sign, and bulk exclusion together, while storing neither implication-valued obligation; this makes the shared claim family thirteen claims. The generic endpoint remains gap-agnostic. The source-order BCS and Nambu adapters additionally expose NonvacuousGapSupportedTransverseMeissnerScreeningAt, which retains the direct nonvacuous self-consistent-gap child, exact established gap route, paper-local admissibility bridge, selected response setup, and direct screening endpoint together. The stronger source-sensitive composition additionally requires independently realized gap, screening, and joining derivations. BCS's join retains its original gap/dispersion/pair-breaking formulas, coherence case II, printed London-current equations, Pippard kernel, and penetration depth. Nambu's join instead retains anomalous nonperturbative pairing, gauge phase, the matrix Ward identity, the Coulomb-omitted collective intermediate, longitudinal cancellation, and the surviving physical transverse response. An inhabited countermodel distinguishes gap values, quasiparticle versus collective excitations, opposing versus aligned currents, and applied versus residual fields while proving that completed child explanations cannot supply a missing joining source. BCS realizes the route through its paramagnetic-plus-diamagnetic response calculation; Nambu realizes it after collective vertex corrections cancel the unphysical longitudinal response while retaining the transverse BCS response. The complete route now also realizes a typed mechanistic explanation: the system-current-field component undergoes a calculated induced and opposing current activity in the valid static transverse response organization, producing bulk field exclusion. Both papers derive this explanation from their full source-stage gap, response, and interpretation inputs before any established shared endpoint exists. A countermodel keeps bulk exclusion true while deleting the current activity, so the phenomenon cannot explain itself. The component composes with the established self-consistent-gap route only through a paper-local admissibility bridge: BCS uses the gapped spectrum in its coherence-factor calculation, while Nambu uses the nonperturbative anomalous solution to establish the Ward identity, continuity equation, and conserving current. Ward constructions, Pippard kernels, penetration depths, and superconductivity mechanisms remain paper-local. Countermodels block inference from a completed gap to a transverse setup, from a calculated current to its screening sign, from an opposing current to bulk field exclusion, and from physical exclusion or theory/model grounding back to the missing response route. They also reject absent-setup grounding and output-only grounding at a non-selected model. A finite positive model realizes the complete screening route and the direct nonvacuous endpoint, and a finite composed witness realizes the gap-supported endpoint. A complementary countermodel realizes generic screening without a nonvacuous gap, proving that screening alone is not gap-supported screening. Direct endpoint-falsification tests cover all six selected indices and all six relation families. A separate twelve-field exact-model audit rejects every changed component. Separate source-valued witnesses now retain the actual BCS equations (5.22), (5.25)-(5.29), case-II coherence channel, London endpoints, gapless normal-current cancellation, Pippard scale, and independent field-expulsion bridge. Nambu's witness retains its noncommuting two-by-two Ward matrix identity, matched self-energy kernel, charged-line insertions, nonzero longitudinal defect, collective cancellation with unchanged transverse response, Coulomb-omitted gapless pair, Coulomb-shifted plasma frequency, and exchange between quasiparticle core and collective cloud. Thirty-one controlled mutations reject altered formulas, mistaken gauge representatives, erased transverse screening, interacting zero modes, and unsupported transport, strong-coupling, or all-orders claims. These source witnesses strengthen fidelity without broadening the generic screening contract or treating local gauge redundancy as a broken physical symmetry.
PhysicsLogic/Framework/RGEndpointMonotonicity.lean: narrow shared renormalization-group irreversibility contract extracted independently from Zamolodchikov 1986 and Komargodski--Schwimmer 2011. It retains a selected nontrivial ultraviolet-to-infrared fixed-point flow, ordered scale evolution, a running quantity with endpoint identifications, weak monotonicity, strict endpoint ordering, an output-led direct result, and setup-bounded TheoryModel grounding. Zamolodchikov's stress-tensor and positive coupling-metric calculation and Komargodski--Schwimmer's dilaton, anomaly-matching, dispersion, optical-theorem, and positive-cross-section calculation remain paper-local. Zamolodchikov's adapter now replays the selected shared flow setup into its stronger paper-local setup before either the conformal endpoint bridge or the running-monotonicity calculation is used; the beta-vanishing and critical-CFT premises remain local rather than being smuggled into the shared vocabulary.
PhysicsLogic/Framework/EffectiveInteractionDynamics.lean: narrow shared organization extracted from Ordonez-Ray-van Kolck 1995 and independently tested by both parts of Epelbaum-Gloeckle-Meissner 1998/1999. It separates perturbative finite-order construction of an effective interaction from nonperturbative full dynamics generated by iteration. The retained model now contains its selected interaction, generated dynamics object, order, and regime together with exactly the seven semantic families used by the shared route. The context owns the low-energy dynamics object, regime, and truncation order and derives the selected interaction from that order, producing one unique selectedModel; a candidate model cannot choose a different dynamics object, EFT regime, or order and certify itself. Each paper constructs its named exact model from that unique selection and proves that it retains the paper adapter's semantics before applying the route. The established result has a checked projection back to the exact selected dynamics and retains that certificate and the complete route directly together with an explicit proposition stating the perturbative-interaction/nonperturbative-dynamics organization. An exhaustive twelve-case technical semantics checks every part of that model-local route in the framework and in each paper adapter. A finite model realizes a direct nonvacuous route that requires the selected order to induce the selected interaction and uses all seven relation families. Exhaustive activity theorems prove that changing any of the four indices or any of the seven relation families destroys that direct route; the eleven-component mutation audit separately checks exact semantic retention. The same raw route now also realizes a structural explanation of the selected mixed organization. A proof-free constraint selects the exact finite-interaction/iteration model, while a separate phenomenon retains the selected interaction, generated dynamics, order, and regime. The source-sensitive form adds an independently realized typed paper derivation without consuming the established endpoint, ordinary explanation, or existing derivational-reduction wrapper. Ordonez-Ray-van Kolck, EGM Part I, and EGM Part II provide distinct source explanations for irreducible-potential iteration, unitary-projected formal iteration, and regulated NNLO Lippmann-Schwinger solution. A finite false-source model keeps the complete route, established organization, and ordinary explanation while denying provenance. A separate theory-model interpretation now treats the finite-order interaction as a mathematical model, keeps each paper's effective theory and represented low-energy dynamics distinct, and transfers only the claims that full dynamics require nonperturbative treatment and are generated by iteration; every adapter proves this exhaustive two-claim transfer. Each transfer is indexed by the pair of the selected dynamics and regime rather than by regime alone. Grounding uses only exact model retention, explicit theory use and world representation, and conditional claim transfer; it consumes no power-counting, construction, iteration, route, or established-result premise. Perturbative construction through a finite order is a model condition, not a property asserted of nature. Countermodels show both that a complete technical route need not supply the interpretation bridges, that exact grounding can hold while the technical route is false, and that even theory-and-world truth of both physical dynamics claims does not reconstruct the finite-order interaction route. Nucleons, pions, potentials, projectors, diagrams, regulators, and scattering equations remain paper-local. The term-level data underlying power counting also remain paper-local; the shared model retains only soundness and completeness through the selected order. The 1999 calculation paper adds a third adapter from its imported NNLO potential through regulated Lippmann-Schwinger iteration, without promoting its cutoff choices or numerical observables into the shared interface. No adapter claims regulator-independent observables, and KSW's amplitude-first resummation is intentionally outside this component.
PhysicsLogic/Framework/RenormalizedPrediction.lean: narrow shared renormalization inference extracted from KSW 1998 and Bedaque-Hammer-van Kolck 1998. It keeps the paper-local parameter-flow calculation separate from the all-scale matching calculation and derives scale-to-scale prediction invariance only through explicit bridges to the mature RG semantics. The technical route also requires one actual target prediction in the selected sector and projects to a direct nonvacuous proposition containing the selected setup, both calculations, running parameters, all-scale matching, and a witnessed common effective prediction at two distinct scales. The established proposition stores exact semantic selection, that direct nonvacuous output, and cross-scale agreement; its complete implication-valued route is reconstructed from these outputs. A separate empirical interpretation distinguishes the target description, each scale-indexed effective description, and the physical system. Only target empirical adequacy plus representation of that same system at every scale yields empirically adequate effective predictions. Both paper adapters first prove a named complete renormalization-route proposition, and the established result exposes its complete setup, both calculations, both exact interpretation bridges, and the reconstructed route. The stronger grounded result retains an independent empirical route as well. The exact proof-free calculation model retains the selected system, target, regime, and observable sector together with the scale-indexed effective descriptions, running parameters, prediction relations, selection predicates, and both calculation predicates. KSW and Bedaque-Hammer-van Kolck each construct a named model from their paper-local context and prove exact semantic retention before either route applies. An explicit theory/model/world interpretation states when a theory uses that same model and when it represents a physical world. Generic grounding requires only exact model selection, setup, and those paper-local bridges; it consumes neither renormalization calculation nor the empirical route. KSW grounds the selected pion-inclusive two-nucleon EFT and scattering problem through effective-range matching; Bedaque-Hammer-van Kolck ground the selected leading-order short-range three-body EFT and low-energy system through the paper's cutoff-correction representation predicate. Every empirically grounded result realizes all eighteen shared claims, including exact semantic selection, through one exhaustive theorem, and both paper adapters expose named realization and theory/world transfer certificates. Countermodels show why vacuously true implication bridges, target mismatch, effective-representation failure, or theory/world claims without the technical route cannot be repaired by all-scale matching. A predictionless countermodel keeps both calculations, both bridges, running parameters, all-scale matching, and extensional cross-scale agreement while blocking both route applicability and the direct endpoint. A separate countermodel grounds the selected setup while parameter flow and route applicability are false, while another proves that false setup cannot be grounded even under universally permissive theory and world claims. A stronger sourced two-body/prediction composition retains exact selection of both independent child contexts, their distinct source explanations, and a third paper-local joining derivation. KSW's joining source preserves the PDS loop, bubble summation, unitarity recovery, pion-inclusive mixed expansion, and full-amplitude RG cancellation; BHvK's preserves the dressed dibaryon, effective-range amplitude, three-body integral equation, individually UV-finite diagrams, cutoff-sensitive sum, one running counterterm, and the original equation-(12) limit-cycle sine ratio. An inhabited countermodel keeps the successful ordinary composition, distinct systems/regimes/targets, and both child source explanations but rejects a missing joining derivation. A fifteen-component mutation audit changes every retained index, scale map, prediction relation, selection relation, and calculation predicate independently, and a completed finite model repeats that audit directly against the nonvacuous endpoint. Beta functions, subtraction schemes, cutoffs, counterterms, amplitudes, and truncation errors remain paper-local.
PhysicsLogic/Framework/PostCalibrationPrediction.lean: narrow shared inference from a completed calibration to a separately calculated target excluded from that calibration and requiring no additional fitted input. KSW 1998 realizes it with a fitted coupled-channel S-wave phase and an unfitted mixing angle; Bedaque-Hammer-van Kolck 1998 with one fitted three-body datum and the remaining energy dependence; and Epelbaum-Gloeckle-Meissner 1999 with nine low-wave contact parameters and the unfitted three-D-one phase shift. Its exact proof-free model retains four selected indices and all five route-used relation families. Each paper adapter proves that this complete model retains its paper-local semantics before applicability. The established result is output-led: exact selected semantics are conjoined directly with validity, calibration, target exclusion, no-extra-input status, and target prediction. The setup, target-calculation contract, and route are reconstructed from those facts. The raw applicable route now also realizes an ordinary structural explanation of the exact calibrated-description/uncalibrated-target phenomenon. Its source-sensitive form additionally requires a typed paper-local derivation relation. KSW retains the coupled S-wave fit and parameter-free mixing prediction; Bedaque-Hammer-van Kolck retain the one-datum limit-cycle-scale fit and cutoff-insensitive energy dependence; Epelbaum-Gloeckle-Meissner retain the low-wave contact fit and parameter- free three-D-one calculation. All three source theorems reconstruct the raw route without consuming the established endpoint or ordinary explanation. A completed-prediction countermodel has the ordinary explanation but no source-sensitive explanation when the derivation relation is false. Grounding instead uses the same exact model plus only the paper-local description-validity facts; it does not require the calibration, target exclusion, no-extra-input claim, or target calculation. A nine-component mutation audit prevents altered calibration or prediction semantics from passing as the selected model. A finite witness realizes the direct endpoint, while a countermodel blocks a vacuous implication-valued calculation with no setup; direct mutations show all four indices and five relations affect that completed proposition. An invalid selected description cannot be grounded, while exact valid grounding need not supply the target calculation or route. The established route also projects to a neutral active prediction sector: its calibrated description and singleton unfitted target are observable only under the complete valid post-calibration setup, and prediction separately requires the actual target calculation. All three clients realize this interface. Countermodels reject a calculated target reused in the fit and a parameter-free target that was never calculated; no empirical-adequacy or probability-role conclusion is added. Parameter-free status, calculation, empirical agreement, and theory/model/world grounding remain distinct. A checked empirical boundary now retains the selected description/calibration/target/regime, calibration and target-calculation residuals, predicted and observed target values, observation tolerance, and truncation allowance. Its exact model bridge retains completed validity, calibration, target exclusion, no-extra-input status, and target prediction without assuming agreement. KSW and Bedaque-Hammer-van Kolck realize completed predictions whose hypothetical target discrepancy exceeds both allowances; Epelbaum-Gloeckle-Meissner realize bounded target agreement while retaining residual cutoff dependence. No constant empirical-agreement predicate substitutes for the prediction, observation, or error budget.
PhysicsLogic/Framework/ThreeBodyPairwiseInputInsufficiency.lean: narrow shared three-body obstruction extracted from Thomas 1935 and Bedaque-Hammer-van Kolck 1998. A calibrated pairwise two-body input is used without an independent short-distance three-body ingredient; a paper-local calculation establishes an instability; explicit bridges say that pairwise sufficiency would imply stability and that the instability excludes stability. The checked reductio derives pairwise-input insufficiency. The established endpoint is output-led: exact selected semantics plus direct validity, calibration, pairwise-only construction, instability, excluded stability, and excluded sufficiency. The complete implication-valued route can be reconstructed from those outputs. Its proof-free model carries four selected indices and all six route-used relation families; each paper-local context owns those indices and exposes one selectedModel, so a candidate cannot select itself by changing them; exact paper-local retention is required independently by model use, representation, model entailment, grounding, and route applicability. Model use, representation, and grounding additionally require the actual selected validity/calibration/pairwise-only setup, but no instability or insufficiency output. A retained finite audit model realizes an actual calibrated setup and instability and has a nonempty off-route sufficiency/stability case. Direct audits now prove that every selected index and relation family changes the nonvacuous endpoint containing validity, calibration, pairwise-only construction, instability, excluded stability, and excluded sufficiency. A false-setup countermodel separates that proposition from vacuous implication bridges, while a mutation audit proves that changing any component fails the original context's exact semantics. The paper interpretations retain the selected indices and pre-calculation setup but do not duplicate the six relation families. Thomas realizes the instability as absence of a lowest three-body energy in the singular limit; Bedaque-Hammer-van Kolck realize it as nonuniqueness and cutoff sensitivity of the resummed amplitude. Thomas's setup-indexed singular calculation replays the shared calibrated boundary and pairwise-only construction facts into SingularPairwiseSetup before it is applied; Bedaque names completed two-body resummation plus the pairwise-only integral equation as a source-native setup that excludes the later cutoff outputs. The ordinary structural-explanation projection executes the instability calculation plus both reductio bridges from the selected pairwise-only setup, without treating provenance as physics. A source-sensitive refinement additionally requires an independently realized typed paper derivation. Thomas supplies a singular-boundary variational derivation; Bedaque-Hammer-van Kolck supply a resummed-equation asymptotic cutoff derivation. A complete endpoint with that derivation relation false still has the ordinary explanation but cannot manufacture a source-sensitive one. Both adapters provide named retention certificates, construct the direct endpoint from their source routes, and recover their source-native setup from any established endpoint. A setup-complete/no-instability countermodel grounds the selected model while falsifying the obstruction. A typed projection into Philosophy/Determination.lean treats the pairwise input as the reduction of the exact selected model and admits that model only when its calibrated setup and stable prediction both hold. The two paper-local instabilities therefore refute nonvacuous stable-prediction determination through an empty admissible domain, without asserting a shared noninjective family. A stable countermodel remains inhabited and determined even with the opaque pairwise-sufficiency predicate false. Finite range, neutron-neutron repulsion, symmetry restrictions, and a running three-body force remain paper-local possible responses, not conclusions of the shared framework. A checked remedy boundary now retains the selected system/input/observable/regime, two-body-calibration, short-distance-instability, and pairwise-prediction residuals, counts of finite-range, repulsive, symmetry, and running-force alternatives, actual selection, two cutoffs and predictions, and the repair residual. Its exact bridge ties the quantitative obstruction to the same calibrated pairwise-only model. Thomas realizes three candidate revisions with none selected; Bedaque-Hammer-van Kolck realize a selected running counterterm and matching running formula while withholding phase locking and two-cutoff prediction agreement. A positive witness supplies the missing agreement and zero repair residual.
PhysicsLogic/Framework/FinitePrecisionTrajectoryPredictability.lean: narrow shared route independently realized by Miller 1964, Portegies Zwart-Boekholt 2014, and Lorenz 1963. A paper-local deterministic classification, an explicit realization of that classification as forward uniqueness of the selected trajectory relation at the reference state and time, two initial states compatible with one finite-resolution input, a paper-local selected-time divergence calculation, and an explicit reliability-exclusion bridge establish only failure of the selected point prediction. The calculated reference trajectory then makes the retained evolution nonvacuously unique at the selected state and time. The established endpoint is output-led: exact selected semantics together with the actual nearby-state setup, a separated selected-time trajectory pair, nonvacuously unique reference evolution, and point-prediction failure. The implication-valued calculation and reliability contracts can be reconstructed from those direct facts. Its exact proof-free model retains seven selected indices and eight route-used relation families. The seven indices are owned by the paper-local context, and every adapter defines its named model through the resulting selectedModel, proves semantic retention, and consumes it in route applicability. A candidate cannot change an index and certify itself by passing that changed value back to modelAt. Generic theory/world membership and grounding require one complete selected pre-output setup: exact selection, valid deterministic evolution, two admissible compatible finite-resolution state descriptions, and the explicit realization of the deterministic classification. They consume no trajectory divergence, reliability exclusion, or established prediction limit. A setup-complete countermodel with identity evolution and no state separation is grounded while failing the direct endpoint. An inhabited finite model realizes a direct NonvacuousFinitePrecisionPredictabilityAt proposition with distinct compatible initial states, unique deterministic trajectories, a calculated separated final-state pair, and point-prediction failure. Direct activity theorems prove that each of the seven selected indices and each of the eight relation families changes that route-used proposition. A separate fifteen-component mutation audit proves that every changed index or relation fails the original exact semantics. Each paper constructs the direct endpoint from its source route rather than using the generic route-to- endpoint theorem as the source analysis. Lorenz's adapter consumes the shared setup directly; Miller and Portegies Zwart-Boekholt replay shared trajectory facts into their stronger local numerical setups before divergence and reliability are calculated. The complete route also realizes a typed structural explanation. Its constraint retains the selected system, both finite-resolution-compatible initial states, time, resolutions, regime, realized deterministic dynamics, actual divergence, and the reliability- exclusion bridge. Its separately typed phenomenon is nonvacuously unique forward evolution together with failed selected point prediction. One countermodel has deterministic nearby trajectories but no divergence; another has deterministic divergence but declares point prediction reliable and lacks the bridge. Neither structurally explains prediction failure. A source-sensitive variant keeps three distinct typed derivations: Lorenz's central nonperiodic-instability argument plus an explicit finite-witness bridge; Miller's controlled parallel n-body protocol and measured separation; and Portegies Zwart-Boekholt's raw arbitrary-precision Brutus validation followed by the same-realization Hermite disagreement. The 2014 source theorem constructs the converged reference and comparison setup internally. A finite countermodel has the complete route, established output, and ordinary explanation but no source explanation, so provenance cannot be inferred from prediction failure. Ontic indeterminism, ensemble failure, numerical convergence, entropy growth, irreversibility, stability topology, return-map evidence, and atmospheric extrapolation are not consequences of the shared component. Its checked value-bearing scope-boundary readout now retains distinct nearby inputs and separated outputs, both positive resolutions and actual distances, two candidate successors of the same reference input, successor count, realization count, two bounded ensemble fractions, and statistical tolerance. The deterministic witness has exactly one realized successor and therefore no ontic branching. The 2014 three-body client realizes pointwise divergence together with agreement of 10,000 ensemble realizations; Lorenz and Miller retain zero tested realizations, so their pointwise limits do not silently establish ensemble reliability.
PhysicsLogic/Framework/CosmologicalPerturbationCollapse.lean: narrow exact collapse-criterion route independently realized by Weinberg 1987 and Press-Schechter 1974. Its proof-free model retains the selected background, perturbation, and regime together with all five relation families used by the route. The ten-claim vocabulary separately exposes exact model selection, the three setup premises, their conjunction, the paper-local calculation, applicability, exact collapse equivalence, the direct nonvacuous model-native criterion, and the established criterion. Both papers construct this exact model and prove a named selected-setup certificate consumed by applicability and grounding. The established result is output-led: it retains that setup and the direct exact equivalence, while checked theorems reconstruct the implication-valued calculation and route. Their concrete grounding theorems use only that selected setup, theory use, world representation, and claim-transfer bridges, never the collapse calculation or result. A converse model has complete grounding with no collapse route, while an output-only model has the exact equivalence but cannot ground without the setup. Eight independent mutations show that no retained component is inert. A finite scoped witness realizes the exact criterion with both the criterion and collapse satisfied. The established route and both paper adapters also project to NonvacuousExactCollapseCriterionAt, which requires the setup and exact criterion directly without asserting collapse. A false-setup countermodel separates it from vacuous implication bridges, and direct activity theorems make all three indices and five relations affect that proposition itself. The framework also projects a satisfied exact criterion into the mature structural-explanation contract using distinct criterion and phenomenon roles. Exact equivalence alone is insufficient: a checked false/false countermodel has an exact criterion but no explanation of actual collapse. Press-Schechter discharges satisfaction from the positive overdensity in its selected setup. Weinberg must receive its paper-local NonlinearCondensationBound as an explicit additional premise. Press-Schechter's adapter consumes its terminal EstablishedSphericalBoundCondensation and extracts the direct setup and exact criterion instead of replaying the spherical calculation. A checked value-bearing distribution boundary now retains the selected background and perturbation, nonnegative strength and collapse threshold, distribution support, selected density, normalization, maximum strength, distribution residual, raw collapsed-tail fraction, and abundance residual. Press-Schechter realizes a satisfied positive-overdensity criterion while withholding distribution support and abundance; Weinberg realizes a normalized supported perturbation distribution while withholding the nonlinear threshold and abundance. The two converse directions and a positive criterion-plus-tail witness prevent an exact collapse test, distribution existence, and thresholded abundance from being conflated. Weinberg's adapter now consumes EstablishedNonlinearSphericalCollapse, which retains the spherical setup and calculated vacuum-energy/collapse equivalence without retaining the implication-valued NonlinearCollapseCalculation. A staged countermodel blocks a vacuous calculation implication from satisfying this boundary. Weinberg's paper-local downstream logic keeps the nonlinear threshold upstream of the maximum-perturbation anthropic cap, and keeps that cap upstream of both the redshift-calibrated quasar lower bound and the cap-indexed intrinsic-vacuum-distribution expectation. The perturbation distribution that supplies the maximum is now a distinct typed object from the intrinsic vacuum-energy distribution assumed smooth and featureless below that cap; neither the empirical route nor a Planck-scale premise can manufacture the missing distributional hypothesis. The complete paper conclusion also retains the calculated missing-mass and cosmic-age assessments rather than dropping them after the near-bound expectation. Vacuum-energy bounds, observer selection, Gaussian statistics, virialization, missing-mass corrections, and abundance spectra remain paper-local.
PhysicsLogic/Framework/ThresholdedCollapseAbundance.lean: narrow shared cosmological-abundance inference extracted from Press-Schechter 1974 and Bond-Cole-Efstathiou-Kaiser 1991. A threshold setup licenses separate paper-local raw-count and missing-mass calculations; a final calculation consumes both outputs and supplies a normalized differential spectrum. Press-Schechter uses initially underdense accretion; Bond et al. use prior first crossings. The proof-free model retains the field, population, raw fraction, completed fraction, spectrum, regime, and all four route-used relation families exactly. Both papers certify that exact model before applicability and ground its actual threshold-counting setup through theory use and world representation without assuming any raw-count, missing-mass, or spectrum output. Their stronger source-input adapters instead execute the paper-local calculations before constructing the shared route: Press-Schechter applies its Gaussian-tail, underdense-accretion, and analytic-spectrum calculations in source order, while Bond et al. execute the sharp-k first-crossing calculation and project its raw tail, prior-crossing completion, and equation-(3.9) spectrum. A typed source-sensitive reduction now records these as distinct derivations: Press-Schechter's maximum-variance Gaussian-tail, accretion, and spectrum route cannot be inferred from Bond et al.'s absorbing-barrier first-crossing route, or conversely, merely because both reach the same normalized abundance. Neither source path assumes a terminal paper result or a shared abundance endpoint. A completed-route countermodel keeps the source relation false and therefore blocks provenance reconstruction. Press-Schechter's paper-local terminal result now also retains the actual displayed maximum-variance chain: equations (7)-(11) for variance, the initial spectrum's second moment, Gaussian density, density-contrast width, and erfc tail; a separate factor-two collapsed-mass equality; and equations (12)-(13) for the differentiated tail and M^(-3/2) exponential number-density spectrum. These are explicit imported calculus equalities, not proofs of the Gaussian integral or derivative. Checked projections and countermodels prevent the named Gaussian, doubling, and spectrum predicates from standing in for those value-level formulas. The source map now also projects their conjunction as a checked analytic-formula output after the terminal spectrum result. Its downstream self-similar endpoint now likewise retains equations (14a)-(14b) for the later density and sigma-squared moments of the derived spectrum. Lean proves the paper's equal-scale reproduction consequence from those formulas, and the self-similarity bridge consumes that conditional formula rather than leaving it inert. A countermodel prevents the older named moment-reproduction predicate from supplying them by itself. Typed countermodels exhibit a raw fraction without missing-mass accounting, setup-licensed accounting without a raw fraction, completed accounting without a differential spectrum, and all three outputs without the threshold setup that would justify them. Technical completion and theory/model/world grounding are independent in both directions: false setup cannot be grounded, but setup-complete grounding still need not supply the raw calculation or route. True theory/world claim tables likewise cannot reconstruct the route. A six-value/four-relation exact-retention mutation audit prevents inert selected data or relations. The model now also has a direct nonvacuous proposition requiring setup, raw count, missing-mass accounting, and normalized spectrum at one selected model. A false-setup countermodel separates that proposition from vacuous implication bridges; a finite witness makes all six selected values and four relation families affect the direct proposition. The established result is exactly the selected direct proposition, and the complete implication-valued route is reconstructed from its direct setup and outputs. Both paper routes reach it from their source-local results. The realized raw count also projects to a typed EnsembleProbabilityContext; the completed fraction and differential spectrum remain downstream roles. Countermodels show that raw ensemble probability supplies neither completion nor the spectrum and does not imply an observed frequency. The same complete route now projects to a typed ReductionAndEmergence.RealizationContext: a proof-free threshold-counting and mass-accounting description realizes a distinct normalized-abundance description, source support retains the raw count, missing-mass accounting, and spectrum-conversion calculation, and the target exhibits only the selected differential spectrum. Countermodels block reduction when spectrum conversion is absent and when matching outputs lack the threshold setup. This is a scoped statistical-to-abundance derivation, not reduction of cosmological dynamics, halo identity, or galaxy formation. Press-Schechter's projection consumes only EstablishedAnalyticMassSpectrum, reconstructing the shared calculation stages from its retained direct outputs. Bond et al.'s projection analogously consumes only EstablishedSharpKMassSpectrum; neither adapter replays a paper-local implication-valued calculation. A separate source-valued physical readout now also retains the two original mechanisms without imposing either on the generic route: Press-Schechter's maximum-variance equation, erfc tail, separately assumed spherical accretion, factor-two completion, equation-(13) density, uncontrolled boundary overlap, and two finite 1000-body experiments; Bond et al.'s independent sharp-k increments, absorbing barrier, reflection, prior crossings, derived factor-two completion, both equation-(3.9) forms, correlated Gaussian and top-hat filter bounds, an at-most-20-percent sharp-k peak discrepancy and comparable general-filter underestimates, failed low-mass particle identification, separate halo calibration, and additional two-barrier merger history. Countermodels distinguish equal normalized abundances with different physical mechanisms and reject invented Press-Schechter first crossings, exact general-filter formulas, particle-level identity from a mean fit, uniquely derived calibration, filter selection from limited simulations, and merger histories without a second barrier. Gaussian-field and first-passage mathematics, spherical dynamics, simulation outputs, and galaxy formation remain paper-local imported or unresolved physics rather than generic framework theorems.
PhysicsLogic/Framework/InflationaryPatch.lean: narrow shared cosmology inference extracted from Guth 1981 and Albrecht-Steinhardt 1982. It requires an admissible selected model and an applicable selected mechanism, then separates initial patch homogeneity, accelerated expansion, observed-region containment, and paper-local bridges to homogeneity and flatness production. Its proof-free calculation model retains the selected model, initial condition, region, mechanism, both targets, and the six proposition-valued relation families used by the deduction. The output-led established result retains exact selected setup, distinct target roles, expansion, coverage, and both produced targets; the implication-valued transfer route is reconstructed from those direct facts. Guth and Albrecht-Steinhardt each define a named paper-local calculation model and prove that it is exactly the model selected by the shared context. The patch calculation, containing cosmological theory, and represented expanded region are separate Lean objects. Model membership and world representation retain the exact selected pre-output setup plus explicit paper-local use and representation bridges. That setup includes admissibility, mechanism applicability, initial homogeneity, and distinct target roles, but excludes accelerated expansion, observed-region coverage, either transfer bridge, and either produced target. A generic setup-only theorem constructs grounding, and a typed countermodel grounds that setup while the patch-expansion route is false. Each paper combines this independent grounding with its separately established route. The model now also exposes NonvacuousInflationaryPatchAt: a direct endpoint that drops exact-record equality and requires the actual setup, both produced targets, and an explicit proof that homogeneity and flatness are distinct targets, without storing either implication-valued bridge. Twelve exhaustive claims expose selected data, admissibility, applicability, the three patch facts, both transfer bridges, both target-production conclusions, target distinctness, and the direct endpoint. Transition completion, graceful exit, reheating, monopoles, deferred curvature physics, and global viability remain outside this framework. The raw applicable route plus distinct targets now also realizes an ordinary structural explanation of the situated expanded patch. A source-sensitive explanation additionally retains one typed paper-local derivation relation: Guth's local sub-horizon patch, expansion, coverage, and horizon/flatness transfer source; or Albrecht-Steinhardt's homogeneous fluctuation region, continued expansion, observed-region containment, and separate homogeneity/flatness bridges. Albrecht-Steinhardt's paper-local thermal setup now also retains equation (1) as a value-level positive-temperature family with the Coleman-Weinberg polynomial/log terms and explicit positive-half-line thermal integral. Its old-inflation setup separately retains p. 1221 equation (2): the vacuum-dominated Friedmann chain, explicit density/GUT-temperature approximations, expansion-time definition, and approximate exponential scale factor. Neither source theorem consumes an established patch, bubble-completion result, defect-formation result, or global-viability conclusion. A countermodel gives the completed ordinary explanation while falsifying the source relation. Countermodels block route-to-grounding and grounding-to-route shortcuts, reconstruction of the route from declared theory/world claims, and treating any context-selected model, mechanism, target, or physical relation as semantically inert. Initial condition and region remain explicit route parameters. A separate finite interpretation now realizes the complete direct endpoint with distinct homogeneity and flatness targets. A coincident-target countermodel can make the older route shape applicable while failing both output-led endpoints, and a false-setup model blocks vacuous implication bridges. Direct activity theorems make every one of the six selected objects and six relation families affect the direct proposition before the independent exact-record mutation audit is applied. Its exact solution context has no consequence type and no naturalness, side-effect, or unacceptability payload.
PhysicsLogic/Framework/BubbleTransitionCompletion.lean: independent shared old-inflation obstruction extracted from the same two papers. It separates bubble-mediated first-order transition, cosmologically sufficient expansion, the paper-local calculation that expansion outpaces bubble formation and connected completion fails, and the bridge to an incomplete-transition side effect. Both papers first prove named selected- setup adapters, then complete their distinct routes. The output-led established obstruction retains exact selected data, the inhabited setup, expansion dominance, failed connected completion, and the side effect. It stores neither implication-valued paper-local contract; checked exposure theorems reconstruct the competition calculation and interpretation bridge from the direct outputs. It also projects to NonvacuousBubbleCompletionObstructionAt, where the setup and three direct outputs hold on one model. Its proof-free calculation model retains the selected model, initial condition, regime, phase, mechanism, consequence, and exactly the five proposition-valued relations used by the route. Guth and Albrecht-Steinhardt each construct a named paper-local model and prove exact retention before any technical inference. Albrecht-Steinhardt's regime is its selected bubble-nucleation rate, and its lifted expansion and completion relations are guarded by that rate and the broken phase. One exhaustive theorem realizes all nine shared claims, including selected- data identity, and both paper adapters expose named exhaustive-realization and grounded-transfer certificates. A countermodel prevents the implication-valued calculation and bridge from counting when the bubble setup is absent, including at the direct endpoint. The framework also imports Philosophy.TheoryModel and distinguishes the selected competition calculation from its containing cosmological theory and represented universe. Model grounding retains only exact selected data, an inhabited first-order expansion setup, and explicit paper-local theory/world roles; it assumes no competition calculation, failed completion, or side effect. Each final paper theorem combines this setup-bound grounding with its separately completed technical route. Further countermodels separate route completion from grounding, grounding from route applicability, output claims without selected setup, and declared theory/world claims from the route. A mutation audit changes the selected model, mechanism, consequence, or any one of the five retained relations and refutes exact selected semantics. A separate finite interpretation realizes the complete obstruction, direct nonvacuous endpoint, and scoped viability-failure route. Direct activity theorems make all six selected objects and all five retained relation families affect the direct endpoint itself, while the older route-fact and exact-record audits remain separate. Initial condition, regime, and phase remain explicit route parameters. Potentials, tunneling rates, percolation thresholds, thermalization, and consequence-acceptability judgments remain paper-local. Its exact viability context has no target type and no naturalness, target-realization, or target-production payload. A separate composed inflation/bubble handoff now retains an actual expanded patch, an actual incomplete-transition obstruction, exact selected model and initial condition, an independent source-local expansion/transition calculation, and either literal mechanism identity or literal mechanism inequality. Guth realizes patch success and graceful-exit failure for the same mechanism; Albrecht-Steinhardt realize a successful fluctuation replacement while the distinct standard-bubble mechanism remains obstructed. Finite countermodels prevent relabeling one mechanism as the other, manufacturing the paper-local handoff from the two endpoints, or transferring the old mechanism's side effect to its replacement. Its source-sensitive composition also exactly selects both child contexts and independently retains the patch derivation, bubble derivation, and paper-local comparison derivation. Guth's token keeps the same-mechanism slow-nucleation/percolation route; Albrecht-Steinhardt's token explicitly requires unequal replacement and standard-bubble mechanisms. An inhabited finite countermodel has ordinary composition and both sourced child explanations while withholding the comparison source.
PhysicsLogic/Framework/CausalDomainDefectFormation.lean: narrow shared defect-formation route realized in Kibble 1976 and reused in Guth 1981's explicitly imported Kibble argument. It separates a nontrivial family of sufficiently separated domains from its selected local order-parameter assignment, requires uncorrelated assigned values, threads the same assignment through collective assembly, and retains a paper-local calculation excluding its global extension and identifying an obstruction before a separate physical-defect interpretation. Its proof-free context owns eight selected values and all ten route-defining relation families and constructs one unique selectedModel. Each client proves exact paper-context retention before applicability. Guth's context is parameterized by the selected bubble family, phase, and defect, so those values cannot be read back from a candidate model. The output-led established result stores exact selection plus direct setup, assembly, failed extension, obstruction, and defect production; it reconstructs the implication-valued route. Both clients provide explicit theory/model/world grounding and exhaustive transfer of seventeen claims. The completed route also projects to a direct nonvacuous formation proposition requiring setup, assembly, failed extension, obstruction, and defect production at one model. The complete route additionally realizes a typed structural explanation. Its constraint retains the exact description, transition, domain family, local assignment, assembly, obstruction, and regime, and is satisfied only by the full selected technical route including the physical-defect interpretation. Kibble's protodomain/vertex/surface route and Guth's bubble/coalescence/Higgs-knot route realize the same scoped endpoint. A countermodel retains a calculated topological obstruction while deleting the interpretation and defect production, and therefore refutes the structural explanation. A converse countermodel declares defect production after collective assembly but omits the global-extension failure and topological route, so the output alone also fails to reconstruct the explanation. The generic grounding constructor requires exact selected-model semantics and an inhabited independent-domain setup but consumes none of those route conclusions. A setup-complete countermodel still lacks assembly and every formation output. Mutation countermodels prove that changing any selected value or relation family fails the original context's exact semantics; a separate finite direct audit shows that all eight selected values and all ten relations affect realized formation, and a physical countermodel shows that changing only the assignment can change whether the route is established. The finite causal witness selects two distinct domains with opposite local order-parameter values while explicitly excluding a third exterior domain; domain membership and causal separation are not constant truth-status predicates. Vacuum manifolds, homotopy groups, walls, strings, monopoles, magnetic charge, production estimates, annihilation, network evolution, and inflationary suppression remain paper-local.
PhysicsLogic/Framework/FiniteRegulatorGaugeInvariance.lean: narrow shared finite-cutoff gauge semantics extracted from Wilson 1974 and Creutz 1980. It separates the regulated lattice setup, exact action and closed-observable invariance, and the compact-integration bridge making gauge fixing unnecessary. Each paper proves the complete route-applicability proposition before deriving the shared result. The established proposition is output-led: it retains the exact selected finite-regulator setup, both invariance outputs, and the no-gauge-fixing output. The calculation and interpretation bridge are reconstructed from those facts when the complete route is requested. Implication-valued calculations and bridges do not count when the finite-regulator setup is absent. It requires orbit completeness before invariant values become representative-independent physical quantities and contains no continuum transfer, simulation, or confinement claim. Its proof-free model retains all four physical indices and all nine semantic relation families used by the route. Wilson and Creutz each name an exact model, prove its retention, and derive a direct NonvacuousFiniteRegulatorGaugeInvarianceAt proposition containing the realized finite setup, both invariance outputs, compact integration, and no-gauge-fixing output. The raw applicable route now also realizes an ordinary structural explanation of the exact selected action-and-closed- observable phenomenon. Its constraint requires exact selected-model identity as well as the complete route, so a record with the same four indices but different relation fields cannot masquerade as the explained calculation. The source-sensitive form additionally requires one typed paper-local derivation. Wilson retains the angular-link gauge transformation, plaquette action, closed-path product, compact periodic integral, and no-gauge-fixing argument; its local route now also retains equations (3.4), (3.6), and (3.8) as selected real-valued link/plaquette propositions before forgetting to the shared endpoint. Creutz retains pure SU(2) links, the Wilson action, invariant group measure, exact local symmetry, and gauge-fixing-independent correlations. A completed-route countermodel has the ordinary explanation but no source-sensitive explanation when its derivation relation is false. A separate direct physical-value proposition requires an actually represented physical state and scoped orbit completeness. A theory/model/world layer grounds the exact selected model together with an actual finite-regulator setup, independently of the invariance calculation and outputs; the final theorem then combines grounding with the technical route. Its two-tier claim semantics transfers ten base claims, including exact model selection, selected setup, and the complete route, or all fourteen claims after orbit completeness is added. Countermodels establish independence in both directions. A finite direct model shows every selected index changes the realized regulated route and every retained relation changes the represented physical-value lane, so the audit does not rest only on record inequality.
PhysicsLogic/Framework/LoopAreaConfinement.lean: narrow shared loop-area-to-confinement inference extracted from Wilson 1974 and Creutz 1980. Its proof-free model retains six selected physical indices and all seven relation families used by the route. Wilson and Creutz each name an exact model and prove its retention before any setup or calculation is assumed. The established proposition is output-led: exact selected setup, area law, linear potential, and confinement are retained directly, while the paper-local area-law calculation and both interpretation bridges are reconstructed by checked eliminators. Eleven exhaustive claims cover exact selection, selected setup, each calculation or bridge, applicability, the three outputs, and the established result. Theory/model/world grounding uses exact selection plus the valid loop/surface/source/positive-tension setup, theory use, world representation, and conditional claim transfer; it uses no area-law or interpretation output. The final paper theorems combine this independent grounding with their separately completed routes. The established result also yields a direct NonvacuousLoopAreaConfinementAt proposition at one actual calculation model. The generic endpoint remains regulator-agnostic, while Wilson's and Creutz's source-order routes additionally expose NonvacuousFiniteGaugeSupportedLoopAreaConfinementAt. That composite keeps the direct finite-gauge child, established gauge route, admissibility bridge, loop setup, and confinement endpoint together. Countermodels establish independence in both directions: setup-bounded grounding can hold while the area law is false, and all three outputs cannot ground a model whose selected setup is false. A finite direct witness shows every one of the six indices and seven relations changes realized route semantics, rather than merely changing record equality. A finite composed witness realizes the regulator-supported endpoint, while a converse model realizes generic confinement with a vacuous gauge child. The complete selected route now also instantiates the mature structural-explanation contract: its typed constraint requires the actual loop setup, area-law calculation, and both physical interpretation bridges, and its phenomenon contains both the rising static potential and confined sources. A countermodel retains all three outputs while deleting selected-regime validity, so output labels alone do not explain them. Wilson and Creutz independently derive this explanatory endpoint from their different calculations. Continuum confinement is not a transferable claim.
PhysicsLogic/Framework/EquilibriumSampling.lean: narrow shared equilibrium-targeted update inference extracted from Metropolis 1953 and Creutz 1980. It keeps detailed balance, the paper-local convergence calculation, equilibrium interpretation, and selected finite-run convergence logically separate. Creutz's adapter now mirrors Metropolis's separation: its imported heat-bath result supplies repeated-update convergence first, and only a distinct interpretation bridge consumes that convergence under the same heat-bath setup to identify the ensemble used for equilibrium measurements. A countermodel blocks the heat-bath setup plus convergence from supplying that interpretation by themselves. Its proof-free exact model retains the selected description, regime, update, and ensemble together with the validity, equilibrium-target, detailed-balance, target-space-accessibility, asymptotic-convergence, and equilibrium-production relation families. The Metropolis adapter supplies target-space accessibility only through its paper-local calculation consuming the certified finite periodic cell, positive proposal width, periodic wraparound, successive particle attempts, finite-probability allowed moves, and the selected update's implementation of that proposal; the shared framework receives only the resulting accessibility fact. Metropolis's paper-local balance route separately retains actual positive canonical state probabilities, symmetric proposal probabilities, the acceptance-weighted uphill transition, and the unsuppressed downhill transition. Lean derives the original directional equality p_r T_rs = p_s T_sr from equation (2), preserves it in the completed sampling result, and supplies normalized physical countermodels showing that discarded rejected attempts or non-Boltzmann population weights destroy that equality. None of these Metropolis-specific transition formulas is imposed on Creutz's distinct heat-bath mechanism. The context owns all four selected indices, and selectedModel fixes their unique combination rather than reading a candidate model's own indices back into the semantics. Both paper adapters construct and certify that exact context-selected model before exposing a complete route-applicability theorem. The established proposition is output-led: it stores exact selection together with the direct NonvacuousEquilibriumSamplingAt proposition, where validity, target, balance, accessibility, asymptotic convergence, and equilibrium production all hold at one selected model. It stores no calculation or applicability proof; the selected setup, calculation contract, interpretation bridge, and complete route are reconstructed from those direct relations. Metropolis and Creutz each derive the output from their source-local route without asserting selected finite-run convergence. A ten-part mutation audit shows that changing any of the four indices fails the original context's exact-selection proposition and that changing any of the six relations invalidates exact retained semantics. A finite source-shaped witness realizes the complete asymptotic route while its selected finite run remains unestablished; direct activity theorems make all four indices and six relations affect route-used propositions, and a second direct mutation audit makes every such change falsify the nonvacuous proposition itself. A separate paper-local theory/model/world grounding treats convergence as a conclusion of the algorithmic model and equilibrium production as a conclusion of the theory and represented sampling process. Grounding requires the exact selected model plus the inhabited pre-convergence setup: validity, target, balance, and accessibility. It assumes neither the convergence calculation nor convergence nor equilibrium production. Metropolis grounds representation with configuration-space accessibility; Creutz grounds it with successive entire-group heat-bath updates and single-link Boltzmann weight. The shared theory/model context requires that exact selected setup in theory membership, world representation, and grounding. The shared layer only combines an established technical route with such independently proved grounding. Balance and target-space accessibility are separate shared premises. Countermodels show that completed equilibrium sampling does not manufacture grounding and that declared theory/world equilibrium claims do not reconstruct the sampling route. A false-setup countermodel cannot be grounded even though both implication-valued calculation contracts hold, while a setup-complete no-convergence model can be grounded without acquiring a route or output. Proposal and acceptance rules, accessibility, heat-bath replacement, Markov kernels, mixing rates, finite-run convergence, physical-time dynamics, and observables remain paper-local. The complete route now additionally realizes a typed structural explanation of the selected asymptotic algorithmic-sampling phenomenon. Its proof-free constraint and phenomenon retain the same four indices but no proofs; satisfaction requires exact selection, the inhabited target/balance/access setup, the convergence calculation, and the interpretation bridge. Metropolis reaches this endpoint by reconstructing its finite model, canonical target, modified update, pairwise balance, and accessibility from source-local calculations. Creutz reaches it with the regulated heat-bath setup while keeping equilibration and equilibrium interpretation distinct. Countermodels exhibit the output without valid setup and convergence without interpretation; a positive model realizes the explanation while finite-run convergence remains false. Thus this is neither physical dynamics nor a mixing-time or finite-run certificate. A stronger source-sensitive explanation retains one typed paper-local derivation. Metropolis's token expands to the pp. 1088-1089 finite-periodic/canonical reductions, symmetric local proposal, downhill-or-Boltzmann acceptance, repeated rejected configurations, reachability, pairwise population flow, equilibration, and interpretation. Creutz's distinct token expands to the regulated SU(2) predecessor, conditional entire-group single-link heat bath, detailed balance, accessibility, equilibration, and interpretation on p. 2309. A countermodel preserves the common route, established endpoint, and ordinary explanation while falsifying the source relation, so common outputs cannot reconstruct either algorithm's derivation.
PhysicsLogic/Framework/ReciprocalTransport.lean: narrow shared Onsager-Casimir semantics for parity-sensitive field-reversed transport. Near-equilibrium fluctuations do not suffice: microscopic reversal must relate the selected dynamics at H to reversed dynamics at -H, and the macroscopic regression law is restricted to an explicit intermediate-time window. A separate ensemble-regression hypothesis and paper-local correlation and coefficient calculations are required to derive L_ij(H) = epsilon_i epsilon_j L_ji(-H). Both paper adapters first prove the complete RouteApplicableAt proposition, and established transport retains that complete route, including both paper-local calculations. The context owns one exact evaluation field and a literally distinct selected transport-variable pair, and separately records the paper-admissible field family. Its unique proof-free model retains the selected process, evaluation field, both selected variables, field-reversal map, time-reversal parity assignment, and kinetic-coefficient family together with all seven route-used relation families. Named projections expose those exact selections, field-paired microscopic reversal, the intermediate regression window, the macroscopic regression law, calculations, correlation result, and reciprocal relation. A selected projection exposes an actual off-diagonal coefficient relation; a singleton variable type cannot realize the route through diagonal identity alone. A separate finite model realizes the direct route with two opposite-parity variables, positive-to-negative field reversal, and asymmetric off-diagonal coefficients satisfying the Onsager-Casimir sign rule. Its NonvacuousReciprocalTransportAt proposition retains the actual setup, regression premise, correlation result, universal relation, and selected cross-variable instance without using exact-record equality. Changing any of the four selected indices or any of the three functions and seven physical relation families destroys that direct proposition. Both paper adapters derive it from their source-local calculations. A stronger structural projection explains the universal field-reversed relation and its selected off-diagonal instance from the exact reversible setup, intermediate-window regression premise, correlation calculation, and coefficient calculation. Its proof-free constraint retains the process, field pair, variables, reversal map, parities, and coefficient family but no reciprocal equality. Onsager realizes it through the zero-field heat route; Casimir realizes it from granular parity, reversal, regression-scope, correlation, and coefficient premises. Reciprocal coefficient outputs in a model with false physical setup do not reconstruct this explanation. The separate theory-model-grounded result distinguishes that exact calculation from the theory using it and the represented transport system. Onsager proves that zero field is fixed under reversal, specializes the shared parity assignment to time-even variables, and obtains ordinary same-field reciprocity. Casimir grounds both declared zero- and magnetic-field routes as distinct exact contexts with their intermediate- time regression scope. A first-class exhaustive theorem realizes all thirteen shared claims, and both paper adapters expose named grounded transfers for every claim. Countermodels show that a completed technical route need not be semantically grounded, that fixed-field reversibility does not supply the H to -H relation, that regression without its time window is inapplicable, that changing any of the fourteen model components changes the selected model, that a second admissible field still fails exact selection, and that even declaring all thirteen theory/world claims true does not reconstruct the regression-and-correlation route. A checked field-reversal boundary now retains the exact selected process, field pair, variables, nonzero field values, forward/same-field/paired trajectory weights, time-reversal parities, and three cross-coefficient values. Its model bridge ties the paired trajectory balance and coefficient entries to the selected calculation. Onsager realizes same-parity magnetic reciprocity at -H while both fixed-field balance and reciprocity fail; Casimir independently realizes the mixed-parity minus sign at -H with the same fixed-field failures. No constant reversibility predicate substitutes for the field values, trajectory weights, parity signs, or coefficients. Thermodynamic variables, dissipation principles, response functions, four-poles, and Hall applications remain paper-local.
PhysicsLogic/Framework/FinitePartitionNonvanishing.lean: narrow shared finite-system induction semantics independently realized by Liu-Sinclair-Srivastava 2018 and Peters-Regts 2017. A proof-free calculation model retains the selected interaction or assignment together with the admissible finite-system class, graph-indexed parameter domain, natural-number complexity measure, and partition-nonzero relation. Each paper supplies that relation through an actual complex-valued finite configuration sum rather than an uninterpreted conclusion. The shared edge-indexed configuration kernel computes hard-core independent-set sums and pinned zero-field Ising sums separately, retains actual graph degree and prescribed spins, enforces constant hard-core activity at every vertex, and calculates the Ising unpinned-vertex induction complexity. One-edge graph witnesses preserve three versus four hard-core occupations, site-dependent cancellation, the original vertex split, disagreement-weighted Ising sums, exact pinning restrictions, and the original pinned-spin partition split. The two independent paper certificates retain seventeen graph- and value-bearing fidelity boundaries. Each adapter fixes the arbitrarily quantified interaction or assignment as the context-owned selectedParameter, constructs the unique selectedModel, and proves exact equality with it. Grounding requires those exact semantics together with an actual admissible complexity-zero graph in the selected parameter domain, while assuming no nonzero base value, induction step, or uniform conclusion. Explicit theory-use and finite-world representation bridges then transfer the selected setup and downstream claims. The Ising adapter uses bounded-degree arbitrarily pinned graphs and unpinned vertex count; the hard-core adapter uses bounded-degree graphs, complex-tube assignments, and vertex count. The established result is output-led and stores selected data, base, step, and uniform nonvanishing directly. An eighth direct NonvacuousFinitePartitionNonvanishingAt claim additionally requires an actual admissible complexity-zero graph with nonzero partition value. Both paper adapters expose that endpoint from explicit zero-complexity graph witnesses and thread the witness through named grounded transfers for every claim. The shared component now also has ordinary and source-sensitive structural projections. Peters-Regts supplies the typed doubleLogInvariantDomainVertexSubsetInduction derivation, whose relation retains the threshold setup, coordinate/contraction calculations, complex invariant domain, occupation-ratio recurrence, final-root cancellation, and empty-graph witness. Liu-Sinclair-Srivastava supplies the distinct correlationDecaySawTreePinnedSpinInduction derivation, retaining the tree uniqueness and correlation-decay route, complex extension, SAW recurrence, pinned cancellation, and zero-unpinned witness. Each source theorem rebuilds the shared base/step route from those paper-local premises; neither source relation stores the shared route, established result, or explanation. A countermodel establishes the ordinary explanation while making the selected derivation relation false, proving that provenance is additional logical content. No finite-regularity or thermodynamic-limit claim is transferable. Countermodels show both that a completed induction does not supply theory/world grounding and that even universal declarations of all eight theory/world claims do not reconstruct the induction route. An empty selected parameter domain can satisfy the universal induction vacuously but fails the direct endpoint and cannot be grounded because it lacks the selected finite-base scope. A finite direct witness separately proves that changing the selected parameter or any selected system class, parameter domain, complexity, or partition relation falsifies the nonvacuous endpoint itself, alongside the exact-selection audit. A separate size-family scope and FiniteRegularityBridgeAt remain necessary even for finite-stage regularity, which still does not imply regularity of the limiting description.
PhysicsLogic/Framework/RandomDisplacementDiffusion.lean: narrow shared stochastic-spread inference extracted independently from Einstein 1905, Smoluchowski 1906, and Linde-Linde-Mezhlumian 1993. It requires a regime-scoped controlled step description, a paper-local directional-bias control, and a paper-local control of inter-step dependence. Independent calculations establish linear mean-square and root-time rms spreading and diffusive transport; the framework imposes no common order on those calculations. A distinct typed constraint and phenomenon now expose the corresponding structural explanation: the complete controlled-step route necessitates all three outputs. This theorem uses route applicability directly rather than the established or nonvacuous endpoint. A finite all-outputs-but-biased model blocks the occurrence-to-explanation converse, while a second model shows that both spread laws without transport do not constitute the selected phenomenon. All three papers additionally realize a source-sensitive explanation whose typed derivation distinguishes Einstein's transition expansion and point-source solution, Smoluchowski's persistent collision flight and gas-kinetic analogy, and the Linde-Linde-Mezhlumian random-phase Hubble-step and Langevin/Fokker-Planck route. These theorems consume raw paper inputs and route applicability, not an established endpoint or the ordinary explanation. A complete common route with a false derivation relation proves that shared diffusion semantics do not reconstruct source provenance. All three papers now establish an explicit shared route-applicability proposition before deriving the established diffusion result. That result is output-led: it retains exact selected semantics, every inhabited setup relation, and all three direct outputs, but no implication-valued calculation or paper-local route order. Named theorems reconstruct the stochastic setup, spread calculation, diffusive-transport calculation, and complete route when needed, preserving the papers' different logical order and mechanisms. A proof-free model records the selected description, system, step model, time, and regime together with the exact validity, step-control, directional-bias, inter-step-dependence, spread, and transport predicates. Each paper proves that this full relation family is the one selected by its adapter. The context owns all five physical indices and exposes one exact selectedModel; changing any physical index or any of the seven retained relations fails that context's exact semantics. Separate direct semantics require all four setup relations and all three outputs to hold at that same model. A finite witness inhabits the complete route, and exhaustive five-index and seven-relation mutations each destroy this route-used proposition. All three paper adapters derive it from their independently anchored established routes. Separate paper-local interpretations state which theory uses that model, which physical process it represents, and what each calculated claim means in the theory and represented world. Einstein grounds the model in molecular-kinetic theory and the selected suspended-particle process; Smoluchowski grounds it in kinetic collision theory and the selected suspension process; Linde-Linde-Mezhlumian ground it in semiclassical stochastic inflation and the selected coarse-grained inflaton process. Only an established technical result plus those explicit bridges yields the stronger grounded result. Grounding itself consumes the exact inhabited pre-output stochastic setup and the conditional theory/world bridges; it consumes neither spread nor transport calculation and no established result. A selected model with false validity or stochastic controls therefore cannot be grounded. Einstein, Smoluchowski, and Linde-Linde-Mezhlumian each also expose the direct structural explanation from their own granular route. Gaussianity, collision geometry, gas analogy, physical-volume branching, stationarity, objective chance, and a common microscopic mechanism remain outside it. Model-level diffusive transport is the actual transport conclusion, not a disguised setup predicate. Transition laws, persistent collision geometry, Gaussianity, drag, diffusion coefficients, osmotic pressure, and numerical factors remain paper-local. The established result realizes four shared claims, including exact selected-model data. Countermodels separate dependence control from directional-bias control, stochastic setup from spread, spread from transport, completed diffusion from theory/world grounding, declared theory/world claims from reconstruction of the stochastic route, vacuous implication-valued calculations from an applicable route, and one-regime validity from transfer. A further pair proves that exact selection without an inhabited setup cannot ground a model, while a complete pre-output setup can be grounded before spread or transport is obtained.
PhysicsLogic/Framework/ThermalDragBrownianTransport.lean: the narrower Einstein-Smoluchowski composition requiring established stochastic diffusion together with thermal setup and sibling hydrodynamic-drag/coefficient and rms- spread calculations. Einstein obtains the coefficient before point-source spread, while Smoluchowski obtains relaxation spread before his later gas-kinetic coefficient; the shared route no longer invents one universal order. Its proof-free model retains the complete nested stochastic model, six additional selected data components, and all four thermal/drag/spread relation families. The nested context owns its five stochastic selections and the parent owns six transport selections; their unique composed selectedModel is required by route applicability and the model judgment. Both papers construct named exact models and expose complete theory/world transfers for all nine claims. Grounding requires exact model selection plus the established nested diffusion, drag-regime validity, and paper-local thermal drive, but no child drag/coefficient calculation, spread calculation, output, or transport route. Countermodels prove both that exact selection alone cannot ground a model and that an inhabited setup can be grounded while the child route remains false. The output-led established result is exact selection together with the direct NonvacuousThermalDragBrownianTransportAt proposition: the nested stochastic controls, drag-regime validity, thermal drive, drag law, coefficient relation, and rms spread all hold at one selected model rather than only through implication-valued calculation contracts. A finite Bool witness realizes that proposition, and exhaustive mutation theorems show that changing any of the eleven selected physical values or eleven route-used relation families destroys it. The older exact-semantics audit still shows that seven top-level data components and four parent relations cannot be erased from the selected model. Both paper adapters bind every parent relation to their selected description, carrier, medium, drag convention, coefficient, spread, time, and regimes, unpack the shared thermal setup to recover the paper-local calculation setup they actually use, then delegate named nonvacuity theorems to the generic projection. The endpoint additionally realizes a typed mechanistic explanation of the rms spread from thermal drive, drag, and coefficient organization. A finite no-thermal-drive model retains stochastic spreading but refutes that explanation, and the projection does not infer ontic randomness. A second, source-sensitive mechanistic projection retains a typed paper-local derivation and its independent proposition-valued realization. Einstein's raw constructor derives osmotic pressure before dynamic equilibrium and independently constructs transition-law/point-source diffusion; Smoluchowski's derives equipartition from collision imbalance before constructing its small-particle diffusion and large-particle relaxation/Stokes branches. Neither source theorem accepts established diffusion, established thermal-drag transport, or the ordinary mechanism as an input. A checked forgetful theorem strips only source provenance from any source-sensitive explanation and recovers the ordinary thermal-drag mechanism from the same physical witnesses. A finite countermodel completes the shared route, established output, and ordinary mechanism while falsifying the source relation, proving that common transport behavior does not reconstruct either derivation. A stronger composed endpoint now requires both child source explanations, their actual two-regime physical handoff, and a third independently realized joining derivation. Einstein's join retains the original transition/Gaussian formulas, both stationary balance equations, and exact coefficient; Smoluchowski's retains both particle-size setups, his original persistent-flight and relaxation/Stokes formulas, different numerical prefactor, and explicit failure of exact agreement. An inhabited distinct-regime countermodel completes both child sources and transport while withholding that joining derivation. Separate source-valued witnesses now retain Einstein's osmotic force balance, actual 6 pi eta a drag, exact scoped diffusion coefficient, normalized symmetric-step variance, Gaussian point-source density, and molecular-count inference; Smoluchowski's distinct witnesses retain noncancelling finite collision counts, the 8/3 persistent-flight prefactor, exponential relaxation, distinct near-agreeing coefficients, unresolved aggregation, and incomplete direct experimental verification. No universal numerical coefficient or common microscopic derivation is asserted, and Einstein's mobility convention is not identified with Smoluchowski's resistance convention.
PhysicsLogic/Framework/LowEnergyEffectiveRangeReduction.lean and PhysicsLogic/Framework/EffectiveRangeBoundStateExtraction.lean: the Bethe and Blatt-Jackson low-energy reduction and its deuteron-data extraction composition. The reduction model retains five selected physical indices and all eleven relation families used by the route. Each paper names its exact context-owned selectedModel, proves a selected-semantics certificate, realizes all thirteen shared claims, including the separately established two-parameter endpoint, and transfers them through theory and represented-world judgments. The zero-energy stage returns controlled reference data together with the scattering-length definition; the reduction consumes both and returns the effective-range definition and phase law as sibling outputs. Bethe and Blatt-Jackson keep their distinct comparison-wave and variational calculations as explicit route hypotheses. Their completed paper-local and shared results retain only the inhabited setup and realized physical outputs; checked reconstruction theorems recover the calculation functions when a source-order or adapter proof needs them. The same output-led boundary applies to both higher-order assessments. Bethe's neutral branch now additionally retains the literal equations (7), (10), (11), (13), and (14): the sine-normalized comparison wave, its explicit k cot(delta) origin-derivative readout, the comparison-minus-exact radial overlap, the zero-energy scattering length, and the energy-dependent/effective-range integrals. Lean checks that equation (7) really normalizes the comparison wave at the origin, that its phase function is tied to the same k and delta, and that equations (10), (11), and (13), together with k_1^2 = 0, produce the exact energy-dependent phase relation before the controlled equation-(14) replacement is used. At the separately selected observable energy, actual k^2 = k * k, nonzero sin(delta), and the same-energy k cot(delta) readout allow Lean to derive both original equation-(17) forms: 4 pi sin(delta)^2 / k^2 = 4 pi / (k^2 + (k cot(delta))^2). The physical S-wave maximum is characterized by cos(delta) = 0; concrete positive-domain countermodels show that neither the wave-square identity nor the physical phase readout can be dropped. Their complete shared reduction now imports the effective-theory truncation vocabulary: the selected two-parameter law is calculation-complete only with its calculated higher-order term and is controlled only when that correction is small. Both papers derive the same ControlledAt proposition through their distinct local mechanisms. A calculated but nonsmall correction is a checked countermodel, and neither empirical adequacy nor potential-shape determination is inferred. The complete route also realizes a typed derivational reduction from the selected short-range scattering description to the two-parameter effective description and its controlled phase behavior. Realization requires the inhabited low-energy setup; source support requires the controlled zero-energy reference and scattering-length definition; macro exhibition requires the effective-range definition, phase law, calculated small correction, and unresolved detailed shape. Both paper adapters consume their applicable routes directly. A non-small-correction model and an output-only false-setup model block promotion of a bare law or declared reduced behavior to derivational reduction. No unique potential recovery or multiple-realizer universality follows. A second, source-sensitive projection pairs the exact model with a typed paper-local derivation token. Blatt-Jackson's stationary-functional and zero-energy-trial route is distinct from Bethe's comparison-identity and interior-replacement route even though both realize the same shared behavior. Their adapters start from raw paper premises, and a finite countermodel proves that a complete route and complete output cannot supply a missing source derivation. The downstream bound-state extraction now also projects its complete parent-and-child route to the mature model-evidence core. A typed channel-parameter estimate is supported only when the selected aggregate evidence package is accessible, both binding and scattering measurements obtain, the parent two-parameter law is active, the bound-state relation is calculated and controlled in the uncoupled scope, and the estimate is both extracted and qualified. Bethe and Blatt-Jackson independently realize this endpoint through their distinct comparison-wave and pole-continuation calculations. A no-data countermodel keeps extraction and qualification labels true but refutes evidence support. No exactness, prediction, potential-shape determination, or theory truth follows. The extraction now also has route-only and source-sensitive structural explanations of that same qualified estimate. Bethe's typed source requires the raw comparison identity, controlled interior replacement, ground-state specialization, and empirical extraction contracts. Blatt-Jackson's typed source instead requires the stationary functional, zero-energy trial reduction, scattering-matrix continuation to k = -iγ with S(-iγ) = 0, and its empirical extraction. Neither source theorem consumes an established shared extraction, nonvacuous endpoint, ordinary explanation, or evidence-support endpoint. A finite converse model retains the complete route, estimate, ordinary explanation, and evidence support while falsifying the source relation. Bethe's observable S-wave cross-section calculation remains a separate paper-local child of the established phase law. At explicitly positive k^2, the printed formula proves cross-section positivity and the 4 pi / k^2 unitarity bound; saturation holds if and only if the actual phase vanishes, and every nonzero phase gives strict suppression. Zero-wave-number and nonzero-phase countermodels block both shortcuts. The need for the next term near that maximum remains separate; neither the phase law alone nor the bound alone licenses the low-order truncation. Blatt-Jackson additionally realizes a paper-local universality explanation from explicitly unequal square and Yukawa wells with shared low-energy parameters and controlled selected phase behavior. Its conclusion retains unresolved detailed shape and higher-order dependence; it is not an arbitrary-potential or all-energy universality claim. The same restricted context has an explicit derivation bridge and checked robust realization, so Lean derives compatible reduction and autonomous emergence without treating the low-energy macrodescription as a unique reconstruction of the potential. Model and represented-world membership require the exact selected low-energy setup: exact context selection, validity, neutral S-wave scope, short range, and low energy relative to the interaction range. Grounding uses only that setup, physical representation, and conditional transfers, never the controlled reference, two-parameter outputs, higher-order outputs, technical route, or established reduction. Each paper supplies its own setup proposition before invoking the generic constructor. One countermodel proves that a false low-energy setup cannot ground even an exactly selected model; another has a complete setup and grounding while the first calculated output and the technical route are false. A 16-component mutation audit proves that every index or relation substitution fails the original context's exact semantics. A finite inhabited witness independently realizes the direct reduction; changing any of the five indices or eleven relations destroys its active setup, output, or unresolved-shape content. The shared established result is definitionally exact selected semantics together with NonvacuousEffectiveRangeReductionAt; it stores neither TechnicalRouteApplicable nor any implication-valued calculation contract. The downstream extraction embeds this exact parent model but depends only on its established order-k^2 endpoint, before either paper's later higher-order analysis. It adds three context-owned selections and eight extraction-specific relation families, including uncoupled S-wave scope and qualification of the reported estimate. Its unique selectedModel exposes all twelve extraction claims. Each paper again supplies that named exact model and exhaustive transfer. Bethe's adapter uses a separate bound-state-relation control proposition at the deuteron energy; policy forbids substituting its positive-energy scattering-accuracy assessment. Both clients explicitly retain deferred tensor-force scope and the qualified status of the reported range. Bethe's paired relation/extraction contracts and Blatt-Jackson's continuation/extraction contracts are consumed to produce direct terminal relation, control, empirical-input, and parameter outputs. Separate theorems reconstruct those contracts when the embedded parent and child routes are replayed; the terminal propositions themselves do not store them. Model and represented-world membership require the exact selected child setup: exact child selection, the established parent two-parameter law, the selected bound state, uncoupled S-wave scope, and both measured inputs. The selected experiment is an aggregate evidence package and can combine several measurements. Grounding delegates to a generic constructor using only that setup, physical representation, and conditional transfers, never the bound-state relation calculation, its control output, the parameter extraction, or the established child result. One countermodel proves that a false parent setup cannot ground the child; another has the complete parent/bound-state/data setup and grounding while the relation calculation and child route are false. A twelve-component child audit proves that changing the parent reduction, any child selection, or any child relation fails the original context's exact semantics, without identifying the papers' comparison-wave and analytic-continuation calculations. The stronger composed audit opens the parent rather than treating it as one opaque field: all thirteen order-k^2 parent components and all eleven child additions are necessary for the direct nonvacuous extraction. Blatt-Jackson's explicit warning that approximate equation (5.3) should not be solved exactly is preserved, as are Bethe's shape qualification and both papers' singlet-range limitations. The established child result is definitionally exact child selection together with the direct composed nonvacuous extraction. Bethe's accuracy result separately retains that a square well would require different triplet and singlet intrinsic ranges, a long-tailed potential can accommodate a common range, and one channel's energy dependence does not select the shape. Bethe's pp. 41 singlet-data limitation is now a separate paper-local route: it combines the failure of neutron-proton singlet data to fix the range with distinct assumptions of approximate proton-proton/neutron-proton singlet-force equality and a borrowed proton-proton effective range. The later charge comparison consumes that qualification without falsely depending on the deuteron triplet-extraction route. Its proton branch also retains the direction and anomalous size of the high-energy departure, the failed tensor-force account, and the unresolved status; its final small force difference is robust only across the considered shapes and supports conditional approximate, not exact, charge independence under a common range-and-shape comparison. KSW 1998 is explicitly rejected as a third client: it imports the standard effective-range expansion to calibrate PDS couplings and RG boundary conditions, but does not perform the controlled zero-energy-reference and small higher-order-correction stages required by this route.
PhysicsLogic/Framework/LargeScatteringLengthResummation.lean: the narrow large-length, low-energy all-orders two-body resummation route independently realized by KSW 1998 and Bedaque-Hammer-van Kolck 1998. Its exact proof-free model retains five selected objects and all five route-defining relations, including an all-orders requirement indexed by the selected resummed object. Its output-led endpoint retains exact selection and the actual setup, requirement, obtained description, and recovered target. Both adapters construct theory/model/world grounding from the inhabited pre-calculation setup only. A positive setup-complete countermodel has full grounding but no applicable resummation route, and a finite positive model realizes the complete technical route. Direct tests make all five selected indices and all five relation families route-active, while a separate ten-component exact-model audit detects every changed field. PDS bubble sums and dressed-dibaryon calculations remain distinct paper-local mechanisms. The applicable route also realizes a typed derivational reduction from the selected large-length two-body description to the selected low-energy target. Realization retains the valid anomalous- length setup and actual all-orders requirement; source support requires the obtained resummed description; macro exhibition requires its recovered target. KSW supplies the PDS loop, bubble sum, and unitarity recovery, whereas Bedaque-Hammer-van Kolck supply the dressed-dibaryon and effective-range recovery. A second source-sensitive projection retains the exact proof-free model plus a typed paper derivation: KSW's PDS-loop/bubble- chain/unitarity token and BHvK's self-energy/dressed-dibaryon/effective-range token have distinct raw realization relations. The generic constructor and both paper adapters consume the applicable route directly, not an established, nonvacuous, or ordinary derivational endpoint. One countermodel has a declared recovered target but no valid source setup; another has the complete technical route and ordinary reduction but a false derivation relation, and therefore no source-sensitive reduction. Its seven directional shared countermodels now use a reduced value-level readout: Q R < 1, Q |a| = 1, inverse-length and cutoff scales, a retained graph order and unsuppressed first omitted graph, complex bare/loop/resummed inverse values, the leading scattering-length-amplitude equations, normalization, target comparisons, and separate theory/model/world mismatches. A checked positive readout has R = 1, |a| = 4, Q = 1/4, an unsuppressed omitted graph, resummed inverse (-1/4,-1/4), and target amplitude (-2,2). Directional changes then separately block the requirement, resummation, recovery, route reconstruction, and grounding. No proposition-pair or Unit truth table replaces these distinctions. The result asserts neither full-theory reduction, universality, equivalence of the two mechanisms, nor unique microscopic recovery.
PhysicsLogic/Framework/FiniteVelocityCommutatorCone.lean: the interaction-dependent commutator-cone route independently realized by Lieb-Robinson 1972, Nachtergaele-Sims 2006, and Hastings-Koma 2006. Its proof-free model retains nine selected physical indices and eleven semantic relation families. Each paper names its exact model, proves semantic retention, and transfers all ten claims through theory and represented-world judgments. Mutation countermodels detect changes to every one of the 20 retained components. Exponential suppression remains distinct from exact microcausality and a universal light speed. Its explicit exact-signal bridge is refuted by an inhabited effective-cone countermodel and is independently consumed by Lieb-Robinson and Nachtergaele-Sims, so the distinction is kernel-checked paper logic rather than an import-only qualification. Lieb-Robinson's paper-local source graph now supplies each basis, differential, Green-function, contour, interpretation, and imported-theorem contract independently before applying it to certified inputs. Its exponential- and slower-tail remarks remain separate class-qualified roots with omitted calculations, while only the actual finite-range result feeds the shared cone and downstream clustering composition. The complete applicable route now also realizes a typed structural explanation. Its constraint retains the exact selected local system, interaction, observables, regions, bound, and regime, whereas its distinct phenomenon retains only finite information propagation. All three papers realize the explanation directly from their route inputs. One countermodel has the velocity phenomenon without the commutator route; a second has the full state-independent cone calculation without the physical velocity interpretation. Neither case counts as this explanation, and no strict no-signalling, relativistic microcausality, universal light speed, or spectral-gap clustering conclusion is added. Its two directional shared countermodels now retain finite interaction range, separated supports, exterior interaction norm, commutator norm and bound, propagation velocity, and interpretation residual. A range-one setup with commutator norm one and claimed bound zero blocks the estimate; a valid bound with nonzero interpretation residual blocks the velocity conclusion. Source-valued witnesses additionally retain the positive finite-time Lieb-Robinson exterior commutator, the sharper metric bound that vanishes at initial time, separate spectral-gap and ground-projection premises, and Hastings-Koma's distinct exponential and power-law tails. The power-law branch has no shared exponential-cone model; odd fermions use an anticommutator, and connected decay does not erase a nonzero ground-sector correction.
PhysicsLogic/Framework/SpectralGapClustering.lean: the corrected correlation-decay route independently realized by Nachtergaele-Sims 2006 and Hastings-Koma 2006. Its proof-free model retains fifteen physical indices and sixteen route-defining relation families. Both papers name the exact selected model, prove semantic retention, and transfer all thirteen claims through full theory-entailment and represented-world judgments. The established route also projects to a direct model-native clustering proposition; a false-setup model blocks vacuous calculation contracts, and separate direct mutations make all 31 components active in that proposition. A typed structural-explanation projection treats the complete gapped-local setup plus propagation, filtering, correction, bound, and decay calculations as the necessitating constraint for the selected corrected-correlation phenomenon. Both papers realize it independently. A countermodel retains a real gapped setup and declared correction, bound, and decay but rejects finite propagation, so neither the gap nor the output label explains the phenomenon alone. A stronger finite-velocity-supported endpoint now retains the direct commutator-cone child, exact cone route, admissibility bridge, gapped setup, and completed clustering together for the paper routes that actually use that source order; generic clustering remains propagation-source agnostic. The exponential routes consume a shared commutator cone only through explicit model-specific admissibility; Hastings-Koma's power-law branch remains direct. The framework does not identify the papers' filter calculations or ground-sector corrections. Its four directional shared countermodels now retain a positive gap and distance, interaction/propagation norms and bounds, frequency-filter and ground-sector-separation residuals, symmetric forward/reverse ground contributions, and an all-distance exponential profile. They exhibit a gap without propagation, propagation without filtering, corrected decay with raw correlation one, and (1/2)^distance clustering at zero gap. No proposition-pair truth table replaces these distinctions.
PhysicsLogic/Framework/NonequilibriumWorkIdentity.lean: narrow shared nonequilibrium-work semantics independently realized by Jarzynski 1997 and Crooks 1999. A declared finite classical process, positive inverse temperature, canonical initial preparation, equilibrium reference free energies, and defined work observable make the identity calculation applicable. A paper-local calculation establishes the exact exponential work identity; a separate mean-work definition and convexity bridge establish the average-work bound. The identity-only and final established propositions are output-led: they retain exact selected setup and direct physical outputs, while checked theorems reconstruct the identity and bound routes. Its proof-free model retains six selected data components: the process, inverse temperature, trajectory work assignment, ensemble-average functional, free-energy-difference assignment, and mean-work assignment. It also retains the five setup relation families used by the route. Jarzynski and Crooks each construct a named exact model and prove that it retains the paper-local semantics before applicability is established. The context owns the selected process and constructs one unique selectedModel; the process-indexed modelAt family remains only for the neutral paradigm view. Exact model identity is required by theory membership and world representation; grounding additionally requires the complete positive-temperature physical setup but no calculated identity, convexity bridge, or bound. Their Hamiltonian phase-space and forward/reverse stochastic path derivations remain paper-local, as do weak-coupling reductions, steady-state relations, sampling claims, and approximations. Jarzynski's paper-local Hamiltonian route additionally requires strictly positive Z_0,Z_1,Y_0,Y_1, proves that its system and full-reservoir canonical densities are positive and integrate to one, and derives positive Z_1/Z_0 and Y_1/Y_0 ratios. Proof-free scalar countermodels separate physical canonical normalization from source-shaped equations satisfied only through totalized zero-partition inverse or division. This Hamiltonian phase-integral machinery remains paper-local rather than becoming a requirement of Crooks's stochastic-path route. Crooks's distinct source-sensitive readout additionally retains positive, normalized forward and reverse three-state transition kernels, actual reversed-protocol path equalities, normalized stationary populations, and the physical same-protocol detailed-balance equation. Its circulating witness has transition probabilities 1/2 and 1/6 and probability current 1/9; its independent balanced witness has zero current and satisfies the same fluctuation route. A Boolean balance report is accepted only when it agrees with the actual transition probabilities, and the common finite-time fluctuation contract neither assumes detailed balance nor assumes its failure. These source-valued checks do not widen the neutral work-identity interface or burden Jarzynski's independent client. Countermodels independently mutate all eleven retained components, and every mutation fails semantic retention, including a changed switching protocol. The final established result is exact selected semantics conjoined with the direct NonvacuousNonequilibriumWorkIdentityAndBoundAt proposition, where the positive-temperature setup, exact identity, mean-work definition, and bound hold together at one selected process. A false-setup countermodel keeps the implication-valued calculation contracts true but fails this proposition. That false setup also cannot be grounded merely by declaring every theory and world claim true. A separate finite witness has positive temperature and nonzero work, free-energy difference, and mean work; exhaustive direct mutation theorems make every one of the eleven retained components destroy the direct complete route itself. The countermodels also block reconstruction of either route from its conclusion and block theory/world declarations from replacing the technical calculation. Both adapters construct the direct proposition from their distinct paper-local outputs and transfer every retained claim to their selected theory and represented process. The same source-ordered route now realizes a typed derivational reduction from a proof-free exact-ensemble work description to a distinct average-work description and scoped free-energy/mean-work inequality. Source support retains the actual identity calculation and identity, the ensemble-mean definition, and the convexity bridge; target exhibition is only the mean-work bound. Jarzynski and Crooks realize this projection directly from granular paper inputs, without consuming the established terminal wrapper. A source-sensitive refinement additionally pairs the exact selected model with a typed paper-local derivation token. Jarzynski's token is realized only by its canonical-Hamiltonian, Liouville, partition-ratio, and Jensen route; Crooks's token is realized only by its forward/reverse path-weight, entropy-work, and Jensen route. Thus the same identity and bound do not erase how either paper obtained them. Countermodels block an identity-plus-coincidental-bound shortcut, a bound-without-identity shortcut, and reconstruction of derivation provenance from an otherwise complete physical route. The projection adds no pathwise law, entropy increase, arrow of time, autonomy, emergence, or complete-theory reduction.
PhysicsLogic/Papers/GoldstoneSalamWeinberg1962.lean: paper-local symmetries, vacua, fields, currents, particles, and spectra, with distinct perturbative, general-current, charge, composite, and outlook deductions. Its shared spectral adapter separately grounds the current calculation in the selected theory current and represented physical spectrum, with an exact paper-data retention certificate plus exhaustive realization and transfer certificates for all six shared claims.
PhysicsLogic/Papers/Anderson1963.lean: paper-local plasma, superconductor, gauge-field, mode, and two-spectrum semantics, including a bare-response pole criterion that places zero-mass support only in the undressed matter spectrum, and checked separation of an uncoupled zero mode from the finite-frequency interacting plasmon. The uncoupled spectral adapter requires absence of long-range Coulomb interaction, certifies every shared spectrum claim, and does not transfer the later conversion.
PhysicsLogic/Framework/CollisionlessKineticPoisson.lean: shared collisionless electrostatic kinetic-Poisson self-consistency, independently realized by Landau 1946 and Bernstein-Greene-Kruskal 1957. Its proof-free physical context separately selects the plasma, primary and background distributions, electrostatic potential, regime, equation branch, and ion-background treatment; a nonvacuous result requires the collisionless kinetic equation, Poisson closure, and their independent coupling. Landau selects a fixed-ion linear Fourier initial-value problem and retains its printed one-sided formulas (6)-(10); BGK selects a stationary nonlinear electron-ion wave and retains its printed equations (1)-(4). Concrete countermodels reject incorrect Poisson signs, restored collisions, substituted background distributions, negative trapped populations, false velocity-distribution damping, unsupported actual-plasma existence, and source explanations without their separate derivation. Damping, trapping, analyticity, and physical realization are not shared conclusions.
PhysicsLogic/Framework/ControlledResonanceModelTest.lean: narrow shared experimental-gravitation logic, independently realized by Pound-Rebka 1960 and Hughes-Robinson-Beltran-Lopez 1960. Its proof-free context retains the actual resonance, distinct configurations, protected reference, finite sensitivity, observed readout, independent model calculation, and distinct affirmative-versus-null branches. Source-valued witnesses separately retain the 74/148-foot gamma reversal, inversion-stability assumption, -(5.13 +/- 0.51) versus -4.92 redshift comparison, 22/104-degree galactic orientations, protected Atomichron/proton references, original P2(x) = (3 * x^2 - 1) / 2, separate nuclear-structure conversion, and finite 10^-20 bound. Exact isotropy, unrestricted angular coverage, exact redshift equality, and whole-theory support remain unestablished.
PhysicsLogic/Papers/LandauDamping1946.lean: paper-local collisionless kinetic setup, normal-mode obstruction, arbitrary-initial-data Laplace solution with value-level equations (6)-(10) for the one-sided transform, inverse contour, transformed distribution, and three-dimensional-to- longitudinal potential reduction, nonvacuous deterministic evolution, analytic continuation, collective-field damping, long- and short-wave asymptotics, initial-data regularity sensitivity, a logically independent moving-pole route to persistent velocity-resolved oscillations, and a separate causal half-space penetration calculation retaining source equations (24)-(26), (35), (37), (39), (41), and (44)-(46): actual dielectric response, reflecting-wall and bulk boundaries, sign-dependent resonant contours, Fourier integration, x^(2/3) far attenuation, distinct below-/above-plasma-frequency profiles, the positive spatial decrement, and the nonexact approximate wall values. The module deliberately derives no entropy-production or microscopic-irreversibility claim. Its seventeen paper-local countermodel theorems now retain actual right-half-plane transform parameter and longitudinal velocity, long-wave formula and residual data, field/distribution amplitudes, wave-number and decrement comparisons, initial-data and moving-pole values, real-valued evolution and response amplitudes, branching alternatives, distinct below-/above-pole contour orientations, sub-/super-resonance frequencies and dielectric values, exact bulk amplitudes, the zero-mode identity, the physical 2/3 exponent, actual positive spatial damping, and separate approximate versus exact wall fields. No Unit/Bool truth table replaces those distinctions.
PhysicsLogic/Papers/BernsteinGreeneKruskal1957.lean: the original stationary nonlinear plasma construction, retaining trapped/passing populations, direct quadrature, inverse trapped-population calculation, nonnegativity, arbitrary-profile scope, singular moment surrogate, and open collision/stability obligations. Its actual stationary equation (4) retains separate positive/negative velocity-direction energy branches; passing populations may therefore be unequal even at the same energy. The distribution also retains its connected orbit component, so distinct trapped wells are not collapsed while passing populations remain common across potential intervals. Electron and ion orbit results retain opposite charge-signed trapping thresholds, real turning roots, a forbidden separating barrier, equal occupation within each trapped well, independently adjustable disconnected wells, and freely assignable passing-direction populations. Seven inhabited countermodels keep these physical implications distinct without imposing trapped-orbit assumptions on Landau's independent plasma route. Its four printed-formula countermodels now retain meaningful setup domains: positive charge and species masses with nonnegative densities/distributions for equations (1)-(4), a signed quadrature and zero turning derivative for equations (6)-(8), and an in-range potential with zero endpoint trapped density for equations (9)-(12). Those domains withhold the corresponding stationary, direct, inverse, and substituted calculations; no constant named-output predicate replaces these BGK distinctions.
Printed-formula countermodels across the active paper library now retain source-shaped physical domains rather than constant named-output predicates. The cross-disciplinary audit spans axial anomalies, black-hole mechanics and entropy, hidden-variable dynamics, boundary layers, excursion sets, gauge and string mass/charge formulas, path amplitudes, helium and Hall response, CMB spectra, renormalization, nebular and stellar dynamics, nonlinear waves, stochastic inflation, and transport. Positive scales, regularity, nonzero denominators, selected directions and cycles, and value-level formula failures remain separate checked facts; no truth-status pair replaces those distinctions.
PhysicsLogic/Papers/PoundRebka1960.lean: the original terrestrial gravitational-redshift experiment, including recoil-free resonance, opposite-Doppler calibration, temperature and monitor controls, source-absorber reversal, offset diagnosis, the explicit inversion-stability premise, separate observed/predicted shifts, and finite-uncertainty model support. It independently realizes the shared controlled-resonance model test without identifying redshift agreement with a nuclear null bound. Its earlier eleven paper-local countermodel theorems retain actual Table-I readings and corrections, 74-foot tower, 148-foot two-way, and six-inch close-baseline values, distinct direction/record alternatives, reported shift and ratio uncertainties, and evidence transfer with zero model-support residual but nonzero theory-support residual. No all-true framework record or enum truth table replaces those distinctions. The counting refinement computes response convolutions, quarter-cycle gates, calibrated gain, thermal shifts, normalized period estimates, reversal residuals, and actual sampling moments. The expanded fidelity matrix has 33 boundaries. The first-four-day table is distinct from the final ten-day result; 513/492 is not the separately printed ratio 1.05. A possible unrounded reconstruction explains why the last displayed row's nonexact arithmetic alone is not evidence of an error in the raw reduction.
PhysicsLogic/Papers/KolmogorovLocalStructure1941.lean: the original local turbulence argument, including conditional velocity-increment laws, local homogeneity and isotropy, high-Re interior scope, two similarity hypotheses, viscous normalization, inertial two-thirds scaling, and longitudinal/ transverse ratios. Its increment-law and derivative countermodels use actual random fields, probability laws, and computed moment profiles. The conditional-law comparison uses two positive-mass base-velocity events, not arbitrary values of a conditional kernel on null events. A constant drift has isotropic increments but anisotropic absolute velocity; R=10^6 does not remove a boundary; lambda=1 and r=L=2 fail the upper inertial bound; and a two-thirds second moment supplies neither the later five-thirds spectrum nor the four-fifths law. No status-enum truth table replaces those distinctions. The technical turbulence semantics remains paper-local until an independent primary-paper client demonstrates genuine reuse.
PhysicsLogic/Papers/Jaynes1957.lean: the complete two-part maximum-entropy, thermodynamic-dictionary, density-matrix, information-loss, and controlled-relaxation argument. Its sixteen paper-local countermodel theorems now retain actual probability, constraint, entropy, variance, canonical-weight, trial-count, population, propagator, rate, correlation, and approximation values. In particular, a broad two-state maximum-entropy assignment has variance 1/4; the array/eigenstate witness checks the measurement formula 1/2 + s^2/4 and equality criterion s=0; identical instantaneous densities admit rates zero and 1/4; an approximate propagator composition has residual 1/20; equal positive rates at a nonzero energy gap fail finite-temperature detailed balance; and the same reduced mean permits global variances four and sixteen across the reliability threshold. No Unit-carrier truth table replaces those distinctions. The exact Jaynes normalization and relaxation semantics remain paper-local until an independent primary-paper client demonstrates genuine reuse. The independent fidelity matrix now has twenty-five physical boundaries: its source-valued thermometer keeps Z_joint=Z_system Z_bath, p_ij=p_i p_j, and lambda=dS_bath/dE_bath=1/T; its rotating nuclear spin has omega=1, lambda=-1, zero energy transfer, zero magnetic field, and the proved <m>=-(1/2)tanh(lambda/2) polarization. Distinct normalized arrays (1,0),(0,1) and (3/5,4/5),(-4/5,3/5) give the same density matrix, while removing correlations changes entropy from log 2 to 2 log 2 without changing the exact unitary entropy or additive mean.
PhysicsLogic/Papers/Nambu1960.lean: paper-local generalized Hartree-Fock self-consistency, nonperturbative gap, gauge-phase family, Ward-identity vertex, gauge-invariant Meissner response, collective pair dispersion, nonlocal quasiparticle charge cloud, Coulomb plasma shift, and explicit approximation-boundary semantics. The paper-local routes now retain value-level equations (2.15), (2.20), (4.4b), (5.9), (6.11), and (8.11): quasiparticle energy and twice-pairing-scale gap, circular anomalous self-energy components, a noncommutative two-by-two Ward matrix relation, selected longitudinal cancellation, the Coulomb-omitted gapless dispersion, and the distinct Coulomb plasma frequency. Its shared screening adapter rebuilds the corrected response antecedent from shared Ward-result, collective-state, and transverse-field facts before rerunning Nambu's paper-local calculation. Its ladder-spectrum grounding requires an explicit representation of the superconductor by the selected quasiparticle vacuum and transfers the complete shared spectrum vocabulary. Its source-sensitive gap-to-screening composition separately preserves the anomalous gap, gauge-phase family, matrix Ward identity, Coulomb-omitted gapless collective intermediate, longitudinal cancellation, and surviving physical transverse current.
PhysicsLogic/Papers/Nakano1956.lean: paper-local arbitrary-time electric field response, pulse and thermal-trace kernel calculations, exact static conductivity extraction, typed equations (1)-(5) with explicit causal and positive-time integrals, beta normalization, thermal trace denominator, Boltzmann spectral weights, current matrix elements, phase, and energy-delta conductivity sum, subsystem decomposition, perturbative pair interaction, one-relaxation-time approximation, and explicit separation of exact result, typical-case approximation, and suggested broader scope. Infinite-sum convergence, integral evaluation, the equal-energy continuation of equation (4), and the delta distribution remain explicit imported mathematics rather than being silently totalized or hidden behind a named output. Explicit representation bridges tie the real/complex formula readout back to the selected current, electric field, kernel family, and static transport value. Formula atoms are projected from the response and static calculation premises, and a finite countermodel blocks named current/conductivity outputs from supplying equations (1)-(5).
PhysicsLogic/Papers/Ramsey1950.lean: paper-local two-state molecular beam, pulse/free/pulse evolution, fixed-field phase accumulation, space-mean energy detuning, fixed apparatus dimensions with selected pulse/free transit times inverse to molecular velocity, distribution-level transit-time variation, exact- versus off-resonant reinforcement, velocity-averaged separated-field resonance, the spin-one-half magnetic-moment specialization and imported Majorana higher-spin extension, calculated limiting regimes versus an interpolated middle interval, pulse-strength and width calculations, reported potassium comparison, two separate probable interpretations, field-uniformity and precision scope, proposed applications, and operational access to the intermediate-region mean splitting. Thirteen checked routes now preserve these stages separately. Nonzero coupling now proves actual two-state mixing normalization, and the full equation-(12) expression is proved to lie in [0,1]. The paper's velocity average retains positive selected and most-probable speeds, both inverse-speed transit times, the original normalized molecular-beam weight 2*y^3*exp(-y^2) on y > 0, and the actual continuous integral of the coherent response at every positive speed. Lean proves normalization, integrability, and the averaged probability bounds. Explicit near-error and weighted dephasing estimates derive separate inhabited frequency sweeps. The doubled harmonic derived from equation (15) remains distinct from the half harmonic literally printed in equation (18), with an actual-integral counterexample to their identification. The averaging contract supplies these physical inputs, not the desired final conclusions. Together with Rabi 1939 it realizes a direct nonvacuous shared resonant-transition spectroscopy route whose ten selected objects and nine relation families are all directly active, together with a stronger normalized two-outcome endpoint independently realized by Rabi's actual equation-(2) transition and Ramsey's actual beam average. Its adapter replays the shared controlled setup, driven transition, and resonance readout through retained pulse/free/pulse, resonance, averaging, interpolation, and line-shape contracts supplied as independent hypotheses. Established physical results do not cache those implication-valued contracts. The shared terminal result is output-led and reconstructs its route. Rabi's resonance-dynamics setup and Ramsey's separated-field setup independently realize the shared pre-output boundary used by both route assembly and grounding; no frequency, response, readout, or quantity output is a grounding premise. No field-free or coherence/decoherence framework is imported. The source-sensitive projection now keeps Rabi's one-region gradient-refocusing and cross-molecule moment extraction distinct from Ramsey's pulse/free/pulse interference and velocity-averaged fringe route. Both source theorems begin with raw paper-local stages rather than complete paper conclusions. A finite converse model has completed spectroscopy, its route, and the ordinary explanation but no source explanation, so a resonance-based extraction cannot certify its own apparatus derivation. A separate source-valued AMO framework audit now retains Rabi's printed Larmor and weak-field transition formulas, opposite deflection gradients, detector minimum, cross-molecule Li-7 assignment, imported spin 3/2, frequency/field-to-g coefficient, exact magnetic moment, and the fact that the displayed values 2.167 * 3/2 and 3.250 are not an exact equality. The journal pp. 527-528 rotating-versus-oscillating distinction is now physical rather than an opaque sign flag: the measured positive magnitude is |mu_signed|, so two genuine moments +mu and -mu retain the same field, Larmor frequency, and nonzero transition probability. A pure oscillating field contains both opposite rotation senses and cannot identify the sign; one selected rotating sense distinguishes them, but that contrast is not represented as a measurement performed by Rabi's oscillating apparatus. Absolute calibration and the hyperfine discrepancy remain qualified. Ramsey's separate witnesses retain both pulses, the drive-free intermediate phase, exact equation-(12) interference, inverse-velocity transit times, positive distribution weights, explicit beam averaging, and an interpolated rather than calculated middle interval. The 0.600 pi selected pulse area, 0.200 weaker comparison, 0.64, 1.23, and 1.4 width coefficients, and distinct 0.6 same-length improvement remain separately active. Longitudinal field averaging does not erase transverse uniformity, and a proposed shielded-region application is not an already performed measurement.
PhysicsLogic/Papers/BardeenCooperSchrieffer1957.lean: paper-local phonon/screened-Coulomb competition, coherent pair variational state, a separately qualified common-pair-momentum persistent-current argument, self-consistent quasiparticle gap with local equation-(2.40), equation-(2.50), and pair-breaking-threshold values, near-critical square-root and continuous thermal gap closure, explicit weak-coupling thermodynamic relations, case-I/case-II coherence-factor matrix elements, Meissner and Pippard response, empirical bridges, and unresolved model extensions. Its shared screening adapter rebuilds the local response antecedent from shared validity, static-field, transverse-field, linear-response, and current-decomposition facts plus the paper-local case-II classification and factor before rerunning the BCS calculation. Its source-sensitive gap-to-screening composition retains the actual variational gap, selected coherence channel, original London-current formulas, Pippard response, penetration depth, and field-expulsion bridge as an independently checked joining derivation.
PhysicsLogic/Papers/Kadanoff1966.lean: paper-local cell variables, scale separation, reduced temperature, weak external field, cell site count, two-valued cell-spin sum, effective magnetic field, nearest-neighbor effective Ising description, explicit free-energy and correlation comparisons, critical-exponent consequences, and the separately qualified effective-coupling regularity extension. The shared coarse-grained-scaling route now consumes the established paper-local cell construction rather than a bare cell label.
PhysicsLogic/Papers/ForsterNelsonStephen1977.lean: paper-local stochastic fluid models A, B, and C; momentum-shell elimination and rescaling; dimension-dependent fixed-point behavior; long-time tails; infrared universality; a nonvacuous transverse-momentum slow-mode reduction from Model C to the Model A infrared description; Galilean Ward-identity reasoning; and explicit perturbative and ultraviolet limitations. Its thirty-two inhabited Forster-Nelson-Stephen fluid boundaries retain P_12=-12/25 and C_12=-12 at k=(3,4,0), genuinely distinct shell and time rescalings, D_A(k)=2k^2, D_B(k)=2, a Model C pulse supported only for 1<|k|<4, generated infrared forcing 1/2, critical dimensions two and four, z_A=2, and z_B=5/3. The Model A all-order argument does not prove the Model B result, and a selected finite-band flow does not establish universality for every finite-band force.
PhysicsLogic/Papers/Mori1965.lean: paper-local orthogonal projection, exact generalized Langevin dynamics, force-memory correlation, the distinct ordinary-force secular cancellation tail, complement-propagator exclusion of that tail from the projected damping kernel, and plateau-value avoidance. The central exact-memory package now retains equations (3.3), (3.8), and (3.10)-(3.12) as componentwise complex-valued propositions: a finite frequency-matrix action, an actual derivative, a causal interval integral, a nonempty selected-component domain with a genuine two-sided covariance inverse, explicit differentiability/ integrability hypotheses, force orthogonality, and both covariance-matrix correlation identities. Plateau resolution and qualified short-memory localization are now sibling consequences of the exact force-memory route rather than an artificial chain. Sections 4-8 are represented directly: canonical scalar-product selection and proposed typicality, time-reversal reciprocity, the good- variable criterion, hydrodynamic slow modes, spin/oscillator/fluid examples, exact projected thermal after-effect dynamics, distinct aged-regression and local-equilibrium transport routes, thermal/mechanical response comparison, ordered-limit qualifications, explicit projected transport coefficients, and the open Mori-Zwanzig comparison. Calculation and assessment contracts remain independent theorem premises; none of the fifteen established-result families stores one as proof payload. Fourteen inhabited fidelity boundaries include a false-setup projection chain in which every implication-shaped calculation is vacuously true but no reduction is established. The shared memory-kernel adapter retains the certified direct-output route, while a separate adapter now applies the projection, orthogonal-dynamics, exact-equation, and force- correlation calculations in source order and realizes the mature derivational-reduction interface before a completed endpoint exists. This does not promote the later short-memory approximation, or assert autonomy or multiple realization. The adapter remains narrow, while the thermal convolution nonvacuously realizes shared retarded-response semantics. Its finite real-sector model now computes the Gram projector and vertical force, solves the full and complementary oscillator generators, and checks the exact causal memory equation. The constant projected correlation and oscillating ordinary correlation are provably different; exact projection alone does not make memory decay.
PhysicsLogic/Papers/Zwanzig1973.lean: the complete nonlinear generalized- Langevin argument through generalized conservative dynamics, the symmetric nonsingular shifted quadratic bath, the solved and integrated bath trajectory, exact history-dependent elimination, conditional canonical bath moments, Gaussian fluctuation-dissipation, the exact particle-plus- oscillator specialization, a distinct Debye-continuum/sinc-kernel route, and the later slow-system delta-localization route. Equations (17) and (19) now remain value-level propositions over nonempty finite system/bath component domains: equation (19) exposes an actual derivative, the nonlinear A-W-L-W-transpose history convolution, and A-W-F noise action, while equation (17) exposes conditional-canonical zero mean and kT-times-kernel covariance with explicit thermal positivity and positive bath quadratic form. The same matrix propagator now defines the shifted initial force, inverse-bath covariance, memory kernel, and equation (18). The particle route retains equations (22)-(24) as actual derivatives, convolution, finite cosine sum, and covariance. Equations (25)-(30) retain the distinct continuum and local models, including the original printed cutoff-squared convention and its separately checked normalization mismatch. Thirteen calculation or interpretation contracts are independent hypotheses rather than outputs of their setups. None of the nine established-stage families stores those contracts as proof payload. The shared adapter retains that direct-output path and now also constructs the exact shared route from exact-elimination, conditional-canonical, bath-moment, and noise calculations before a canonical-noise endpoint is packaged. Eleven inhabited fidelity boundaries include a staged false-setup chain that makes every calculation through exact elimination vacuously true without establishing the result, while preserving the special-bath, distribution-role, exact/local, and continuum/Markov distinctions. The exact elimination also realizes the mature derivational-reduction interface, independently of the continuum and Markov approximations. The strengthened paper also independently uses the shared finite residual-covariance operation. An actual positive oscillator bath realizes fluctuation- dissipation, while a nonsingular negative-energy bath excludes a physical canonical covariance and a finite bath retains nonzero-lag correlations.
PhysicsLogic/Papers/OrdonezRayVanKolck1995.lean: paper-local low-energy field selection, the original equations-(1)-(3)/(14) chiral-index chain nu = 4 - A + 2 L - 2 C + sum_i V_i Delta_i, Delta_i = d_i + f_i / 2 - 2, Delta_i >= 0, and A = 2, C = 1 => nu = 2 L + sum_i V_i Delta_i, irreducible-potential construction, reducible dynamical iteration, third-order momentum-space potential, regularization and coordinate conversion, radial solution, empirical fit, and explicit short-range and higher-order limitations. The finite vertex-list readout keeps the source sum structural, checks the two-nucleon specialization and nonnegative index, and includes a negative-index countermodel when equation (3) is omitted; none of that widens the shared effective-interaction contract. The momentum route now also retains preprint p. 10 equations (15)-(16) as a selected scalar matrix-element package: the literal static -(2 g_A/F_pi)^2 one-pion-exchange coefficient, isospin and spin-momentum factors, pion denominator, C_S and C_T contacts, and the parity-forbidden zero first correction. The package is tied to the selected leading and first-order potential objects through their matrix-element map; a name-only countermodel blocks replacing those equations by order labels.
PhysicsLogic/Papers/Zamolodchikov1986.lean: the original two-dimensional c-theorem route through stress-tensor correlations, the trace identity, Callan--Symanzik evolution, separately established positivity of both the coupling-space metric and the running c-function, strict differential decrease away from fixed points, explicit RG integration, and fixed-point identification with the Virasoro central charge. The printed normal coordinates and no-linear-term expansion in equations (11)-(12) separately establish stationarity of every c-gradient component at both fixed points; inhabited countermodels reject deriving that claim merely from vanishing beta, a vanishing directional derivative, or central-charge matching. Its complete route realizes the shared RG endpoint-monotonicity framework while keeping the local field-theory calculation explicit. The shared adapter reconstructs the paper-local selected-flow setup from the shared flow facts plus the retained beta-zero and conformal-endpoint facts before invoking either endpoint identification or the c-theorem calculation.
PhysicsLogic/Papers/KomargodskiSchwimmer2011.lean: the four-dimensional a-theorem route through anomaly matching, the spectator dilaton, low-energy scattering, the forward amplitude, a dispersion relation, the optical theorem, and positivity of the total cross section. Separate routes retain the moduli-flow argument, general-flow extension, running a-function, free-scalar check, and stated open questions; the general unitary flow realizes the shared RG endpoint-monotonicity framework. Its forward-positivity adapter reconstructs the low-energy dilaton theorem from the supplied shared coefficient assignment before building the dispersion sum rule.
PhysicsLogic/Papers/Heisenberg1927.lean: operational quantity definition, stationary-state position and momentum restrictions, gamma-ray microscope accuracy and recoil, energy-time resolution, an independent selected Gaussian transformation whose equations (3)-(6) now retain the printed position Gaussian, Jordan integral, exponential q-p kernel, transformed momentum Gaussian, and selected p_1 q_1 = h/(2 pi) product, experiment-relative value partitions, coherent versus intermediately measured transitions, the high-excitation obstruction, observation-defined trajectories, exact and finite free packets, the grating and radiative-jump thought experiments, causal interpretation, qualified resonance fluorescence, weak quantization, and the coupled rotor-rack energy distinction. Its 53 claims and 18 semantically certified routes retain every proof-stage correction while its direct measurement adapter proves disturbance without identifying that claim with prepared-state dispersion.
PhysicsLogic/Papers/Kennard1927.lean: transformation-related coordinate and momentum probabilities with pointwise M M* density formulas, Kennard's doubled-variance precision, Gaussian saturation, the general equation-(27) positivity route, alternative and joint observation interpretations, and simple-motion scope. Its adapter constructs an exact shared model, proves semantic retention, directly packages the shared state-dispersion outputs, and realizes and grounds both the shared state-dispersion route and the independent amplitude-derived exact-observation probability route. Its state-dispersion provenance theorem starts from the general amplitude factorization and nonnegative remainder rather than an established shared inequality, keeping the pp. 338-339 derivation distinct from Robertson's.
PhysicsLogic/Papers/BornCollisions1926.lean: the full original collision paper's discrete and continuum frequency rules, asymptotic flux balance, directional elastic and inelastic scattering, excitation thresholds, qualified dipole and evidence assessments, practical-indeterminism interpretation, and open radiation extension. Its elastic route supplies the scattering realization of the shared amplitude-to-outcome-probability component without exporting Born's paper-local channel meanings.
PhysicsLogic/Papers/RocekVerlinde1991.lean: the original-author v1 routes for bosonic parent-action reduction, one-loop dilaton correction, compact holonomy completion, vector/axial quotients, mode and singularity interpretation, and the N=2 Legendre extension. Only the first local reduction route feeds the shared parent-action component.
PhysicsLogic/Papers/DeLaOssaQuevedo1992.lean: the earliest available author revision's abelian review, non-abelian parent path integral, determinant and dilaton correction, SO(N) examples, leading black-hole applications, and explicit unresolved global-equivalence assessment. Its local parent route now retains value-level equations (3.2), (3.3), (3.10), and (3.15): a finite Lie-index curvature with actual partial derivatives and commutator sum, the multiplier-curvature worldsheet integral, the selected bar-h/f-inverse/h predual-action integral, and the real logarithmic determinant shift of the dilaton. Functional path integration and determinant evaluation remain explicit source contracts rather than invented internal mathematics. Its adapter shares the local reduction route while preserving the unknown multiplier range, duality group, and global CFT relation.
PhysicsLogic/Papers/HamiltonGeneralMethod1834.lean: the original 1834 varying-action calculation, positive final and negative initial endpoint momentum readouts, separate parameter/energy derivative recovery of complete motion integrals, initial and final characteristic equations, transformed and relative coordinates, explicit selected-to-relative, relative-to-binary, and binary-to-Newtonian system links, the general three-point pairwise-force specialization with nine full and six relative endpoint-integral counts, centre/relative action and energy splitting, translation/rotation constraints, ternary pentagon and four-point heptagon geometry counts, the stated arbitrary-multiple-system extension, arbitrary binary quadrature, Newtonian conic and Lambert specialization, exact and first-order action corrections, and time principal function. The perturbation branch now retains Hamilton's printed p. 296 equations (O5) and (P5) as paper-local real-valued formulas: the rigorous correction keeps the second-part living-force term, the approximate expression drops it, and explicit imported integral linearity identifies their difference as the higher-order remainder. A checked countermodel blocks the printed pair from making the first-order expression exact without remainder control. Characteristic-equation verification now branches from signed endpoint derivatives without inheriting the stronger complete-recovery route. Its shared adapter combines the positive final derivative route with the later first-order-equation verification while leaving living force, the initial endpoint sign, the system-specialization chain, ternary recovery, invariant multiple-system geometry, binary motion, Kepler formulas, and perturbations local. Its twelve directional paper-local countermodels are now value-bearing: stationary action fixes both endpoint displacements and energy variation while remaining dynamically impossible; varying action retains 5=4-1+2*1, conservation, and a dynamically possible neighbor; signed endpoint derivatives are (2,-3), complete recovery requires six parameters and the energy derivative 2=t, the ternary counts are (9,9)/(6,6), and the pentagon reduction is 10-1=9. Binary quadrature leaves a three-body problem unsolved, and exact correction reuses the checked nonzero-remainder model. No proposition-pair or action/variation status truth table replaces these Hamilton distinctions. The predominant-mass approximation now consumes the established multiple-system geometry route instead of depending on varying action alone.
PhysicsLogic/Papers/JacobiPDEReduction1837.lean: the original 1837 theorem that any complete integral of the time-dependent principal equation recovers mechanical motion, together with constrained and explicitly time-dependent scope, autonomous reduction, the critique of Hamilton's second equation, homogeneous-force stability tests, the Kepler example, general characteristic-system reduction and converse, and the broader Pfaff comparison. The endpoint-defined principal function and the arbitrary complete integral remain separate selected scalar functions; only the arbitrary complete-integral reconstruction feeds the shared component. The p. 104 Hamilton-Jacobi relation and pp. 107-109 derivative recovery relations are retained as paper-local value packages with explicit evaluation points and name-only countermodels.
PhysicsLogic/Papers/AlbrechtSteinhardt1982.lean: the original new-inflation argument, including the radiative finite-temperature potential, exact versus near-Coleman-Weinberg tuning, the trusted T^4 exp(-F_bubble/(kT)) saddle rate, independently supplied bubble percolation, saddle breakdown above strong coupling, multiple thermal fluctuation paths, order-one phi ~ T and R_initial ~ 1/T scaling, the full phi_ddot + 3 H phi_dot + V' = 0 Klein-Gordon equation, N = H tau, R_final = R_initial exp(N), and delta_H < 3.6e-11. Thirty-three inhabited physical boundaries separate a large converted fraction from bubble connectivity, full accelerated field dynamics from an unsupported overdamped truncation, sixty exact exponential e-foldings from observed containment, nonthermal-monopole suppression from allowed thermal monopoles, unobserved from globally absent domain walls, and selected cosmological success from deferred thermalization, baryogenesis, curvature, and perturbation-spectrum calculations. The concrete paper witnesses agree with the independent reusable bubble-transition framework.
PhysicsLogic/Papers/Robertson1929.lean: Hermitian means and rms deviations, the one-particle Schwarz-commutator proof, conjugate-variable specialization, angular-momentum inequality and extremal saturation, and the author's polynomial-operator scope statement. Actual complex 2 x 2 observables and normalized state vectors verify [X,Y] = 2 i Z; the same observables produce either a saturated bound of one or a zero bound with dispersions 4/5 and 3/5. Hermitian 3 x 3 integer-spin generators realize the original l=1,m=0 and l=1,m=1 branches, including their component variances, J^2 = 2, and exact extremal saturation. Thirty-four inhabited physical boundaries prevent loss of conjugation, normalization, Hermiticity, centered moments, ordered commutators, absolute values, state dependence, angular assumptions, or the distinction between state dispersion and apparatus disturbance. Its adapter constructs an exact shared model, proves semantic retention, and grounds the same shared route while keeping commutator analysis local. Its shared established result is constructed directly from the retained rms, commutator-bound, and product outputs. The terminal general result retains the scoped setup, direct commutator-bound outputs, and the printed real-valued normalized-wavefunction, doubled Schwarz overlap, mean/rms, and h |C0| / (4 pi) formulas. The source's bilinear pairing is checked pointwise against the conjugate-first convention. Its two norm factors give |<[A,B]>|^2 <= 4 (Delta A Delta B)^2; nonnegative rms values then give the product bound. That inequality is no longer a supplied calculation conclusion. Calibration connects the numerical inequality to the selected product relation. The conjugate branch checkedly substitutes unit coefficient magnitude to obtain h / (4 pi); the angular branch retains M_z, M^2, the M_x M_y - M_y M_x = -h M_z / (2 pi i) action formula, transverse rms squares, Delta M_z = 0, the oriented component bound, and l(l+1) >= m(m+1), with m = l checked as equality of the reduced relation. All shared endpoint consumers accept the terminal result instead of replaying the Schwarz calculation, and none of these source-specific formulas is promoted into the neutral shared framework. A separate source-sensitive adapter intentionally starts earlier, from the one-particle setup and raw integration-by-parts, Schwarz-commutator calculation, so the terminal result cannot manufacture derivational provenance.
PhysicsLogic/Papers/WittenIndex1982.lean: proposition-valued index model and the actual c -> c + 2*pi/L gauge identification and periodic physical wavefunction, identity-connected Gauss-law/Weyl constraint, terminating U^p|Omega> tower, UV=VU=0, V^2 ~ U^r, exclusion of the cubic invariant by two spinor components, distinct pseudo-invariant V|Omega> multiplet, unresolved signed branches, and fixed-theta (T_z)^N=T orbit with unit winding and one index contribution from every parallel flux eigenvalue. Its independent physical boundaries also distinguish nonadmissible large-field deformations, missing gauge quotients, incomplete operator algebra, finite-volume limits, and sector sums.
PhysicsLogic/Papers/WittenDynamicalBreaking1981.lean: global vacuum-energy and the printed E=f^2 Goldstino current-algebra residue, finite-order nonrenormalization, equations (28)-(31) with both supersymmetric-mechanics supercharges and their actual Pauli axes, the spin-dependent Hamiltonian, an arbitrary growing two-zero superpotential, its integral solution, the source's W~x^4/integral W~x^5 illustration, and the opposite-tail normalizability obstruction. Its 2+1-dimensional sixth-order scalar potential, Higgs-triplet SU(2)->U(1) vacuum, unresolved symmetric vacuum, and monopole pair retain charges +1/-1, magnetic flux, the Bianchi-reduced (2*pi*a/e)*Q, exact two-zero-mode saturation, undeformed signed cancellation, mixed-species zero modes, and genuine discrete-breaking unequal weights. Twenty-nine physical fidelity boundaries also preserve the four-dimensional zero-mode obstruction, gravitational and technicolor qualifications, and explicit unresolved four-dimensional conclusion.
PhysicsLogic/Papers/Adler1969.lean: paper-local axial current, Ward identity, loop diagram, regulator prescription, anomalous term, renormalization, neutrino-scattering, massless-symmetry, conserved-generator, and PCAC semantics. Six checked routes distinguish formal field equations from the linearly divergent triangle calculation, physically select the vector-gauge-invariant prescription, derive the vertex and scattering consequences, establish current nonconservation despite gamma-five invariance, and retain the controlled two-photon extrapolation and note-added all-orders qualification. The paper-local value layer retains equation (30) and now also Appendix A equations (A11) and (A22): the formal equation-of-motion sigma-model PCAC divergence and the actual anomaly-modified quantum divergence are distinct selected values. A nonzero electromagnetic anomaly proves their inequality before, and independently of, the controlled two-photon decay approximation; inhabited countermodels also separate vector gauge invariance, the real-photon spin restriction, and heavy-fermion decoupling.
PhysicsLogic/Papers/SeibergDuality1994.lean: the conjectural magnetic SQCD dictionary, six anomaly checks, conditional conformal-window bound, dual-of-dual test, one-flavor mass deformation, and a grounded qualified assessment that never promotes consistency evidence into a duality proof. Its shared mass-flow adapter now establishes exact selected semantics plus the direct nonvacuous endpoint requiring the selected setup, calculations, outputs, evidence, and nonproof boundary together; the complete route is a checked reconstruction from that output-led result. Its seven directional paper-local countermodels are now value-bearing: (N_c,N_f)=(3,6) gives magnetic and second-dual rank three, the proposed charges and six anomaly coefficients (3,-3/2,3,-10,7/2,-18), D(M)=3/2, the second-dual F-terms, and a one-flavor condensate -1 with reduced magnetic rank two. The separate (3,5) boundary retains the broken-SU(2) instanton coefficient, Lambda_L^(2N_c-1)=m Lambda^(2N_c-2), and the matched confining coefficient; it is not incorrectly left as an open case. Completed checks still do not prove duality or supply grounding. No proposition-pair truth table replaces these magnetic-SQCD distinctions.
PhysicsLogic/Papers/KutasovSchwimmer1995.lean: the original adjoint-SQCD proposal parsed into adjoint-superpotential, stability, magnetic-dictionary, anomaly, one-flavor mass, polynomial-vacuum, and qualified self-dual routes. Imported SQCD results, expected exact marginality, and unresolved free-field questions remain explicit. Together with Seiberg 1994, only its narrow magnetic mass-deformation consistency route enters the shared framework, including the same direct nonvacuous endpoint. Its six directional paper-local countermodels are now value-bearing: (k,N_c,N_f)=(2,3,4) gives magnetic rank five, meson/trace counts (2,1), baryon occupations (1,2)->(2,3), and all six normalized anomaly coefficients; a one-flavor mass has F-term values (0,-1), condensate -1, two-color Higgsing, and reduced rank three. The polynomial witness retains four stable vacua out of six magnetic candidates and det M-B*Btilde=1; the self-dual witness retains expected marginality but no established fixed point. Completed consistency routes still do not prove duality or supply grounding. No proposition-pair truth table replaces these adjoint-SQCD distinctions.
PhysicsLogic/Papers/Bell1964.lean: proposition-valued Bell framework and concrete singlet directions, checked derivation and violation of the original inequality, plus checked EPR, exact no-go, robustness, and nonlocality deductions. Bell's first section-III illustration now retains the pure-spin polarization, uniform hidden hemisphere, sign response, zero-weight boundary, spherical-average calculation, rotated-direction calibration, and derived cos theta expectation before concluding that a single-spin hidden-variable account exists. Bell's section-II predetermination now requires an actual hidden-state value and two distinct magnet settings, not merely response functions on a possibly empty domain. The candidate model's equation-(1) responses are now explicitly required to realize the outcomes inferred by the EPR route; a countermodel shows that abstract predetermination alone does not localize an unrelated candidate model. Three further inhabited boundaries reject empty hidden-state, empty-setting, and singleton-setting response domains. A composed paper theorem connects the nonvacuous remote-prediction result to the nonvacuous shared local-response result through Bell's explicit EPR and candidate-realization bridges. Its shared deterministic-response adapter now requires an actual local functional representation and establishes generic factorization at every hidden state. The adapter now also distinguishes the response-function calculation from the candidate deterministic completion using it and the separated spin-pair experiment it represents. Dichotomic outcomes and normalization occur in the theory-use bridge, while separation and operational locality occur in the world-representation bridge. A named paper certificate fixes the exact unrestricted and proposed local response functions together with a nonempty hidden-state domain and two distinct settings independently of both bridges; the shared semantics require that setup in model use, representation, and model entailment. At fixed settings, an explicitly supplied hidden-state value also realizes witnessed common-cause support screening; this is not hidden-state-averaged probabilistic independence. The established response directly stores the nontrivial domain, exact and generic factorization, total support, and no-signalling outputs; a theorem reconstructs its complete route. Its exhaustive certificate covers all six shared claims, and the grounded Bell adapter transfers that vocabulary to the candidate theory and represented experiment. Framework countermodels show that determinism and rectangular singleton support alone do not establish Bell locality, and that a completed technical route does not itself supply theory/model/world grounding. A two-field mutation audit rejects changes to either retained response object. The direct response proposition now also requires one actual setting pair and hidden-state value, realizing screening, total support, and possibility-level no-signalling at that same witness. Universal factorization over an empty setting scope is a checked countermodel, while a finite inhabited model makes both response-function fields directly active. Complete factorization outputs over a singleton setting type still cannot establish theory/model/world grounding. Hidden-parameter generality and probability normalization are separate premises. A signed-average countermodel isolates positivity as an essential input to Bell's hidden-state averaging step; a finite-speed countermodel separately shows why spacelike separation is required before remote influence is classified as instantaneous. The final Lorentz route stores the signal's temporal and spatial separation and checks the reversal of causal order under a suitable subluminal boost.
PhysicsLogic/Papers/EPR1935.lean: the original completeness argument with separate reality and completeness criteria, single-system and separated-system routes, an explicit single-system joint-representation obstruction from which Lean derives the paper's first alternative, conditional remote states, and the concrete position-momentum calculation. Its pp. 779-780 equations (7)-(18) are now retained as a value-level conditional-wavefunction package: two basis expansions of one joint state, continuum momentum and position branches, phase factors, Dirac-delta position localization, selected eigenvalue shifts, and the noncommutator. The Planck constant is strictly positive, and the displayed delta is interpreted operationally by its evaluation action on test functions. The position eigenstate and its remote conditional partner retain their distinct distributional actions, including the printed factor of h; the joint continuum state has an explicitly nonzero distributional pairing. The exact state is not square-normalizable, and no finite-resolution regularization is silently supplied. The sum and integral evaluations remain imported mathematics. Independently inhabited countermodels show that all twelve printed equations can still hold for a zero fake delta and zero joint state unless those operational requirements are stated. The actual paper calculation now realizes the shared framework's EPR idealization control directly, with the physical conversion hbar = h / (2 pi) rather than identifying the two Planck constants. The remaining route keeps checked wave-function incompleteness, the simultaneous-measurement objection, and the explicitly unconstructed alternative theory. Its remote certainty-and-non-disturbance step realizes the narrow shared framework also used by Bell 1964. The established shared result retains EPR's named exact correlation model, prediction-readout bridge, non-disturbance bridge, and complete selected route, while the completeness reductio remains paper-local.
PhysicsLogic/Papers/Bohm1952.lean: both original 1952 papers parsed into separate Schrödinger-decomposition, configuration-guidance, one-particle, many-body transition, apparatus measurement, equilibrium, contextual observable, EPR, radiation-field, and completion/scope routes. The module distinguishes the continuity and Hamilton-Jacobi calculations from the added actual-configuration and guidance postulates; proves only equivariance from the shared flow while retaining general relaxation as an author expectation; derives effective packet selection without fundamental collapse; and realizes supplemented deterministic completion and predictive-versus-ontic probability through the mature philosophy and paradigm layers. Its selected electron gives the universal completion law a concrete governed-system witness; an empty-system countermodel blocks a vacuous completion. Its certified source routes additionally retain p = grad S, v = grad S / m, stationary zero particle motion with positive total energy and balanced classical/quantum forces, one actually occupied apparatus packet with two squared-amplitude Born weights, distinct apparatus-hidden-variable distributions, and EPR correlations with changed remote motion but unchanged operational marginal. Twenty-five physical fidelity boundaries block the corresponding invalid substitutions. The polar formulas now use actual coordinate fields and derive the local Born current from the source certificate; a nodal-wave boundary prevents upgrading a conserved density to a node-free polar chart. The equilibrium certificate now retains almost-everywhere trajectories of the very map used for Born transport: actual derivatives equal the current divided by positive density, with initial values and calibrated coordinates and clock. A normalized endpoint-only loop fails this guidance condition. Normalization, existence of regular flow, and common measure pushforwards remain separate explicit analytic inputs; global existence is not claimed. The deterministic-motion route now also derives actual coordinate continuity and uniqueness on a regular interval from the guidance ODE and an explicit uniform spatial Lipschitz bound. Selected-state evolution is identified with all such trajectories, and state decoding recovers their actual configurations. Its universal determinism premise remains separate from this interval result. Its explicitly nonlocal configuration-space dynamics is not mapped to the shared deterministic-local-response framework. Comparison with Dürr-Goldstein-Zanghì 1992 earns only the narrow guided-density equivariance component. That component retains both density maps and the common guided-evolution relation in a named exact model. Its established result is defined by the direct initial-agreement, common-evolution, and later-agreement endpoint. The two paper adapters ground the selected pre-output setup without using propagation, later agreement, or the completed technical route, and transfer all nine shared claims only after the separate route and grounding certificates are combined. Each of the five selected physical indices now changes the direct nonvacuous equivariance proposition, as does each of the three retained semantic families. Bohm's wave density is computed through densityOfWave, and both adapters bind common evolution to their exact wave, ensemble, times, and regime. The original Durr-Goldstein-Zanghi author TeX and PDF now also ground the paper-local equations (3.8)-(3.18) at the actual value level: v_k = (hbar / m_k) Im(grad_k psi / psi), rho = |psi|^2, both printed complex-current forms, ensemble continuity, and the exact current-flux substitution. Equations (5.17)-(5.19) retain the occupied disjoint environment branch and psi_Y(x) = Psi(x,Y), while equation (6.1) keeps normalized conditional Born probabilities distinct from an actual unique configuration and ontic chance. Physical witnesses realize traveling, time-reversed, and stationary waves, exact (9/25,16/25) conditional probabilities, environment selection, and wave-rescaling invariance. Sixteen inhabited fidelity boundaries exclude wrong mass/current/Born formulas, zero-wave nodes, missing flux substitution, incorrect environment conditioning, overlapping branches, autonomous conditional evolution, and multiple actual configurations. None of this paper-specific physics is inserted into the shared guided-density framework.
PhysicsLogic/Papers/GRW1986.lean: the original objective-localization model parsed into separate random individual-process, deterministic ensemble master-equation, free-particle suppression, selective trajectory, constituent amplification, rigid-body, parameter-calibration, scoped measurement, energy-increase, phase-space diffusion, and limitation routes. Free, trajectory, constituent, rigid-body, and energy routes keep independent local setups, including the necessary master-equation physics. Calibration consumes the free, trajectory, amplification, and rigid results; measurement consumes amplification and calibration, while phase space uses the free result. These are certificate dependencies, distinct from the physical assumptions within each local setup. Its amplification calculation also requires the sourced macroscopically distinct pointer-branch pair and one-localization coherence-destruction premise before it can conclude selected branch decorrelation; the shared Zeh/GRW adapter reconstructs and replays that local setup. The parameter route also realizes the neutral unification contract: one GRW dynamics acts on microscopic constituents and the derived macroscopic center of mass, while one admissible parameter choice yields practical microscopic agreement and rapid, time-scoped macroscopic classical behavior. Its phase-space route also realizes exactness-aware recovery: retained stochastic diffusion prevents the approximate phase-space description from becoming exact deterministic classical mechanics. The module realizes the mature objective-stochastic-localization paradigm while distinguishing statistical-mixture formation from the additional definite-pointer bridge. The selected apparatus and pointer record make universal dynamics and macroscopic definiteness nonvacuous; an empty-scope model satisfies only the weaker law package. Comparison with Bohm 1952 does not earn a shared technical measurement framework because the two papers use physically different outcome-selection mechanisms. The original selective operation (2.7) now restricts the same Gaussian integral to a result region, and (2.8) computes its weight from the kernel's coordinate trace. Complementary regions recover the nonselective map. Positive-weight conditioning has unit trace; a half-weight subensemble and a zero-probability selection cannot be passed off as normalized states. Positivity and trace-class operator interpretation are not inferred from unit trace, and no actual individual record follows from this bookkeeping. Equation (3.3) now uses the squared norm of the actual nonselective kernel, with a positive normalized density expansion and physical endpoint states. Trace-square differentiation and Hamiltonian trace cyclicity are separate mathematical inputs; strict Gaussian purity loss and final mixedness are derived. Mixedness is not called a proper stochastic ensemble or an actual outcome. The finite diagnostics also compute purity and coherence from positive density matrices: a mixed state can retain coherence 1/4 and have purity 5/8. Unit trace supplies neither purity nor positivity. These matrix controls also exhibit different pure-preparation supports with the same mixed density. They are not solutions of the continuous GRW evolution. The trajectory route now retains the forward selective equation (5.1), actual trace loss (5.2), and the common finite-window Gaussian estimate (5.3). It derives the exponential survival bound and long-time extinction, with survival probability computed from a measure on ordered real jump times and localization centers. Actual Hamiltonian conjugation and Gaussian jumps determine each branch kernel. The history law is weighted by that branch's trace; normalization, positivity/regularity, Poisson counts, projectivity, and selected-kernel representation remain explicit mathematics. The probability-to-trace equality is then derived by integral interchange. A positive no-test probability gives a lower survival bound, and three concrete history controls separate counts, test-time survival, and continuous confinement. Full continuous stochastic existence is not proved. Practical accuracy is an independent approximation input: a near-one upper bound does not prove high survival. The fixed-diffusion infinite-frequency limit and the nonselective full-region control remain distinct, and an expected localization count is not a realized count. Its directional paper-local countermodels are value-bearing. They retain N=100, elementary rate one and amplified rate 100, branch separation two against localization distance one, the coordinate damping exponent -4, localized kernel exp(-4) for input kernel one, and the reduced evolution relation density derivative=-(1-exp(-4))=Hamiltonian term 0+localization term -(1-exp(-4)) with zero residual. Finite Gaussian localization suppresses a nonzero coordinate kernel but cannot erase it exactly. A separate exact-erasure control satisfies the algebraic master term but violates equation (2.10). These numbers are illustrative test values, not the paper's calibration. The named-equation converse keeps a valid reduced evolution relation while withholding the printed localization formulas. Spontaneous localization requires stochastic outcomes and the printed formulas; the complete witness has equal mixture weights, energy-increase rate one from hbar^2 lambda alpha/(4m), internal spread 1/2 against localization distance one, and exactly one realized pointer record. Rate addition without differently located constituents blocks branch decorrelation; a center-of-mass-localized but internally broad body blocks rigid protection; and a definite pointer leaves the exhaustive measurement residual nonzero. No proposition-pair, status-enum, or Unit-carrier truth table replaces these GRW distinctions.
PhysicsLogic/Papers/Wilson1974.lean: paper-local link, plaquette, loop, surface, quark-path, transfer-matrix, coupling-regime, and continuum-limit semantics. The finite-gauge route now retains selected equation-(3.4), equation-(3.6), and equation-(3.8) link/angle/plaquette values with explicit site, boundary-link, configuration, and finite-gauge-coupling relations. Its nine directional paper-local countermodels are now value-bearing: the selected gauge pair has zero orbit residual while equation (3.4) fails, the compact angular link and plaquette action with phase one respectively withhold equations (3.6) and (3.8), and the tiled-area witness retains A/a^2=4 against leading power three. The normalized isolated loop is 1/2, while a unit-separation vacuum loop shields area four down to one; hopping and vacuum-loop weights one withhold the no-free-quark inference. Positive strong tension, zero weak tension, and an uncontrolled mean-field jump do not establish transition order, and nonzero scaling, Euclidean, and Lorentz residuals withhold continuum confinement. No proposition-pair or finite-gauge status truth table replaces these Wilson distinctions. Exact finite-spacing gauge invariance is separated from the representative-to-physical interpretation bridge; the strong-coupling plaquette expansion is separated from the area-law-to-confinement bridge; and the regulated no-free-quark result is not promoted to continuum QCD, restored Lorentz invariance, or continuum string equivalence. Together with Creutz 1980, it exposes a complete finite-regulator gauge-route applicability theorem. Its shared gauge adapters reconstruct the local lattice setup from the shared finite-regulator setup, then apply the retained compact-integration bridge to the calculated action and loop invariance proofs; no-gauge-fixing is not a cached sibling output. Its strong-coupling setup also realizes a complete shared loop-area setup and applicability theorem before deriving the narrow inference from a calculated area law through a linear-potential bridge to regime-scoped confinement. That complete route now also proves the direct nonvacuous shared loop-area proposition and the stronger finite-gauge- supported endpoint at Wilson's named model. It separately realizes the shared structural explanation only after the spanning-surface calculation and binding interpretation are both present; the lattice construction and strong-coupling calculation remain paper-local.
PhysicsLogic/Papers/Creutz1980.lean: paper-local pure SU(2) lattice construction, heat-bath Boltzmann update, independent-start and finite-size checks, Wilson-loop fit, confinement-based scale setting, and qualified asymptotic-freedom comparison. The numerical reliability route is required before the fitted area law is used, and neither perturbative scaling agreement nor absence of an observed transition is promoted to a continuum proof. Its regulated gauge inputs separately establish the complete shared gauge-route applicability proposition. The shared gauge adapters rebuild Creutz's local SU(2) setup from shared finite-regulator input and apply the invariant-group bridge to the calculated action and loop invariance proofs. Its loop-fit route separately exposes the full selected loop/surface/source/tension setup and shared applicability proposition. It independently realizes the narrow shared loop-area confinement inference and proves the direct nonvacuous shared proposition and stronger finite-gauge-supported endpoint at Creutz's named finite-cutoff model. Its fitted area law and separate potential and confinement interpretations also realize the structural-explanation endpoint. The paper-local fit now retains ln W(C) = -K A(C) + O(P(C)), its lattice-unit rewrite, W(S) = exp[-(A + B S + C S^2)], and C = a^2 K; these displayed formulas do not widen the shared loop-area contract. Its equilibrium-sampling provenance theorem separately retains the p. 2309 conditional entire-group single-link heat bath, detailed balance, accessibility, equilibration, and interpretation instead of inferring that route from the common sampling endpoint. Its algorithm, fitting procedure, and evidential conclusion remain local.
PhysicsLogic/Papers/Stanley1968.lean: paper-local spherical and finite-component vector-spin models, normalized-partition reduction, stationary-point and normalization calculations with a distinct finite site-count index, equation-(24)'s explicit -beta psi_infty = -1/2 - 1/2 ln(2K) + F/N + remainder accounting with its separately vanishing normalized-log remainder, a noncritical free-energy limit, ten-term free-energy and susceptibility support, an exact linear-chain check, a qualified m-spherical heuristic, and the appendix's unresolved critical-index order of limits. It realizes the neutral large-parameter paradigm without importing gauge-theory coupling or diagram topology. The linear-chain route now retains equation (28)'s finite-spin Gamma/Bessel formula and equation (29)'s limiting square-root/log free energy, explicitly identified with the selected spherical free energy, in its checked endpoint. Its paper-local countermodel theorems retain actual scope and value data: a one-dimensional Bessel witness with nonzero two- and three-dimensional residuals, tenth-order free-energy/susceptibility agreement with an eleventh-order departure, actual uniformly convergent free energies with unequal critical indices, a stable family with uniform free-energy and entropy convergence but no specific-heat transport, and a converged noncritical free energy with vanishing remainder but failed equation-(24) stationary accounting.
PhysicsLogic/Papers/THooft1974.lean: paper-local color-index surfaces, the journal-p. 465 chain r = g^(V3 + 2 V4) N^I, F = L + I, 2 P = 3 V3 + 4 V4, V = V3 + V4, r = g^(2 P - 2 V) N^(F - L), F - P + V = 2 - 2 H, and r = (g^2 N)^(V3 / 2 + V4) N^(2 - 2 H - L), with the pointwise g^2 N identity kept separate from the large-rank/small-bare-coupling trajectory, Euler-characteristic rank exponents, fixed-rescaled-coupling trajectory retained in the specialized asymptotic-organization conclusion, planar one-boundary dominance, conditional dual-string comparison, light-cone block representation, planar Hamiltonian reconstruction, and unresolved discrete-spectrum binding criterion. It realizes the mature large-rank paradigm and, with Witten 1979, the narrow shared planar-diagram route with actual nonplanar and additional-boundary correction witnesses. Checked specializations retain the planar one-boundary rank power and fixed-rescaled-coupling rewrite; a separate checked theorem reconnects that pointwise rewrite to the fixed trajectory only when both hypotheses are supplied, while a finite countermodel prevents equations (3.2), (3.4), (3.5), and (3.7) from manufacturing equation (3.6) without the vertex/dot count in equation (3.3). Its five directional paper-local countermodels are now value-bearing: the rank-four witness keeps g^2 N=1, the exponents (1,0,-1) for planar one-boundary, extra-boundary, and one-handle diagrams, and the corresponding relative corrections (1/4,1/16). A planar two-boundary diagram has exponent zero and is not leading; the topological string analogy retains a mesh but no continuum bridge, and the planar Hamiltonian retains continuous free spectrum but no established discrete interacting spectrum. The finite-rank witness gives N=3 and 1+1/3+1/9=13/9, so leading order is not exact. No proposition-pair truth table replaces these planar-gauge distinctions. That shared framework now projects its fixed-coupling nonplanar sector back into the mature large-rank paradigm only after explicit varying-family and planarity-classification premises. Constant-family and overlapping planar/nonplanar countermodels prevent a technical selection from masquerading as nonvacuous topological organization.
PhysicsLogic/Papers/SeibergWitten1994.lean: concrete electromagnetic charge vectors and Dirac pairing; exact BPS charge-period logic; conditional singularity and monodromy reconstruction with three pairwise-distinct named singularities and explicit exclusion of additional selected singularities; effective-theta/Witten-charge preservation under the T^{-2} relabeling and the separate P T^{-2} infinity-matrix factorization; the elliptic curve, differential, and period solution; checked monopole-vacuum equations; and explicit condensation-to-Higgs-to-gap-to-confinement reasoning. The infrared monopole is connected to a finite-energy semiclassical gauge-Higgs soliton with degree-one asymptotic Higgs winding and nonzero quantized flux, while the real-axis continuation now retains path connection, real electric periods, imaginary magnetic periods, and nonreal period ratios before its no-jump conclusion; wall crossing remains an explicit scope limitation. This independent active client now realizes the shared charge and discrete-vacuum frameworks.
PhysicsLogic/Papers/GeneralizedGlobalSymmetries2014.lean: paper-local higher-form defect, charged-operator, Maxwell-current, background-field, loop-order-parameter, infrared-no-order, and photon-spectrum semantics. Six checked routes derive positive-form Abelianity from continuous defect-exchange witnesses and faithful fusion, plus linking action, a compact-spacetime selection rule, electric and magnetic Maxwell one-form symmetries, their mixed anomaly, and the photon as a Goldstone mode of both broken symmetries. The sixth route captures the generalized Coleman-Mermin-Wagner argument: continuous d-q<3 or discrete d-q<2 scope, a charged order parameter, divergent infrared potential, and the source's exp(-V) expectation law yield a checked zero-expectation limit and an unbroken symmetry. Countermodels retain the dimension, form degree, potential, expectation, breaking, and other-order values, separating low dimension from actual divergence, divergence from suppression without the loop law, and selected no-order from absence of other transitions. The Maxwell line operators realize the shared charge framework, while the final spectral conclusion realizes the shared broken-symmetry spectrum framework with separate theory/model/world grounding for the electric and magnetic current sectors and paired exhaustive certificates.
PhysicsLogic/Papers/MerminWagner1966.lean: the original magnetic no-order argument with value-bearing spin, exchange, Brillouin-zone, field, magnetization, and susceptibility semantics. Two checked routes separate the Bogoliubov/operator estimate, finite mode and denominator bounds, uniform equation-(11) family, thermodynamic equation-(12) transfer, logarithmic two-dimensional and arctangent one-dimensional infrared bounds, distinct small-field scalings, and post-thermodynamic spontaneous limit from the source's finite-second-moment qualification, precise axial anisotropic exception, open nonmagnetic transitions and susceptibility, and distinct crystalline and classical comparisons. Countermodels block finite-zero-to-thermodynamic inference, generic-anisotropy extrapolation, and promotion of magnetic no-order to absence of every order channel. The magnetic route now realizes the shared infrared-order-suppression framework using its actual post-thermodynamic small-field limit and an explicit spontaneous-breaking bridge.
PhysicsLogic/Papers/KosterlitzThouless1973.lean: the original finite-core, dilute neutral-vortex and iterated-dielectric argument, with fifteen source claims and five checked routes for microscopic setup, original screening/phase classification, factorized conventional-order suppression, solid and material-dependent scope qualifications, and winding-barrier metastability. It distinguishes original equation (19) from the rescaled equation (21), proves the solid's L versus sqrt(L*r) contour scalings, excludes charged-superfluid protection through its finite-energy vortex free energy, and explicitly contracts Heisenberg winding through the third spin component. Eighteen inhabited fidelity boundaries retain these exclusions, separate shell density, polarizability, dielectric response, and renormalized binding. Its microscopic route retains integer phase winding and local irrotationality away from vortex cores; its metastability route derives thermodynamic protection from the positive logarithmic vortex-pair barrier rather than assuming divergence. It does not substitute a later BKT recursion.
PhysicsLogic/Papers/Maldacena1997.lean: D3 stack dimension, charge and five-form flux; explicit four-dimensional N = 4 U(N) worldvolume data with six real adjoint scalars at the superconformal point; explicit alpha' -> 0 scaling with distinct bulk-radial and inter-brane separation data; fixed stretched-string and Higgs scales followed by an independent coincident-brane conformal specialization; the full equation-(2.2) D3 metric with positive-radial scope, physical harmonic readout, and separate worldvolume, radial, and sphere warp coefficients; checked disappearance of its constant term only after that formula is supplied; radius and explicit AdS_5 x S^5 near-horizon metric coefficients; proper-energy redshift equations; fixed positive near-extremal worldvolume energy density, the displayed U_0^4 = (2^7/3) pi^4 g^2 mu relation, the separate fixed-U_0 limit input, a checked finite-horizon deduction, and an explicit finite-temperature premise before Hawking flux; boundary data; and compositionally checked sector, duality, calculational, and interpretive routes. Its local supergravity result now separately realizes prediction-grounded classical recovery: a controlled singleton observable approximation is not treated as classical until the proper-energy window, local calculation, and correctness bridge supply the behavior.
PhysicsLogic/Papers/GubserKlebanovPolyakov1998.lean: point-indexed boundary source/operator coupling and its exponentiated CFT expectation; admissible bulk extension and proposed on-shell functional dictionary; controlled leading-large-N correlator transfer; asymptotic conformal symmetry; massless scalar, graviton, higher-partial-wave, and massive-string dimension routes; and separately retained expectations, deferrals, regime limits, and open leg-factor obligations. Its inhabited variation-sector approximation now also realizes prediction-grounded classical recovery only through the separate leading-large-N classical-supergravity reading.
PhysicsLogic/Papers/WittenHolography1998.lean: Witten's original source-indexed CFT/bulk generating-functional proposal, controlled classical-saddle correlator prescription, general massive-scalar mass-dimension route, three protected Kaluza-Klein spectrum families, spin-structure-sensitive Hawking-Page transition, and conditional Hamiltonian state/operator extension. The proposal, controlled approximation, imported calculations, quantitative evidence, and additional Hamiltonian assumptions remain logically distinct. Its thermal branch now retains the original section-3.2 beta(r_+) and I(X_2)-I(X_1) formulas as selected scalar readouts; Lean checks their small/large-radius signs before the action crossing enters the spin-selected saddle route.
PhysicsLogic/Papers/AMPS2012.lean: complementarity postulates with physical content, including a unitary black-hole S-matrix, exterior semiclassical equations, dim H_M = exp(S(M)), and quantitative no drama; entropy data, explicit B(omega)/C(omega) Bogoliubov kernels whose creation strength is evaluated from the stored C(omega) itself, operational infalling-vacuum annihilation conditions, transmission, creation-norm and eigenstate-defect data; separate projection, prediction, measurement-performance, and number-state propositions; a countermodel excluding prediction-to-state conflation; distinct ordinary low and mined high modes; distinct Page-time and scrambling-extension ages; mining premises, scrambling expectation, and compositionally checked incompatibility, extension, and resolution deductions.
PhysicsLogic/Papers/Jarzynski1997.lean: paper-local switching protocols, trajectory work, Hamiltonian and density data, partition functions, and ensemble averages. The isolated route selects the initial point on the unique trajectory through each final phase point, uses that same final-to-initial correspondence in Liouville transport and work-energy balance, checks the pointwise Boltzmann cancellation, and derives the partition ratio from explicit integral obligations; an exact full-reservoir route repeats the checked correspondence and derivation in the combined phase space. Full-ratio endpoint invariance yields path/rate independence before a dependent quasistatic-reference route derives the central law; direct weak-coupling partition reduction depends only on the exact full-ratio route, not the quasistatic transfer. The limiting identities are checked separately. The Jensen route is stated on the actual trajectory-work ensemble and must consume the explicit mean-work definition before deriving the average-work bound. The Gaussian cumulant calculation yields an exponential-average formula that must be combined with the certified Jarzynski equality; countermodels delimit trajectory-level, mean-label, and free-energy-identification overclaims. Proof-free numerical countermodels retain selected initial and final phase points, forward flow, inverse selection, transported densities, thermal versus interaction energy, reservoir degrees, and the canonical marginal residual; equal endpoint densities do not select an inverse trajectory, weak coupling does not make a small reservoir canonical, and a large reservoir alone does not establish canonical system sampling.
PhysicsLogic/Papers/Onsager1931.lean: paper-local coupled-process, chemical-transition, anisotropic-crystal, fluctuation-regression, dissipation, stationary-flow, magnetic-field, and approximation-regime semantics. It proves the Part I reciprocal heat-conduction conclusion only from explicit regression, correlation, and coefficient-identification calculations. The fluctuation branch now also retains equations (4.3)-(4.10) as a represented real-valued readout and checks that its opposite-sign delayed correlations plus microscopic-reversal symmetry force omega_3 = 0; an explicit countermodel keeps (4.3)-(4.9) with nonzero omega_3 while denying (4.10). Countermodels separate entropy positivity from reciprocity, equilibrium from detailed balance, microscopic reversibility from its macroscopic bridge, zero-field from magnetic same-field reciprocity, and the anisotropic result from the deferred general transport theorem. With Casimir 1945 it realizes the narrow shared reciprocal-transport inference. The source-sensitive structural layer now retains this as Onsager's reversal-fixed zero-field heat/fluctuation route, distinct from Casimir's parity- and field-paired route with an independently assessed regression hypothesis. A completed reciprocal relation and ordinary structural explanation cannot reconstruct either source token.
PhysicsLogic/Papers/Casimir1945.lean: paper-local equilibrium fluctuation statistics, velocity-parity and magnetic-field reversal, the explicitly independent ensemble-regression hypothesis, thermomolecular pressure, heat-current representative ambiguity, electrical four-poles, resistance, and Hall parity. Its general reciprocity result now retains Casimir's selected equations (18a)-(18c) and (18 prime) as value-level even-even, odd-odd, and mixed-parity coefficient equalities; zero-field equalities use an explicit reverseField zeroField = zeroField premise, and a reduced countermodel rejects name-only reciprocity. Its zero- and magnetic-field adapters construct distinct exact selected contexts; Onsager's independently checked heat adapter, each construct the complete shared reciprocal-transport applicability proposition before deriving a coefficient relation. Its thirty-three inhabited Casimir transport boundaries retain Delta S=-3, Gaussian covariance values 1/2 and 1/4, an independent 1<2<10 regression window, zero instantaneous derivative with nonzero lagged displacement, Q_small=8, Q_large=10, Knudsen pressure values 3 and 6, and R_12(+H)=2=R_21(-H) with field-odd Hall values +1 and -1. Virtual entropy cancellation does not eliminate irreversible entropy production. Broader linear-response machinery remains paper-local or unformalized.
PhysicsLogic/Papers/LeeYang1952.lean: the paired original partition-zero papers, with finite positive-coefficient partition polynomials separated from the thermodynamic limit; zero-free analyticity separated from its single-phase interpretation; nonvacuous zero accumulation separated from both a possibly vacuous universal neighborhood law and the physical singularity bridge; and the Ising/lattice-gas dictionary, circle theorem, one-dimensional root gap, two-dimensional exact transition, and unresolved finite-field/root-distribution scope represented as distinct checked routes. It exercises Paradigm/ThermodynamicLimit.lean but does not by itself earn a shared partition-zero or phase-transition framework. Together with BBCKK 2004, it now realizes the narrower shared Framework/PartitionZeroPhaseBoundary.lean result. That established result stores the actual finite-family, boundary, accumulation, and singularity outputs; its full implication route is reconstructed by theorem. The p. 406 transition adapter reaches it only after an actual selected transition is supplied; conditional zero localization alone does not create one. Its finite-volume setup also requires an actual finite-size witness, so an empty size family cannot make the universal finite-stage claims vacuous. Its theory/model/world grounding uses only the selected finite family, finite pressure and density definition, regularity, and explicit interpretation bridges; it does not assume zero accumulation, singularity, or a phase boundary. A separate one-way ordinary structural-explanation route stops before the converse singularity-to-boundary bridge: the actual transition and finite regular family explain accumulated zeros and the singular limit. A stronger source-sensitive route adds the typed Lee-Yang localization derivation and reconstructs raw applicability from it. A completed correspondence plus ordinary explanation with the derivation relation set false cannot recover the source-sensitive explanation.
PhysicsLogic/Papers/BiskupBorgsChayesKotecky2004.lean: the original Pirogov-Sinai paper on first-order partition-function zeros. It keeps Assumption C, contour representation, cluster expansion, metastable free energies, distinguishable Gibbs phases, the periodic torus phase sum, and the imported preceding zero theorem as separate propositions and routes. Theorem B retains its actual L >= L_0 threshold, kappa = tau / 4, phase-subset-dependent U_{kappa/L}(Q) region, exclusion of the closed half-width regions for competing phases, analyticity on the larger complex domain, nonzero analytic finite metastable weights, their distinct exp(-tau L/8) logarithmic and derivative corrections, (ell!)^2 M_0^ell normalized derivative bounds, alpha - 2 exp(-tau/2) overlap nondegeneracy, and the original ell! (C_0 L^d)^(ell+1) zeta(z)^(L^d) (sum q_m) exp(-tau L/16) remainder bound. The unrestricted regular finite family at physical controls comes from the finite lattice model, not from applying the restricted complex phase-sum theorem to every torus or control. Standard Ising, perturbed Ising, and Blume-Capel consequences consume the general zero-control result explicitly. With Lee-Yang it earns only the finite-family, zero-accumulation, limiting-singularity, and physical phase-boundary correspondence; all contour and model-specific machinery remains paper-local. Its direct shared-result adapter combines the actual physical-coexistence boundary on pp. 109-110 with the zero route on pp. 112-115; the controlled phase sum alone still does not create a boundary. Its ordinary explanation uses the one-way route and actual boundary; a stronger typed source derivation combines the controlled phase sum, distinguishable-phase coexistence, physical boundary, and imported zero-location control to reconstruct that route and source-sensitively explain accumulation and singularity without consuming the converse physical bridge. Its selected finite size supplies the shared nonempty-family premise. Its paper-local FinitePartitionFamilySetup supplies shared grounding with finite partition definition and regularity, not the controlled torus phase sum or the subsequent zero-location calculation. Seven additional inhabited boundaries reject a below-threshold phase sum, an ambient complex domain without the required phase-subset exclusion, an incorrect kappa/L width, thermodynamic regularity inferred from a complex phase sum, nonzero finite phase weights inferred from partition analyticity, the identification of the 1/8 and 1/16 suppression exponents, and overlap nondegeneracy inferred from a single-phase derivative bound.
PhysicsLogic/Papers/LiuSinclairSrivastava2018.lean: the original correlation-decay route to a Fisher-zero-free complex neighborhood for the bounded-degree zero-field Ising model. It separates the imported regular-tree uniqueness theorem, real contraction calculation, complex invariant-domain construction, Weitz self-avoiding-walk recurrence, pinned-spin induction, final cancellation exclusion, and external deterministic-approximation bridge. Its finite pinned-graph induction explicitly realizes the base, step, selected-model-data, and route-applicability semantics of the narrow shared Framework/FinitePartitionNonvanishing.lean interface. It now exposes the output-led established shared result before the Fisher-zero theorem projects uniform nonvanishing. The framework imports Paradigm/ThermodynamicLimit.lean, but reaches finite-description regularity only through a separately supplied size-family scope and interpretation bridge; neither finite regularity nor nonvanishing implies regularity of the limiting description. Its finite induction model now retains the exact bounded-degree pinned-graph class, complex-neighborhood interaction domain, unpinned-vertex complexity, and pinned-partition relation selected by the source. It is grounded separately in the zero-field Ising theory and represented finite Ising graph family for each nearby interaction and explicit zero-unpinned base graph. Grounding remains independent of the nonzero base calculation and induction step, with exhaustive realization and transfer certificates for all eight shared finite claims. The same witness projects the established induction to the direct nonvacuous endpoint.
PhysicsLogic/Papers/PetersRegts2017.lean: the original hard-core occupation-ratio proof of the strong univariate Sokal conjecture. It separates the elementary angle theorem, regular-tree rational dynamics, parabolic optimality input, double-log coordinate, uniform real contraction, complex invariant domain, unequal-input convex reduction, vertex-subset induction, final-root cancellation argument, univariate exhaustion, external interpolation consequence, and the appendix counterexample to a literal multivariate product domain. Its empty-graph base and vertex-subset step explicitly realize the same shared route contract as Liu-Sinclair-Srivastava. It likewise exposes the established shared result before the multivariate tube theorem projects uniform nonvanishing; both papers keep their correlation, recurrence, and domain physics local. Its finite induction model is grounded separately in the hard-core theory and represented finite hard-core graph family using an explicit vertex-count-zero graph in the selected tube. The model exactly retains the bounded-degree graph class, graph-indexed complex-tube assignment domain, vertex-count complexity, and multivariate partition relation at the selected assignment. Grounding is independent of the empty-graph nonvanishing calculation and vertex-subset step. The paper adapter exposes exhaustive realization and grounded transfer certificates for all eight shared finite claims once an explicit vertex-count-zero graph in the selected tube is supplied, and it projects the route to the direct nonvacuous endpoint.
PhysicsLogic/Papers/EinsteinBrownian1905.lean: the original molecular- kinetic Brownian-motion argument, with independent osmotic-pressure and transition-law routes joined only when the diffusion coefficient is eliminated to recover the molecular count. Its first route explicitly retains the contrast between the classical no-wall-force prediction and molecular-statistical osmotic pressure. Its original equations (1) and (2) now genuinely determine the following unnumbered diffusion-coefficient display by cancelling an explicitly nonzero concentration gradient; a uniform force-free equilibrium satisfies both equations without determining that coefficient. The formalization keeps external Stokes transport, continuum reduction, point-source solution, and numerical calculations explicit, derives actual Gaussian moments and interval probabilities, and preserves Einstein's unresolved identification of the prediction with observed Brownian motion. Its shared stochastic model is grounded from Einstein's inhabited mesoscopic symmetric-step setup in molecular-kinetic theory and the selected suspended-particle process before the Taylor and point-source calculations transfer diffusion claims. Its selected-data theorem retains Einstein's symmetric displacement law, independent-step control, coefficient-dependent moment laws, and diffusion- equation transport predicate in the shared model. Its source-sensitive diffusion/thermal-drag composition additionally exposes the original transition and Gaussian formulas, both force/flux balances, and exact inverse-Stokes diffusion coefficient through an independent joining source. Its predictive route retains disjoint measured intervals and actual history-event probabilities. Its prospective molecular-count method retains finite-sample moments, separate calibration and sampling errors, and derived uncertainty intervals instead of assuming experimental recovery. Its actual mesh process also gives an exact finite-step second moment and conditional readout inference at the selected observation time without assuming an exactly Gaussian finite-step law. Clock separation, joint increment independence, aligned population models, and conditional finite-to-continuum error transfer remain distinct obligations.
PhysicsLogic/Papers/SmoluchowskiBrownian1906.lean: the independent collision-imbalance and persistent-direction account, separating empirical exclusions, equipartition, microscope-visible averaged motion, small-particle and large-particle regimes, relaxation and Stokes drag, diffusion, and suspension stability. It preserves the explicit numerical- factor disagreement with Einstein, treats agreement as strong support rather than proof, and leaves aggregation unresolved. Together with Einstein 1905 it realizes the narrow shared stochastic-diffusion interface and its source-sensitive thermal-drag composition without identifying their historical derivations. The third joining source retains the original persistent-flight and relaxation formulas, both particle-size regimes, and the logically explicit failure of exact coefficient agreement. Its model is grounded from the inhabited small-particle collision setup and diffusion-regime validity in kinetic collision theory and the selected suspension process; that interpretation is not manufactured by the completed random-flight calculation. Its selected-data theorem retains the collision and persistence controls, path-dependent spread laws, and coefficient-bearing transport predicate.
PhysicsLogic/Papers/LindeLindeMezhlumian1993.lean: the stochastic-inflation argument now includes the original paper's controlled ordinary-diffusion route before its branching extension. Random-phase Hubble-time field steps yield linear variance and root-time rms spread in the flat-potential regime. Its separate Langevin/Fokker-Planck calculation now retains the literal beta-dependent Langevin, comoving Fokker-Planck, and continuity formulas over a typed P_c readout, with Hubble positivity, differentiability, and the Ito/Stratonovich convention boundary explicit. The physical-volume branch separately retains the selected Stratonovich backward generator, adjoint generator, expected-volume equation, endpoint derivative, and backward/forward branching equations over distinct u and P_p readouts; the initial-field and final-field reproduction terms are not interchanged. Projection theorems expose both formula bundles from their calculation contracts, and a finite countermodel blocks named diffusion or branching outputs from supplying the displayed equations. This is the third realization of Framework/RandomDisplacementDiffusion.lean, grounded from the inhabited flat-potential random-phase Hubble-step setup in semiclassical stochastic inflation and the selected coarse-grained inflaton process; it remains logically distinct from physical-volume branching and stationary measure claims. Its selected-data theorem retains the flat-potential validity and drift restriction, random-phase and independent-step controls, field-variance laws, and ordinary comoving diffusion relation.
PhysicsLogic/Papers/BondColeEfstathiouKaiser1991.lean: the original excursion-set analysis, separating a typed continuous resolution history from its selected scale and threshold interpretation, exact sharp-k first-passage logic along that history, numerical general-filter histories, qualified N-body comparison, two-barrier merger and bias calculations, and explicit low-mass and galaxy-formation limits. The sharp-filter route retains the unrestricted Gaussian, the reflected absorbing density in equation (3.1), independent increments, equations (3.5)-(3.7), the Langevin force covariance and power spectrum, and the prior-crossing origin of the factor of two. The original equation (3.9) contains an apparent printed threshold-power mismatch; the formalization preserves that literal typography separately from the physically reflection-derived Gaussian result, and a nonunit-barrier countermodel rejects both their identification and the previously accepted hybrid. For Gaussian and top-hat filters it additionally distinguishes the unrestricted drift-only one-point Gaussian from the non-Markov absorbing survival process and retains the source's integer upcrossing, downcrossing, first-crossing, and rate inequalities. All four established stages retain setup plus direct physical outputs, not proof-carrying calculation wrappers. The N-body assessment additionally records the original quantified peak comparison: at most 20 percent sharp-k overestimate and comparable Gaussian/top-hat underestimates. Together with Press-Schechter 1974 it realizes only the narrow thresholded collapse-abundance route; its stochastic process, filtering, halo calibration, simulation, and merger semantics remain paper-local.
PhysicsLogic/Papers/FermiPastaUlam1955.lean: the original finite nonlinear- chain numerical experiment, with the weakly nonlinear fixed-end setup, finite-difference and modal-analysis protocol, the printed equation-(4) discrete sine transform and original equations (5a)/(5b), repeated as (5a) in the reprint, particle/modal energies, independent total-energy and linear-control checks, quadratic-mode transfer and near return, cross-force finite-time nonmixing evidence, and the conjectural quasi-state proposal represented as separate routes. Figure 1 supplies the distinct selected values N=32, alpha=1/4, (delta-t)^2=1/8, approximately 30,000 cycles, five displayed modes, and higher-mode energy bound 20. The omitted nonlinear potential is retained as a separately evaluated correction, so the reported modal-energy sum is not identified with the separately checked conserved total. First-mode return is the numeric inequality |E_return-E_initial| <= E_initial/100, derived independently of the equipartition interpretation. The formalization distinguishes this modal return from exact full-state recurrence, finite observed failure of equipartition from asymptotic nonthermalization, and validated numerical evidence from an analytic theorem. Together with Zabusky-Kruskal 1965, it realizes the narrow Framework/ValidatedNumericalNearReturn.lean interface; with Zabusky-Kruskal and Creutz 1980, it also realizes the lower-level Framework/ValidatedNumericalPrediction.lean interface. Its near-return adapter grounds the finite calculation separately in the weakly nonlinear chain theory and selected finite physical chain. The same raw finite-difference/modal-energy source derivation also realizes the lower-level source-sensitive numerical-prediction explanation without first packaging an established prediction. Its 37 fidelity boundaries now include actual cycle-indexed phase histories. Modal energies are computed from coordinates and velocities; the mean and high-mode tail use the declared active mode set. A strict tail bound proves finite non-equipartition; individual high-mode bounds alone do not. Figure 9 separately averages kinetic energy over cycles 1..nu for modes 1,3,5,7 of the Figure 6 broken-linear case, with reported effective N=16, squared step 1/64, cutoff 5/128, and a 25-percent slope increase. Its numeric test is independent of the mixing assessment. The validation uses optional linear controls and a separate energy-drift tolerance, not a universal one-percent control log. The weak nonlinear force bound is evaluated on the actual bond force, not fixed to one tenth. Equal finite phase records with conserved modal energy can have a continuation whose kinetic averages converge to equipartition. A harmonic flow preserves energy while reversing the phase-space state. These diagnostic histories are not solutions of the nonlinear FPU equations. Long observation times now compare the actual cycle clock to a selected characteristic linear period. The p. 987 positive-matrix analogy has an independent imported-result route with normalized eigenrays, not raw-vector convergence. The nonlinear proposal uses actual quadratic iterates and cone-occupation averages over every nonvanishing initial orbit. A weak quadratic map has only zero-or-one limiting values per cone but no uniform finite partition of initial directions, so the two source formulations are not silently equated. Both remain conjectural. The public dynamics API and a nine-theorem independent quadratic client separate unique evolution, fixed direction, and decay of the actual vector. A separate consumer constructs its own frequency-two oscillator and applies the shared exact-return-to-observable-return theorem without importing this paper or its control witnesses. The reported effective N is no longer identified with active cardinality. A positive energy calibration now relates reported modal sums to total energy; the velocity projection is retained separately from the displacement projection. The literal sine formula loses a terminal coordinate if all listed coordinates are free, and its boundary at N differs from the chosen N+1 interior-count convention. A nonzero fixed-end example derives the conversion from two explicit Parseval calculations and distinguishes the printed particle-energy sum from the Hamiltonian. The checked relative one-percent return survives common positive calibration; an unconverted absolute bound need not. The independent oscillator client checks that distinction in rescaled energy units too. The original report explicitly distinguishes the squared step in its captions from the positive cycle duration. The checked clock now has delta-t=sqrt(1/8) and t_n=n*delta-t; it rejects the earlier unsquared 1/8 reading, a negative step, and exact elapsed time inferred from a rounded cycle report. The 30,017-cycle control is constructed diagnostic data, not a recovered original computation log. Four independent internal client theorems exercise the clock with their own sqrt(2)/4 step. The additional force-derived energy refinement computes the Hamiltonian from the same quadratic, cubic, or broken-linear potential and actual phase samples, counting each bond once. Explicit component evaluation inputs, not an assigned energy-conservation flag, connect reported modal and nonlinear readouts to that Hamiltonian. The validation route requires the resulting sampled drift bound with both endpoint errors. Relative precision needs a resolved positive physical reference. Neither energy constancy nor small net nonlinear potential supplies Newton's law or weak bond forces. An independent three-moving-site cubic client computes H=41/8 with unequal readouts 83/16 and 81/16; its combined bound is 163/640, not the reported-drift budget 83/640. These remain paper-local semantics, not a new shared framework or reconstruction of the original runs.
PhysicsLogic/Papers/ZabuskyKruskal1965.lean: the original KdV numerical experiment introducing solitons, with the isolated pulse calculation, checked finite-difference evolution, pulse-train identification through measured width and speed, nonlinear identity-preserving interactions, unresolved close-overlap mechanism, phase-focusing near recurrence, and qualified long-time thermalization expectation represented as distinct routes. It distinguishes near profile reconstruction from exact state recurrence and realizes the same narrow validated-near-return interface as Fermi-Pasta-Ulam while keeping KdV and soliton physics paper-local. Its validated run also realizes the lower-level numerical-prediction interface. Its near-return adapter separately grounds the finite-difference calculation in the KdV theory and represented periodic KdV system. Its periodic-KdV validation, soliton-focusing, and waveform-reconstruction source derivation is also retained by the lower-level source-sensitive numerical-prediction explanation. Its six directional paper-local countermodels are now value-bearing: an isolated pulse with positive dispersion, peak contrast three, and width one withholds equations (2)-(4), whereas the calculated witness retains width two and speed one. The eight-pulse train satisfies separate percent-level width and one-fifth speed checks but leaves the close-interaction residual nonzero; exact momentum coexists with energy drift 1/100000, first-profile residual 1/100 and poorer second residual 2/100 withhold exact state recurrence, and finite recurrence does not exclude later equipartition. No proposition-pair or pulse/status truth table replaces these Zabusky-Kruskal distinctions.
PhysicsLogic/Papers/Miller1964.lean: the original parallel-trajectory stellar-system experiment, retaining deterministic reversible equations, first-integral and reduced-step controls, exponential phase-space separation, encounter amplification, inverse-square collective scaling, qualified irreversibility, individual prediction limits, and the unresolved ensemble question as distinct routes. Its narrow point-predictability route realizes the shared finite-precision trajectory component. The parallel branch now retains p. 253 equation (2) as the literal logarithm of the summed squared position and velocity differences, while the encounter branch retains p. 251 equation (1), the angular-error amplification factor, and the stated tau / ln f e-folding time. Lean checks the unit-distance normalization, strict amplification, and positive e-folding consequence; countermodels prevent named separation or encounter calculations from manufacturing those formulas.
PhysicsLogic/Papers/PortegiesZwartBoekholt2014.lean: arbitrary-precision validation and approximate-versus-converged resonant three-body comparison, separating convergence, individual trajectory disagreement, the first integral-time dissolution criterion's independent energy/radius/outward- motion conditions and surviving bound binary, all four 10,000-member initial-condition classes, majority-only energy control, tested timestep thresholds, four distinct survival half-lives, selected ensemble recovery, and untested extrapolations. Its individual-comparison route realizes the same shared finite-precision trajectory component while its physical escape and ensemble conclusions remain paper-local.
PhysicsLogic/Papers/Lorenz1963.lean: finite deterministic dissipative flow, separate central and noncentral instability deductions, bounded finite-memory numerical integration, Saltzman's original dimensional convection equations, both distinct temperature Fourier modes, the exact Rayleigh threshold 27 pi^4/4, and the severe three-mode reduction. Its complete Jacobian, both characteristic polynomials and equilibria, separate convection-instability threshold 470/19, and exact exp(-287/30) volume factor distinguish shrinking phase volume from converging trajectories. Lorenz's idealized two-branch return map retains its undefined midpoint, opposite slopes, distinct preimages, and every printed periodic cycle; exact surrogate calculations and finite numerical evidence still do not prove nonperiodicity of the physical flow. Atmospheric predictability remains conditional. Its selected nearby-state divergence route is the third independent realization of the shared finite-precision trajectory component; the real atmosphere is not identified with the finite model.
PhysicsLogic/Papers/Noether1918.lean: paper-local variational problems, finite-parameter, infinitely-many-parameter, arbitrary-function, and mixed transformation groups, exact calculation interfaces for both theorems and converses, a theorem-II route deriving selected Euler-Lagrange equations from the remaining equations, and checked theorem-I divergence relations in both the finite and non-arbitrary-function infinite-parameter cases. The finite coefficient contract now retains equation (13) as a value-level sum of selected Euler expressions times generator variations equaling the selected current divergence, with a projection theorem and countermodel separating that formula from a relation label. The theorem-II calculation now supplies the exact intermediate variational and integration-by-parts inputs, not equations (15) or (16). Noether1918/ArbitraryFunctions.lean derives the weighted divergence formula for every smooth compactly supported test family, proves vanishing boundary jets, and uses an explicit Gauss formula plus Mathlib's fundamental lemma to derive the pointwise adjoint identities. The coefficients are actual ordered derivatives of coefficient times Euler expression on the same history. The source certificate exposes those same pointwise identities. Operator independence, a positive function count, and an inhabited regular history are explicit; stronger differential irreducibility remains separate. Noether1918/EulerDependence.lean replaces opaque remaining/dependent equation predicates by actual selected Euler expressions. Its reduction supplies a universal reconstruction on smooth trial fields, zero-preserving recovery maps, and explicit initial or boundary jets, not the desired equations. Lean derives their vanishing from the same history's identities and remaining equations. Each theorem-I case retains a separately qualified converse. Mixed-group output explicitly records that its divergence relations are independent of its theorem-II identities. Both consequence routes inherit their forward-theorem outputs through semantic route certificates; separate multidimensional-conservation and one-dimensional-first-integral routes, plus the philosophy-layer Noether bridge, consume the certified finite relation output at the retained parameter count rather than recomputing a one-generator surrogate; the mixed-group result, Hilbert's improper energy criterion with its Euler-expression/derivative current construction and identically divergence-free remainder, and countermodels delimit the theorem's scopes. The thirteen algebraic countermodels retain value-bearing Euler expressions, generator variations, alternating derivative coefficients, injective parameter modes, distinct histories, current decompositions, and equation residuals. They explicitly separate sourceful from zero divergence, mixed outputs from their independence, nonlinear first-integral dependence, and conservation from impropriety; no Unit-carrier truth table replaces those distinctions. Four coordinate-current controls and two actual adjoint-identity controls are joined by two equation-recovery controls and three first-integral controls, bringing the fidelity matrix to twenty-four boundaries. An independent kinetic gauge client verifies the density invariance for arbitrary local shifts, operator independence, and all inputs before using the library to derive an off-shell identity and residual balance. It also constructs an actual differential recovery, realizes a nonconstant on-shell history, and checks that reversing the selected equation requires an initial value. A remaining equation at just one point does not supply the neighborhood needed to differentiate its vanishing. Noether1918/FirstIntegrals.lean now derives constancy of the actual selected currents on connected open one-dimensional history domains using Mathlib's mean value theorem. No supplied integral-existence predicate or mandatory nonlinear-dependence flag remains. A free-particle family has independent space and time translations but the nonlinear relation 2E = P^2; different histories have different conserved values. Actual derivative controls exclude a single constant across disconnected regions, a compulsory zero value, and empty-domain realizations. An independent harmonic-oscillator client derives conserved nonzero energy even though its boundary term and Lagrangian density vary with time. Noether1918/FiniteCurrents.lean defines the corrected variation, B = A - f delta x, and actual coordinate divergence on the same history. The finite on-shell and sourceful routes use that identity and regularity to derive zero divergence or source balance, respectively. An independent free-scalar client checks gradient energy and the negative Laplacian before deriving a nonzero, nonconstant, divergence-free current. The coordinate-current API is now shared with Einstein 1916 through Framework/Conservation.lean. Their different source arguments separately derive its nonvacuous result. An external transport client imports neither paper and tests continuity, uniform production, domain restriction, and background-current subtraction through six public-API proof uses.
PhysicsLogic/Papers/HohenbergKohn1964.lean: paper-local potentials, nondegenerate ground states, densities, universal and decomposed energy functionals, with the universal term explicitly equal to fixed kinetic plus mutual Coulomb-repulsion energy rather than an opaque internal-energy label, and a theorem-I route that derives both strict variational inequalities, potential-difference antisymmetry, and the reductio from explicit principles. Additive-constant transport and nondegenerate state uniqueness are separate inputs. Its theorem-I route independently realizes the shared density-potential gauge determination framework without conflating static constant shifts with time-dependent gauges. Its theorem-II route proves exact ground-energy attainment and a bound over every representable density, rather than only one selected competitor. A separate footnote-11 route proves that positivity and integer normalization alone do not logically establish representability, without asserting a physical counterexample. The remaining routes cover the corrected equation-(35) momentum-kernel/polarizability equality K(q) = (2 pi / q^2) (1 / alpha(q) - 1), equation (36)'s dielectric definition, the checked equation-(37) dielectric rewrite on its explicit common denominator domain, equations (38)-(40)'s small-q polarizability series, derivative singularity at 2 k_F, and q^-4 large-momentum decay, and equations (44)-(46)'s transferred small-q kernel series, derivative singularity, and q^2 large-momentum growth. Equation (47) then retains the position-space kernel as a distribution on test functions, with the origin delta and distributional Laplacian explicit, while equation (48) retains G[n]-G[n0], the perturbation-square integral, the gradient-square integral, and the higher-gradient remainder. These limit formulas feed the explicit 2 k_F nonanalyticity and inverse-cube Friedel profile, the checked finite-gradient obstruction, and the conditional gradient expansion with equation (63)'s divergence-reduced local energy density: one second-order gradient-square term, three distinct fourth-order invariants, an explicit sixth-order remainder, and equation-(64) integration to the global value. Equation-(83) partial summation then has an explicit three-dimensional local energy density, local-density kernel, opposite half-displacement density differences, divergence/higher-order remainder channels, and equation-(64) integration back to the global residual functional. Equation (84) now fixes that local-density kernel through a summable countable reciprocal-momentum Fourier series with positive box volume, nonzero momentum and dielectric denominators, and the complex exp(-i q . r') plane wave. The equation-(84) 1/epsilon subseries remains distinct from equation (37)'s 1/(epsilon - 1) exact-kernel rewrite. Scope countermodels include failure of universality when internal energy depends on the varied external potential, failure of a named gradient expansion to supply equation (63), failure of a named kernel to supply equation (84), and failure of a named partial-summation label to supply equation (83).
PhysicsLogic/Papers/RungeGross1984.lean: the fixed-initial-state, gauge-qualified time-dependent density-functional argument, including the Taylor-current, continuity, equation-(6) density-separation, boundary, hydrodynamic, stationary-action, and effective-orbital routes. It independently realizes the shared density-potential gauge determination framework while retaining fixed initial conditions, the original equation-(6) derivation, and open representability and practical scope. Its six paper-local countermodel theorems now retain actual density, potential-jet, divergence, gauge-shift, phase, action/Hessian, functional-residual, approximation, initial-state, and derivation values. In particular, the equation-(6) witness has a nonzero right-hand side but zero density derivative; spatial potentials (0,1) and (2,3) are gauge-equivalent without literal equality; and a zero first variation with Hessian values 2,-2 is stationary but not minimal. No Unit-carrier or status-enum truth table replaces those distinctions. Its independent fidelity matrix now has twenty-one physical boundaries. The original k+1 current and k+2 density derivatives, occupied-support integral -18, zero boundary flux, both fixed hydrodynamic initial conditions, and A[n]=B[n]-int(nv) are retained inside the certified source routes. The exact Kohn-Sham witness has density two, external potential one, Hartree term two, exchange-correlation derivative three, and effective potential six; Taylor-flat nonanalytic futures, nonzero boundary flux, zero occupied support, missing initial current, and omitted exchange-correlation terms are independently ruled out.
PhysicsLogic/Papers/LandauSuperfluidity1941.lean: paper-local quantum-liquid operators, the explicitly supposed potential-below-vortex ordering, phonon-roton spectrum, low-temperature excitation thermodynamics, zero-temperature wall-excitation threshold derived from both actual branch dispersions, an explicitly attained quadratic-roton minimum and proven-positive critical speed, rotating-vessel two-motion statistics, nonliteral two-fluid interpretation, two-velocity hydrodynamics, and second sound. The spectrum first feeds a separate dilute-gas heat-capacity route; the absolute-zero flow branch remains independent of it, while the later rotating-vessel route consumes the thermodynamic result before reaching two motions. The low-temperature statistical regime is kept distinct from the lambda-point endpoint. Its selected wall-channel result realizes the shared subthreshold-excitation component through an exact paper-context model-retention certificate, without claiming exclusion of vortices or every dissipative process. A source-facing theorem starts from the operator/spectrum premises and direct wall-flow calculation rather than accepting EstablishedSubthresholdFlow. Its thermal and normal-density routes now use actual momentum integrals through the shared excitation-response component, deriving heat from energy families and equation (3) from radial moment identities. Explicit quantum-statistics bounds preserve the dilute approximation's scope.
PhysicsLogic/Papers/BogoliubovSuperfluidity1947.lean: paper-local weak Bose gas formalized in 24 source atoms and 13 certified routes. It keeps the exact pair-potential Hamiltonian, interaction-sign stability restriction, weak-excitation linearization, commutation-preserving canonical diagonalization, and phonon-to-molecular spectral asymptotics separate before deriving equilibrium occupations, the positive velocity threshold, and stationary frictionless condensate-quasiparticle motion. A sibling threshold branch derives the molecular momentum distribution and zero-temperature depletion; only then are the small-depletion, weak-coupling, low-temperature, and excluded-short-range-repulsion conditions assessed. The later exact zero-density two-body scattering replacement, free-energy and virial-pressure calculation, hard-sphere and weak-attraction comparison, and semi-phenomenological real-liquid proposal remain distinct downstream routes. Its complete motion route independently realizes the unchanged shared subthreshold-excitation component through an exact paper-context model-retention certificate. A source-facing theorem executes the complete microscopic-to-threshold chain and motion calculation without accepting EstablishedFrictionlessMotion; molecular depletion and real-liquid extensions remain outside that route.
PhysicsLogic/Papers/FeynmanTwoFluid1954.lean: paper-local liquid-helium density-mode ansatz, variational energy, phonon-roton interpretation, dilute-excitation thermodynamics, moving two-fluid description, current-conservation diagnosis, impurity mass estimate, and qualified scope. Its fixed-momentum upper-bound route independently realizes the shared momentum-resolved variational component through an exact paper-context model-retention certificate, a direct nonvacuity theorem, and a structural explanation of only the selected upper-bound relation. The structural route executes the ansatz and Eq. (18) calculation directly; it does not consume the terminal established spectrum. The thermodynamic and moving-fluid stages additionally retain selected Eq. (25)-(26) and Eq. (39)-(43) formula packages rather than only named outputs; all established stages avoid storing implication-valued calculations. Its moving-fluid result now also retains Feynman's multiply connected ring argument: integer phase winding and locally irrotational flow can carry nonzero permanent circulation. The original expectation of accuracy near the structure-factor maximum and the appendix's experimental impurity-mass disagreement are explicit. Its actual Bose-current derivative now consumes the shared excitation response with the original number normalization. The literal n^2 coefficient and differentiated n(1+n) response remain distinct.
PhysicsLogic/Papers/FeynmanCohen1956.lean: paper-local return-flow construction across eighteen source-distinct routes: Landau and simple-mode benchmarks, localized continuity failure, foreign-atom mechanism, exact symmetrization and controlled linearization, qualified vortex picture, diffraction and identity scope, corrected Kirkwood and residual integrals, separate norm and numerator calculations, variational quotient, optimization, momentum regimes, error budget, and thermodynamic scope. It also carries typed equation-(9), equation-(61), and equation-(63) scalar packages tied to the selected momenta, structure factor, corrected correlation data, return-flow strength, energies, and reported gaps. The staged packages survive into the simple benchmark, improved spectrum, and optimized gap, and a countermodel blocks a named output from replacing the printed formulas. It has twelve formal nonimplications and uses the shared variational component as a dependent refinement of Feynman 1954 while supplying its own exact paper-context model-retention certificate and direct inhabited-route theorem.
PhysicsLogic/Papers/GirvinMacDonaldPlatzman1986.lean: paper-local lowest-Landau-level projection with exact Gaussian cyclotron subtraction, actual noncommuting complex density matrices and exponential commutator, a positive finite spectral measure with evaluated zeroth and first moments, oscillator-strength rather than static-weight fractions, an unsaturated 98% density mode, and explicit density-dark excitations below every proposed gap. Its remaining paper-local semantics retain the qualified gap condition, magneto-roton dispersion, crystallization interpretation, large-wave-vector scope, finite-thickness and disorder assessment, and static response. Its projected single-mode upper bound independently realizes the shared momentum-resolved variational component through an exact paper-context model-retention certificate, a direct nonvacuity theorem, and a structural explanation of only the selected upper-bound relation. The structural route executes the unprojected diagnosis, projected construction, and projected energy calculation in source order before any terminal projected bound exists. Nine established stages retain only named direct outputs; the source graph explicitly certifies the unprojected diagnosis and projected trial before the energy quotient, and a staged countermodel blocks all nine vacuous calculation contracts. Twenty inhabited fidelity boundaries additionally separate incorrect operator order, commuting densities, unprojected structure factors, filled Landau levels, negative spectral weights, zero denominators, exact first moments, invisible lower states, incomplete saturation, and false many-body gaps.
PhysicsLogic/Papers/Laughlin1983.lean: paper-local odd-Jastrow state selection, independent variational evidence, plasma mapping, two fractional-charge calculations, excitation algebra, compression-gap reasoning, localization, and scoped Hall response. It realizes shared charge assignment, evidence semantics, and the gapped-fluid route without promoting a generic quantum Hall framework.
PhysicsLogic/Papers/Haldane1983.lean: paper-local spherical monopole geometry with literal radial-field, Dirac-flux, angular-momentum, lowest-Landau-level energy/degeneracy, and magnetic-length formulas; finite 2S=m(N-1), finite N/(2S), and explicit thermodynamic nu -> 1/m formulas; operator flux/angular-momentum shifts, fixed-field m-hole production, N+1 degeneracy, and opposite e/m charge formulas; hard-core exact versus general variational state assessment, conditional hierarchy recursion, continued-fraction observables, and the unresolved interaction-dependent existence problem. The readouts are tied to the selected sphere, radial field, electron gas, parent state, operators, excitations, and charge assignments; countermodels block merely named monopole, parent-filling, or fixed-field outputs from supplying those equations. It realizes grounded shared charge assignment, the exact fractional-Hall quasihole-charge route, and the gapped-fluid route. The fixed-field charge calculation remains independent of the parent gap, which is retained as an explicit author assumption only in the gapped-fluid and hierarchy routes. Its thirty-two inhabited Haldane hierarchy boundaries include an actual six-flux monopole with seven Landau states, finite filling 1/2 versus thermodynamic 1/3, three fixed-field holes of charge e/3, parent/child fluxes 15, 19, and 11, and the separate continued fractions [3,+2]=2/7 and [3,-2]=2/5. Their charges and Hall resistances are respectively e/7, e/5, 7/2, and 5/2; all printed hierarchy formulas remain compatible with zero child gap.
PhysicsLogic/Papers/Kitaev2001.lean: paper-local Majorana-chain semantics for the exactly solvable endpoint modes and parity doublet, boundary-root phase distinction, exponentially small finite-chain splitting, parity- resolved 2pi cycle, Z2 Majorana number and loop diagnostic, quadratic Pfaffian formula, weak-pairing odd-Fermi-point criterion with explicit gap opening, and the qualified 4pi Josephson-current proposal. Material realization and fault-tolerant gates remain open. Together with Oreg-Refael-von Oppen 2010, its boundary calculation now independently realizes the narrow shared Framework/BoundaryMajoranaMode.lean route. Its source-anchored adapter also projects the completed route to a direct nonvacuous boundary-mode proposition and to a structural explanation whose constraint includes the actual boundary calculation. Its separate grounding path consumes only BoundaryMajoranaGroundingSetup, before bulk classification or boundary-mode outputs. Together with Fu-Kane 2009, its localized parity branch independently realizes Framework/ParityResolvedFractionalJosephsonResponse.lean and projects its completed response to the direct nonvacuous shared endpoint.
PhysicsLogic/Papers/FuKane2009.lean: paper-local quantum-spin-Hall semantics for the superconducting-magnetic interface Majorana mode, BdG and Andreev spectrum, protected parity crossing, bulk parity-transfer interpretation, fixed-parity fractional Josephson response, finite-temperature switching rate, telegraph-noise spectrum, and proposed HgCdTe probe. The junction result retains the original magnetic-barrier transmission, epsilon_0(phi) = sqrt(D) Delta_0 cos(phi/2), both occupation energies epsilon_0(phi) (N_0 - 1/2), and the exact I_0(phi) = (1/2) sqrt(D) e Delta_0 sin(phi/2) current. Its thermal result separately retains the two printed switching rates, conditional bath symmetry, quasiparticle versus two-dimensional variable-range-hopping activation, the two-pi thermal equilibrium current, and the Lorentzian noise spectrum; the zero-frequency formula is derived rather than assumed. Concrete transparent and magnetic junctions, two different thermal baths, and nineteen inhabited fidelity boundaries prevent these source equations from collapsing into named predicates. Its interface route makes the known SSH zero-mode result an explicit imported theorem hypothesis, keeps the subsequent BdG self-conjugacy inference separate, and is a third independent client of Framework/BoundaryMajoranaMode.lean. Its later Josephson route separately realizes the shared parity-resolved fractional-response component without promoting the QSHI anomaly or noise calculation into generic semantics. Its interface adapter also exhibits the direct nonvacuous shared mode, and its interface route realizes the shared structural explanation. Its Josephson adapter exhibits the direct nonvacuous shared response. The shared mode grounding consumes MajoranaInterfaceSetup, not the completed interface result.
PhysicsLogic/Papers/Gamow1928.lean: paper-local semantics for the nuclear potential and classical obstruction, rectangular-barrier calculation, damped outgoing state and decay constant, radial barrier transfer, qualified Geiger-Nuttall comparison, and the unknown-potential and gamma-preparation scope. Actual waves and currents distinguish standing amplitudes, leading tunneling factors, and exact scattering probabilities. Complex-energy time evolution derives damping and finite-region survival; conservation and leading normalization derive equation (5). The separate Coulomb model derives a base-corrected log slope and combines model-transfer and Taylor errors without identifying the conflicting printed exponents. The normalized survival curve gives correctly conditioned future escape probabilities; the damped and radial routes jointly realize the nonvacuous shared memoryless-decay endpoint. Its named setup bridge maps two local nuclear barrier setups, comparable potential profiles, and energy ordering to the shared pre-output grounding boundary. Its source-facing mechanism theorem reaches both selected decay explanations before constructing the Geiger-Nuttall comparison. Its stronger source-sensitive theorem records separate lower and higher damped-outgoing radial-transfer derivations and exposes either derivation from the resulting explanation.
PhysicsLogic/Papers/GurneyCondon1928.lean: paper-local semantics for chance-governed radioactivity, overlapping interior and exterior wavefunctions, overlap-sensitive rates, the conditional energy-rate trend, incoming-alpha scattering consistency, and the field-emission analogy. Because the original letter prints no tunneling integral, its local value layer retains source-faithful inequalities instead: positive overlap below an explicit selected smallness scale, a positive decay rate and observation duration, the corresponding escape probability in (0, 1), and conditional strict energy/overlap/rate ordering with equal-duration probability comparisons. The letter's explicitly recalled exponential law receives normalized survival and correctly conditioned age-independent future-probability semantics, with countermodels separating positive rate, survival, conditioning, and positive observation duration. Its independent setup bridge preserves the two selected potential pictures, comparable profiles, and energy ordering without assuming wave-overlap or decay outputs. Its source-facing mechanism theorem executes the two setup-and-overlap routes without using the conditional comparison or the objective-chance classification. Its source-sensitive theorem records the two interior/exterior wave-overlap derivations separately rather than identifying them merely because they realize the same shared route. Together these two papers independently realize Framework/FiniteBarrierMetastableDecay.lean.
PhysicsLogic/Papers/OregRefaelVonOppen2010.lean: paper-local spin-orbit-coupled quantum-wire semantics retaining the perpendicular wire axes, four-term BdG Hamiltonian, homogeneous spectrum and two gapped phases, distinct 4e^2/h and 2e^2/h transport plateaus, Zeeman- and pairing-interface gradient matrices and oscillator branches, chemical-interface decay and wavefunction-matching coefficients, the weakly split pairing-sign Majorana doublet, and fractional h/e versus conventional h/(2e) Josephson flux periods. Fifteen inhabited fidelity boundaries keep those physical distinctions independent. Vortex action remains an expectation, detailed braiding remains deferred, and material realization and fault tolerance remain open. Its chemical interface independently realizes the shared boundary-Majorana route without promoting semiconductor, Zeeman, Josephson, or braiding vocabulary into the framework. Its source-anchored adapter projects that route to the same direct nonvacuous boundary-mode proposition and structural explanation. Its separate ChemicalInterfaceGroundingSetup contains only the shared pre-output physical setup.
PhysicsLogic/Papers/Parker1969.lean: paper-local quantum-field theory in an expanding universe, separating canonical commutator propagation, continuity-based scalar statistics, Bogoliubov pair production and infinite-volume representation change, adiabatic invariance, Parker's minimization postulate for physical particle operators, radiation- and dust-era no-creation conditions, heuristic backreaction, the rough present-epoch estimate, and conformal no-creation for massless nonzero-spin fields. Together with Hawking 1975 it realizes the narrow shared Bogoliubov particle-production inference, while Parker's time-local particle definition and cosmological conclusions remain paper-local. Its Bogoliubov route retains equations (13), (28), (39), (40), (52), and (55): the selected operator ansatz, hyperbolic coefficient parameterization, unitary implementation, normalization, occupation, and density formulas. It keeps the production calculation without silently manufacturing Parker's later physical particle criterion. A separate downstream route realizes the neutral description-relative particle-content paradigm only after consuming the minimization-selected observation-time operator: the same scalar-field state is initially vacuum and has positive nonvacuum content under that physically selected description. A separate bridge still prevents positive occupation from silently becoming nonvacuum status. Its shared context owns six selected indices and all seven route-used relation families and constructs one named model, with an exact paper-semantics certificate consumed by applicability. Its output-led established result retains exact selection plus the directly realized vacuum-to-production facts and reconstructs the calculation route. Grounding uses the same exact model, Parker's actual incoming-vacuum setup, and his explicit theory/world bridge without assuming mode mixing or any later production output. Its pp. 1061-1062 adapter now projects the route to a direct nonvacuous result containing the actual incoming vacuum, selected coefficient relation, positive occupation, and produced-particle conclusion. The same granular inputs now realize a typed structural explanation: its proof-free constraint retains Parker's selected creation coefficient, while its distinct phenomenon contains the incoming vacuum, represented positive occupation, and produced particles. A shared countermodel with that terminal phenomenon but no selected mode expansion blocks the converse. A stronger source-sensitive explanation now retains Parker's typed canonical transformation/vacuum/creation-coefficient derivation. Parker's full calculation first projects to a narrower source calculation that omits vacuum persistence, pair statistics, stimulation, and density; the source theorem then starts from that setup, calculation, and interpretation rather than a terminal production result.
PhysicsLogic/Papers/Hawking1975.lean: paper-local semiclassical collapse, asymptotic in/out mode mixing, nonzero negative-frequency production, a selected last-escaping horizon ray trace with logarithmic phase, selected late-time wave packets dominated by high incoming frequencies, greybody thermality, spin and mass extensions, Kerr-Newman shifts and superradiance, renormalized integrated flux, quasi-stationary evaporation, black-hole thermodynamics, and the qualified Planck endpoint. Its heuristic pair picture is kept separate from the derivation. It realizes the exact Bogoliubov production inference shared with Parker and the compensation-to-generalized-entropy- nondecrease inference shared with Bekenstein. Its beta-row model carries the same context-owned exact-retention certificate, while a thirteen-component framework mutation audit makes every index or relation change fail the original exact semantics. A nonvacuous finite witness realizes the complete vacuum-to-positive-occupation route and its direct realized result, with direct component-activity checks. Its pp. 206-207 adapter projects the beta-row route to that result without absorbing collapse or future-null-infinity interpretation into the shared component. Those same source-local inputs realize the shared structural mode-mixing explanation, without identifying Hawking's collapse and ray tracing with Parker's expansion mechanism. The stronger source-sensitive explanation records a distinct asymptotic in/out beta-row derivation. It stops at equations (2.5)-(2.10) and excludes the later ray-tracing, thermal, greybody, and evaporation routes. A complete shared route with a false source relation has the ordinary explanation but neither paper's source-sensitive one. The collapse route also realizes description-relative particle content for the same incoming-vacuum field state under the asymptotic outgoing description, without treating particle descriptions as conscious observers or arbitrary relabellings. Bogoliubov grounding uses Hawking's actual incoming-vacuum setup and explicit theory/world bridge without assuming the beta-row calculation or particle- production result. Its p. 203 thermodynamic route now branches from steady thermality and explicit entropy bookkeeping without absorbing the later p. 219 renormalized-flux calculation; backreaction remains the separate premise for evaporation. Its separate generalized-entropy model retains the process, both entropy-change functions, and all five route-used predicates; its exact certificate is consumed by route applicability and by exact theory/model membership. Its context fixes generalizedEntropyProcess before constructing the unique selectedModel, so a candidate cannot change the process and remain exact. Its shared compensation adapter rebuilds the local thermodynamic setup from shared process, account, horizon-exchange, and fluctuation facts plus the paper-local mechanical and area-law analogies before invoking the thermal interpretation. Entropy-model grounding delegates to the generic route-independent constructor using the certificate, Hawking's pre-compensation thermodynamic setup, and explicit theory/world bridges, without assuming the compensation calculation or nondecrease. The completed Hawking route separately proves direct nonvacuous generalized-entropy balance at that named process.
PhysicsLogic/Papers/Bekenstein1973.lean: paper-local black-hole entropy logic from the Kerr mechanics analogy and inaccessible information through merger-based area scaling, the semiclassical one-bit coefficient estimate, the statistical generalized second law, oscillator and beam tests, fluctuation resolution, individual-quantum accounting, and the finite-box Geroch engine. Together with Hawking 1975 it realizes only the narrow generalized-entropy balance inference; information loss, area coefficients, radiation, and all example calculations remain paper-local. Its named Section V route branches from the inaccessible-information result without consuming the tentative one-bit normalization; the oscillator, beam, and Geroch tests explicitly rejoin the coefficient route where they use Eqs. (15)--(18). Its named eight-component shared model is constructed from a context that fixes bodyCaptureProcess, then certified against that context before the compensation route can be used. Its shared compensation adapter rebuilds the local body-capture setup from shared process, account, horizon-exchange, and fluctuation facts plus the paper-local horizon-crossing fact before invoking the information calculation. Theory/world grounding delegates to the generic constructor using the certificate, Bekenstein's pre-compensation body-capture setup, and explicit bridges, without assuming compensation or nondecrease. The completed capture route separately proves direct nonvacuous generalized-entropy balance at that named process. Its typed entropy source separately reconstructs the mechanics, inaccessible-information, actual body-capture, compensation, and statistical-interpretation chain before realizing the source-sensitive explanation. A completed common balance and ordinary explanation cannot reconstruct either paper's missing source.
PhysicsLogic/Papers/KaplanSavageWise1998.lean: paper-local scattering channels, subtraction scales, scale-indexed coupling and amplitude values, scale-weighted coupling derivatives, beta-formula and running-solution values, interaction terms, regimes, and fits; checked PDS, literal complex-valued equation-(5) loop and equation-(6) bubble-amplitude readouts with on-shell, zero-power-loop, and non-pole obligations, value-level RG matching, a loop-to-resummation-to-unitarity chain, a separate minimal-subtraction scope theorem contrasting natural p/Lambda counting with the large-length p << 1/|a| window, mixed resummation, explicit-pion, and a D2 chain whose requiredness is derived from scale-indexed amplitudes with and without the term, whose same-order contribution uses shared power counting, and whose Weinberg inconsistency is a checked contradiction rather than an imported obstruction; scale-cancellation, empirical-support deductions through an explicit author-interpretation bridge, and coupled-channel deductions with explicit matrix components, observable values, mixed calculation orders, fit-parameter status, and scope countermodels. Its pion-inclusive running-coupling and full-amplitude matching route realizes the shared renormalized-prediction component.
PhysicsLogic/Papers/BedaqueHammerVanKolck1998.lean: paper-local short-range three-body EFT, large-scattering-length, resummation, integral- equation, distinct intermediate-asymptotic and on-shell momentum roles, asymptotic-phase, Lambda-star phase locking, two-cutoff solution agreement, datum-to-Lambda-star calibration, cutoff, running-force, prediction, numerical-check, and bound-state semantics. The original author source fixes the exact 3 sqrt(3)/(4 pi) channel threshold, distinguishes the bosonic channel from the protected spin-3/2 quartet and coupled spin-1/2 nucleon equations, and separates the exact characteristic root from the quoted s0 ~= 1.0064. Its sine-ratio coupling repeats after Lambda -> Lambda exp(pi/s0) without becoming constant or admitting its poles. One fitted a3 = 1.56 a2 datum yields the distinct r3 = 0.57 a2 and B3 = 1.5/(M a2^2) predictions; the independently rounded helium values retain their nonzero 0.468 A and 0.079 A residuals. Twenty inhabited countermodels reject stronger false readings. Five checked routes establish the nonperturbative cutoff obstruction, the leading one-parameter running three-body force, low-momentum prediction invariance, one-datum predictive consequences, and the qualified shallow-state and triton extensions. Its pairwise-only cutoff obstruction independently realizes Framework/ThreeBodyPairwiseInputInsufficiency.lean, while its promoted running-force route realizes Framework/RenormalizedPrediction.lean. Its pairwise-input context fixes the dressed dibaryon description, on-shell amplitude observable, and low-energy regime before constructing the shared model. Its grounding boundary additionally requires completed two-body resummation and the pairwise-only three-body equation, but no nonuniqueness, cutoff sensitivity, or insufficiency output. Its ordinary shared explanation starts from the pairwise-only route; its source-sensitive refinement additionally retains the resummation, three-body equation, and asymptotic cutoff derivation and stops before the running-force remedy.
PhysicsLogic/Papers/Thomas1935.lean: paper-local finite-range and singular neutron-proton interaction models with the original finite-support potential, exterior A exp(-lambda r)/r deuteron, exact signed binding relation, and both pair potentials. The singular route retains the genuine A(1/r-lambda) contact limit, 4 pi A^2=2 lambda, two distinct neutron-proton coincidence channels, the mixed three-body kinetic term, and the explicitly absent triple-contact condition. Its separate variational input retains both contact-surface corrections rather than reusing a divergent finite-range quadratic form. Physically inhabited countermodels share identical deuteron data while producing distinct double-contact amplitudes and three-body energies. The paper retains its observed-mass constraint, disjunctive physical alternatives, and numerical-scope qualifications. Its singular route proves absence of an algebraically least three-body energy and realizes the shared pairwise-input insufficiency framework without selecting one remedy. Its shared context fixes the singular interaction, triton binding observable, and nuclear regime before constructing the model, and its calibrated relation retains both physical contact equations. The shared instability adapter reconstructs the singular local setup from the supplied shared calibration and pairwise-construction facts before invoking the variational calculation; the reverse adapter recovers that source setup from the output-led endpoint. An ordinary theorem explains the instability from the shared route, while a distinct source-sensitive typed theorem retains that setup and calculation without consuming the endpoint or selecting a remedy.
PhysicsLogic/Papers/EpelbaumGloeckleMeissner1998.lean: paper-local chiral pion-nucleon Hamiltonians, eta/lambda projection, Bloch-Horowitz energy-dependent reduction, Okubo unitary decoupling, pion-number recursion, finite-order potential construction, complete two-nucleon term accounting through the first correction, leading three-nucleon cancellation, and explicit regularization, Delta, and numerical open obligations. Its certified routes retain orthogonal complementary projector actions; the original kappa_i and nu_A counting formulas; the full spin/isospin pion-exchange potential and independent scalar/tensor contacts; projection graphs without nucleon-only denominators; and the equal-and-opposite rational three-body contributions. Twenty-two physical countermodels reject formula substitutions and preserve the distinction between internal unitary cancellation and iterated old-fashioned recoil.
PhysicsLogic/Papers/EpelbaumGloeckleMeissner1999.lean: paper-local realization of the Part-II two-nucleon calculation: imported and renormalized NNLO potential, sharp and exponential regulation, Lippmann-Schwinger iteration, all nine published NNLO coefficients and their explicit 4 + 4 + 1 S/P/S-D projected contact formulas, distinct NLO/NNLO fit windows and sharp/exponential cutoffs, an unfitted three-D-one prediction, the complete selected NLO/NNLO/experimental deuteron table, nonobservable D-state probabilities, the actual 47.1/2.5 GeV spurious state scales, and an explicitly incomplete Delta extension. Lean checks that binding-energy improvement need not improve the quadrupole moment. It independently realizes both finite-order-interaction plus iterative dynamics and post-calibration prediction, with separate theory/model/world grounding.
PhysicsLogic/Papers/Einstein1916.lean: paper-local coordinates, metrics, metric connections, equations of motion, curvature tensors, bodies, sources, energy tensors and traces, field equations, coordinate-dependent total matter-plus-gravity energy complexes, approximation regimes, and phenomena; checked routes from Einstein's two motivations through covariance, metric interpretation, connection-built geodesic motion with the original Gamma^tau_(mu nu) = -{mu nu;tau} Christoffel index order, the complete signed four-index equation-(43) metric-curvature formula, and a separately checked curvature-contraction dependency retaining the original upper-to-last-lower trace, the geometric and coordinate vacuum equations, the trace-adjusted sourced equation under its displayed sqrt(-g) = 1 condition, separated from its relativity limitation, and its separately checked coordinate-scoped conservation validation, the covariant matter balance, the explicit frictionless-fluid Euler specialization that consumes that preceding balance certificate, the generalized Maxwell systems with value-level covariant equations (59), (60), (62), (63), (65), (66), and (66a), explicit coordinate-derivative laws and a checked potential-curl-to-cyclic-identity step, plus the separate three-dimensional dictionary (61), (60b), (64), (63a), and (65a), field-current force density, electromagnetic energy balance, and free-charge recovery of the matter balance with open matter-ontology scope, the Newtonian limit, and the scoped redshift, 1.7-arcsecond solar-deflection, and 43-arcsecond-per-century Mercury conclusions. Seventeen inhabited fidelity boundaries now include computed Lorentzian, spherical-coordinate, Ricci-flat tidal, source-sign, and volume-derivative controls. These pointwise witnesses do not assert global solution existence.
PhysicsLogic/Papers/Rosen1940.lean: paper-local formal-versus-physical two-metric semantics across Rosen's paired Parts I and II. Part I now retains equations (7)-(10) as a selected four-coordinate component package: the gravitational/flat connection difference, its metric-derivative formula, the Ricci rewrite, and kappa = sqrt(g / gamma), tied to the selected metrics and tensors. Both metric determinants must be nonzero, without requiring either Lorentzian determinant to be positive; a checked degenerate-metric countermodel separates this from the square-root domain. Part II independently retains the exact printed motion formulas m=m_0*d_sigma/ds=m_0/w=m_0*sqrt(gamma_44/g_44) and the separately qualified weak-field approximation m approximately m_0*(1-phi). Equal inertial and gravitational masses need not be constant: the same reference rest mass two gives proper masses two and one when the selected gravitational metric changes. Sixteen physical countermodels additionally separate a fixed physical flat background from dynamical gravitational fields, shared coordinate motion from identical physical intervals, force-free potential from the proposed absolute-frame light-drag effect, and matter expansion in fixed flat space from expanding geometry. The physical-flat-background, empirical-agreement, absolute-frame, cosmological, and open foundational routes remain separate and do not turn covariance into background independence or Rosen's deferred Miller proposal into established evidence. A computed metric-jet adapter supplies the actual equations-(7)-(10) package and independently realizes the shared geometry contract; flat auxiliary curvature neither erases its coordinate connection nor imposes vacuum on the gravitational metric.
PhysicsLogic/Papers/Schwarzschild1916.lean: paper-local coordinate systems, exact point-mass metric, reduced vacuum equations, integration constants, approximation, worldline, orbit, and frequency-law semantics; checked exact integration and uniqueness, finite-order nonuniqueness assessment, Mercury and circular-orbit deductions, and a separately qualified molecular expectation. Equation (14)'s areal-radius line element and equations (15)-(18)'s equatorial first integrals and reciprocal-radius orbit equation are value-level paper-local formulas; a named orbit output cannot replace the latter package. Its exact-solution and orbital routes realize the shared vacuum-metric-dynamics interface without importing post-1916 horizon semantics.
PhysicsLogic/Papers/Nordtvedt1968.lean: paper-local test-element and self-gravitating-body scopes, operational mass-ratio calibration, general weak-field metric coefficients, stationary two-body cancellations, Brans-Dicke comparison, virial sphere reduction, and nonstationary oscillatory terms. It realizes the existing equivalence-principle semantics while keeping the paper's coefficient calculations and unresolved coordinate interpretation local.
PhysicsLogic/Papers/HughesRobinsonBeltranLopez1960.lean: paper-local finite evidence logic for a selected galactic P_2 inertial-mass anisotropy model. The chlorine and lithium observations now retain the printed 22/104-degree sidereal comparison, 9190-Mc/sec and 30-kc/sec atomic readout, 4.3-ppm versus 5.0 +/- 1-ppm nuclear widths, 8-cycles/sec residual allowance, and the 10^-10 and 10^-20 ratios as proposition-valued data tied to the selected objects; the oxygen 10^-10 comparison remains its own branch. Lean checks the finite ratio hierarchy while the Coulomb and central-potential conversions remain explicit imported physical hypotheses. It independently realizes the shared controlled-resonance model test using the bounded selected P2 model, protected references, finite nuclear sensitivity, and separate source-calculation branch. Its seven paper-local countermodel theorems now retain actual P2, angular, frequency, field, linewidth, ratio, conversion, scope, and evidence data: a 22/22-degree collapsed pair with zero prediction/rotation residuals still fails both scans; equal finite bounds cannot establish stronger nuclear sensitivity; and the evidence witness has zero bounded-model-support residual but nonzero theory-support residual. No Unit/Bool framework or constant relation replaces those distinctions.
PhysicsLogic/Papers/Penrose1965.lean: paper-local nonspherical collapse, positive-area future trapping with both independent null expansions negative, future-directed optical-scalar focusing, compact-boundary construction, and the original signed-degree transport contradiction on a noncompact Cauchy surface. The checked degree argument derives the shared topology obstruction. Sixteen inhabited fidelity boundaries distinguish one-sided convergence, marginal trapping, finite caustics, signed preimage counts, physical alternatives, and stronger singularity claims.
PhysicsLogic/Papers/HawkingOpenUniverses1965.lean: paper-local expanding equation-(1) Robertson-Walker metric with all three K=-1,0,+1 branches, a separate flat/open theorem scope, compact hyperbolic quotient with a noncompact deck-translation cover and explicit incompleteness descent, and both original large-sphere past-null convergences. Its 0 <= delta < epsilon perturbation calculation proves strict positivity independently for both null families, while the weaker global alternative retains the unique timelike Ricci eigenflow, noncompact causal cover, complete spatial hypersurface, pointwise positive density bound, and uniform flow-tilt bound. Twenty inhabited fidelity boundaries preserve compact-versus-cover topology, strict trapping, two-sided control, curvature-divergence nonimplication, and the deferred closed-universe extension.
PhysicsLogic/Papers/Friedmann1922.lean: paper-local homogeneous-curvature cosmology, the stationary/nonstationary split, Einstein and de Sitter stationary cases, radius-equation reduction, monotone first- and second-kind worlds, periodic worlds, an actualWorldKindAt relation with existence-plus-uniqueness determination, a checked open-alternatives adapter, and explicit cosmological-constant and illustrative-period qualifications. Its ten directional paper-local countermodels are now value-bearing: equations (4)-(5) can hold at R=1, c=kappa=1, lambda=0, R'=0, R''=-1/2, and rho=3 while equation (6) fails for A=2; positive mass can fail equation (9); the subcritical witness has roots one and two with a negative between-root radicand; the monotone creation radii are zero and two. Period identification retains an integer multiple of a calculated period and finite existence, whereas the unbounded-time witness retains genuine recurrence. The calculated period selects neither temporal reading, and the original 5*10^21-solar-mass, 10^10-year illustration leaves actual-world determination open. No proposition-pair or temporal-status truth table replaces these Friedmann distinctions.
PhysicsLogic/Papers/Lemaitre1927.lean: paper-local homogeneous variable-radius cosmology, field equations and energy conservation, constant-total-mass expansion, exact radius-ratio redshift, the near-source velocity-distance approximation, and original 43-object velocity catalog with 42 selected nebulae after excluding NGC 5194 because of its NGC 5195 association. Its value-bearing calibration retains absolute magnitude -15.2, log_10(r/parsec) = 0.2m + 4.04, declining 1/sqrt(1+r^2) distance weights, directed 300 km/s solar motion, asymmetric 0.4-to-2.5 distance uncertainty, distinct weighted 625 and unweighted 575 km/s/Mpc estimates, and their nonzero 6.25 and 3 km/s rounded-mean residuals. The Einstein static, current expanding, and asymptotic initial radii are respectively 2.7e10, 6e9, and 2.7e8 parsecs, while the separately rounded y = 0.0465 is not falsely identified with their exact ratio. Twenty inhabited fidelity boundaries retain these distinctions and leave the radiation-pressure origin as a suggestion rather than a result. The original scan corrects the archived OCR's erroneous 48-object catalog reading.
PhysicsLogic/Papers/Hubble1929.lean: paper-local construction of the selected nebular distance sample, the literal p. 170 rK + X cos(alpha) cos(delta) + Y sin(alpha) cos(delta) + Z sin(delta) = v equation of condition with the fit residual kept explicit at the data boundary, individual and grouped proportional fits, residual and independent pre-conclusion validation checks, a roughly linear first-approximation conclusion over a restricted range, a downstream NGC 7619 consistency check, and a possible but unestablished de Sitter interpretation. A proof-free observational readout retains the actual 24-object and 9-group samples, 465/513 fits with 50/60 uncertainties, 500 adoption boundary, 150/110 residuals, four-object Virgo scope, all-22 1.4-million-parsec/745-km/s mean check, downstream 7.8 versus 7 million parsecs, and separate de Sitter prediction residual without replacing observational distinctions by enum-to-Prop truth tables.
PhysicsLogic/Papers/RiessEtAl1998.lean: paper-local classified supernova sample, cross-band and light-curve distance reductions, scoped FRW likelihood with separate nonnegative-matter and nonbouncing-big-bang domain restrictions, two-component acceleration bridge, named-systematic assessment with unresolved evolution, and separate age and eternal-expansion routes. Terminal propositions retain the paper's 15-object primary sample, magnitude excess, method-specific flat-Lambda fits, significance ranges, q_0, age, and eternal-expansion outputs. Its source-sensitive shared explanation is derived directly from the raw observation, distance, likelihood, deceleration, and robustness calculations.
PhysicsLogic/Papers/PerlmutterEtAl1999.lean: paper-local matched low- and high-redshift samples, cross-filter and stretch standardization, Fit A/B/C progression, the printed selected-Fit-C double integral that marginalizes the joint four-parameter probability density over cal M_B and alpha, primary acceleration interpretation, identified error budget with grey-dust and evolution loopholes, and qualified comparison with the partially overlapping Riess analysis. Terminal propositions retain the 54-object Fit C result, the nuisance-marginalized cosmology probability, joint and flat density estimates, 99-percent positive-Lambda confidence, zero-Lambda dimming requirement, and both dimensionless age estimates. Its source-sensitive shared explanation is derived directly from the raw standardization, Fit A/B/C, interpretation, and systematic-refit calculations.
PhysicsLogic/Papers/FixsenEtAl1996.lean: paper-local full-mission FIRAS reduction, calibrated monopole detection, Planck residual fit, original 2-21 cm^-1 band and 320-sample external-blackbody calibration, systematics-qualified temperature, dipole, spectral-distortion, imported energy-release, and deferred-calibrator routes. Section 4 separately retains thermometry 2.730 +/- 0.001 K, color 2.7255 +/- 0.0009 K, and dipole 2.717 +/- 0.007 K, including the shared color/dipole frequency calibration. The dipole retains 3.369 + 0.003 = 3.372 mK, 0.004 mK statistical and 0.006 mK Galactic-systematic contributions, the rounded 0.007 mK uncertainty, distinct one-sigma and 95-percent directional intervals, and a separately imported 371 km/s Doppler interpretation. Section 6 retains the printed equation-(3) linear fit and equations (4)-(7) Bose-Einstein, chemical-potential derivative, optical-depth y, and Compton-shape formulas as selected value-level packages tied to the FIRAS spectra, temperature, Galactic contaminants, and distortion objects. A source-valued Table 4 witness retains the 2.27 cm^-1 bin, 5 kJy/sr residual, 14 kJy/sr uncertainty, and nonzero 4 kJy/sr Galactic foreground; the 2.728 +/- 0.004 K temperature retains its systematics-dominated 95-percent confidence qualification. The mu and y fits retain their separate redshift epochs and are not jointly fitted. Eighteen independent physical countermodels separate the reported calibration, method, dipole, and distortion claims from stronger unsupported interpretations, including the independently imported Wright energy-release conversions.
PhysicsLogic/Papers/Kibble1976.lean: paper-local finite-temperature symmetry breaking, including the original one-loop scalar-plus-gauge effective potential, gauge-dependent critical temperature, and strictly nonzero below-critical order parameter from equations (3)-(5); random nonequilibrium protodomain formation explicitly consumes those formulas, correlation-scale input, separate wall, string, and monopole topology routes, distinct S¹ string and S² monopole shortest-path production estimates with separate illustrative domain families and actual normalized orientation-configuration sums: two favorable three-domain chambers out of eight give 1/4, while two favorable four-domain chambers out of sixteen give 1/8. Rational unit-circle and unit-sphere vacuum vectors retain their actual signed triangle/tetrahedron coefficients, origin enclosure, and enclosing-versus-semicircle/hemisphere distinctions. Independent unbiased orientation weights and the continuum shortest-path reduction remain separate explicit assumptions; bias, correlations, missing obstruction geometry, raw-versus-normalized weights, and the distinct simplex arities have inhabited physical countermodels. The paper also retains wall and string evolution assessments and explicitly unresolved present-density, string-mechanism, and pi_3 obligations. Its shared adapter exports only the selected domain-to-vacuum-value assignment and the causal-domain assembly, obstruction, and monopole-formation route, with an exact paper-context retention certificate for the shared model. Its local grounding input is a valid selected transition plus independent protodomains, not a shared-framework implementation detail.
PhysicsLogic/Papers/Guth1981.lean: paper-local cosmological models, initial conditions, phase transitions, conserved quantities, monopoles, bubbles, Higgs orientations, bubble and monopole counts, rates, an explicit structural definition of the horizon problem from causal disconnection and thermal uniformity, a separate structural flatness diagnosis from Hubble tuning and conserved curvature, a source-anchored bridge to generic problem targets, a phase-attached real-valued readout for equations (3.5) and (3.8)-(3.13) that retains the shifted false-vacuum density, temperature-form Friedmann equation, halted and unchecked curvature branches, bounded-relative cooling approximation, exponential scale factor, and Hubble relation without promoting those formulas into a generic cosmology framework, an explicit distinction between slow nucleation and the presumed subcritical percolation regime, converted volume fraction and connected phase completion, and cosmological consequences; checked routes expose the family-level topology-and-coalescence logic of Kibble monopole production, the causal bubble-radius bound in equation (4.1), the explicitly order-qualified inverse-volume monopole estimate in (4.2), Preskill's independent observational abundance bound in (4.3), the resulting coalescence-temperature bound and four-order supercooling estimate in (4.4), and the separate weaker strong-transition revision in (4.5); inhabited countermodels prevent a named horizon bound, causal radius inequality, Kibble density estimate, or revised temperature estimate from supplying the missing source formulas, independent Preskill observation, or superseded stronger coarse limit, including the selected bubble-to-Higgs-orientation assignment, pairwise causal independence, and uncorrelated assigned orientations, with an exact paper-context retention certificate for the shared defect-formation model, uses a paper-local GUT-transition and independent-bubble setup for grounding, and distinguish successful horizon/flatness and monopole mechanisms from the original scenario's graceful-exit nonviability and the open status of proposed repairs. The sharp-nucleation assessment supplies only its conditional physical outputs; separate source-mapped establishment requirements derive why the proposed repair remains unestablished. Its local-patch source relation separately retains the preprint's locally prepared sub-horizon region, accelerated expansion, observed-region coverage, and distinct horizon/flatness transfer before any established shared patch or graceful-exit result is used.
deprecated/paper-formalizations/: retired paper-first formalizations and their source maps, coverage proofs, and target documents. They remain available for comparison but are outside the active package.
PhysicsLogic/Logic/Formula.lean, Argument.lean, and Route.lean: auxiliary source-map syntax and structural validation, including transitive route dependency inheritance, topological-order checks, and premise-sensitive propagation of epistemic justification statuses to route outputs.
PhysicsLogic/Logic/Semantics.lean: reusable propositions stating that a source claim, each inference step, and every output of a named route holds under a paper-local Lean interpretation. Its checked step-lookup interface lets coverage proofs certify the exact premise-to-conclusion rule declared by a source-map step without copying the paper's semantic vocabulary into the shared library. Conclusion-only certification is restricted by its Lean type to steps whose declared premise list is literally empty; the policy audit checks the same invariant for every active paper. For ordinary non-reductio routes, ordered step soundness computes output truth compositionally. Witten 1982 now follows the same discipline across its full graph: ordinary and twisted calculations inherit the finite-volume index logic, while the chiral interpretation inherits both index multiplicity and the computed zero-mode charge sequence. The ordinary calculation distinguishes the true-invariant U-tower candidate from the pseudo-invariant V multiplet and now retains the preceding gauge logic: periodic gauge shifts plus Gauss law make the Cartan variables periodic, while identity-connected Weyl transformations plus Gauss law make physical states Weyl invariant. Both source calculations now have direct paper-local endpoints: the periodic endpoint retains pure-theory scope, weak-coupling reduction, Cartan gauge constraints, Cartan/Weyl data, and the signed branch result together, while the twisted endpoint retains pure-theory scope, sector-classification data, and I=N together. A separate electric-flux refinement keeps ordinary zero flux on the unresolved periodic branch, gives zero index to nonzero ordinary and transverse twisted sectors, and gives unit index to each parallel twisted sector. The twisted calculation now exposes its complete nonzero-index, zero-state, finite-volume, and large-volume chain before applying the separately qualified boundary-condition expectation. Its true-invariant branch selection remains a separate author-qualified proposition. The deformation argument also realizes the shared protected-prediction paradigm: admissible connection, index protection, and value transfer are distinct propositions, and the periodic-volume theorem consumes that adapter. Bell 1964 distinguishes unrestricted bipartite outcomes from Bell-local response functions: the EPR-predetermined outcomes are connected to the candidate completion by an explicit realization bridge, locality is an explicit factorization equation, the shared applicability result retains the exact selected response pair, and the established result stores the nontrivial response domain and physical outputs while reconstructing the route separately. Remote influence is witnessed by changed outcomes under changed distant settings, equation (15) is checked from explicit normalized positive-average laws, and downstream routes inherit their EPR and no-go inputs from certified predecessors. Its final physical route separates the Lorentz causal-direction principle from the checked boosted-frame order reversal. Maldacena 1997 likewise represents its original v1 complex coupling dictionary by explicit real-component equations for g, gYM, theta, and the RR scalar chi, rather than an opaque correspondence predicate; its symmetry evidence records SO(2,4), SO(6), N=4, and the doubled superconformal supersymmetry rather than comparing arbitrary symmetry labels. Its sector argument now identifies the worldvolume and near-horizon theories through two explicit decompositions of the same D3 low-energy system with the same asymptotic closed-string spectator sector, rather than inferring identity from bare survival in a common limit. Its supergravity calculation now realizes the shared regime-and-accuracy approximation semantics: admissible boundary data, reliability, and an explicit calculation-correctness bridge are all required before exact bulk predictions are transferred to the supergravity description. Its paper-local reliability condition preserves both the direct gN >> 1 branch for g <= 1 and the original footnote's S-dual N/g >> 1 branch for g > 1.
PhysicsLogic/Papers/*/SourceMap.lean: primary-source provenance and paper ordering; these files do not substitute for the formal logic.
PhysicsLogic/Papers/*/Coverage.lean: exhaustive interpretations from every source-map atom to a proposition in the primary semantics or an explicit paper-local context, plus checked output theorems for every named route. RouteSemanticallyCertified strengthens this with soundness of every individual source-mapped step. Every active benchmark now uses the stronger certificate for every route: Witten 1981, Witten 1982, Bell 1964, Maldacena 1997, AMPS 2012, Jarzynski 1997, Noether 1918, Hohenberg-Kohn 1964, Kaplan-Savage-Wise 1998, Epelbaum-Gloeckle-Meissner 1998, Einstein 1916, Guth 1981, and Gubser-Klebanov-Polyakov 1998, Knox 1995, Scott-Srednicki-White 1993, Goldstone-Salam-Weinberg 1962, Anderson 1963, Landau 1941, and Bogoliubov 1947. A source step classified as a reductio hypothesis introduces a temporary assumption; it is not asserted globally, while all uses and the discharged conclusion remain ordinary checked semantic obligations. Adding an unmapped atom or omitting a required certificate fails the build or policy audit.
docs/targets/witten-index-1982.md: benchmark scope and acceptance criteria.
docs/targets/witten-dynamical-breaking-1981.md: original vacuum-energy, perturbative-protection, lower-dimensional model, four-dimensional obstruction, qualified proposal, and open-question routes.
docs/targets/bell-1964.md: original-paper scope and logical cautions.
docs/targets/maldacena-1997.md: original-v1 D3-brane scope and epistemic distinctions.
docs/targets/amps-2012.md: original-v1 contradiction routes, extensions, scope limits, and acceptance criteria.
docs/targets/jarzynski-1997.md: original-v1 isolated, reservoir, limit, ensemble-consequence, thermostat, and practical-scope routes.
docs/targets/riess-et-al-1998.md: original-v1 sample, calibrated-distance, FRW-fit, acceleration-interpretation, systematic, age, and fate routes.
docs/targets/perlmutter-et-al-1999.md: original-v1 standardization, Fit A/B/C, systematic-budget, residual-loophole, age, ontology, and qualified cross-check routes.
docs/targets/noether-1918.md: original finite-group, arbitrary-function, converse, on-shell, mixed-group, and Hilbert-energy routes.
docs/targets/hohenberg-kohn-1964.md: original exact density theorems, nearly uniform response, gradient limitation, slowly varying expansion, and partial-summation scope.
docs/targets/landau-superfluidity-1941.md: original quantum-liquid, phonon-roton, zero-temperature threshold, two-motion, hydrodynamic, and qualification routes.
docs/targets/bogoliubov-superfluidity-1947.md: original weak-gas diagonalization, quasiparticle, equilibrium-threshold, frictionless-motion, approximation-scope, and proposed-extension routes.
docs/targets/kaplan-savage-wise-1998.md: original pionless PDS, large-length power counting, explicit-pion completion, scale cancellation, fit warning, and coupled-channel scope.
docs/targets/mayer-1949.md and docs/targets/haxel-jensen-suess-1949.md: independent original nuclear-shell routes, their exact relation-retaining shared models, and the distinction between Mayer's square-well ordering and the Haxel-Jensen-Suess isotropic-baseline/anharmonic/Yukawa construction; Mayer's qualified Table I order, thallium crossing, and pair-filling caveat remain paper-local.
docs/targets/epelbaum-gloeckle-meissner-1998.md: original chiral projection formalism, unitary decoupling, recursive construction, two- and three-nucleon calculations, and open-program scope.
docs/targets/gubser-klebanov-polyakov-1998.md: original boundary generating-functional proposal, conformal-symmetry, correlator, spectrum, controlled-regime, and open-program routes.
docs/targets/ryu-takayanagi-2006.md: original static minimal-area proposal, exact and qualitative checks, finite-temperature interpretation, and open-extension scope.
docs/targets/lewkowycz-maldacena-2013.md: original density-matrix, replica, Einstein, cone, AdS/CFT, reflection, and extension-scope routes.
docs/targets/knox-1995.md: original single-sky estimator, instrument-design, likelihood-forecast, consistency-test, cosmological-correction, and cosmic-confusion routes.
docs/targets/goldstone-salam-weinberg-1962.md: original perturbative, current-spectral, charge, composite, and outlook routes.
docs/targets/anderson-1963.md: original plasma response, gauge invariance, bare-response spectrum criterion, superconducting mode conversion, analogy, and scope routes.
docs/targets/thooft-1974.md: original double-line color counting, topological large-rank expansion, planar dominance, light-cone surface, Hamiltonian reconstruction, and conditional binding routes.
docs/targets/stanley-1968.md: original vector-spin definitions, normalized-partition derivation, supporting checks, heuristic comparison, proposed uses, and critical-index order-of-limits scope.
docs/targets/einstein-1916.md: original motivation, covariance, metric, motion, field-equation, conservation, fluid, electromagnetic, Newtonian-limit, and prediction routes.
docs/targets/nyquist-1928.md: original frequency-balance, transmission-line, circuit-noise, carrier-scope, and Planck-replacement routes.
docs/targets/callen-welton-1951.md: original perturbative-dissipation, equilibrium-fluctuation, generalized-relation, Brownian, vacuum, acoustic, and interpretation-scope routes.
docs/targets/kubo-1957.md: original weak-response, operational-scope, canonical-relaxation, separate static-limit, correlation, magnetic and conduction, reciprocity, fluctuation-dissipation, sum-rule, and Einstein-relation routes.
docs/targets/epr-1935.md: original reality-criterion, completeness, noncommuting-pair, separated-system, remote-prediction, incompleteness, objection, and open-theory routes.
docs/targets/wetterich-1993.md: original exact effective-action flow, endpoint, exact-potential, qualified-truncation, and grounding routes.
docs/targets/wegner-houghton-1973.md: original infinitesimal shell, exact-generator, fixed-point, invariant-projection, epsilon-expansion, large-n, and qualified finite-integration routes.
docs/targets/bond-cole-efstathiou-kaiser-1991.md: original Gaussian hierarchy, sharp-k first crossing, correlated-filter numerics, N-body assessment, merger/bias, shared abundance, and qualified-scope routes.
docs/targets/tknn-1982.md: original magnetic Bloch, bulk Kubo, curvature-integrality, Harper/Diophantine equations (9) and (11), tight-binding, conditional deformation, and flux-limit routes.
docs/targets/niu-thouless-wu-1985.md: original many-body twist, thermodynamic averaging, integer Chern, conditional fractional, nonrigorous parent-state, and bulk-scope routes.
docs/targets/fu-kane-2009.md: original QSHI junction spectrum, local and bulk parity accounting, fractional Josephson response, switching-rate, telegraph-noise, and experimental-scope routes.
docs/targets/chandrasekhar-1931.md: original nonrelativistic comparison, relativistic equation-of-state, index-three-polytrope mass, ideal maximum- mass interpretation, and scoped synthesis routes.
docs/targets/oppenheimer-volkoff-1939.md: original relativistic hydrostatics, equations (11)-(19) cold-neutron formula package, numerical family, turning-point mass curve, free-energy stability, Tolman comparison, and qualified stellar-scope routes.
docs/targets/evans-cohen-morriss-1993.md: original proposed segment measure, thermostatted reversal, finite probability-ratio, molecular- dynamics, second-law, and qualified-scope routes.
docs/targets/gallavotti-cohen-1995.md: original dissipative-reversible, chaotic-hypothesis, SRB construction, long-time fluctuation-ratio, numerical-comparison, and qualified-scope routes.

The two Hall papers independently earn PhysicsLogic/Framework/TopologicalTransverseResponse.lean. The shared component contains only the gapped closed two-parameter family, response-curvature identity, integrality calculation, integer-unit normalization, and explicitly conditional gap-preserving stability. Magnetic Bloch momentum and many-body boundary twist remain distinct paper-local realizations. Its proof-free model retains all nine selected indices and all eleven route-used relation families. Each context owns one exact selected model, and route applicability consumes equality to it. Both paper adapters prove exact semantic retention and construct the direct established response from their paper-local setup and three outputs before recovering the generic route. Theory/model/world grounding requires the actual selected gapped-family setup but does not assume curvature identity, integrality, normalization, or the quantized-response route. A positive countermodel grounds the exact model while the technical route is false; exhaustive mutation theorems reject all nine index and eleven relation changes. The established result is definitionally the direct nonvacuous proposition containing the full gapped-family setup and all three calculation outputs at one model. A finite witness makes every retained index and relation directly active, while a vacuity countermodel proves that implication-valued calculations without setup cannot be grounded or counted as an inhabited response route. The five directional shared countermodels now retain a positive gap and parameter-cycle area, response unit, curvature integral, integer invariant, selected and comparison responses, curvature/integrality/normalization residuals, and the minimum deformation gap. A checked positive witness has unit gap, unit cycle, curvature and invariant one, and response one; separate witnesses falsify the curvature identity, integrality, normalization, other response, or actual gap openness. TKNN's eight paper-local witnesses retain magnetic flux 3/1, a gapped family, Kubo and phase-patching residuals, gap index three, Diophantine coefficients (s,t)=(0,1), and Landau level one, subband responses (0,1,0) with integer total one, distinct linear and strong electric fields, a nonzero tunneling rate, and interacting/disordered comparison strengths. NTW's seven witnesses retain a finite twist gap and size/correlation scales, fixed-twist responses 0,2 with average one, nondegenerate versus degree-three sectors, Chern-sum and parent-derivation residuals, bulk response and edge residual, and a gapless interacting, disordered comparison. No proposition-pair or Unit truth table replaces these distinctions. The optional deformation stage is also output-led. Its applicability route requires the established integer response, a selected connecting deformation, actual gap preservation, and a paper-local conditional stability calculation; its established endpoint stores only the direct response, open-gap setup, and stability output. That endpoint now realizes the mature protected-prediction contract between typed source and target ends of the selected deformation, preserving the response, integer witness, and response unit. TKNN's shared adapter still needs an independent open-gap premise because the original paper explicitly says gap nonclosure was unproved, while Niu-Thouless-Wu includes the open-gap condition in its selected deformation setup. Countermodels prevent a vacuous conditional calculation, a missing open gap, or a bare stability label without the source quantization from establishing the transfer.

The shared component now also records derivational provenance without collapsing the two constructions. A proof-free TopologicalTransverseResponseSourceConstraint stores the exact selected model, a typed paper-local derivation token, and its proposition-valued interpretation. TKNN realizes its token only from the magnetic-Bloch, bulk-Kubo, state-derivative, Stokes, boundary-phase-winding, integrality, and normalization stages. Niu-Thouless-Wu realizes a different token only from the many-body fixed-twist Kubo calculation, short-range/thermodynamic boundary insensitivity, twist averaging, first-Chern identification, integrality, and normalization. Both raw routes realize SourceStructuralTopologicalTransverseResponseExplanationAt; neither may consume the established or nonvacuous shared response.

The source-sensitive result extends through deformation only by also consuming the raw gap-preserving setup and conditional stability calculation. TKNN still requires an independent proof that the gaps remain open; NTW uses its explicit open-gap deformation setup. A finite converse model retains the completed response, ordinary structural explanation, open-gap stability, and protected transfer while making the source relation false. Thus common topological output and protection do not manufacture common derivational provenance.

TKNN 1982 and Haldane 1988 independently earn the coarser PhysicsLogic/Framework/GappedBandHallQuantization.lean. Its ordinary shared route retains the selected periodic noninteracting gapped-band setup, a paper-local integer-index calculation, and a paper-local transport normalization rooted in the same setup. The shared contract does not order those outputs: TKNN locally reaches integrality before normalization, while Haldane's Streda calculation supplies the signed index and response relation together. A separate value-bearing PhysicalSourceGappedHallReadout now retains TKNN's nonzero magnetic field, magnetic Bloch boundary winding, original r = s_r q + t_r p and 2 |s_r| < p branch, and sigma_xy = (e^2/h)(t_v + N - 1) formula without identifying them with Haldane's zero-net-flux honeycomb model. Haldane's paper-local source atoms retain all four coefficients of the printed honeycomb Bloch Hamiltonian, the opposite valley momentum commutators, the original relativistic Landau ladder, and its valley-signed, field-odd unpaired zero mode. The shared source readout retains the exact M ± 3 sqrt(3) t2 sin(phi) masses and distinguishes the number-density shift Delta n = e B/h from the printed electric charge-density shift Delta rho = e^2 B/h; the original Streda relation is sigma_xy = d rho/dB, not an additional multiplication by e. Its e = 2 witness also keeps the continuum and lattice half-indices dimensionless until their sum is multiplied by the conductance quantum. It separates trivial, anomalous, critical, spin-doubled, and Zeeman-metal realizations. The proof-free ordinary model retains all seven selected physical indices and all ten route-used relation families. Both adapters construct one named model, prove exact retention, exhaustively realize all nine shared claims, and derive grounding from the selected pre-output gapped-band setup plus paper-local interpretation inputs. Grounding assumes neither calculation nor response output. Converse models separate grounding from calculation, and a seventeen-component mutation audit detects every retained index and relation family. The established result is the direct nonvacuous proposition containing the complete setup, integer index, Hall conductance, and normalization relation at one actual model; both calculations and the route are reconstructed from it. A finite witness realizes it, while a countermodel blocks vacuous implication-valued calculations from masquerading as a completed physical route. A separate countermodel shows that a response plus an index-unit normalization relation does not itself supply the integer-index predicate. Named adapter theorems expose the seven indices directly and project the direct proposition from both papers. Haldane's occupied-band predicate is restricted to the anomalous description, and its Fermi-gap predicate is restricted to both that description and the selected honeycomb system rather than silently ranging over foreign models. Haldane's separate same-sign branch still selects one paper-local deformation object and requires both continuity and preserved gap along that object before transporting the zero-Hall index; the shared source readout independently distinguishes its zero-index phase.

Haldane's directional paper-local countermodels are now value-bearing. They retain canceling local fluxes (1,-1) with nonzero chiral hopping phase, anomalous corner masses (-1,1) and index one versus equally gapped trivial masses (2,2) and index zero, the continuum and lattice half-contributions, independently falsifiable Bloch coefficients, valley Landau terms, non-unit-charge number/charge density and direct Streda response, independent continuous-gap-closing and gapped-discontinuous deformations, and spin multiplicity two with Zeeman shift two against gap one. The named Streda setup itself now requires opposite masses and positive probe/Planck values. A checked positive witness realizes the source boundaries. No proposition-pair or status-enum truth table replaces these Haldane distinctions.

The complete shared route now also realizes the route-bounded RouteStructuralGappedBandHallQuantizationExplanationAt. Its constraint and phenomenon are distinct proof-free types. Satisfaction requires exact model selection, the inhabited gapped-band setup, and both calculations; necessity is proved by applying those calculations rather than by unpacking the established endpoint. TKNN reaches this theorem from magnetic-Bloch, Kubo, and phase-patching inputs. Haldane reaches it independently from opposite-mass weak-field spectral flow, filled-level counting, and the Streda relation. A model with all terminal response relations but no physical gapped-band setup shows that the phenomenon does not explain itself. The claim is limited to the selected integer-normalized response and does not add disorder, interaction, plateau, bulk-boundary, or universal-topology conclusions.

A second, source-sensitive projection keeps the two derivations distinct. GappedBandHallSourceConstraint retains the selected model, a typed paper-local derivation token, and its proposition-valued interpretation. TKNN realizes its token from magnetic-Bloch, Kubo-curvature, Stokes, and boundary-phase inputs; Haldane realizes a different token from opposite-mass weak-field Landau levels, spectral-flow counting, and the Streda relation. The generic source theorem requires both the realized token and the raw shared route. A finite countermodel retains the completed quantization, the route, and the response while making the source relation false, proving that shared output cannot manufacture derivational provenance.

Transfer-Complete Shared Components

The following reused framework contracts now have named paper-level theorems that transfer every retained shared claim to both a selected theory and a represented physical world through explicit grounding:

partition-zero/phase-boundary correspondence: Lee-Yang 1952 and BBCKK 2004; its output-led endpoint stores the actual finite-family, boundary, accumulation, and singularity outputs, its two-stage finite audit model realizes them, and direct activity theorems show that every selected index and relation family changes a route-used proposition;
tripartite sharing constraints: Coffman-Kundu-Wootters 2000 and AMPS 2012, with a context-owned exact selected model, retention of all tangle or entropy functions, an output-led conditional result, and grounding bounded by the actual three-party setup but independent of the monogamy or entropy-inequality output; the conditional exclusion now projects, only with an actual dominant demand, to a direct nonvacuous endpoint. CKW exposes that endpoint under explicit selected-pair saturation, while AMPS exposes it before thermal outgoing-mode entropy supplies the contradiction. Its composed bipartite-entanglement handoff distinguishes CKW's actually entangled dominant AB pair from AMPS's actually entangled competing BC pair: the first realizes an inhabited composed sharing endpoint, while the second contradicts the completed sharing exclusion through its positive entropy witness. Exact ordered subsystem placement, witness/demand equality, and paper-local tangle or strong-subadditivity calculations remain separate; finite models exclude missing calculation handoffs, missing sharing bounds, and relabeling one pair as the other. The source-sensitive composition also retains separate entanglement, sharing, and pair-to-demand derivations; an inhabited countermodel has both child source explanations and ordinary composition but lacks the independent handoff derivation. Its complete bound-plus-dominance route also realizes a typed structural explanation of the excluded positive competing demand. A distinct-setup countermodel retains that exclusion while removing the sharing bound, so the output does not explain itself. Its saturated finite audit model has positive demand and capacity, an implication-without-dominance countermodel blocks vacuous completion, and all ten retained fields directly change the nonvacuous endpoint;
anomaly-selected vacuum multiplicity: Witten 1982 and Seiberg-Witten 1994;
finite-symmetry vacuum counting: Witten 1982 and Seiberg-Witten 1994;
linear-response transport: Nakano 1956 and Kubo 1957;
accelerated-frame gravity: Einstein 1911 and Einstein 1916;
ground-density variational semantics: Hohenberg-Kohn 1964 and Kohn-Sham 1965, with selected-density admissibility and direct nonvacuous attainment/minimization retained;
broken-symmetry mode conversion: Nambu 1960 and Anderson 1963, with source-sensitive mode-conversion explanations checked to entail the shared ordinary mechanism while preserving their distinct derivations;
macroscopic coherence suppression: Zeh 1970 and GRW 1986, with exact retention of five selected physical indices and five relation families, branch-pair-setup-bounded grounding, eight-claim transfer, directional setup/output countermodels, a direct seven-fact nonvacuous stopping point, exhaustive direct mutation of all five selected indices and five relation families, and a typed mechanistic-explanation projection in which the environmental or localization process produces coherence suppression while the separate interpretation predicts unavailable interference. A converse model retains both outputs without mechanism action. A second, source-sensitive mechanistic projection retains the derivation of that process rather than only its selected mechanism token. Zeh's source requires dense-spectrum environmental correlation, equation (9)'s branch-dependent environment states, matrix-element suppression, autonomy, and noncommunication. GRW's source requires randomly timed localization, universal constituent-wise application, a macroscopically distinct pointer pair, amplified decorrelation, and an interference bridge. Neither source theorem accepts an established endpoint or ordinary explanation. A checked forgetful theorem strips only source provenance and recovers the ordinary mechanism from the same physical witnesses. A finite converse model completes both while falsifying source realization, so the common endpoint cannot identify universal linear environmental decoupling with objective stochastic collapse dynamics. Mixture, collapse, branch deletion, and outcome selection remain outside the shared projection. A checked value-bearing boundary readout now makes that stopping point substantive: it retains distinct weighted branches, coherence magnitude and operational threshold, full-state and reduced-pointer purities, a mixture-transition count and residual, and a selected-branch count and residual. Zeh realizes suppressed coherence and a diagonal reduced pointer with full purity one, zero mixture transitions, and no selected branch; GRW realizes the same suppression with full purity falling from one to one-half, one mixture transition, and exactly one selected pointer branch. A separate checked converse retains the produced mixture while withholding branch selection;
linear relative-state measurement: Everett 1957, Zeh 1970, and Rovelli 1996, with exact retention of thirteen selected objects and seven relation families, an output-led fifteen-fact endpoint, calibrated-setup-bounded grounding independent of correlation and record outputs, eighteen-claim transfer, converse models, and a twenty-field mutation audit. Each completed alternative is also exposed as a calibrated, present, correlated, relatively definite record branch. Everett and Rovelli independently map that branch to the neutral operational-observer contract through explicit physical-system, interaction, information-production, and information-availability bridges; Zeh is not promoted without those semantics. A completed-measurement countermodel with absent observer relations blocks name-based observerhood;
trapped-surface stability: Penrose 1965 and Hawking 1965, with exact retention of nine selected indices and five route-used relation families, route-independent grounding, seven-claim transfer, converse models, and a fourteen-component mutation audit;
adiabatic closed-cycle phase: Berry 1984 and Arovas-Schrieffer-Wilczek 1984;
planar exchange statistics: Wilczek 1982 and Arovas-Schrieffer-Wilczek 1984;
finite-velocity commutator cones: Lieb-Robinson 1972, Nachtergaele-Sims 2006, and Hastings-Koma 2006;
spectral-gap clustering: Nachtergaele-Sims 2006 and Hastings-Koma 2006, with a direct model-native completed clustering route, a false-setup vacuity countermodel, and fifteen selected-index plus sixteen relation-family direct mutations; the cone-supported source order now has its own direct endpoint and a countermodel showing generic clustering does not manufacture a finite-velocity cone; the complete route also realizes a typed structural explanation with a propagation-missing countermodel;
Bogoliubov particle production: Parker 1969 and Hawking 1975, with exact context-owned six-index/seven-relation model membership and incoming-vacuum-bounded, output-independent grounding; Parker's equation (52) coefficient norm and Hawking's equation (2.10) beta-row sum remain local; a nonvacuous route witness and direct activity audit cover all thirteen retained components; both routes realize a typed structural explanation of the distinct vacuum-to-outgoing-particle phenomenon, while a no-mode- expansion countermodel blocks occurrence-to-explanation; distinct typed Parker and Hawking source constraints additionally prevent a common completed route from erasing canonical-creation-coefficient versus asymptotic-beta-row provenance;
gravitational ray deflection: Einstein 1911 and Einstein 1916;
gapped incompressible fluids: Laughlin 1983 and Haldane 1983;
fractional Hall quasihole charge: Laughlin 1983, Haldane 1983, and Arovas-Schrieffer-Wilczek 1984, with a direct ten-component realized endpoint audit and three nested route-binding selections kept separate;
post-calibration prediction: KSW 1998, Bedaque-Hammer-van Kolck 1998, and Epelbaum-Gloeckle-Meissner 1999;
brane worldvolume decoupling: Maldacena 1997 and Itzhaki et al. 1998. Its exact proof-free model retains all five selected indices and all eight route-used relations. Each paper-local context owns its five physical selections and exposes one unique selectedModel. Model use, representation, entailment, grounding, and route applicability require that exact model; both papers supply their named retention certificate independently of the later survival and mutual-decoupling calculation. A thirteen-component mutation audit shows that every index or relation change fails the original context's exact semantics. The setup requires pairwise distinct parent, worldvolume, and asymptotic-bulk descriptions. The established result is output-led: it combines exact selection with NonvacuousBraneWorldvolumeDecouplingAt, which retains setup, survival, both sector assignments, and both decoupling directions but no implication-valued calculation. That calculation is reconstructed from the realized outputs. The completed D3 and D2 routes also project to a typed derivational- reduction endpoint whose parent object retains the open-string description, asymptotic spectator, brane system, and limit, and whose reduced object retains the surviving worldvolume description. Realization requires setup, survival, and sector membership; support and exhibition require the full mutual-decoupling decomposition. Survival-only and one-way-decoupling countermodels block weaker routes. A separate proof-free source description now retains the exact model and a typed paper derivation. Maldacena's token requires the D3 setup, fixed-U scaling limit, superconformal specialization, and open-string calculation. Itzhaki et al.'s token requires the D2 setup, its field-theory scaling, and the D2 decoupling calculation. That D2 scaling explicitly retains positive alpha' tending to zero, fixed U, fixed field-theory energy, and gYM^2 = gs / sqrt(alpha'). Both source routes yield the same reduced description and behavior without identifying the derivations. A completed route with an always-false source relation has no source-sensitive reduction. The projection asserts no AdS/CFT, physical equivalence, emergence, multiple realization, or unique recovery. Grounding requires the selected setup and no survival or decoupling output. False-setup and setup-complete/no-decoupling witnesses guard both boundaries, while a distinct-role finite model makes all five selected data and eight relation families directly mutation-sensitive;
finite-precision trajectory predictability: Miller 1964, Portegies Zwart-Boekholt 2014, and Lorenz 1963, with shared setup replay at the divergence and reliability stages and a direct structural explanation of deterministic point-prediction failure;
equilibrium noise-dissipation: Nyquist 1928, Callen-Welton 1951, and Kubo 1957, with an inhabited frequency-resolved equality and direct activity for all nineteen retained components, plus a typed structural-explanation projection and an equation-only/no-readout countermodel;
field-free magnetic interference: Aharonov-Bohm 1959 and Berry 1984, with distinct split-beam and exact transported-box source tokens, ordinary and source-sensitive structural explanations, and a false-source converse;
forward-amplitude positivity: Adams et al. 2006 and Komargodski-Schwimmer 2011, with five context-owned selected indices, a unique model retaining fourteen relation families, an exact-model certificate consumed by route applicability, setup-bounded output-free theory/world grounding, an output-led established endpoint with reconstructible audit contracts, grounding-without-result countermodels, a direct nonvacuous positivity proposition with source-anchored paper realizations, a false-forward-setup vacuity countermodel, nineteen direct mutations, and nineteen exact-retention mutations. The complete dispersive route also realizes a typed structural explanation of the identified positive coefficient; a positive-coefficient/analytic-branch model with no optical theorem refutes the shortcut from sign to explanation. Adams grounds its regulated channel setup and maps its direct established positivity result; Komargodski-Schwimmer grounds the low-energy theorem and constructs the direct dispersive result before reconstructing the route; its five shared countermodel theorems now retain actual regulator/cut, analytic/crossing, contour, optical, cross-section, spectral-weight, integral, coefficient, interpretation, and grounding residuals. Adams's five paper-local scope countermodels additionally retain the stable-vacuum kinetic sign, controlled constant-gradient background, negative leading coefficient, Goldstone fluctuation equation and widened cone, regulated cut/pole locations and power-corrected sum rule, zero-interaction strictness failure, and the massless G_N s^2/t graviton pole;
body-dependent self-gravity response: Nordtvedt 1968 and Eardley 1975, with exact retention of seven selected objects and nine relation families, inhabited-setup-bounded and output-free grounding, twelve-claim transfer, grounding-without-route models, an output-led established endpoint with explicit unequal-body and unequal-response witnesses, source-anchored paper realizations, a theorem excluding false-setup grounding, a separate false-common-field vacuity countermodel, direct activity for all seven indices and nine relation families, and a sixteen-field exact-model mutation audit. The complete route also realizes a typed mechanistic explanation: the body comparison, distinguished responses, common external field, and paper-local effect remain separate roles. A response-collapse countermodel retains both the effect calculation and attribution but refutes the mechanism. A second, source-sensitive activity now keeps Nordtvedt's general- metric and stationary-bound-system derivation distinct from Eardley's field-dependent-mass, compact-sensitivity, and scalar-dipole derivation. Both are rebuilt from raw paper-local premises rather than established outputs; a checked forgetful theorem recovers the ordinary response mechanism from either source-sensitive explanation, while a completed common route with its ordinary mechanism but a false source relation proves that neither derivation can be reconstructed from the shared result. Nordtvedt's independent paper-fidelity certificate additionally checks the original weak-field values omega = 6, coefficient -1/8, binding fraction 1/10, test response 1, massive response 79/80, external field 2, and distinct accelerations 2 and 79/40. Separate inhabited controls distinguish test-body universality from massive-body universality and reject Einstein cancellation, a vanishing external field, or vanishing gravitational binding as substitutes for the Brans-Dicke effect. Eardley's paper-local semantics additionally retain the original seven-row neutron-star table, sensitivity-dependent pair-force cross term, scalar charge (1-s)*M/(2*omega+4), complete eccentric-orbit dipole decay, separately rounded PSR 1913+16 estimate with observed mass function kept distinct from reduced mass, and the original varying-gravity/inertia/clock equations. Physical witnesses establish ordinary-matter and identical-body dipole cancellation, negative decay for unequal sensitivities, and a black-hole companion with zero scalar charge and clock variation but nonzero dipole decay. Distinct selected orbital positions and unequal selected sensitivity values now force the actual nonzero scalar dipole and negative decay, while result-level theorems independently derive the identical-PSR and black-hole-companion alternatives;
spin-orbit shell closure: Mayer 1949 and Haxel-Jensen-Suess 1949, with context-owned exact 18-component retention, named exact selected-setup grounding, seventeen-claim transfer, Mayer's checked Table I twiceJ + 1 = capacity formulae for the selected high-j rows, converse models, and an eighteen-component semantic mutation audit in which every change fails the original exact semantics, plus a shared mechanistic-explanation projection that keeps empirical prediction short of physical explanation without the separate account bridge, and separate ordinary/source-sensitive structural explanations so shared route logic cannot manufacture paper provenance;
thresholded collapse abundance: Press-Schechter 1974 and Bond et al. 1991, now also realizing a scoped derivational reduction from threshold counting and mass accounting to the normalized differential spectrum through direct source-input routes, independently of their terminal-result compatibility adapters;
boundary Majorana modes: Kitaev 2001, Oreg-Refael-von Oppen 2010, and Fu-Kane 2009, with source-anchored direct nonvacuity adapters, a false-setup vacuity countermodel, and nine selected-index plus twelve relation-family activity mutations, plus a typed structural-explanation projection whose converse model retains two classified gapped phases but no boundary solution; governed source-valued witnesses additionally retain Kitaev's paired-chain criterion and nonzero finite-wire splitting, the nanowire critical surface B^2 = Delta^2 + mu^2 and double-mode pairing wall, and Fu-Kane's 2 pi Hamiltonian versus 4 pi fixed-parity branch;
parity-resolved fractional Josephson response: Kitaev 2001 and Fu-Kane 2009, with direct nonvacuity adapters, a false-setup vacuity countermodel, six selected-index plus eleven relation-family activity mutations, and a typed structural-explanation projection that rejects both branch-only and uninterpreted-current routes;
three-body pairwise-input insufficiency: Thomas 1935 and Bedaque-Hammer-van Kolck 1998, with a typed nonvacuous stable-prediction determination projection, ordinary plus distinct source-sensitive structural explanations, and countermodels for label independence and source-provenance self-reconstruction;
bulk-boundary scalar mass-dimension semantics: Gubser-Klebanov-Polyakov 1998 and Witten 1998.
scalar-correlator composition: Gubser-Klebanov-Polyakov 1998 and Witten 1998, consuming both shared child results plus exact paper-local links and a distinct two-point scaling calculation.
balance-law conservation: Noether 1918 and Einstein 1916;
equilibrium sampling: Metropolis et al. 1953 and Creutz 1980, with balance, target-space accessibility, asymptotic equilibration, and equilibrium interpretation retained as distinct obligations;
reciprocal transport: Onsager 1931 and Casimir 1945, with a finite opposite-parity, field-reversed realization and direct activity for all four selected indices, three retained functions, and seven physical relation families; their shared reversible setup projects to a typed physical field-reversal symmetry, while a finite countermodel keeps that symmetry short of macroscopic regression and coefficient reciprocity. Typed source-sensitive explanations separately retain Onsager's zero-field heat derivation and Casimir's parity/field-reversal/independent-regression derivation, with a countermodel blocking source reconstruction from the completed shared route; their value-bearing field-reversal boundary separately retains nonzero H, -H, trajectory balance, parity, and selected cross coefficients;
remote correlation prediction: EPR 1935, Bohr 1935, and Bell 1964, with Bohr retaining the original separated double-slit pair, alternative position/momentum values, and explicit rejection of joint measurement and common reality, while Bell retains its concrete spin-singlet data and separated-measurement stage; all three give direct source-sensitive structural explanations of inhabited certainty without disturbance;
vacuum metric dynamics: Einstein 1916 and Schwarzschild 1916, with an output-led direct endpoint, reconstructed equation and motion bridges, and selected-physical-setup-bounded grounding;
random-displacement diffusion: Einstein 1905, Smoluchowski 1906, and Linde-Linde-Mezhlumian 1993;
transverse Meissner screening: BCS 1957 and Nambu 1960;
protected-index transport: Witten 1982 and Strominger-Vafa 1996, with a direct output-led source-to-target endpoint, pointwise transfer calculation, a typed structural explanation of the situated target indexed prediction, a target-occurrence-without-explanation countermodel, and seven selected-object plus nine relation-family direct mutations; Strominger-Vafa separately retains its Cardy logarithmic-growth and charge-substitution formulas locally;
planar diagram expansion: 't Hooft 1974 and Witten 1979;
RG endpoint monotonicity: Zamolodchikov 1986 and Komargodski-Schwimmer 2011, with a direct model-native endpoint, a false-setup vacuity countermodel, and ten selected-index plus ten relation-family direct mutations;
exact regulated scale flow: Wegner-Houghton 1973 and Wetterich 1993, with output-led full and projected results, setup-bounded grounding, a direct nonvacuous full-flow-plus-projection endpoint, and exact/direct audits of six selected indices and four route relations; Wegner-Houghton now separately retains the original p. 403 equation-(2.20) value-level sharp-shell formula with its shell logarithm/open-line quotient, momentum renumbering, volume, field, and trace contributions, plus an idempotent shell-erasing retained-configuration projection and explicit angular integral, Fourier-sum, positive projected-Hessian, derivative, and primed-momentum obligations. Wegner-Houghton also separately retains the pp. 405-406 controlled-epsilon coefficient package for v4, v2(k), eta, and y_1s as selected truncated values tied to the invariant n-vector expansion; source-valued framework controls independently check the selected v4 = 1/180, v2 = 59/60, eta = 1/5400, and y1 = 59/30 without adding them to the neutral endpoint. Wetterich separately retains the original equation-(2) value-level trace formula partial_t Gamma_k = 1/2 Tr[(Gamma_k^(2) + R_k)^(-1) partial_t R_k] with an explicit positive scale path satisfying dk/dt = k, plus regulator-derivative, actual two-sided inverse, trace, and differentiability obligations. The formula is derived from the connected trace calculation and retained by the paper-supplied shared relation, without adding Wetterich-only conventions to the neutral framework. Separate controls retain the modified Legendre subtraction, independent infrared/ultraviolet endpoint conditions, distinct Goldstone and radial denominators, truncation-without-error-control, zero-momentum regulator caveat, and unproved constrained-action equivalence;
homogeneous cosmic expansion: Friedmann 1922 and Lemaitre 1927, with an exact eight-index/nine-relation shared model, source-ordered field-equation, branch-selection, and interpretation stages, and a typed structural explanation. Both papers now realize that explanation directly from their original calculation inputs before a terminal paper or shared expansion result exists. Friedmann executes the stationary/nonstationary split, nonstationary reduction, root classification, and monotone-world calculation before applying a separately reconstructed curvature-radius interpretation; Lemaitre executes the variable-radius field equations and constant-mass increasing solution before applying his explicit expansion interpretation. Distinct typed source constraints retain those reconstructed-versus-explicit derivations even though both explain the same shared phenomenon. A finite false-provenance countermodel shows that a completed route does not itself realize either paper derivation. Their terminal-result adapters remain compatibility paths.
finite-parameter congruence focusing: Raychaudhuri 1955 and Penrose 1965, with exact retention of eight selected indices and ten route relations.
qualified nebular distance-velocity calibration: Lemaitre 1927 and Hubble 1929. Lemaitre locally retains its exact equation-(22) period/radius/Doppler chain and separate equation-(23) nearby-source R'/R = v/(c r) formula; those source-specific redshift semantics are not exported into the shared qualified-fit contract.
causal-domain defect formation: Kibble 1976 and Guth 1981, with output-led established semantics, exact selected-model and independent-domain grounding, a setup-complete countermodel with no formation output, a direct nonvacuous endpoint, and an eighteen-component direct activity audit.
exact quantum error recovery: Calderbank-Shor 1996 and Steane 1996, with a context-owned exact model retaining twelve selected indices and fifteen route relations; output-led intermediate and terminal results record direct recovery facts and reconstruct calculation routes, both papers provide direct encoded-state and environment-action setup witnesses for grounding, setup-complete grounding remains independent of every recovery output, recovery outputs cannot replace the selected setup, and a finite witness makes all twenty-seven model components directly active. The complete route additionally realizes a typed mechanistic explanation: complementary syndrome/recovery operations act on a supported environment-coupled error, organized production is arbitrary-error reduction, and the separate prediction is restoration plus environmental decoupling. Countermodels block both prediction without recovery activity and organized reduction without decoupling. Both papers now also reach this explanation directly from source-stage inputs, before a terminal paper result or shared recovery endpoint is available. Calderbank-Shor executes nested-code construction, supported decoherence, bit recovery, phase recovery, and arbitrary-error restoration in order. Steane executes the coset construction, supported defection, basis-one recovery, basis-two recovery, and final restoration and disentanglement in order. Steane's paper-local basis-two calculation now also retains author-TeX equation Cij as the finite signed (-1)^(wt(j and l)) syndrome sum over complex state-coordinate amplitudes; that normalization is not promoted into the shared route. The generic route-to-mechanism theorem now obtains the direct nonvacuous endpoint without passing through an established-result wrapper. A stronger source-sensitive activity pairs the ordinary recovery activity with a typed paper derivation and an independent realization relation: Calderbank-Shor supplies nested-code Fourier decoding and logical-state-independent ancilla/environment factorization, whereas Steane supplies coset parity checks, the residual-entanglement intermediate, and final apparatus/environment disentanglement. A checked forgetful theorem recovers the ordinary recovery mechanism from either source-sensitive explanation. A finite countermodel retains the complete shared route and ordinary mechanism while falsifying the source relation, so common recovery behavior cannot reconstruct historical derivational provenance. The older terminal-result projections remain compatibility adapters. A genuinely carrier-polymorphic NoCloningExactRecoveryHandoff now also composes the actual selected recovery model with an independently selected no-cloning model through proposition-valued unknown-state identification, distributed-encoding, syndrome-privacy, and independent-copy relations. Its stronger sourced result retains exact selection of both child contexts, their independent recovery and no-cloning explanations, and a third physically specific encoding-compatibility derivation. Calderbank-Shor's version retains both nested-code expansions and the separate syndrome ancillas; Steane's retains the selected coset, equation Cij, and both parity-check apparatus records. Independently typechecked downstream clients supply the no-cloning arguments from Wootters-Zurek and Dieks, respectively, while countermodels reject an actual independent copy and a missing compatibility derivation even when both child explanations hold. The independent paper-local coding results now also retain their actual binary-entropy formulas: Calderbank-Shor distinguishes the weakly self-dual classical dimension from the encoded quantum dimension, retains R = (n - 2k) / n >= 1 - 2 H_2(d / n), and separately retains the abstract's 1 - 2 H_2(2t / n) achievable rate. Steane retains the distinct code dimensions k_1 + k_2 = n + K, the proved two-distance Hamming upper bound, the general Gilbert-Varshamov lower bound only under its explicitly unproved simultaneous-code conjecture, the separately proved equal-distance case, and the printed inverse-entropy window and numerical estimates. Independent countermodels prevent a named rate from replacing either paper's formulas, prevent a counting bound from replacing its abstract error-rate formula, and prevent a conjectural numerical window from establishing general code existence or noisy-channel capacity. A separate finite source-grounded witness now also computes Calderbank-Shor's exact printed sixteen-word Hamming table and signed 1/4 logical amplitudes, Steane's printed simplex generator and parity-check matrix, their distinct coordinate conventions, eight-word logical cosets, GF(2) syndrome equations, and actual syndrome-directed single-qubit recovery. Every syndrome identifies the physical error without revealing the logical coset; equal same-qubit amplitude/phase syndrome values retain distinct basis-tagged apparatus records. A first-plus-second-qubit error aliases a single-qubit syndrome and flips the recovered logical coset in both source conventions. Nine new independent physical fidelity boundaries reject Boolean-only parity certificates, invented syndrome records, collapsed correction bases, erased Calderbank-Shor relative phases, mixed Steane cosets, and unsupported two-error recovery. No collapse, threshold, or fault-tolerance claim is imported into the shared recovery framework. The general coherent refinement additionally binds both paper routes to actual local recovery matrices and binary X/Z component equations. Their certified exact-recovery results expose restored reduced density and a normalized common environment factor. Four further fidelity boundaries use actual isometric basis-recording and relative-phase interactions to distinguish coherent recovery from basis-only recovery and private apparatus probabilities.
subthreshold excitation stability: Landau 1941 and Bogoliubov 1947, with exact retention of seven selected indices and fifteen route relations; both source-facing paper chains directly realize distinct typed derivations of the shared structural explanation before any terminal paper or shared endpoint is available; a provenance countermodel prevents the shared route and ordinary explanation from identifying those derivations.
momentum-resolved variational bounds: Feynman 1954 and GMP 1986, with exact retention of eleven selected indices and seventeen route relations; an inhabited route and exhaustive direct activity for every component; both source-facing calculation chains directly realize the typed structural explanation before any terminal paper or shared endpoint is available; Feynman's terminal established spectrum supplies the shared adapter without replaying its variational contract, and its false-setup countermodel blocks seven vacuous local calculations; GMP's terminal established projected bound likewise supplies its adapter without replaying the unprojected, projection, or energy contracts, and its staged countermodel blocks all nine vacuous paper calculations; Feynman-Cohen 1956 is a dependent reuse client whose full local route reaches the shared component only after independently established trial, norm, numerator, quotient, and upper-bound outputs. The two terminal routes remain compatibility adapters. A countermodel shows that a declared inequality without the quotient route does not explain itself.
one-parameter localization scaling: Abrahams et al. 1979 and MacKinnon-Kramer 1981, with context-owned exact retention of eight physical indices and fourteen relation families; both project to one direct nonvacuous scoped-scaling proposition, while their analytic and finite- numerical methods remain paper-local; both realize the ordinary shared structural explanation from the applicable route and separately realize source-sensitive refinements from their source-local derivations, while a converse model keeps the endpoint, route, ordinary explanation, and phenomenon but refutes source-provenance self-reconstruction.
resolvent-decay localization: Anderson 1958 and MacKinnon-Kramer 1981, with distinct selected kernels and descriptors; each context owns five selected indices, and both papers project to one direct nonvacuous scoped-localization proposition that stores no implication-valued route contract; the complete route is reconstructed from direct descriptor, decay, localization, and scope outputs. Grounding requires each paper's physical propagation setup but no decay or localization result. A countermodel realizes every direct output at a non-selected model and proves that those outputs cannot ground it. Mutations of every index and all eight predicate families destroy that proposition as well as failing exact selected semantics.
operational error-disturbance: Heisenberg 1927, Bohr 1935, and Ozawa 2003, with the corrected microscope, fixed-diaphragm slit and local recoil, and operator-universal calculations kept distinct by their selected measurement data and paper-local predicates; all remain distinct from prepared-state dispersion uncertainty, and Bohr's local recoil does not become remote EPR mechanical disturbance.
magnetic mass-deformation consistency: Seiberg 1994 and Kutasov-Schwimmer 1995, with fundamental one-color and nilpotent-adjoint-chain k-color Higgsing kept distinct through their selected condensates and rank data; F-term response, condensate, Higgsing, reduced parameters, and rank matching are separate calculations with exact retained outputs, while countermodels separate every missing stage, outputs from setup, consistency evidence, and duality proof. The output-led established result is exact selection plus a direct nonvacuous proposition requiring setup, all five calculations, all five outputs, evidence, and explicit nonproof at one model; a positive finite witness and direct mutations of all ten indices and eleven relation families audit that endpoint itself. Complete direct outputs under the wrong selected description cannot establish or ground themselves.
exact exterior vacuum-metric solutions: Schwarzschild 1916 and Kerr 1963, with static point-mass integration and algebraically special rotating-mass construction kept distinct; vacuum verification, exact expression, asymptotic matching, and scoped regularity are sibling paper-local certificates rather than a shared chronology. Schwarzschild keeps asymptotic behavior as a problem condition and continuity in the integration; Kerr keeps vacuum/expression and flatness/ring-scope pairs in their local routes. Checked countermodels reject all three artificial predecessor arrows. Grounding now requires SelectedExteriorVacuumSetupAt: exact model selection plus an actual physical metric, governing field equation, exterior-vacuum situation, and paper-local construction, with none of the four outputs. Schwarzschild's construction setup stops at the determinant-preserving polar construction rather than importing the reduced field-equation calculation; Kerr's stops at the selected null tetrad rather than importing the already-calculated branch equations. Kerr's exact- expression adapter additionally consumes its value-level displayed stationary line-element formula; the Euclidean-radius quartic remains paper-local and is not promoted into the shared interface. Each context owns its four selected indices, and mutations of every index and all eight relation families directly fail exact selected semantics. Kerr's eleven paper-local countermodels are now value-bearing: zero time/azimuthal derivatives coexist with vacuum residual one; a nonzero imaginary rotation component can accompany an exact Type-D vacuum metric; r=1, theta=0, m=a=0, du=dt=k=1 yields line elements -1; r=2 with R=x=1 violates the radial quartic by twelve; the ring R=a=1, z=0 remains exceptional; and EIH orders (2,1), zero approximate higher multipole, no exact invariant definition, and a desired but unsampled interior preserve the original scope. No status enum or proposition wrapper replaces these Kerr distinctions. The established route also projects definitionally to selected semantics plus a model-native nonvacuous proposition requiring the physical setup and all four realized outputs; the implication-valued calculation contracts and complete technical route are reconstructed from those outputs. A false physical setup cannot ground, while setup-complete grounding with false outputs does not manufacture the route. The complete route also realizes a typed structural explanation: its constraint retains the exact selected metric, exterior situation, boundary, construction, and applicable route, while its distinct phenomenon is the direct nonvacuous exact exterior solution. Schwarzschild and Kerr expose separate paper theorems for this projection. Completed outputs with the physical setup removed fail the explanation, so this adds no generic GR, uniqueness, horizon, interior, or global-causal claim. The applicable route now yields that direct phenomenon without an established-result detour. A stronger source-sensitive constraint keeps Schwarzschild's determinant- preserving spherical reduction, exact integration, continuity, and point- source scope distinct from Kerr's algebraically special null congruence, degenerate stationary branch, asymptotically flat transformation, and ring scope. A finite countermodel retains the common route, established endpoint, and ordinary explanation while denying source derivation, so shared exact metric behavior cannot certify historical provenance. The same twelve mutations falsify the direct solution proposition itself. A construction mutation also directly breaks construction selection and the indexed vacuum output. The distinct paper-local constructions carry the route difference without an inert enum. Uniqueness, free motion, EIH parameter identification, multipoles, horizons, and global causal structure remain paper-local or outside the source scope.
self-gravitating equilibrium mass limits: Chandrasekhar 1931 and Oppenheimer-Volkoff 1939, with their ultrarelativistic index-three-polytrope and relativistic numerical turning-point constructions kept paper-local; each supplies an explicit bridge from its calculation, finite mass, and retained scope to its distinct maximum-equilibrium interpretation. Each context owns seven selected components, and mutations of every component and all eleven predicate families directly fail exact selected semantics. Every selected value also changes a predicate used by the route, independently of whole-model equality. The established endpoint is output-led: selected semantics plus the direct setup, equation-of-state, equilibrium-mass, finite-limit, scope, and maximum-interpretation facts. Its contracts and applicability route are reconstructed. Chandrasekhar and Oppenheimer-Volkoff separately expose source-native physical setups for grounding, before the n = 3 selection or relativistic hydrostatic reduction is calculated. A setup-complete grounded model can still have every downstream output false. Chandrasekhar's paper-local setup also retains positive electron and mass densities, molecular weight, hydrogen-atom mass, Planck constant, and light speed, together with a nonnegative ion/electron ratio. Its exact n = rho/(mu H (1+f)) equation stays distinct from the qualitative usually-negligible-f approximation: positive f strictly changes the density, while exact agreement with the dropped-f formula would force f = 0. The shared framework's source-shaped validation model likewise uses a positive ratio and keeps its exact correction and approximation premise independently mutable. Oppenheimer--Volkoff's original pp. 378-380 now also distinguish the selected equilibrium's 0.71 M_sun gravitational mass from its greater fixed-particle-number proper rest mass: M_rest = N m_n and M_binding = M_rest - M_gravity > 0. Their approximately ten-percent excess is represented by an explicit nonzero approximation tolerance, not an invented exact M_rest = 1.1 M_gravity; both exact and genuinely nonexact source-valued witnesses satisfy the same physical contract. This neutron-star accounting is absent from Chandrasekhar's neutral shared route. Stability, realistic high-density matter, nonstatic evolution, horizons, and black holes remain paper-local or unresolved. The complete applicable route also projects to a typed structural explanation. Its proof-free constraint and phenomenon both retain the body, matter, gravity, equation of state, equilibrium construction, mass, and regime, while satisfaction requires the full calculation and separate maximum-equilibrium interpretation bridge. Chandrasekhar and Oppenheimer-Volkoff expose direct and granular paper adapters. The former reconstructs the equation-of-state, polytropic-mass, and interpretation stages; the latter reconstructs relativistic equilibrium, the cold-neutron family, mass curve, and qualified scope. A finite scoped mass without interpretation fails the phenomenon, and a declared maximum-mass output with invalid equilibrium setup fails the explanation. Thus the projection explains only the selected model's equilibrium limit, not a universal mass bound or dynamical stellar fate. A source-sensitive projection now keeps the two derivations distinct. Chandrasekhar's token requires the relativistic electron equation of state, imported index-three polytrope calculation, and separate ideal-limit interpretation. Oppenheimer--Volkoff's different token requires the GR hydrostatic reduction, cold-neutron numerical family, turning-point mass curve, stability and Tolman branches, and qualified high-density scope. The generic source theorem consumes the realized token plus the raw shared route. A countermodel retains the complete result, route, and phenomenon with a false source relation, proving that a common maximum-mass shape does not identify the calculation that produced it. The stellar paper countermodels now also retain their source-shaped values instead of enum truth tables. Chandrasekhar keeps the relativistic density threshold, pressure/composition and four-thirds relations, polytropic index, gram and solar reports, density-profile mismatch, and model/world values. Oppenheimer--Volkoff keeps regular hydrostatics, the cold-Fermi pressure and density formulas, sampled rise/turn/drop masses, free-energy curvature and a possible continuity jump, repulsive-pressure correction, compactness, contraction-time bound, and central-density grounding mismatch. These witnesses block setup-to-calculation, turning-point-to-stability, exact-equation-to-physical-domain, vanishing-denominator, nonzero-ratio-to-zero-ratio, exact-to-dropped-composition, formal-pressure-to-positive-pressure, ideal-to-actual-matter, and static-limit-to-horizon shortcuts without identifying the two stellar constructions.
critical-collapse scaling: Choptuik 1993 and Evans-Coleman 1994, with separate threshold-outcome, mass-scaling, and vanishing-mass calculations; Choptuik additionally retains its paper-local printed M_BH = 2 r_BH horizon readout, separately formalizes the preceding apparent-horizon threshold 2 M_BH = r_BH, proves the two formulas incompatible at positive radius, and retains the tolerance-bounded equation-(12) fit c_f |p - p*|^gamma, and Table II interval 0.366 <= gamma <= 0.380 through its calculation and complete conclusion without promoting those one-paper formulas into the shared layer; typed countermodels showing that threshold outcomes do not imply a mass fit, a positive fit does not supply its limiting bridge, completed outputs do not reconstruct their setup, and technical completion and physical grounding are independent in both directions. The established result is output-led: it retains exact selected semantics and a direct nonvacuous model-native scaling proposition requiring an actual threshold setup and all six completed outputs at one model, while reconstructing the three route contracts only when needed. Grounding requires the threshold setup but no outcome, mass-fit, limiting, route, or terminal result. A false-setup witness blocks vacuous implication-only success, and a route-shaped finite model makes all nine selected indices and twelve relation families directly mutation-sensitive. A source-sensitive structural projection additionally distinguishes Choptuik's adaptive Einstein-scalar threshold search and mass fit from Evans--Coleman's Gaussian radiation-fluid numerical route. Their independent self-similar ODE construction is not used to obtain that shared token. A false source relation can coexist with the complete route and all outputs, so numerical and conjectural status and local/global similarity scope remain paper-local. Source-sized scalar countermodels retain the 3.44 echo period, family-indexed residuals and fitted exponents, the Table II interval, actual one-sided vanishing mass, and a nonzero visibility residual. Radiation-fluid countermodels retain local and exterior metric data, transient near-critical similarity, the 0.129 redshift exponent, distinct 0.36 and 0.37 numerical matter exponents, and the absence of a proved visible singularity or universal matter exponent.
linear state-replication obstruction: Wootters-Zurek 1982 and Dieks 1982, with basis-state copying, deterministic output uniqueness, the calculated linear superposition output, and comparison with the required clone output retained as separate obligations; twelve shared claims transfer through exact paper-local interpretations whose contexts own all nine selected indices, typed countermodels block each missing stage and output-to-setup reconstruction, and a finite three-state/four-output model realizes the output-led direct obstruction. Grounding requires exact selection, the inhabited two-state setup, and deterministic output uniqueness, but no calculated output, mismatch, route, or obstruction. All nine selected indices, the clone-output function, and all eight relation families are active in that physical route, independently of the older exact-semantics mutation audit. Both papers derive the direct nonvacuous proposition from their source-local calculations; polarization, spin, EPR protocols, statistics, and causal mechanisms remain local. Dieks's repeated-trial and one-run conclusions additionally realize the narrow nonvacuous operational signal-exclusion interface, independently of Minkowski's stronger light-cone propagation realization. His p. 272 multiplier calculation separately retains signed sqrt(2)/2 coherent branch amplitudes, the orthogonal (N/2,N/2) occupation sector, and exact probabilities (1/2,1/2,0); source-level countermodels prevent either named branches or matching classical probabilities from replacing that actual quantum calculation. The direct obstruction now also realizes a typed structural explanation: the constraint retains the exact selected states, device, ready state, linear output, required clone output, deterministic uniqueness, and output mismatch; it necessitates the distinct arbitrary-replication exclusion phenomenon. The necessity proof rederives exclusion rather than consuming the endpoint's stored conclusion. A model with the exclusion and terminal outputs but no valid replication setup blocks the converse. A typed source constraint now distinguishes Wootters-Zurek's six-input polarization and apparatus-record derivation from Dieks's five-input spin-multiplier derivation. Both raw routes invoke the same substantive contradiction without consuming their completed obstruction paths. A further model has the completed obstruction, valid route, and exclusion phenomenon but no source-sensitive explanation when the derivation relation is false. Separate original-source physical controls now retain Wootters-Zurek's normalized polarization and sqrt(2)/2 example, actual complex apparatus-record overlap and two-by-two reduced photon density matrix, Tr(rho^2) purity, physically distinct record rays versus phase-equivalent unequal vectors, and partially coherent nonorthogonal records. Independent witnesses retain overlap -1 with purity 1, overlap 0 with purity 337/625, and overlap 3/5 with purity 11017/15625. The common actual record-state construction now comes from FiniteQuantumState.TwoBranchRecordState, shared with Zeh. Wootters-Zurek retains the symmetric VV/HH embedding into a full two-photon density and a separate apparatus trace. The main route derives pair mixedness for physically distinguishable records and pure-clone exclusion from explicit density identifications, not free mixed-output or mismatch conclusions. It no longer excludes unequal phase-equivalent records: their actual pair is pure but the general density comparison still forbids the tensor-square clone. A pure correlated pair can have mixed single-photon marginals and is not the tensor-square clone. The source also retains nonzero ordered alpha beta tensor-square cross terms, equal stimulated/spontaneous emission, random companion polarization, and explicitly unfinished experiment. Dieks now has a genuine electron-spin multiplier with orthogonal x+/x- states and a z+ superposition rather than an abstract nonorthogonal-photon surrogate. His coherent burst retains exact (1/2, 1/2, 0) Born probabilities; an illustrative N = 4 independent-copy hypothesis gives half-split probability 3/8 while actual linear evolution gives zero. Thirty-two mutations separately reject apparatus, tensor, emission, singlet, orthogonality, occupation, signalling, and epistemic-scope collapses. Dieks's joint burst now has actual machine-record/occupation basis states, signed real sector amplitudes, and an off-diagonal coherence of 1/2 or -1/2. Different source phases give identical observable occupations, equal machine records do not destroy occupation-sector orthogonality, and false coherence or orthogonality reports cannot replace the physical equations. The independent Born-rule countermodel remains normalized without silently deriving probabilities from the branch state.
entropy-production fluctuation structural explanation: Evans-Cohen-Morriss 1993 and Gallavotti-Cohen 1995, with a typed qualified-ratio constraint retaining the selected dissipative setup, source-specific reversal pair, represented probabilities, implication-valued probability-weight calculation, and qualified scope, but no calculated ratio. The calculation necessitates the distinct leading probability-ratio phenomenon. Reversal and represented probabilities alone do not calculate the ratio, while a finite converse model declares the ratio in an invalid setup and hence has no structural explanation. ECM's adapter consumes its equation-(8) calculation without an established ratio or second-law result; GC's adapter consumes its SRB weight calculation without an established fluctuation- symmetry result. No output-led endpoint is converted into an explanation. A stronger source-sensitive projection retains two noninterchangeable typed derivations: ECM's proposed finite-segment natural weight plus fixed-shear aggregation, and GC's SRB/Markov-partition time-reversal Jacobian ratio. Each is extracted from direct paper inputs before invoking the generic source theorem. A completed qualified route and ordinary explanation with an unrealized source relation has no source-sensitive explanation, so the common leading ratio cannot manufacture derivational provenance.
complete-integral structural reconstruction: Hamilton 1834 and Jacobi 1837, with a typed constraint retaining the selected first-order equation, complete parameter family, endpoint evolution, and separate momentum, parameter-selection, dynamics-recovery, and completeness calculations, but no solved-motion or complete-integrals output. Applying those contracts in source order necessitates the distinct complete-motion phenomenon. A finite output-without-valid-setup model blocks the converse, while another model realizes the explanation together with forward branching and therefore refutes any explanation-to-determinism shortcut. Both adapters consume source-local calculations rather than established recovery or shared terminal bundles.
holographic region-entropy structural explanation: Ryu-Takayanagi 2006 and Lewkowycz-Maldacena 2013, with a typed constraint retaining the selected boundary/bulk descriptions, region and anchored surface, area and entropy values, native observables, physical duality, dictionary, surface-selection and area-entropy bridges, area calculation, and normalization, but no final entropy agreement. The route necessitates the selected boundary entropy value and matching native boundary/bulk predictions. RT consumes its static proposal directly; LM consumes replica fixed-point, continuation, Einstein, cone, and AdS/CFT calculations rather than established intermediate or shared terminal bundles. Direct entropy outputs on an unselected region do not explain themselves, and no full prediction-relation equivalence follows. RT's Brown-Henneaux, large/small regime, cutoff, global-AdS3, and BTZ interval formulas remain explicit paper-local route outputs rather than being folded into this shared explanation contract.
adiabatic-cycle transport quantization: Laughlin 1981 and Thouless 1983, with setup, adiabatic following, integrated transport, selected integer index, and index-to-unit correspondence retained as separate calculation stages. The output-led established result stores exact selected setup and the five direct outputs, then reconstructs the implication-valued route; fourteen shared claims transfer through paper-local interpretations, typed countermodels block every missing stage and output-to-setup reconstruction, and a direct nonvacuous transport proposition makes all ten selected indices plus twelve relation families active in the completed physical route. Grounding requires exact selected setup but no following, transport, index, correspondence, or quantization output; flux, Hall conductance, Bloch bands, Chern classes, and finite-torus physics stay local. A proof-free typed source constraint now gives the route a source-sensitive structural explanation. Laughlin's token retains current/phase rigidity, the ideal Landau-gauge flux calculation, and the dirty mobility-gap extension. Its ideal branch now also retains equations (7)-(9) as a selected scalar state-center/energy readout: y_0, the -Delta A/H_0 center shift, and both equation-(9) energy values are proposition-valued source formulas, and Lean checks their linear-energy consequence before the existing equation-(11) current/conductance chain is used. Its qualified-error route also retains the actual printed equation (abs (Delta R_H / R_H)) = (R_H / R)^2, derives the negative Hall-resistance deficit -R_H^3 / R^2, and preserves thermal-error dominance as speculation. Independent countermodels separate mobility gaps from density-of-states gaps, ideal from dirty transfer integers, reversible edge thermalization from Hall error, and the signed correction from an arbitrary resistance label. Thouless's token instead retains the adiabatic current calculation, Bloch derivative substitution, two-parameter integral, and first-Chern interpretation. Both execute the raw shared route and invoke the same checked integer-unit necessity theorem without using a completed transport endpoint. A finite model with completed quantization and a valid route but a false derivation relation blocks the provenance converse.
calibrated residual-background detection: Penzias-Wilson 1965 and Fixsen et al. 1996, with exact retention of ten selected indices and fourteen relation families. Each paper-local context owns the ten indices and constructs one selectedModel, so a candidate cannot select itself by supplying different observational data. Separate calibration, component-separation, uncertainty, robustness, interpretation, and detection bridges; the established result is exactly selected semantics plus a direct nonvacuous model-native detection proposition retaining setup and all eight outputs at one model. The six calculations or bridges are reconstructed afterward. Countermodels block every missing stage and output-to-setup reconstruction. A false-setup witness blocks vacuous implication-only success, while a route-shaped finite model makes all ten selected indices and fourteen relation families directly mutation-sensitive. Both paper adapters replay the shared selected setup at calibration, separation, uncertainty, and robustness stages, rebuild their horn or FIRAS local setup before each paper-local calculation, and use a named exact selected-setup witness for theory/world grounding. Exact selection and outputs without setup cannot ground, while setup can ground without detection outputs. The framework now also owns the common observation-procedure, instrument implementation, performed raw-record, and operational-value assembly independently repeated by both papers. Their temperature representations remain parameters: completed detection plus an assigned represented value yields a recorded measurement, and only faithfulness yields an operational physical value. Countermodels block both detection-to-assignment and recorded-but-unfaithful value promotion; cosmological interpretations remain paper-local. Penzias-Wilson additionally checks both a source-valued positive accounting witness and a negative witness retaining the calibrated 4080 Mc/s foreground budget while withholding the 3.5 K residual. The actual paper argument now separately retains the central 0.8 K ohmic loss, a nonnegative actual ground back-lobe strictly below 0.1 K, and the distinct calibration, atmospheric, and ohmic uncertainties 0.3, 0.3, 0.4 K. Thus the rounded 0.9 K antenna allowance strictly exceeds the central-ohmic-plus-back-lobe contribution; central-component subtraction lies above 3.5 K and at most 3.6 K. The arithmetic 0.3 + 0.3 + 0.4 = 1.0 K checks compatibility with the reported residual budget without inventing a confidence level or statistical error-propagation rule. Six independent physical countermodels separate rounded allowances, central estimates, strict bounds, uncertainty components, and rounded versus central residual subtraction. A separate explicit component-error model now computes candidate actual temperatures; three additional countermodels prevent treating central estimates or their arithmetic bounds as exact physical values. Its proof-note countermodel preserves the 404 Mc/s, 16 K and 4080 Mc/s, 3.5 K measurements without supplying the lambda^0.7 spectral conclusion. FIRAS retains its actual Section 6 equations (3)-(7), Table 4 Galactic foreground and confidence-qualified temperature. Its external blackbody calibration, three unequal and partly correlated temperature methods, finite-beam-corrected dipole, rounded systematic uncertainty, and separate distortion epochs remain paper-local. Its approximate 400 MJy/sr figure-caption peak is used only as a scale witness; values inside the mu and y bounds are logical counterexamples, not claimed experimental central estimates. Separate source-valued controls now retain the complete 6.7 - 2.3 - 0.9 = 3.5 K horn budget, its independent atmospheric and ohmic uncertainties, ten-month observation scope, and the separate 404 MHz proof-note comparison. FIRAS retains 6068 sky pixels, four components, two Galactic templates, a strictly nonzero Table 4 residual below 50 ppm, 2.728 +/- 0.004 K at 95% confidence, 3.372 +/- 0.007 mK dipole amplitude, and the distinct |mu| < 9e-5 and |y| < 15e-6 bounds. Nineteen mutations reject exact blackbody claims, zero residual, pure detector-noise uncertainty, exhaustive foreground exclusion, and derivation of cosmology from one horn frequency.
Schwarzschild master-equation reduction: Regge-Wheeler 1957 and Zerilli 1970 independently retain odd/even parity, coupled radial equations, calculated master-variable transformations, tortoise coordinates, effective potentials, homogeneous master equations, and explicit no-stability scope. The established route projects to NonvacuousSchwarzschildMasterEquationReductionAt and from there to a typed, nonvacuous derivational-reduction result. The latter retains the parity-resolved coupled problem, master description, effective potential, homogeneous equation, and explicit no-stability scope. A false-setup countermodel blocks vacuous implication contracts, and all thirteen selected indices plus thirteen relation families directly change the completed reduction. The compatibility adapters retain their output-led paths from completed odd/even results. Separate source adapters now execute Regge- Wheeler's parity-resolved odd calculation and Zerilli's corrected-system, transformation, potential, equation, and scope calculations in source order, realizing the derivational interface before a completed shared endpoint exists. A source-sensitive refinement pairs the exact selected model with a typed paper-local derivation token: Regge-Wheeler must discharge its harmonic/canonical-gauge/odd-radial relation, while Zerilli must discharge its corrected-even-system/nonunique-transformation relation. The common master-equation shape therefore cannot erase derivational provenance. A completed route with an everywhere-false derivation relation still realizes the ordinary reduction but not the source-sensitive one. Neither path imports a stability analysis. Vishveshwara 1970 is a downstream odd-parity consumer only, so its later Kruskal boundary argument remains outside this shared reduction. Its paper-local setup nevertheless retains value-level equations (4.6a), (4.7a-c), and (4.8a-b): the tortoise logarithm, Q/V_eff definitions, odd wave equation, h_0 reconstruction, and positive-imaginary-frequency specialization. A checked master/stability boundary now retains the selected objects, positive exterior potential and formula residual, nonzero master amplitude, homogeneous residual, boundary-calculation count, outer-decay and inner-regularity residuals, and admissible growing-mode count. Its exact bridge ties those values to the selected master model and its explicit no-stability scope. Regge-Wheeler and Zerilli independently realize valid odd/even homogeneous equations while withholding boundary exclusion; Vishveshwara realizes a positive odd potential while an even growing mode remains. A separate positive witness supplies the missing boundary mismatch and excludes the growing mode.
scoped Schwarzschild linear mode stability: Regge-Wheeler 1957 and Vishveshwara 1970, with wormhole matching and Kruskal regularity kept as distinct selected inner boundaries. The output-led established result is exact selected semantics plus one direct nonvacuous proposition retaining the small linear setup, odd/even exclusions, real-frequency behavior, completeness scope, linear conclusion, and explicit nonlinear exclusion; the complete implication-shaped route is reconstructed from these facts. Theory/model/world grounding requires the exact selected perturbation, parity, frequency, and boundary setup but no boundary calculation, exclusion, completeness assessment, or stability output. Regge-Wheeler and Vishveshwara prove this setup from different named source-local inputs. A false-setup countermodel blocks vacuous implication contracts, and all eleven selected indices plus fifteen relation families directly change the direct endpoint. Converse countermodels ground setup without stability output and reject output-only grounding. Regge-Wheeler's stability adapter accepts only its output-led scoped conclusion and extracts all earlier physical results from that certificate; no arbitrary-data or nonlinear stability theorem is imported. A narrower GrowingModeExclusionRouteApplicableAt now projects both papers to a typed structural explanation: their distinct inner/outer boundary calculations necessitate only the selected odd/even growing-mode exclusions. The projection does not consume completeness or the terminal stability result, and a checked output-without-boundary-calculation model blocks the converse. The checked stability-scope boundary separately retains odd/even analyzed, growing, and total mode counts, regular-packet count and amplitude bound, and nonlinear deviation and bound. Its exact bridge ties the growing-mode and real-frequency counts to the selected stability model. Regge-Wheeler realizes a complete non-growing linear family with an excessive nonlinear deviation; Vishveshwara retains one non-growing analyzed even mode out of two total modes and a regular packet while withholding both completeness and nonlinear control. A positive witness retains complete odd/even expansions and a nonlinear bound, so these absence-of-entailment checks do not assert instability. The stronger master/stability composition now formally distinguishes an independently derived odd master equation from an adopted prior result. Regge-Wheeler must supply its original harmonic/canonical-gauge/radial derivation before the wormhole mismatch; Vishveshwara explicitly adopts the earlier tensor/master machinery and retains corrected radial equations, Kruskal divergence, odd-dipole gauge removal, even divergence, missing even completeness, and its absent rigorous arbitrary-data proof. Inhabited countermodels reject both reclassifying adoption as independent derivation and manufacturing a missing joining argument from otherwise complete child calculations.
gauge-field mass generation: Englert-Brout 1964 and Higgs 1964, with broken and residual generators, their massive and massless gauge fields, nonzero vacuum order, longitudinal-mode response, and approximation scope kept explicit. Exact context-owned retention covers eleven selected values and fourteen relation families, while a separate model-native nonvacuous endpoint drops equality and retains the actual setup and six realized outputs, including distinct direction roles, without storing any implication-valued calculation or bridge contract. The established result is exactly selected semantics plus that direct endpoint, while the complete route is reconstructed from its outputs. Theory-model grounding requires the selected setup but no mass, residual, longitudinal, or scope conclusion. False-setup and setup-complete/no-mass countermodels keep those boundaries active, and typed eleven-index plus fourteen-relation mutations all destroy the direct endpoint; lowest-order and linearized paper-local calculations remain distinct. The adapters also keep Englert-Brout's Abelian mass separate from its selected compact-group mass, and Higgs's U(1) bare mass separate from its selected semisimple component mass; each group calculation is replayed from the shared setup before its mass-to-broken-direction bridge is used. Englert-Brout's p. 322 Abelian tensor, mu^2 = e^2 <phi_1>^2, compact tensor, and mu_a^2 = -<phi|T_a T_a|phi> are now literal proposition-valued formulae with four-component momentum, metric, complex polarization, coupling, vacuum-order, mass-square, and generator-expectation readouts. Their established routes retain them, while a reduced countermodel prevents a named gauge-mass calculation from supplying the printed mass equations. The direct endpoint now also realizes a typed mechanistic explanation: the broken-direction gauge field is the component, the broken-vacuum longitudinal response is the activity, the nonzero locally gauge-invariant broken vacuum with distinct residual roles is the organization, and selective massive/massless gauge response is the phenomenon. The separate mass calculation supplies prediction. An output-complete model with an invalid broken-vacuum organization blocks the converse. This explains mass generation conditional on the selected vacuum; it does not explain why the vacuum broke or promote either calculation to an all-orders quantum result. A proof-free source constraint now also retains a typed derivation token and its proposition-valued realization. Raw source inputs establish the route before either paper obtains a source-sensitive structural explanation: Englert-Brout uses lowest-order polarization, compact-generator selection, rotated vacua, and qualified scope, whereas Higgs uses linearized U(1) equations, zero-coupling mode conversion, semisimple selection, and conjectural quantum scope. Both explanations entail the same selective mass phenomenon, while a completed shared route with an unrealized source token has no source-sensitive explanation. Source-sized QFT countermodels now distinguish Englert-Brout's order-zero transverse polarization and positive pole from an independent higher-order zero pole, and realize rotating and stabilizing generator masses from their actual vacuum-square expectations. Higgs's solved classical equation has field-strength divergence -1, while an independently selected quantum inverse propagator is nonzero at the candidate massive pole; its positive broken mass and zero residual mass are physical values. The equation-(4), perturbative, quantum, and residual-direction caveats are not represented by Boolean, evidence-status, mass-status, or generator-role truth tables.
entropy-production fluctuation symmetry: Evans-Cohen-Morriss 1993 and Gallavotti-Cohen 1995, with conjectured finite-segment-measure and chaotic- SRB modes kept distinct. Each paper-local context owns thirteen selected indices and constructs one exact model carrying eighteen relation families; every index or relation mutation fails that model equality. The established endpoint is exactly selected semantics plus one direct nonvacuous proposition containing the dissipative reversible setup, paired windows, represented probabilities, scoped leading ratio, finite negative production, and long-time suppression. Calculation contracts and route applicability are reconstructed from those outputs. Each paper derives a source-native complete setup and bridges it to the shared setup before grounding; a setup-complete grounded countermodel still makes every output false. A false-setup countermodel blocks vacuous implication contracts, and every selected index or retained relation mutation breaks the direct endpoint. Both papers derive that endpoint from their own source-local routes without strengthening their qualifiers. The shared result records negative entropy production neutrally: ECM's explicit finite-time "second-law violation" interpretation remains paper-local and is not projected onto GC. Finite-time versus leading-long-time scope remains preserved. Source-sized statistical countermodels distinguish ECM's normalized 1 / 2 segment weight from an independently observed 1 / 3 weight despite exact slope agreement. GC retains its two positive contraction samples, separate negative invariant-mean witness, zero-weight negative tile, and reversible dynamics with missing hyperbolic directions; source caveats are not represented by status truth tables.
exact memory-kernel reduction: Mori 1965 and Zwanzig 1973, with orthogonal projection and shifted-quadratic bath elimination retained as distinct source derivations. Both routes calculate an exact history-dependent reduced equation, eliminated-sector memory, a residual force, and the force-correlation/noise-memory relation. A typed proof-free source constraint now feeds two independent projections of the raw paper calculations: a source-sensitive derivational reduction and a structural explanation of the exact-memory phenomenon. Neither consumes completed force-correlation, canonical-noise, or shared endpoint bundles. A converse model has every exact output, a reconstructed route, and the ordinary derivational reduction, but neither source-sensitive result when the source-derivation relation is false. Mori's short-memory plateau argument and Zwanzig's Debye/Markov limit remain paper-local and are not promoted into the exact shared phenomenon.
unitary similarity decoupling: Głazek-Wilson 1993 and Bogner-Furnstahl-Perry 2007, with finite-similarity and continuous-flow modes kept distinct. The output-led result is exact selection plus the direct qualified transformation, suppression, band, and preservation facts; calculation contracts and the route are reconstructed. Grounding requires the source-local qualified setup but no decoupling output. Exact retention covers seven selected indices and thirteen relation families. A separate Representation.InterpretationContext distinguishes the actual unitary mathematical isomorphism from scoped physical equivalence based on an independent selected-content preservation calculation and output. Countermodels block both inference from unitarity to preservation and the converse. Głazek-Wilson select spectrum preservation; Bogner-Furnstahl-Perry select two-body observable preservation without extending it to omitted induced many-body content. The same complete route now satisfies a distinct proof-free structural constraint and necessitates a qualified band-decoupling phenomenon. Terminal outputs with invalid unitary setup do not explain themselves, and an explanation for the selected sector and content does not extend to omitted sectors or content. A stronger typed source constraint now distinguishes the two original derivations: the 1993 divergence diagnosis and finite-similarity calculation versus the 2007 hard-interaction diagnosis, continuous flow, momentum suppression, and two-body preservation calculation. Both raw routes establish the shared explanation without consuming completed paper or framework endpoints. A checked model with every terminal output and a reconstructed route but a false source-derivation relation still has no source-sensitive explanation. Głazek-Wilson's opening diagnosis now also retains its actual journal pp. 5863-5864 three-level Hamiltonian: diagonal (Lambda,m,m), four cutoff-sized high/low entries g Lambda, and two degenerate low/low entries g m, all tied to the selected bare, free, and interaction Hamiltonians and cutoff. The source map exports that exact matrix as its own certified claim; inhabited countermodels independently separate degenerate mixing from ultraviolet jumps and reject named obstacle sectors with incorrect cutoff scaling. Its solvable-model branch retains journal p. 5870 equations (4.2)-(4.3) as a selected real-valued readout, including positive cutoff and nonzero-denominator assumptions, representation links to the selected cutoff, observable, interaction, counterterm, and transformed interaction, plus an explicit relation from that interaction to the transformed Hamiltonian, and the checked reference-cutoff values u(Lambda_0) = f and <z|V'|z'> = -g-f for every nonnegative model-label pair. A named running counterterm no longer stands in for those equations. Bogner-Furnstahl-Perry's explicit continuity in its selected flow parameter and its counterterm, momentum-space, numerical-convergence, and omitted-three-body claims stay paper-local. Its nuclear momentum branch now retains author-TeX equation (6) as a selected real-valued derivative/integral formula with the -(k^2-k'^2)^2 V_s term, 2/pi radial kernel, and dominance-qualified exp(-s (k^2-k'^2)^2) leading-term relation; a named suppression label no longer stands in for that source equation, and the source map exposes the conjunction as a checked formula-package output. Its flow route now also retains actual finite Hamiltonian matrices, two-sided unitary similarity, H_s = U H U† = T_rel + V_s, the anti-Hermitian generator eta = (dU/ds)U† = [T_rel,H_s], both actual matrix commutators in dH_s/ds = [[T_rel,H_s],H_s], and the distinct inverse-fourth-root resolution law lambda^4 s = 1. Its numerical convergence route now consumes the actual ordered free-resolvent kernel (E-T_rel)^(-1)V_s, a nonzero eigenvector, a nonpositive source energy, and the exact geometric Born-series criterion |eta| < 1. The initial repulsive eigenvalue -2 gives divergent partial sums; the evolved -1/2 gives a genuinely convergent series. Nineteen inhabited source-specific boundaries reject arbitrary anti-Hermitian generators, missing double commutators, an incorrect inverse-square scale, nonunitary congruence, insufficient eigenvalue reduction, the divergent |eta|=1 boundary, finite truncation, reversed resolvent order, positive source energies, and zero eigenvectors. Its five directional paper-local countermodels are now value-bearing: the selected witness retains s=1, off-diagonal momenta (0,1), equal initial and evolved matrix elements, and zero derivative/integral contribution, so equation (6) and actual suppression fail despite the named sector. It also retains zero unitary defect with a (0,1,1) continuity jump, equal two-body observables within numerical tolerance, a size-four basis with errors 2 -> 1 and Weinberg magnitude 2 -> 1/2, and two-body-only triton energies (-7,-8) at lambda=(2,1) with omitted contribution one. No proposition wrapper or dependency-status truth table replaces these nuclear distinctions, and all five source-valued countermodels are independently required by the compiled nuclear fidelity certificate.
thin viscous boundary-layer reduction: Prandtl 1904 and Blasius 1908, with the full viscous equation governing the selected full flow, seven further setup relations, separate momentum and continuity reductions, and their coupling. The established result is selected semantics plus all eleven relations stated directly; its implication-valued calculation route is reconstructible but is not stored in the endpoint. Grounding requires each paper's checked eight-relation source setup and no reduction output. A finite role-typed projection additionally realizes a scoped derivational relation: the physical setup realizes the full/reduced descriptions, both equation reductions supply micro support, and equation coupling supplies macro exhibition. Each paper now also constructs that result directly from its source setup and calculation, before any output-led established reduction is packaged. A stronger source-sensitive derivational projection requires a typed paper-local derivation plus that applicable route: Prandtl retains the original thin-wall-layer scaling and omission argument, while Blasius retains the explicitly imported program and his own order counting. A separate ordinary structural projection entails the coupled reduction phenomenon without source provenance; its source-sensitive refinement adds the typed derivation, exposes it, and entails the ordinary explanation. A complete output-led reduction, ordinary derivational bridge, and ordinary explanation with the derivation relation made false realizes neither source-sensitive result. Prandtl's route retains its short-wall-path and negligible- curvature inputs locally; Blasius's route retains streamwise-diffusion omission, curvature contribution, and explicit boundary conditions locally. BoundaryLayerVelocityMatchingReadout now gives those boundary conditions physical content: matching both tangential and normal fluid velocities to the selected wall, and recovering the outer tangential velocity as the wall distance grows. Prandtl's wall may move. Blasius's original p. 4 instead requires u(x,0)=0, v(x,0)=0, and u(x,infinity)=U(x) before any flat-plate specialization. Both papers realize stronger shared velocity-matched reductions, and independent witnesses distinguish wall slip, wall penetration, failed outer-flow recovery, and moving walls. Prandtl also retains its original p. 487 steady planar momentum and continuity equations as real-valued derivative formulas with explicit density, viscosity coefficient, regularity, selected fields, and the selected wall/free-fluid velocity boundary data. The displayed PDE and its coefficients remain paper-local, while its velocity-matching semantics project to the reusable shared refinement. These are separate formal realizations, not independent discoveries: Blasius explicitly imports Prandtl's small-friction program and adds his own order-counting calculation. The shared friction boundary is now value-bearing: BoundaryLayerFrictionContrastReadout retains friction, layer thickness, wall-velocity jump, outer second derivative, outer and wall viscous effects, negligibility tolerance, and global-flow difference. It checks delta^2 = friction, the two viscous scaling equations, outer negligibility, and wall significance. Prandtl's original pp. 486-488 and Blasius's original pp. 4-5 independently realize this contrast with distinct witnesses; small friction therefore cannot be read as global irrelevance. Their remaining scope witnesses are also value-bearing: Prandtl retains inviscid residual versus wall slip and limiting-flow difference, abstract outputs versus the displayed equation pair, surface-path length versus its admitted maximum, pattern agreement versus drag/vorticity agreement, and cylinder suction versus outer-wall separation. Blasius retains potential adherence/vorticity failures versus the independent Helmholtz pressure-boundary objection and distinguishes an instantaneous velocity jump from finite-duration uniform acceleration. No fluid region, flow-description, reduction, path, boundary, introduction, or start-protocol enum truth table substitutes for these distinctions. A separate source-valued framework audit now checks Prandtl's displayed momentum and continuity equations, short-wall-path scope, neglected streamline curvature, boundary-generated vorticity, necessary-but-not- sufficient adverse pressure, nonvanishing global effect at zero limiting thickness, and actually performed local cylinder suction with separation retained at the outer wall. Blasius's distinct branches retain his imported Prandtl program, independent order counting, nonzero normal-curvature term, original far-field profile derivative 2, matched coefficient 1.3266 bounded by 1.326 and 1.327, local wall stress, one-face integral, exact two-face drag, and the strictly larger rounded 1.327 report. They also retain the explicitly truncated 0.65 separation root, qualified 11%-12% offset, impulsive versus uniformly accelerated starts, and viscosity-dependent thickness and drag at equal reduced onset. Independent controls reject each erased assumption and forbid universal drag, sufficient adverse pressure, global suction suppression, exact wake prediction, universal series convergence, or an already proved uniform zero-viscosity limit. Countermodels separate setup from reduction and reduction from coupling. This adds no Navier-Stokes limit or error-bound claim. A finite model realizes all eleven physical relations, and direct activity theorems cover all fifteen selected data and eleven relation families; separation, curvature choices, profile calculations, and unsteady-flow applications remain paper-local.
Broken-symmetry spectra now distinguish Goldstone's nonzero Hessian null direction and separately bridged current pole; Nambu's gapped quasiparticles, zero-energy collective pair, and Ward cancellation; Anderson's 4 pi n e^2/M Coulomb plasma; and the Maxwell photon as a Goldstone of an electric one-form global symmetry. Wilson/'t Hooft charges, the mixed anomaly, and intact local gauge redundancy are separately governed.
Gauge-field mass generation now distinguishes Englert-Brout's transverse lowest-order Abelian polarization, different compact-group broken/residual masses, and chiral pseudovector Ward pole from Higgs's classical B = A - (ev)^(-1) dphi, massive field equation, independent radial scalar mass, zero-coupling limit, and semisimple residual direction. Neither argument silently becomes an all-orders quantum proof.
Cosmological defect formation now retains Kibble's actual scalar-plus-gauge thermal potential, critical temperature, unequal correlation and penetration lengths, and distinct wall/string/monopole homotopy classes with conditional 1/4 and 1/8 initial fractions. Guth's independent bubble junction, conditional entropy dilution, and exponentially failed old-inflation percolation remain separate; no graceful exit is invented.
Exact gravitational exteriors now retain Schwarzschild's determinant gauge, original radial cube substitution, four metric coefficients, and relativistic orbit correction alongside Kerr's twisting Type-D stationary metric, exact implicit Cartesian quartic, Kerr-Schild one-form, mass/spin assignment, excluded ring, and zero-spin reduction. Original papers are not retroactively credited with interior solutions, global event horizons, maximal extensions, or an exact invariant no-hair theorem.

The milestone list above is not the complete inventory. Every active shared framework component has policy-enforced required-theorem and retained-route contracts, and every registered component-to-paper realization exposes a checked transfer of each retained claim to both a selected theory and represented physical world.

These certificates preserve the narrow shared vocabulary. They do not import paper-local mechanisms or stronger interpretations into the framework layer.

Build

python3 scripts/check_all.py

Literal complete-line audit registrations are counted through a bounded, content-keyed index rather than repeated full-file regex scans. Differential tests preserve exact names, leading whitespace, duplicate counts, LF boundary semantics, and changed-source behavior. This is a text-check optimization, not a Lean parser or a replacement for the source, axiom, fidelity, and elaborated dependency audits. Its focused tests run with python3 -B scripts/test_policy_line_index.py and in the standard suite.

The standard verification includes duplicate-key integrity for its Python governance policies, primary-source JSON portfolio, and versioned physical- countermodel governance manifest. The manifest independently retains named physical controls, declaration-local source fragments, and forbidden collapsed-witness regressions across the shared technical frameworks. It is validated by schema, duplicate-key, deletion, and mutation checks alongside independently checked equivalence of indexed forbidden-pattern matching with direct regex searches, single-read exhaustive retired-foundation identifier audits, source provenance, an explicit declaration-scoped proof-trust boundary, the formalization policy, direct independent physics clients for every philosophy and paradigm module, an explicit ten-family classification of every source-certified primary paper, actual cross-family elaborated declaration dependencies for every domain-neutral foundation, physically justified and audited scopes for narrowly specialized paradigms, independently reviewed three-family grounding for every active philosophy module and every domain-neutral paradigm, two independent primary-paper clients for every shared technical framework, explicit proposition-valued nonvacuity contracts for all shared frameworks, two independent primary-paper clients actually using each nonvacuous physical result, source and elaborated Lean audits that every framework-composition edge actually consumes its child's nonvacuous physical result, an elaborated Lean audit that clients use their directly imported foundational and technical semantics, exhaustive independent review of every public paper conclusion and source route, inhabited countermodel boundaries whose actual retained and rejected propositions cannot unfold to True or False, complete and synchronized paper editions with independently checked source-derived per-paper and aggregate theorem, claim, step, route, and fidelity-boundary inventories, the Lean library build, and a kernel-checked foundational-axiom audit of the independent fidelity certificates and representative results from quantum foundations, gravitation, cosmology, statistical mechanics, condensed matter, nuclear physics, fluid dynamics, plasma physics, holography, and supersymmetric field theory. The named audit resolves declarations from a Lean-parsed block, so inline entries, multiline entries, and intervening documentation all receive the same dependency check. Core-only regression fixtures reject direct and indirect untrusted axioms and distinguish documentation from executable entries. Every standard run also exhaustively audits the reviewed production declaration inventory through a shared proof-dependency traversal that independently covers every elaborated production declaration, including generated theorems, proof-valued definitions, and unused axioms. Source-authored theorem and lemma declarations are separately cross-checked, including inline and multiline attributes, rather than relying only on the manually reviewed declaration list, rejecting unexpected axioms while first verifying that every non-auxiliary production declaration depends only on Lean's foundational axioms. Remaining compiler-assisted decisions are permitted exclusively inside named theorems in paper SourceMap.lean and Coverage.lean modules, counted separately for finite provenance and semantic route coverage, and checked against their actual elaborated source modules and source-authored theorem owners. The source audit excludes nested comments, quoted strings, non-theorem declarations and metaprogramming commands, nested lookalike paths, and every framework, foundation, main paper, and fidelity module. Use --skip-build to reuse an existing verified Lean build, or --legacy-axiom-trace when the much slower verbose declaration-by-declaration trace is specifically required. An external-client-style Lean check exercises quantum-foundation, electronic-structure, condensed-matter, cosmology, plasma, nuclear-EFT, holography, supersymmetry, and statistical-physics public APIs without adding assumptions or strengthening the original conclusions. It additionally compares independent Everett/Rovelli operational-observer realizations, Wu/Bohm calibration-versus-faithfulness semantics, and Penzias-Wilson/FIRAS operational temperature assignments without identifying their distinct physical systems or source-specific premises.

Casimir's main heat-current route now derives the antisymmetric column condition from reciprocal bulk operators tested on arbitrary regular functions. It derives nonuniqueness from distinct actual currents and keeps the original tensor separate from the convention-selected symmetric representative. Kernel reciprocity, macroscopic-equivalence interpretation and vacuum/shape selection remain explicit inputs; one temperature profile cannot replace the arbitrary-test condition.

The independent CasimirHeatRouteClient now constructs all five main-route premises together, with positive conductivity, an actual energy-density rate of 6, and a normal-current difference of 4. Its exact theorem-type checks exclude hidden assumptions about the setup or result. A second choice preserves bare vacuum/shape agreement and local reciprocity but fails selection, with a nonzero skew jump at the sample boundary. This identifies the missing global interface condition; it is not a counterexample to the original paper. The fixture does not assert the paper's unrelated statistics or electrical routes.

Casimir's heat-current fidelity boundary now uses actual differentiable tensor-generated currents, rather than assigned derivative readouts. The paper-local refinement retains both conditions in the original equation (18): antisymmetry and vanishing column divergences. Its positive-temperature cube witnesses have equal bulk divergence but distinct currents; a spatially varying antisymmetric tensor fails the missing column condition. An independent client preserves a nonzero bulk operator. Boundary exchange, vacuum extension, and sample-shape conventions are not inferred from these local results.

The separate tests/consumer Lake package now adds an actual external dependency test. It reconstructs finite Gibbs-quench work logic, a deterministic finite-resolution prediction limit, Bell's three-setting inequality, full-sky cosmic-variance logic, local geodesic focusing, nuclear amplitude expansions, signed and spectral Hall response, coherent molecular spectroscopy, supported quantum-error recovery, self-consistent plasma phase mixing, and Brownian joint-law and coordinate distinctions using only public technical and foundational APIs. Its own elaborated audit checks real theorem dependencies, rejects paper imports and canned countermodels, and permits only the three foundational proof axioms. python3 -B scripts/check_external_consumer.py stages this source-only consumer in a temporary directory against the exact locked Mathlib revision; no consumer build artifacts enter the source fixture. Add --compare-reference to compare indexed public-API dependencies, including absent ones, against fresh Lean collector traversals.

The in-repository downstream audit uses an immediate-dependency fast path for public-API queries, with Lean's fresh transitive collector as the fallback. Its mandatory differential examples compare 304 queries against the original collector, including type-only, opaque, inductive, quotient, missing-name, and unrelated-client cases. Complete axiom traversals, forbidden-dependency checks, namespace scans, and individual #print axioms remain unchanged.

Expensive verification can also be split into independently reproducible stages without changing the default complete audit. Run python3 -B scripts/check_all.py --skip-build --list-checks to inspect the stable identifiers. --check trusted-axioms isolates the long foundational proof audit; repeated --check options preserve canonical stage order. --from-check trusted-axioms --through-check axiom-inventory runs an inclusive named window, and --from-check downstream-reuse resumes at the remaining client, graph, and integrity gates after an externally interrupted run. Use --check external-consumer for the isolated package check. Governance regression tests verify the default full inventory, canonical numbering, inclusive windows, optional build/legacy stages, and rejection of invalid selections.

The standard sequence begins with a lightweight policy-keys preflight and ends with exhaustive policy-integrity regressions. All sixteen previously required checks remain mandatory; the preflight is an additional seventeenth check, not a substitute. This lets a bad source, physical contract, or client fail before the expensive regression suite. --check policy-keys scans only governance keys and explicitly reports that semantic regressions were not run. It cannot produce a complete-suite result. The standalone integrity command still runs its full suite by default. Successful full runs retain the same semantic checks; this ordering improves failed-run latency, not physical assurance.

Within policy integrity, source/governance regressions run before the compiled meaning-inspection suite. A source failure returns a failing status and reports that the compiled suite was not run; successful runs still execute every check. Failure-injection regressions exercise every scheduling boundary in both normal and full-source-reference modes. This reduces failed-run latency, not the amount of semantic scrutiny required or the cost of a successful complete audit.

Add --report /absolute/existing/cache/directory/new-run.json to retain a machine-readable result. The parent directory must already exist outside both the project and the selected reference archive. Reports are published atomically and never replace an existing file, including one created during the checks. Keep them outside the repository; they are verification artifacts, not production sources.

Schema version 2 records the exact source-snapshot file hashes and aggregate digest, Python runtime, selected and completed stage identifiers, each actual command and return code, per-stage elapsed times, and final result. Only a successful run of every standard stage, including the build and unchanged input boundaries, sets complete_standard_suite to true. A successful selected window or --skip-build run is explicitly narrower. Optional legacy tracing does not substitute for any standard stage.

The schema's assurance record explicitly states that these are automated check results: they do not establish physical fidelity, human semantic review, or completion of the project. These limits apply even when complete_standard_suite is true. A recorded review of a particular semantic scope is separate evidence, not global approval. Historical schema-1 reports lack this explicit record and must not be interpreted as stronger evidence. Likewise, fidelity-ledger coverage and registered source-family counts are not counts of human-reviewed or physically certified papers. The runner and standalone audits now state these limits in their terminal output.

Ordinary check failures, source invalidation, unreadable inputs, and command launch errors produce non-success reports when publication is possible. Child signal return codes remain signed in their stage records; the runner returns the conventional 128 + signal exit status. Invalid destinations or report-publication errors return status 2 without printing a successful final summary. Cleanup failure after successful publication instead produces a warning naming the leftover temporary file; it does not change the recorded verification result. An interrupted or killed runner need not produce a report; absence of a report is not evidence of success. These local records are not signed attestations, clean-checkout builds, runtime dependency-cache hashes, or a certificate of physics fidelity beyond the checks actually executed. The snapshot guarantee concerns the observed stage boundaries, not undetected transient edits made and restored inside a running check.

After extending a paper formalization, update its readable edition and structured source-derived catalog inventory with python3 scripts/sync_html_papers.py --write. The synchronizer also repairs existing displayed theorem, route, claim, and fidelity-countermodel counts; the independent HTML audit verifies those numbers against actual Lean declarations, including theorem names written on the next line and multiple source-map constructors on one line. The separate elaborated Lean fidelity audit additionally checks every paper's catalogued claim, route, and physical countermodel counts against the actual compiled argument.

The original Witten 1982 and Seiberg-Witten 1994 vacuum calculations now provide a source-sensitive composition benchmark: the shared anomaly and discrete-vacuum frameworks retain three independent source explanations and a separate physically meaningful joining derivation. Witten's finite-volume index, hypothesized gluino condensate, and additional infinite-volume identification remain distinct. Seiberg-Witten's mass-deformed route instead retains the Z_8 -> Z_4 -> Z_2 sequence, exact local monopole equations, distinct mutually nonlocal monopole/dyon charges, and independently realized two-vacuum agreement.

Bell 1966 now has twenty physically inhabited Bell boundaries and an actual spin-half source model. The binary threshold lambda=-1/2 still selects the allowed eigenvalue +1; the formerly used ternary Real.sign 0=0 would instead make the construction impossible. The certified routes retain three incompatible Stern-Gerlach outcomes 1,1,sqrt(2), noncommuting zero-meet projectors, and cumulative Born intervals [0,1/2) and [1/2,1) with equal quantum probability and distinct deterministic values.

Knox 1995 now has twenty physically inhabited Knox boundaries. Its actual five-mode full-sky calculation retains quadrupole variances 8/5 and 2/5, fixed detector weight with distinct pixel noise, the original chi-square degrees 5 and variable V=5, foreground cross-pixel covariance 1/2, distinct squared scalar/tensor correction factors, and baryon nuisance shifts exceeding both conditional forecast errors.

The original D-brane regime calculation now has twenty-one inhabited D-brane boundaries. Its source witness retains N=3, g_eff^2=16, and N^4=81, separate curvature and local-dilaton control, a genuinely inhabited large-rank D2 window, an infinite NS5 throat, and D6 ALE orbifold geometry with a nonextremal horizon and actual asymptotic Hawking flux.

Nakano's electrical-conductivity paper now has twenty-six inhabited Nakano transport boundaries. Its certified approximation route retains the original frequency selection, the double-commutator memory kernel f(t)=(2+cos(t))/2, an independently assumed exponential tail, and zero-frequency conductivity 2/pi; doubling the static scattering weight changes the result to 1/pi.

Evans and Coleman's radiation-fluid collapse now has forty-six inhabited Evans-Coleman boundaries. Its similarity route uses actual reduced equations, profile fields, and calibrated exterior limits. The report labels n=1.1485 and beta=0.36 remain distinct estimates. Setup does not assume a solution or exact reported index; the mass ratio is calculated from the metric. Index admissibility follows conditionally from the boundary-value calculation, without uniqueness or an exact printed decimal. Actual center, similarity-boundary, and sonic regularity now replace the scalar regularity proxies and are retained in the complete result. C2 metric and C1 fluid extensions must match the selected profile's fields. A center-regular model can still have divergent boundary density and fail the Einstein equations. The acoustic principal matrix now comes from derivatives of the actual printed fluid fluxes. Its two nondegenerate characteristics have nonzero fluid amplitudes and lie inside the metric light cone. A separate main claim identifies the selected sonic surface with the incoming branch, without assuming local-attractor correspondence. Independent moving-fluid tests check the matrix coefficients and distinguish fluid-frame direction from coordinate motion; vacuum degeneracy is not interpreted as sound propagation. The local-asymptotic representation is explicitly an author expectation. It now means convergence of the actual critical evolution's four rescaled fields to the same constructed profile, not a freely assigned relation. The pointwise limit shares its physical fields with the separate only-critical expectation; it implies neither exact spacetime equality nor a flat radial tail. Finite numerical comparison no longer assumes that interpretation or a solved profile; exact sampled metric agreement can coexist with failed field equations. The mass route retains the reported eta_c=1.018828234 and K=3.27, both numerical grids, and the finite observed scaling range. The central density and boundary lapse now use actual profile traces. A lapse-defined inverse proper-time clock transfers the coordinate density scaling to its proper-time limit, retaining the clock and field bindings in the result. Three countermodels reject a wrong clock and unbound density or boundary-lapse readouts. Curvature still uses a separately supplied identity for curvature computed from the actual metric derivatives. Its central readout is bound to a radial limit through the proper clock. A regular flat-metric countermodel rejects even a divergent scalar readout with the radiation formula and correct density if that geometric binding is absent. Observed redshift is a separate conditional deduction using normalized observers and actual photon trajectories. The continued metric matches the selected precritical profile; position derivatives and both covector geodesic equations constrain the photons. Endpoints are derived, with emission at t=0 and reception at one fixed positive radius. Lean proves reception requires t>0, and derives boundary-lapse matching by continuity. Three new controls reject non-affine momentum, a different selected metric, and precritical-only reception. Continuation and the required photon family remain explicit hypotheses, not constructed solutions for the critical spacetime; the required transport calculation, outgoing visibility, and a measure-zero proof are not supplied. Full paper fidelity is not claimed. The intermediate route now selects the actual radial-metric observable in Figure 4, without inferring unplotted fluid agreement, and retains an approximate departure scale tied to the actual later mismatch radius. A remote exterior discrepancy cannot stand in for breakdown at that inner scale. Only-critical persistence is a separate neighborhood-wide expectation, and eventual nonpersistence needs that expectation: a smooth field can depart at a later finite time and still return to the profile near the critical point. Three additional mass-route boundaries distinguish finite fits from a zero mass limit, calibrated report values from exact physical thresholds, and finite polar-slice estimates from exact horizons. Common relative-error control and physical-family realization are separate explicit inputs to the shared mass-limit deduction, not consequences of the finite report.

Hannay's classical adiabatic-holonomy paper now has twenty-four inhabited Hannay holonomy boundaries. One witness realizes all nine source equations with dynamical angle 1, geometric angle 1, and total angle 2. Its noncircular (A,L)=(1,4) hoop has angle -pi^2/2, while a provably different circular hoop has angle -2 pi; a nonspinning driven top still retains geometric rotation 1/2.

Two-dimensional melting now has twenty-four inhabited Halperin-Nelson melting boundaries. Its actual triangular Burgers charges sum to zero, nonzero fugacity realizes all three source RG equations with genuine angular-integral Bessel functions, and positive I_1(2) makes the bulk flow strictly greater than the shear flow. eta_6=18 k_B T/(pi K_A) distinguishes hexatic orientation from translation, and floating stability requires both lambda_M<0 and K_R>16 pi. The quoted exponent near 0.44817 remains approximate.

The four-dimensional a-theorem now has twenty-eight inhabited Komargodski-Schwimmer a-theorem boundaries. Its source-valued routes retain ghat=exp(-2 tau)g, separate Euler and Weyl anomalies, an independently controlled spectator and tuned vacuum, the exact positive optical dispersion integral, nested running tails, and the original scalar-loop value a_UV-a_IR=1/(5760 pi^2) without claiming gradient flow.

The original Gurney-Condon nuclear letter now has twenty-eight inhabited Gurney-Condon nuclear-decay boundaries. Its certified scattering calculation retains the 4 million volt emitted alpha, uranium range 2.7 cm, faster incident alpha 5, exterior turning radius 2, and inverse-square force 5/2. Independent countermodels reject missing wave tails, unconditional energy-rate ordering, invented quantitative tunneling formulas, and misidentification of the field-emission analogy as a nuclear derivation.

The original Vishveshwara Schwarzschild analysis now has twenty-five inhabited Vishveshwara Schwarzschild-stability boundaries. Its nonzero master mode has m=1, r=3, l=2, V_eff=4/27, and Q''=31/27; the infinity-decaying branch grows to exp(2) at the horizon. A removable nonstationary dipole coexists with stationary source rotation, and the k=2-i damped resonance retains independent radiation boundaries, complete odd modes, incomplete even modes, and uncontrolled nonlinear deviation.

The original stochastic-inflation paper now has twenty-three inhabited Linde-Linde-Mezhlumian inflation boundaries. Its certified routes retain delta_phi=H/(2 pi), <phi^2>=H^3t/(4 pi^2), D=H^3/(8 pi^2), and e^3/2 rising daughter domains. Most importantly, raw physical volume is P_p(t)=15 exp(2t) while only tilde P_p(t)=15 is stationary; the spectral gap, both absorbing Planck boundaries, unequal clock densities, and nonstationary comoving density remain independent.

Minkowski's original spacetime lecture now has twenty-nine inhabited Minkowski spacetime boundaries. Its certified route realizes beta=3/5, gamma=5/4, upper-hyperboloid coordinates (3/4,5/4)->(0,1), proper time 4 from separation (5,3), orthogonal four-acceleration, a unique retarded null separation (5,3,4), and potential e/r=2/5. Charge product 6 does not become the proposed mass product 10, and a checked approximation does not prove universal gravity.

Everett's original relative-state paper now has thirty-two inhabited Everett relative-state boundaries. Unequal amplitudes 3/5 and 4/5 give weights 9/25 and 16/25; the four two-observation histories have weights 81/625, 144/625, 144/625, and 256/625. Their mixed-branch measure 288/625 is not the counting fraction 1/2, and the positive finite exceptional measure 81/625 is not erased by its genuine Born-product history tail (9/25)^(n+2). Decay of that one history does not imply decay of the entire exceptional set. Local noncommuting disturbance remains distinct from remote noninteraction.

Landau's 1941 helium paper now has forty-six inhabited Landau superfluidity boundaries. Its original zero-momentum quadratic roton has Delta=8, mu=4, energy minimum at p=0, and wall-speed minimum 2 at p=8. Simultaneous motions rho_n=1, rho_s=3, s=1/2, T=2, v_n=3, and v_s=-1 give zero mass current, entropy current 6, and thermal current 12. These integer response coefficients admit an arithmetic four-atom partition; the separate actual phonon response 3/2 excludes every exact subset partition of one hundred unit-mass atoms. The author's nonliteral microscopic interpretation remains a separate input. Actual thermal functions distinguish a three-dimensional population from its activation factor, heat from energy, and a weak gap inequality from one-percent response accuracy. Sound readouts now come from one thermodynamic potential and actual propagating-wave families. The four linearized balances yield a coupled characteristic and explicit errors in equation (9)'s approximate sound formulas. The same phonon-roton thermal and normal-response functions derive the low-temperature estimate; actual mode limits also require the pressure limit and vanishing coupling errors. Amplitude rescaling makes the actual fields arbitrarily small without changing their speeds or mixing corrections. The lambda limit has separate thermal-prefactor control. A leading-phonon diagnostic has u_1=2, u_2=1 at T=2 and a genuine second-sound limit 2/sqrt(3) at zero temperature; a different response family agrees at T=2 but has limit zero. Other potential-based controls distinguish held-variable conventions and show why vanishing superfluid density alone is insufficient. Restoring positive normal viscosity produces an actual nonzero wave residual, not merely a different assigned scalar. These are ideal-model diagnostics, not numerical predictions for physical helium or nonlinear vessel solutions.

Callen and Welton's original generalized-noise paper now has forty-five inhabited Callen-Welton noise boundaries. At hbar=k=T=1 and omega=log(2), the upward/downward ratio is 1/2, the dissipative difference is 1, and the fluctuation sum is 3. The zero-point energy log(2)/2 and Planck term log(2) remain distinct; resistance pi gives quantum noise 3log(2) and classical noise 2. Brownian spectra 9log(2)/pi and 10log(2)/pi are not white, dipole resistance is 4/3, and wall pressure 3/pi^2 doubles volume pressure 3/(2pi^2). The source energy balance 10=2+8 does not complete the proposed future theory. The strengthened classical controls compute their oscillator energy and actual Dirac-measure integrals. A two-bin quantum spectrum has a controlled low-frequency bin but violates the integrated classical tolerance; a positive-frequency continuum satisfies the pointwise quantum formula while its total noise integral diverges. Zero-probe, reactive-response, peak/RMS, and angular-measure controls separately guard the response comparison.

Anderson's original plasma paper now has thirty-four inhabited Anderson conductor boundaries. Carrier data n=1, e=2, and M=1 give response K=4, plasma gap omega_p^2=16pi, screened field ratio 1/5, and 1+2=3 polarizations. Crucially, the normal plasma retains gapless matter despite its gapped gauge sector; only the distinct superconductor is fully gapped. Conducting spectral weight 1 gives Z=0, ordinary weight 1/2 gives Z=1/2, and charge moves from the dressed particle to the surface without particle loss. The gravitational mode has signed frequency square -4pi G rho, so 3+2=5 polarization counting does not establish a stable massive graviton or complete the non-Abelian and baryon-gauge programs.

Regge and Wheeler's original Schwarzschild paper now has twenty-six inhabited Regge-Wheeler boundaries. At M=1, r=3, and l=2, the lapse is 1/3, the tortoise derivative is 3, and the gravitational potential is 4/27; frequency 1 gives effective wave number squared 23/27. The negative-frequency mode decays at both ends but fails smooth continuation through the two-ended wormhole; equal and unequal incoming/outgoing strengths are both allowed. The independent even constraint is not implied by its equation-(29) first-integral transport or a later Zerilli potential. Static sources occur on both wormhole sides, and a nonzero quadratic residual blocks any nonlinear-stability claim.

Zeh's original measurement paper now has twenty-eight inhabited Zeh measurement boundaries. The actual complex x- and y-spin projectors both average to I/2 without determining preparation or selecting an outcome; the trace formula presupposes rather than derives the measurement postulate. The printed energies 10^-42 eV and 10^-7 eV give microscopic ratio 10^35, while the dipole coupling weakens as R^-3. Unequal retained branch weights 9/25 and 16/25 now come from an actual finite composite ket; global and reduced purities are computed from its density and partial trace. Reduced purity depends on environmental-record overlap: orthogonal records give 337/625, while overlap 3/5 gives 11017/15625 with nonzero coherence 36/125. Two populated branches or unequal record vectors alone do not imply reduced mixedness. These numbers are diagnostics, not values printed in Zeh; dynamical coupling estimates remain separate. The source also retains distinct sugar/ammonia tunneling scales, two anticorrelated EPR records, and a globally symmetric sum of individually asymmetric components.

Young's original two-dimensional melting paper now has twenty-one inhabited Young melting boundaries. Genuine angular-integral Bessel functions support the nonzero-fugacity recursion, and triangular Burgers fusion (1,0)+(0,-1)=(1,-1) produces the quadratic channel absent for square vectors with composite squared length 2. The equal-force exponent is 0.3696, dislocations erase shear without erasing orientational correlations, and vacancy/interstitial contributions distinguish the true bulk modulus from the dislocation-only result without determining the correction sign. The later disclination transition and competing first-order melting remain unproved.

When the large primary-paper archive is kept outside the published checkout, set PHYSICSLOGIC_REFERENCE_ROOT to the local references/ directory before running check_all.py. Both the complete artifact/checksum audit and the policy check's original-source passage comparisons then read that external archive. Without the variable, both continue to use the repository-local references/ directory.

The active lane intentionally avoids technical mathematical proofs and calculations. Those may later be imported from specialist libraries; until then, they appear as explicit hypotheses of checked Lean theorems.

Recorded Estimates And Exact Values

The Penzias-Wilson 1965 and FIRAS 1996 adapters now distinguish a performed, represented temperature estimate from exact possession of its central value. Their actual-temperature relations are independent of the calculations, and Lean checks that changing those relations leaves each complete source result unchanged. Reported uncertainties, detection bridges, and FIRAS's Planck fit and systematic qualifications remain part of the source routes. Exact-value strengthening requires a separate faithfulness premise, not an inferred one.

Sixteen source contracts and twelve mutations guard this distinction. An independent consumer realizes a 300 K recorded estimate with a 299 K actual temperature and bounded bias, then uses the public interface to reject exact physical equality to the recorded center. This is an adapter correction, not a claim that every measurement formalization has already passed this audit.

Rabi 1939 now makes the same estimate/exact-value distinction while keeping its physical moment parameter separate in the resonance and molecular dynamics. The source retains nominal 0.5% absolute and 0.1% relative accuracy, separate from the tentative 0.2-0.3% line-minimum shift assessment. The source route and independent epistemic ledger preserve that author expectation. A symmetric diagnostic dip with 1% half-width and a 0.4% displacement shows why width and symmetry alone cannot establish the proposed shift bound. A calibration-only model derives the field-scale factor in moment extraction and its cancellation from ratios only when common. Three additional inhabited fidelity boundaries and an independent common-standard consumer test why relative moment information need not fix an absolute moment. The quoted accuracies are not silently promoted to hard bounds or confidence coverage.

Ramsey 1950 now calibrates its quoted pulse-area prescription to the actual coupling, interaction length and beam-speed scale used by the source dynamics. The on-resonance integral is derived exactly for double resonance and with the retained error bound in the more general near-resonance regime. Two inhabited countermodels and an independent coherent-evolution consumer show why a quoted area needs physical calibration and why equal areas do not fix the frequency response or width scale. The numerical optimizer remains an explicit source input.

Its calculated-profile comparison also retains the two numerical FWHM error bounds. A resolved nominal gap gives actual profile narrowing; ratio control requires a positive lower bound for the reference width. Four inhabited controls and an independent eight-theorem profile client reject dropping an error or treating positive actual width as resolution of the error-bound denominator. The comparison concerns the near and conventional calculated profiles, not the exact coherent or observed response. The original numerical roots and validation budgets remain explicit inputs.

Ramsey's weak-excitation argument also distinguishes the incident beam from the transition-selected speed law. Lean derives the quadratic signal limit, the normalized selected density 2 y exp(-y^2), and its inverse-square enhancement relative to the incident density. A finite-field theorem retains the phase regime under which halving the coupling relatively favors slower molecules. Three inhabited boundaries exclude a uniform small-phase claim, unqualified coherent speed ordering, and conditioning at zero drive. A fresh six-theorem physical-beam client audits these APIs independently; no linewidth is deduced from selection alone.

That selected-speed law now enters the normalized cosine-squared interference average explicitly, including its weak-field limit. Positive peak normalization preserves a separately computed FWHM. Mean-speed substitution and unqualified relative accuracy near a weak peak are rejected by inhabited counterexamples; the controlled near-frequency sweep retains the actual peak-referenced error bound. A separate seven-theorem client tests these APIs without production diagnostic witnesses. Fixed nonzero detuning can leave the near regime as the field weakens, so the near-model limit is not silently identified with an exact-experiment limit.

Figure 2's width labels and equation (22)'s nominal coefficients are now separate dimensionful evaluations, including the distinct near and broad frequency scales. The empirical route retains their nonzero Table I residuals. The former displayed-precision check is correctly identified as coarse consistency, not decimal rounding. Three inhabited boundaries and an independent five-theorem client protect these distinctions.

KSW's pionless RG output now retains a real subtraction-scale coupling family. Lean differentiates the imported equation-(11) solution on its non-pole domain, derives the printed beta equations, and recovers the zero-scale boundary data. The source beta-function atom includes actual derivative semantics, and sampled couplings are identified with the real family. Three inhabited controls reject one-point sampling, vacuous zero-scale weighting, and inclusion of the pole. A separate six-theorem client uses three public APIs with independent physical parameters. No claim is made to derive the solution from scale independence alone.

The pion-inclusive route now has separate actual retained-model derivatives, literal pion corrections, and the inhomogeneous D2 running term. Its computed- order scope is expressed with formal amplitude coefficients at powers n - 1: full invariance, coefficient completion, and no omitted p^-1 or p^0 terms derive retained agreement through p^0 and explicit higher-order compensation. Five new fidelity boundaries and a seven-theorem independent client prevent promotion to all-order equality, confusion with pionless flow, or unqualified zero-scale continuation. These are local derivative and formal-coefficient tests, not a global RG solution, convergent expansion, or nuclear fit.

Hohenberg-Kohn's response route now derives actual nonanalyticity from its punctured-neighborhood derivative divergences. Finite isotropic gradient kernels are polynomials in q^2, and their analyticity is proved. They cannot agree with the exact singular kernel on any neighborhood of 2 k_F; this direct obstruction does not assume a Fourier-tail calculation. The Friedel tail has an explicit additive inverse-cube envelope limit with positive frequency and nonzero amplitude, retaining cosine nodes and allowing smaller corrections without claiming exact equality. Five new fidelity boundaries and an eight-theorem independent client verify these distinctions. The Fourier calculation, nearly-uniform approximation, and separate slowly- varying expansion remain explicit obligations.

The slow-gradient expansion now distinguishes order and scale limits using actual coefficient sums, replacing the former shared Boolean status wrapper. The paper-local source calculation identifies the same scaled density shape, energy-density readout, fourth-order sum, absent fifth order, and sixth-order remainder. The explicitly assumed asymptotics then give orderwise eventual error budgets and the sixth-order coefficient limit. Three further fidelity boundaries and nine independent client theorems separate asymptotic behavior, fixed-scale convergence, and summation to the physical target. None proves the author's expectation or supplies a uniform numerical error estimate. The actual fourth-order error also realizes an inhabited controlled truncation in the existing shared framework, without inferring empirical adequacy or extracting the one-paper series vocabulary prematurely.

Finite Work Sampling

The Jarzynski 1997 parsing now separates exact ensemble validity, failure within a declared sampling budget, convergence of the actual finite exponential-work estimator, and accuracy of a selected observed dataset. The original pp. 7 and 9 do not turn rare-event difficulty into a prohibition of every finite experiment. Ten source routes and eight additional fidelity boundaries retain this distinction. The Gaussian variance label is also identified with the actual normalized work-law variance.

Constructed canonical Hamiltonian quenches realize an exact identity and rare-tail dominance while a ten-trial budget is insufficient, yet prove eventual convergence and reliable larger counts. Correlated repetitions can retain all canonical marginals without converging. A selected 100-trial dataset can be exact without its experiment meeting the confidence target. The IID moment calculation is a sufficient semantic diagnostic, not a proof of the general paper or an author's necessary hypothesis.

The independent three-state consumer derives a different canonical law, one-trial error probability 1/5, and a five-trial exact estimate. It uses the shared canonical integration and probability-role selection APIs without importing paper files or canned production witnesses. The new general sampling vocabulary stays paper-local until a second independent source justifies extraction.

Cosmological Posterior Logic

The Riess 1998 and Perlmutter 1999 routes now require actual normalized posterior evidence for acceleration, separately from positive-Lambda preference. Shared semantics retain the two-component threshold Lambda > M/2, nuisance marginalization, proper normalization, the coasting boundary, and the distinct flat-prior threshold. Riess's method-specific Gaussian likelihoods and Perlmutter's supplied correlated-error joint density remain different constructions. Numerical probability bounds are explicit imported calculations, not new fits or proofs of physical truth. Five additional paper-fidelity boundaries and an independent sixteen-theorem finite posterior client test these distinctions. The main results and shared adapters retain the evidence, so an interpretation flag cannot bypass it.

PhysicsLogic0.1.0