[{"data":1,"prerenderedAt":4},["ShallowReactive",2],{"CBoMbQbYVa":3},"# Mathematical Verification Components in Lean 4\n\n[![Lean verification](https://github.com/solanaqubits/leanbook/actions/workflows/lean_action_ci.yml/badge.svg)](https://github.com/solanaqubits/leanbook/actions/workflows/lean_action_ci.yml)\n\nMachine-checked mathematical components built with Lean 4 and Mathlib: algebraic\ninvariants, finite computations, conditional protocol properties, and explicit\nscalar models. Browse the proofs by subject, inspect their assumptions, and reuse\nthe components in larger formal developments.\n\n**[Knowledge base](knowledge/README.md)** · **[Results and value](knowledge/SUMMARY.en.md)** ·\n[Technical reference](docs/verification-details.en.md)\n\n[Reservoir indexing status](docs/reservoir-readiness.en.md): eligibility checked;\nregistry inclusion remains unconfirmed. The Lake package identifier is\n`lean-verification-components`.\n\n[Verification policy α–ζ](VERSIONING.md) · [Trust boundaries and conformance](docs/verification-hierarchy.en.md)\n\n## Proof sections\n\n| Section | Focus |\n|---|---|\n| [Collatz and discrete dynamics](knowledge/collatz/README.md) | Finite orbits, congruences, and coefficient bounds |\n| [Explicit logarithmic bounds](knowledge/riemann/README.md) | Prescribed analytic functions |\n| [Almost-complex algebra](knowledge/hopf/README.md) | Algebraic identities and cross products |\n| [Polynomial functionals](knowledge/lamzouri/README.md) | Integrals, quotients, and exact minima |\n| [Coordinate geometry](knowledge/finsler/README.md) | Forms, polarization, and diagonal transformations |\n| [Proof certificates and DAGs](knowledge/proof-graphs/README.md) | Conditional checker soundness |\n| [Cryptographic algebra](knowledge/cryptography/README.md) | Diffusion, traces, folding, and commitment identities |\n| [Quantum algebra, photonics, and mechanics](knowledge/quantum-physics/README.md) | Matrices, symmetries, and prescribed energy models |\n| [Finance and mechanisms](knowledge/finance/README.md) | Balances, reserves, fees, and portfolio risk |\n| [Distributed consensus](knowledge/distributed/README.md) | Quorums, reachable Log Matching, and operational Leader Completeness |\n| [Registry and audit](knowledge/verification/README.md) | Selected suites and axiom dependencies |\n\n## ALCC certificate verification\n\n[Canonical byte verification, CLI, and trust boundaries](docs/alcc.en.md).\n\n## Verified snapshot\n\n[Combined synchronization v0.7.48](docs/release-v0.7.48.en.md) reconciles all completed streams and preserves their verification boundaries.\n\n**300 direct imports in MasterSuite**, **349 library Lean sources including Verification.lean**.\nThe separate `AlccVerifyMain.lean` CLI, auxiliary tooling and test fixtures are outside\nthis library-source metric.\nThe [v0.9.0 publication](docs/release-v0.9.0.en.md) has a confirmed strict-build\nfailure; its successful-beta qualification is withdrawn. See the\n[correction and validation boundary](docs/v0.9-build-correction.en.md).\nThe last successful beta remains v0.8.0. The\n[300-module extension](docs/toward-300.en.md) describes the source additions.\n\nALCC is an additive batch on top of v0.7.48, released with a new full-validation checkpoint; see the\n[public integration record](docs/release-v0.8.0.en.md).\nThe [bounded Prometheus synchronization](docs/prometheus-lean-sync.en.md) adds nine\nconditional model modules and their public verification scope.\n[Release v0.7.47](docs/release-v0.7.47.en.md) adds granular provenance reports,\nan explicit pinned native IO adapter and sequential replay-registry recovery.\nThe Lake package metadata retains version 0.7.1; checkpoint tags follow the\nseparate [hierarchical version policy](VERSIONING.md).\n\n[Native adapter](tools/provenance_native/README.md) ·\n[Snapshot format](docs/quota-codec-v1.en.md) ·\n[Snapshot reader](docs/quota-snapshot-reader.en.md) ·\n[Profile reader](docs/quota-profile-reader.en.md).\nRecovery preserves acknowledged challenges relative to a retained completed log\nand an independent trusted prefix. Physical WAL/fsync, anti-rollback storage,\nconcurrent atomicity and hardware authorization remain external obligations.\nNative conformance tests do not prove cryptographic security or FFI refinement.\nThe explicit qutrit Spec build is preserved.\n\n[Composite epoch safety](knowledge/02_distributed_systems/DistributedTendermintEpochTransitionSafetyMasterContract.md)\nand [checked header chains](knowledge/02_distributed_systems/DistributedTendermintHeaderChainEpochAuthContract.md)\ncompose conditional agreement, actual historical slashing and structural history checks.\nTrusted roots, signature authenticity, commitment binding, commit consistency and\ncomplete offence references remain explicit premises; delivery and liveness remain open.\n\n[HCTK scalar partition](knowledge/03_quantum_physics_and_optics/HCTKScalarPartition.md)\nproves algebraic partition, transfer, explicit three-store capture and regularization properties. Physical stability,\nvacuum charge transport and a topological interpretation are not established.\n\n[All-round handover agreement](knowledge/02_distributed_systems/DistributedTendermintHandoverRoundInduction.md)\nuses strong round induction under explicit honest prevote/precommit rules and\nuniversal honest quorum intersection. Registered local executions connect checked\nlock replacements to transcript Polka. Delivery, liveness, signature authentication\nand complete protocol refinement remain open.\n\n[Checked lock handover](knowledge/02_distributed_systems/DistributedTendermintLockHandoverContract.md)\nprovides adoption, conditional round-zero agreement and justified local replacements;\nthe all-round theorem adds global history rules, not automatic network guarantees.\n\n[Weighted quorum intersection](knowledge/02_distributed_systems/DistributedTendermintQuorumIntersectionEpochTransitionContract.md)\nprovides common-mass, total-variation and directed honest-weight-loss criteria\nfor a shared honest validator across epochs. Strict and non-strict quorum thresholds\nare distinguished. This does not establish lock handover or protocol agreement.\n\n[Stable epoch identity](knowledge/02_distributed_systems/DistributedTendermintEpochIdentityContract.md)\nresolves old certificates against historical identity maps and preserves global\nslashing keys and unbonding liabilities. Exclusion from the entire certified\nhistorical offender set protects a subject from that penalty; inequality with\none former index owner alone is insufficient. History authentication and quorum\nhandover remain external obligations.\n\n[Evidence windows and delayed withdrawal](knowledge/02_distributed_systems/DistributedTendermintUnbondingPeriodContract.md)\nuses finite queues and two-phase slots. No-Escape covers liable tranches and\ncertificates included before admission closes; unseen-certificate delivery is\nnot guaranteed. Clock synchronization, network delays and concurrent execution\nremain external obligations.\n\n[Slashing replay protection](knowledge/02_distributed_systems/DistributedTendermintSlashingReplayProtection.md)\nuses checked (height, validator) keys, rejects invalid input without state changes,\nand preserves accounting across finite sequential request lists. Database durability,\nconcurrent execution, reorganizations and unbonding remain outside the model.\n\n[Pedersen opening extraction](knowledge/04_cryptography/CryptoPedersenCommitmentOpeningExtractionContract.md)\nproves scalar/vector special soundness and checked extraction. The conditional\nBulletproofs bridge needs additional opening forks; obtaining them from the\noriginal protocol and probabilistic forking remain open obligations.\n\n[Certified Tendermint slashing](knowledge/02_distributed_systems/DistributedTendermintSlashingPenaltyContract.md)\nproves exact rational penalties, protection of honest stake, a strict\nconfiscation bound and conditional growth of the honest share.\n[Scope policy](docs/verification-scope-policy.en.md) separates validated metadata\nfrom executable checking mechanisms and binds evidence to exact checked inputs.\n\n[Qutrit circuit refinement](knowledge/03_quantum_information/QuantumQutritDecoderCircuitRefinement.md)\nconnects an executable three-gate finite interpreter to the explicit unitary\ndecoder and Kraus channel on all complex input matrices. It preserves reference\nsystems and rejects four deliberately incorrect gate configurations.\n\n## Release v0.5.88\n\n[Explicit qutrit decoder](knowledge/03_quantum_information/QuantumQutritSecretSharingExplicitDecoder.md)\nconstructs the basis permutation D|u,v>=|v-u,2v-u> and proves both unitary\nidentities and full-state factorization. Three explicit Kraus operators recover\nall logical matrices from every pair and preserve arbitrary external references.\n\n## Release v0.5.87\n\n[Qutrit two-of-three secret sharing](knowledge/03_quantum_information/QuantumQutritTwoOfThreeSecretSharingContract.md)\nproves an explicit modulo-three isometric code, perfect single-share privacy\nand CPTP recovery from every pair. The same recoveries preserve arbitrary\nexternal references, while no single share permits exact recovery.\n\n## Release v0.5.86\n\n[Subsystem erasure correctability](knowledge/03_quantum_information/QuantumErasureCorrectabilityContract.md)\nconstructs the partial-trace Kraus channel and identifies its complement with\nthe lost subsystem. Exact recovery is equivalent to independence of the lost\npart, with reference preservation. Explicit fixed-factor and entangled-auxiliary\ncodes are verified alongside the repetition-code obstruction.\n\n## Release v0.5.85\n\n[Reference-preserving recovery](knowledge/03_quantum_information/QuantumReferencePreservingRecoveryContract.md)\nextends exact recovery to every finite reference with the same recovery channel,\nderives reference/environment factorization and proves the normalized maximally\nentangled-state criterion by matrix-block extraction. Bell coherence regressions\ninclude the impossibility of full-qubit dephasing recovery.\n\n## Release v0.5.84\n\n[Knill-Laflamme recovery necessity](knowledge/03_quantum_information/QuantumKnillLaflammeRecoveryNecessity.md)\nproves scalar structure of composite Kraus operators and derives the general\nKnill-Laflamme conditions from arbitrary exact CPTP recovery. Together with the\nprevious sufficiency and environment criteria, it establishes the finite-dimensional\nequivalence and rules out exact recovery of full-qubit dephasing.\n\n## Release v0.5.83\n\n[General Knill-Laflamme recovery](knowledge/03_quantum_information/QuantumKnillLaflammeGeneralRecoveryTheorem.md)\nderives coefficient Hermiticity and constructs the spectral certificate using\nMathlib. It proves exact CPTP recovery of every complex logical matrix from\ngeneral Knill-Laflamme conditions, without a supplied diagonalization certificate.\nThis is sufficiency; necessity and an executable numerical decoder remain outside scope.\n\n## Release v0.5.82\n\n[Recovery with certified unitary diagonalization](knowledge/03_quantum_information/QuantumUnitaryKrausDiagonalizationRecoveryContract.md)\nuses complex Kraus mixing with the exact transpose bridge W=U^T. It derives\nnonnegative normalized spectral weights and preserves the physical channel.\nThe explicit CPTP recovery from module 183 then recovers every complex logical\nmatrix. A unitary diagonalization certificate is supplied as input; existence\nof such a certificate and the general recovery equivalence are outside scope.\n\n## Release v0.5.81\n\n[Orthogonal error recovery](knowledge/03_quantum_information/QuantumOrthogonalErrorRecoveryContract.md)\nconstructs a recovery CPTP channel for diagonal Knill-Laflamme data. Normalized\nerror adjoints are completed with reset operators on the unused output space.\nThe channel recovers every complex logical matrix, including coherences, and\nhandles zero error weights. General non-diagonal coefficient reduction and the\nfull recovery theorem remain open.\n\n## Release v0.5.80\n\n[Knill-Laflamme environment criterion](knowledge/03_quantum_information/QuantumKnillLaflammeEnvironmentCriterion.md)\nproves the equivalence between compressed Kraus-product scalar identities and\nconstancy of the complementary channel on an encoded space, for all complex\nlogical matrices. Isometric encoding with positive logical dimension yields a\nnormalized positive environment state. Complex regressions check the ordinary\ntranspose convention. Recovery CPTP maps and full error correction remain open.\n\n## Release v0.5.79\n\n[Complementary quantum channel](knowledge/03_quantum_information/QuantumComplementaryChannelContract.md)\nconstructs the environment output of a supplied Kraus/Stinespring representation,\nproves its CPTP properties and both partial-trace identities, and relates a given\nisometric environment change to the unchanged main channel and conjugated\ncomplement. Examples cover unitaries, reset, dephasing and zero padding.\nThe joint matrix need not be pure; information absent from both marginals can\nremain in correlations. General dilation uniqueness, minimality, quantum\ncapacity and general recovery maps are outside scope.\n\n## Release v0.5.78\n\n[Utilization feedback stability](knowledge/01_defi/DeFiLendingUtilizationFeedbackStability.md)\nextends the existing rational kinked rate to a real projected feedback law,\nwith an exact rational bridge. It proves invariant unit-interval bounds,\ncontraction conditions across the kink, finite-time disturbance bounds and\nzero-noise convergence to a specified equilibrium. Rational trajectories and\ninteger-rate rounding have explicit correspondence theorems. A large-step\nexample cycles between zero and one while remaining bounded by projection.\nThe response law is a prescribed model, not a proof of market stability,\nliquidity or economic solvency.\n\n## Release v0.5.77\n\n[Tendermint evidence accountability](knowledge/05_distributed/DistributedTendermintAccountableSafety.md)\nconstructs explicit accusations and a deduplicated offender set for conflicting\nvotes, uncertified precommits and unjustified lock switches. Conflicting commits\nforce strictly more than one third of the total weight into that set.\nNo-framing is proved for reachable core histories under a sufficient view of an\nexternally authenticated complete reference transcript. The checker verifies\nrelative prevote coverage; it cannot establish the reference's own completeness.\nMissing evidence is rejected. Concrete signatures, slashing, evidence deadlines,\ndynamic membership and deployed-protocol equivalence remain outside this result.\n\n## Release v0.5.76\n\n[Conditional range extraction](knowledge/04_cryptography/CryptoBulletproofsRangeWitnessExtraction.md)\ncomposes actual IPA tree extraction with polynomial/grid interpolation from\ncertified openings of A,S,V. It returns a range witness opening the original V\nor a concrete nontrivial zero relation among the original generators, including\nblinding generators. Vector agreement is derived rather than assumed.\nObtaining the supplied openings, rewinding, runtime bounds and Fiat–Shamir/ROM\nsecurity remain outside this result. This release also names the existing scope\nranks alpha/beta/gamma and documents delta iterations in parallel streams.\n\n## Release v0.5.75\n\n[Stinespring dilation](knowledge/03_quantum_information/QuantumStinespringDilationContract.md)\nconstructs an isometry from supplied rectangular Kraus operators, recovers the\nchannel through the existing partial trace and identifies its dual map.\nJoint density matrices and their recoverability are proved. Exact regressions\ncover unequal dimensions, dephasing and redundant zero Kraus blocks.\nMinimality, uniqueness and general unitary extension are outside this module.\n\n## Release v0.5.74\n\n[Finite-grid range interpolation](knowledge/04_cryptography/CryptoBulletproofsRangeInterpolation.md)\nturns pointwise equalities on an injective Y/Z grid for fixed witnesses into a\nformal polynomial identity, bit constraints and a natural range bound under\nexplicit no-wrap hypotheses. This is not a full transcript witness extractor.\nThe release includes targeted regressions, a checked grid interface and the\napproved X/Y/Z verification policy.\n\n## Release v0.5.73\n\n[CPTP channel contract](docs/release-v0.5.73.en.md) proves quantum trace-distance\ncontraction, dual effect pullback and trace preservation for Kraus channels, with\nan additional theorem for the existing abstract CPTP interface. Identity and\nunitary channels preserve distance; basis-state reset and dephasing demonstrate\nloss of distinguishability. Stinespring dilation, full equivalence of channel\nrepresentations and relative-entropy DPI are outside this module.\nThe updated verification workflow retains incremental caches and runs a single\nfull final release gate.\n\n## Earlier additions in v0.5.72\n\n[Bad debt accounting](docs/release-v0.5.72.en.md) allocates authorized writeoff\nlosses first to reserves and then to supplier claims, preserving the accounting\nbalance with fixed cash. It proves indexed debt consistency, supplier-share price\ndecline, exact integer loss allocation and explicit rounding bounds. The signed\ndebt-ledger/index gap is separated from reconciliation dust. Actual uncollectibility,\nwithdrawal liquidity, economic solvency and specific protocol mechanisms remain\noutside scope. Full Bulletproofs range extraction, Tendermint accountability,\nPython, JSON/SHA-256 and SimLab obligations remain open.\n\n## Earlier additions in v0.5.71\n\n[Liquidation accounting](docs/release-v0.5.71.en.md) connects liquidation admission\nto indexed debt repayment, splits the collateral bonus between liquidator and a\nseparate treasury, and conserves both asset balances. The checked integer policy\nhas explicit rounding bounds and distinguishes the debt-ledger/index gap from\nreconciliation dust. Health-factor improvement is conditional. Oracle accuracy,\nmarket execution, debt recoverability, economic solvency and deployed-contract\ncorrespondence remain outside scope. Full Bulletproofs range extraction,\nTendermint accountability, Python, JSON/SHA-256 and SimLab obligations remain open.\n\n## Earlier additions in v0.5.70\n\n[Trace distance and measurement contraction](docs/release-v0.5.70.en.md) proves\nmetric laws on density matrices, an attained maximum over effects, the equal-prior\nHelstrom identity and TV contraction under finite POVM measurements and classical\npostprocessing. A binary spectral POVM attains the maximum over all finite outcome\ncounts. General quantum-channel contraction, numerical spectral certification and\nphysical implementation remain outside scope. Full Bulletproofs range extraction,\nTendermint accountability, Python, JSON/SHA-256 and SimLab obligations remain open.\n\n## Earlier additions in v0.5.69\n\n[Holevo–Helstrom state discrimination](docs/release-v0.5.69.en.md) proves the optimal\nbinary state discrimination bound without commutation assumptions, attainment by a\nspectral projector, freedom of selection at zero eigenvalues, Bayes decision rule\noptimality and classical postprocessing contraction of optimal guessing probability.\nExact noncommuting qubit regressions give trace norm 1/sqrt(2). Certified numerical\nspectral algorithms, sampling, physical implementation and general quantum DPI remain\noutside this model. Full Bulletproofs range extraction, Tendermint accountability,\nPython, JSON/SHA-256 and SimLab obligations remain open.\n\n## Earlier additions in v0.5.68\n\n[Recursive IPA tree extraction](docs/release-v0.5.68.en.md) proves deterministic\nextraction from a supplied complete accepting four-branch tree. It recovers full\nwitness vectors or explicit nonzero coefficients of a zero combination of the\nroot generators. Relation lifting preserves evaluation and nontriviality; the\nchecker validates every branch against the actual verifier's derived contexts.\nHonest trees recover their exact vectors at every depth. The tree has n^2 leaves,\nseparate from the 2k group elements of a single IPA transcript. Probabilistic tree\nconstruction, full range extraction and bitness, computational binding, HVZK,\nFiat-Shamir/ROM, Tendermint accountability, Python, JSON/SHA-256 and SimLab\nobligations remain open.\n\n## Earlier additions in v0.5.67\n\n[Local Bulletproofs witness extraction](docs/release-v0.5.67.en.md) proves a\none-step IPA extraction dichotomy from four accepting folded-witness responses\nwith a common prefix and distinct nonzero challenge squares: an original witness\nor explicit nonzero coefficients of a zero generator combination. Generator\nindependence is not assumed. The checked interface rejects invalid inputs.\nThree-point Vandermonde interpolation recovers the range-reduction polynomial's\ncoefficients; it does not establish bitness. Full recursive extraction,\nprobabilistic transcript-tree construction, computational binding, HVZK and\nFiat-Shamir/ROM remain open, as do Tendermint accountability and external Python,\nJSON/SHA-256 and SimLab obligations.\n\n## Earlier additions in v0.5.66\n\n[Debt-index accrual and rounding reconciliation](docs/release-v0.5.66.en.md)\nproves interval composition, the strict subdivision effect and guarded accrual,\nborrowing and repayment accounting. Natural accrual preserves balance by assigning\nthe interest residual to suppliers. Index-derived reconciliation dust is at most\nn-1 and is explicitly separated from independent ledger/index drift. Local error\nbounds do not imply a uniform global bound over arbitrary update chains. Debt\nrecoverability, default freedom, withdrawal liquidity and deployed-contract\nrefinement remain outside scope. Tendermint accountability, Bulletproofs security\nand external Python, JSON/SHA-256 and SimLab obligations remain open.\n\n## Earlier additions in v0.5.65\n\n[Kinked utilization rates and rounding](docs/release-v0.5.65.en.md) proves exact\nutilization admission, continuity and monotonicity of the borrow curve, convexity\nunder ordered slopes, supply-rate monotonicity and conditional spread. Executable\nnatural arithmetic has explicit rounding order and end-to-end error bounds against\nthe rational lift of the same encoded parameters. The checked quote rejects U>1\neven when rounding would hide the excess. Rate order is an instantaneous property;\npool solvency, defaults, withdrawable liquidity and accrual over time are outside\nscope. Deployed-contract refinement and external Tendermint, Bulletproofs, Python,\nJSON/SHA-256 and SimLab obligations remain open.\n\n## Earlier additions in v0.5.64\n\n[Classical POVM data processing](docs/release-v0.5.64.en.md) proves stochastic\npostprocessing of finite POVMs, support preservation and classical KL contraction\nunder absolute continuity. Bistochastic channels cannot decrease Shannon entropy;\nbinary symmetric noise strictly increases it for nonuniform inputs when\n0\u003Cepsilon\u003C1/2. Deterministic merging provides the entropy-decrease counterexample\nfor general stochastic channels. Singular infinite KL and general quantum Umegaki\nDPI remain outside scope. The exact real analysis is noncomputable; no numerical\nlogarithm implementation is certified. External correspondence, Tendermint\naccountability and Bulletproofs security obligations remain open.\n\n## Earlier additions in v0.5.63\n\n[Weighted Tendermint core safety](docs/release-v0.5.63.en.md) proves quorum\nintersection, same-round uniqueness and cross-round commit safety from reachable\nstates. Strict >2/3 quorums retain safety at exactly one-third Byzantine weight;\na concrete reachable conflict is exhibited above that boundary. Executable guards\ncheck actual certificates and unique signers. This is a fixed-height safety\nabstraction, with full implementation refinement, liveness, signatures and\nattributable slashing evidence outside scope. External correspondence and\nBulletproofs security obligations remain open.\n\n## Earlier additions in v0.5.62\n\n[Lending liquidation health factor](docs/release-v0.5.62.en.md) proves\nexact liquidation accounting, conditional health improvement, residual debt\ncoverage and directed integer rounding. Zero debt has no numeric health factor.\nExecutable guards distinguish liquidation admission from preserving coverage;\ncounterexamples show why admissibility alone does not ensure either health\nimprovement or residual coverage. Oracle truth, market execution, pool-wide\nsolvency and external correspondence obligations remain outside these guarantees.\n\n## Earlier additions in v0.5.61\n\n[Bulletproofs multi-range aggregation](docs/release-v0.5.61.en.md) proves\nblock-weighted polynomial reduction, formal coefficient recovery and honest\ncomposition with the recursive IPA. The single-block verifier equals module 159.\nThe IPA payload contains exactly 2(a+b) group elements and two scalars;\nthe proof body and envelope with public commitments are counted separately.\nWitness extraction, binding, HVZK, Fiat-Shamir/ROM and external correspondence\nobligations remain open.\n\n## Earlier additions in v0.5.60\n\n[POVM information entropy](docs/release-v0.5.60.en.md) proves the general\nMaassen-Uffink lower bound for finite POVMs and density matrices through\nHadamard interpolation, Naimark phase contractions and spectral mixtures.\nThe overlap uses the Euclidean operator norm. Exact Pauli examples attain one\nbit; noncommuting qutrit measurements can share a zero-entropy eigenstate.\nFinite sampling, quantum side information and numerical logarithm certificates\nare outside this exact analytic model. Existing cryptographic and external\ncorrespondence obligations remain open.\n\n## Earlier additions in v0.5.59\n\n[Constant product with virtual reserves](docs/release-v0.5.59.en.md) proves exact\nreal-reserve solvency, the retained-fee product identity, fixed-fee price impact\nand executable natural swaps with directed rounding. Successful finite chains\nwith variable valid fees have nondecreasing product. Fees remain in trading\nreserves; external-price value preservation and MEV/arbitrage security are not\nasserted. Existing Bulletproofs security and implementation obligations remain open.\n\n## Earlier additions in v0.5.58\n\n[Bulletproofs batch verification](docs/release-v0.5.58.en.md) proves perfect\ncompleteness, equivalence to one expanded MSM, paired permutation invariance and\nan error bound of at most 1/q relative to individual verification. The probability\nbound applies to a fixed batch with fresh independent uniform field weights.\nScalar checks reject invalid challenges deterministically. Original IPA transcripts\nare retained. Knowledge extraction, computational binding, HVZK, Fiat-Shamir/ROM\nand implementation of secure randomness remain open.\n\n## Earlier additions in v0.5.57\n\n[Bulletproofs algebraic range reduction](docs/release-v0.5.57.en.md) proves\nformal polynomial equivalence with bit constraints, natural range recovery under\nexplicit bounds, the corrected public IPA target and honest composite completeness.\nKnowledge extraction, computational binding, HVZK and Fiat-Shamir/ROM remain open.\nAn identity of formal polynomials is distinguished from equality at a fixed challenge.\n\n## Earlier additions in v0.5.56\n\n[Bulletproofs inner product algebra](docs/release-v0.5.56.en.md) proves the\nhalving invariant, recursive completeness, equivalence of expanded verification\nand an exact payload of 2k group elements plus two scalars for dimension 2^k.\nKnowledge extraction, range reduction, HVZK and Fiat-Shamir/ROM remain outside scope.\nLogarithmic proof size does not imply logarithmic verifier work.\n\n## Earlier additions in v0.5.55\n\n[Stable Marzullo event merge sorting](docs/release-v0.5.55.en.md) proves\nstable ordering, exact insertion-sort equivalence and the comparator-call bound\nN * ceil(log2 N). The merge-based backend preserves peak and safe-hull semantics.\nRational bit complexity and the complete consensus runtime remain outside scope.\n\n## Earlier additions in v0.5.54\n\n[Linear interactive Pedersen range proofs](docs/release-v0.5.54.en.md) prove\nnatural bit ranges, fixed-opening completeness, two-transcript witness extraction\nand equality of full joint special HVZK distributions. The simulator includes\ncorrelated bit commitments with the fixed aggregate. Computational binding,\nFiat-Shamir/ROM and malicious-verifier security remain outside scope.\n\n## Earlier additions in v0.5.53\n\n[Discrete concentrated-liquidity reference arithmetic](docs/release-v0.5.53.en.md)\nproves directed token rounding, finite-grid swap budget bounds, and nonnegative\nposition-derived liquidity through tick crossings. This executable exhaustive\nreference model does not establish equivalence to Solidity SwapMath/TickMath,\nefficient execution on wide price grids, or a complete pool lifecycle.\n\n## Earlier additions in v0.5.52\n\n[Executable Marzullo interval consensus](docs/release-v0.5.52.en.md) proves rational\nevent-sweep overlap counts, exact maximal peak intervals and deterministic\nselection by length and left endpoint. The computed safe hull equals the existing\nreal-valued thresholdHull. A selected peak need not contain true time; its\ncontainment in the safe hull is non-strict. Full NTP and physical clock control\nremain outside scope.\n\n## Earlier additions in v0.5.51\n\n[Informationally complete POVMs](docs/release-v0.5.51.en.md) connect measurement\ninjectivity to a positive definite, invertible frame operator and exact quantum\nstate reconstruction through its canonical dual. The module proves the d²\noutcome bound, constructs a tetrahedral qubit SIC-POVM and exhibits states that\nbasis measurements cannot distinguish. Finite-sample statistics, numerical\nconditioning and SIC existence in arbitrary dimensions remain outside scope.\n\n## Earlier additions in v0.5.50\n\n[Mixed-state no-broadcasting](docs/release-v0.5.50.en.md) proves that a pair of\nfinite-dimensional density matrices admits one exact CPTP broadcasting channel\nif and only if the states commute. Correlated outputs and degenerate spectra are\nincluded. Necessity uses a constructed symmetric logarithmic derivative and an\noperator sum of squares. Infinite dimensions, approximate broadcasting and\nphysical implementations remain outside scope.\n\n## Earlier additions in v0.5.49\n\n[FROST threshold Schnorr signatures](docs/release-v0.5.49.en.md)\nproves partial and aggregate verification for any signing set at or above the\nthreshold, canonical session contexts and independently recomputed alternative\ncoalitions. A single response error is rejected; opposite errors can cancel in\nthe aggregate. ROM security, nonce-use enforcement, DKG/VSS and serialization\nremain outside scope.\n\n## Earlier additions in v0.5.48\n\n[Raft joint-consensus reconfiguration](docs/release-v0.5.48.en.md)\nproves reachable Election Safety, Log Matching and Leader Completeness for one\nold-to-joint-to-new transition, with historical commit-index soundness and local\nconfiguration rollback. Arbitrarily many reconfigurations, snapshots, Byzantine\nfaults, crash/recovery and liveness remain outside scope.\n\n## Earlier additions in v0.5.47\n\n[Finite-field Shamir sharing](docs/release-v0.5.47.en.md)\nproves t-of-n interpolation over ZMod q, joint PMF secrecy below threshold,\ngroup-point reconstruction and finite weighted linearity. The explicit secret-shift\nequivalence preserves every observed share. VSS, active share forgery, DKG,\nrefresh, threshold signatures and efficient DLOG decoding remain outside scope.\n\n## Earlier additions in v0.5.46\n\n[Vector Pedersen commitments](docs/release-v0.5.46.en.md)\nproves vector linearity and weighted homomorphism, perfect hiding through a uniform\nPMF, exact collision relations and conditional logarithm extraction. Equal bases\nand known relations yield explicit alternate openings. Generators are an indexed\nfamily, not a linearly independent basis. Computational binding, parameter\ngeneration, coordinate opening proofs and ZKP protocols remain outside scope.\n\n## Earlier additions in v0.5.45\n\n[Group ElGamal weighted homomorphism](docs/release-v0.5.45.en.md)\nproves group and exponential decryption correctness, scalar uniqueness,\nfinite weighted homomorphism, algebraic rerandomization and nontrivial malleability.\nDecryption returns a group point; scalar uniqueness does not provide an efficient\ndiscrete-logarithm decoder. IND-CPA/IND-CCA proofs, DDH reductions, concrete curves\nand serialization remain outside scope.\n\n## Earlier additions in v0.5.44\n\n[BLS aggregation in bilinear groups](docs/release-v0.5.44.en.md)\nproves individual and aggregate completeness, common-message aggregation and\ncomposition of valid partial signatures. Pairing injectivity is derived from\ncyclicity and nondegeneracy. A concrete scalar model witnesses the assumptions.\nRogue-key and error-cancellation counterexamples delimit what verification\nestablishes. Concrete curves, hash-to-curve, serialization, PoP and computational\nsecurity reductions remain outside scope.\n\n## Earlier additions in v0.5.43\n\n[Signed Byzantine broadcast](docs/release-v0.5.43.en.md)\nproves Agreement and CommanderValidity in f + 1 synchronous rounds with ideal\nsignatures, n >= f + 2 nodes and at most f static Byzantine faults. Signature\norigins and dissemination follow from execution transitions. Final honest\nlieutenant views coincide. A delayed-chain counterexample establishes why the\nround-length filter matters. Computational signature security, asynchrony and\ndynamic faults remain outside scope.\n\n## Earlier additions in v0.5.42\n\n[Three-generals oral Byzantine broadcast](docs/release-v0.5.42.en.md)\nproves that Agreement and CommanderValidity cannot both hold for three nodes\nand at most one static Byzantine fault in synchronous oral messages. Honest\nlocal-state equality is derived inductively in three constructed executions\nfor every fixed finite horizon T. General n \u003C= 3f, signed messages, randomized\nprotocols and termination without a common finite bound are outside scope.\n\n## Earlier additions in v0.5.41\n\n[Finite-group Schnorr aggregation](docs/release-v0.5.41.en.md)\nproves partial and aggregate algebraic completeness for a static key vector in\na cyclic prime-order group. Accepted partial responses with a common challenge\nassemble into an accepted aggregate. A naive rogue-key witness exhibits key\ncancellation and a passing signature. A common ring identity connects the real\nscalar model and modular specialization. AGM/ROM security, hashed-coefficient\nrogue-key resistance, interactive MuSig2/BIP327 and serialization are outside scope.\n\n## Earlier additions in v0.5.40\n\n[Coordinated attack impossibility](docs/release-v0.5.40.en.md)\nderives delivery-removal indistinguishability from deterministic local transitions.\nFor every fixed finite horizon, Agreement and ValidityZero force retreat on every\ninput and delivery schedule, contradicting ReliableSuccess. The model permits\nsynchronous rounds and arbitrary message losses, with no sender-visible delivery\nfeedback. Regressions cover zero rounds, an always-retreat protocol, lost\nacknowledgements and commuting delivery removals. Unbounded stopping times,\nrandomized agreement, quantum channels and Byzantine behavior are outside scope.\n\n## Earlier additions in v0.5.39\n\n[Exact unitary no-cloning](docs/release-v0.5.39.en.md)\nderives overlap constraints from unitary evolution and tensor factorization.\nPure states cloned by one unitary with a fixed blank must be orthogonal or have\nidentical density matrices. Global phases are handled explicitly. CNOT copies\nthe computational basis and entangles a superposition. Universal cloning in\ndimension at least two and joint cloning of the four BB84 states are impossible.\nGeneral CPTP cloning, mixed-state no-broadcasting and physical QKD security are\noutside scope.\n\n## Earlier additions in v0.5.38\n\n[Finite POVMs and Naimark dilation](docs/release-v0.5.38.en.md)\nproves the finite-dimensional Naimark theorem, preservation of Born probabilities\nand density matrices, and unitary extension with a fixed pure ancilla. Partial\ntrace yields the canonical Lueders instrument. Identical POVM effects need not\ndetermine identical state updates. The constructions are noncomputable; minimality,\ninfinite-dimensional spectral measures and physical circuit synthesis are outside scope.\n\n## Earlier additions in v0.5.37\n\n[Quantum depolarizing channel and CHSH damping](docs/release-v0.5.37.en.md)\nproves Kraus completeness, trace preservation and complete positivity for every\nfinite ancilla dimension. It derives Bloch scaling, channel composition, the noisy\nE91 singlet, CHSH damping and key QBER. The physical parameter range is [0,1].\nChannel capacity, key secrecy, DI-QKD and finite-key statistics are outside scope.\n\n## Earlier additions in v0.5.36\n\n[Quantum E91 correlations and CHSH violation](docs/release-v0.5.36.en.md)\nderives all nine correlations from singlet Born probabilities, proves the exact\nCHSH value -2 sqrt(2), and separates key, test and discarded rounds. It proves\nclassical bounds for finite local laws and separable qubit mixtures. The explicit\nXZ intercept/resend instrument on the supplied singlet produces a separable state.\nUniversal Tsirelson bounds, device-independent secrecy and finite-key statistics\nare outside scope.\n\n## Earlier additions in v0.5.35\n\n[Operational Multi-Paxos consensus](docs/release-v0.5.35.en.md) derives slot\nAgreement across ballots from reachable protocol transitions and Promise snapshots,\nwithout an external SingleVote premise. One phase-one certificate supports multiple\nslots; replica execution preserves comparable chosen prefixes. Safety tolerates\narbitrary message delays and duplicates. Liveness is not proved; progress requires\nadditional leader, quorum, delivery and scheduler assumptions.\n\n## Earlier additions in v0.5.34\n\n[BB84 QBER from Born measurement](docs/release-v0.5.34.en.md) derives a\ntrace-preserving intercept-resend channel with prefactor one half. The sifted\nerror probability is exactly one quarter under full interception, and f/4 for\nindependent interception with probability f. For m independent sifted rounds,\ndetection probability is 1-(3/4)^m; evasion remains possible on every finite sample.\nThe model assumes ideal Z/X preparations, projective measurement and an\nauthenticated classical channel. Full QKD secrecy is outside its scope.\n\n## Earlier additions in v0.5.33\n\n[Linear-optical quantum teleportation](docs/release-v0.5.33.en.md) derives ten\nKraus operators from the Bell analyzer on an invariant twenty-dimensional sector.\nSuccess is one half for every density operator. Conditional Pauli corrections\nrecover the input exactly, with squared Uhlmann fidelity one. The unconditioned\nchannel gives Bob the maximally mixed state. The scheme assumes an ideal supplied\nBell resource, ideal optics and detection; deterministic teleportation is outside scope.\n\n## Earlier additions in v0.5.32\n\n[Linear-optical Bell analyzer](docs/release-v0.5.32.en.md) derives a unitary\nnormalized ten-dimensional two-photon evolution from balanced splitters.\nIt computes all four Bell outputs and derives positive, complete detector POVM\neffects and the Born identity. Psi-plus/minus are identified without error;\nPhi-plus/minus have identical outcome distributions. Success is one half for\nthe uniform ensemble and one for a Psi-only ensemble. The result concerns this\nfixed ideal scheme; the universal bound for arbitrary optical networks is outside scope.\n\n## Earlier additions in v0.5.31\n\n[Observed-remove set and causal add-wins](docs/release-v0.5.31.en.md)\nderives fresh tags from operational counters and proves add-wins for concurrent\noperations and complete post-operation snapshots. Componentwise metadata union is\nan unconditional join semilattice. Equal included updates give equal states;\nauthentic reliable snapshots and explicit fairness imply dissemination and,\nafter updates cease, stabilization. The causal-broadcast adapter and counterexamples\nto tag reuse and premature tombstone collection are included. Tombstone GC,\nORSWOT compression and linearizability remain outside scope.\n\n## Earlier additions in v0.5.30\n\n[State-based LWW register and strong convergence](docs/release-v0.5.30.en.md)\nderives unique stamps from fresh writes and constructs a join semilattice on\ncompatible states. Equal included update sets give equal register payloads.\nFair sending and reception of reliably available useful snapshots imply information\ndissemination; after writes cease, replicas stabilize to the global maximum.\nAn incremental causal-broadcast adapter and collision/stale-write counterexamples\nare included. Consensus, linearizability and physical-time ordering are outside scope.\n\n## Earlier additions in v0.5.29\n\n[Causal broadcast and delivery safety](docs/release-v0.5.29.en.md) connects\nindependent broadcast causality with operational delivered-prefix counters and\nbuffer guards. Prefix integrity, at-most-once delivery, exact causal-past timestamps\nand causal delivery order are proved. Eventual delivery requires reliable arrival\nand per-message weak fairness. Reordered arrivals and weakened-guard counterexamples\nare covered. The fixed-group model excludes failures, total-order guarantees and\nphysical delay bounds.\n\n## Earlier additions in v0.5.28\n\n[Postselected photonic controlled-Z](docs/release-v0.5.28.en.md) derives\nK(T)=diag(T,T,T,2T-1) from a unitary six-mode optical network and its\n21-dimensional two-photon lift. At T=1/3 the accepted branch is CZ/3,\nwith success probability 1/9 for every normalized input. Pauli conjugation,\ngraph-state entanglement and reduced density matrices are proved.\nThe model uses ideal coincidence postselection; nondestructive heralding,\nlosses, detector noise and scalable KLM implementations are outside its scope.\n\n## Earlier additions in v0.5.27\n\n[Vector clocks and causal order](docs/release-v0.5.27.en.md) proves exact\ncorrespondence between independently defined event causality and vector comparison.\nThe causal-past invariant gives injective timestamps and detection of causal\nincomparability. Executable traces cover reordered delivery and outstanding messages;\na two-process bridge preserves the older clock API. The model uses fixed processes,\nunbounded counters and authentic immutable timestamps, without a delivery-liveness claim.\n\n## Earlier additions in v0.5.26\n\n[Raymond tree message complexity](docs/release-v0.5.26.en.md) connects\nactual isolated protocol send counters to sharp diameter and height bounds.\nFinite completion is proved separately. Complete k-ary trees have exact\nnode counts, diameter 2h and worst-case sends 4h=4 floor(log_k N), with IsBigO.\nThe binary height-three regression requires 12 messages. Concurrent load,\namortization, random traffic and physical delays are outside this extension.\n\n## Earlier additions in v0.5.25\n\n[Two-photon Hong–Ou–Mandel interference](docs/release-v0.5.25.en.md) derives\nthe unitary normalized two-photon lift, output probabilities and balanced bunching.\nA unitary gauge connects the real and complex conventions. Independent labeled\npaths give the distinguishable baseline and exact HOM visibility. Temporal\nwave packets, partial distinguishability, losses and detector imperfections\nare outside this finite model.\n\n## Earlier additions in v0.5.24\n\n[Complex beam splitter and MZI](docs/release-v0.5.24.en.md) adds the lossless\nunitary convention U=B†DB, output probabilities derived from complex amplitudes,\nexact Solaris intensity bridges and a certified interference visibility model.\nA static phase offset preserves the extrema and contrast. The pi/2 reflection\nphase is model-specific; Maxwell equations, dispersion, polarization and physical\nnoise are not modeled.\n\n## Earlier additions in v0.5.23\n\n[Balanced Deutsch-Jozsa oracle classification](docs/release-v0.5.23.en.md) adds an\nexplicit support bijection, exact binomial counts for positive n, the empty\nzero-qubit family, and equivalence between balance and zero amplitude/probability\nin the existing runDJ circuit. Counts 0,2,6,70 and a first-bit projection witness\nare proved. Efficient enumeration, asymptotic density and hardware are not claimed.\n\n## Earlier additions in v0.5.22\n\n[General Chandy-Lamport snapshots](docs/release-v0.5.22.en.md) add consistent cuts,\nexact ordered FIFO channel records, and conditional termination on finite directed\nnetworks. Termination requires root reachability, eventual message progress and\nweak fairness of local snapshot reactions. Explicit executions demonstrate the\nnon-FIFO recording anomaly and the need for reachability. Causal permutation\nequivalence, failures, dynamic topology and overlapping snapshots are not claimed.\n\n## Earlier additions in v0.5.21\n\n[Schnorr identification](docs/release-v0.5.21.en.md) adds perfect completeness,\nalgebraic witness extraction from two accepting transcripts with one commitment\nand distinct challenges, and exact equality of real and simulated transcript\nPMFs. The simulator has no secret input. Perfect special HVZK covers fixed or\nindependent honest-verifier challenges. Malicious-verifier security, computational\nhardness, polynomial runtime and Fiat-Shamir signatures are not claimed.\n\n## Earlier additions in v0.5.20\n\n[Pedersen homomorphic sums](docs/release-v0.5.20.en.md) add exact linear-combination\nidentities and PMF hiding over a finite prime-order group. Aggregate hiding needs\nan independent uniform mask with a nonzero weight. Collisions with distinct\nmessages yield an algebraic DLOG extractor; computational hardness is not proved.\nThe aggregate concerns a scalar weighted sum, not the full vector of messages.\n\n## Earlier additions in v0.5.19\n\n[Raymond tree mutual exclusion](knowledge/09_distributed_systems/DistributedRaymondTreeMutex.md)\nproves token conservation, mutual exclusion and effective holder routing. Starvation\nfreedom requires delivery, weak local fairness and finite CS occupancy. Isolated\ncompleted entries cost exactly twice the initial tree distance in messages. A reachable\ncounterexample establishes that raw holder pointers can form a two-cycle during transit.\n\n**3585 strict build jobs**, **66 public live tests**, no warnings or skips.\nAll 164 root-inclusive Lean sources match private snapshot `d4a72dfb`.\nSee the [public release report](docs/release-v0.5.19.en.md).\n\n## Earlier additions in v0.5.18\n\n[Shor LCM/GCD recovery](knowledge/03_quantum_physics_and_optics/QuantumShorOrderRecoveryGCD.md)\nproves conditional recovery from certified divisors and the equivalent spectral GCD\ncriterion. Modular validation alone establishes a multiple of the order. A formal\ncounterexample shows that taking every candidate denominator can pass the check\nwhile returning a proper multiple. Candidate selection and sampling probabilities\nremain outside scope.\n\n**3547 strict build jobs**, **65 public live tests**, no warnings or skips.\nAll 163 root-inclusive Lean sources match private snapshot `5e714619`.\nSee the [public release report](docs/release-v0.5.18.en.md).\n\n## Earlier additions in v0.5.17\n\n[Shor continued fractions](knowledge/03_quantum_physics_and_optics/QuantumShorContinuedFractions.md)\nadds executable candidates, strict Legendre recovery and the bound\n**2·floor(log₂ Q)+1 Euclidean stages**. The correct reduced denominator is r/gcd(s,r).\nExact recovery is conditional; modular validation alone admits multiples of the order.\nBit complexity, repeated-sampling analysis and integer factorization are outside scope.\n\n**3546 strict build jobs**, **64 public live tests**, no warnings or skips.\nAll 162 root-inclusive Lean sources match private snapshot `189077d1`.\nSee the [public release report](docs/release-v0.5.17.en.md).\n\n## Earlier additions in v0.5.16\n\n[Suzuki–Kasami mutual exclusion](knowledge/09_distributed_systems/DistributedSuzukiKasamiMutex.md)\nproves reachable token conservation, mutual exclusion and queue invariants.\nEventual service requires reliable delivery, weak fairness and finite CS visits.\nA reachable counterexample refutes LN ≤ RN at the holder; retained-token reentry\nneeds no artificial sequence increment. The operational serialization and exclusions\nare documented explicitly.\n\n**3543 strict build jobs**, **63 public live tests**, no warnings or skips.\nAll 161 root-inclusive proof sources match private snapshot `ef9c4813`.\nSee the [public release report](docs/release-v0.5.16.en.md).\n\n## Earlier additions in v0.5.15\n\n[Shor order-finding core](knowledge/03_quantum_physics_and_optics/QuantumShorOrderFindingCore.md)\nconstructs padded modular multiplication, its orthonormal orbit spectrum and the\ncoherent decomposition of the accessible input |1⟩. The actual QPE marginal is\nderived as a uniform mixture of spectral components. The nearest-sample bound\nis **4/π² per component**, giving an individual contribution of **4/(rπ²)**\nto the mixture. Recovering the order, continued fractions, factorization and\nphysical gate synthesis remain outside scope.\n\n**3542 strict build jobs**, **62 public live tests**, no warnings or skips.\nAll 160 root-inclusive proof sources match private snapshot `110558af`.\nSee the [public release report](docs/release-v0.5.15.en.md).\n\n## Earlier additions in v0.5.14\n\n[General Quantum Phase Estimation](knowledge/03_quantum_physics_and_optics/QuantumPhaseEstimationGeneral.md)\nderives output amplitudes from an explicit controlled-power cascade and inverse\nFourier transform. It proves Fourier unitarity, exact dyadic recovery, normalized\nprobabilities and a nearest-sample success bound of **4/π²** for every real phase.\nThe supplied target eigenstate is normalized; its preparation, gate synthesis,\nhardware noise and the full Shor algorithm remain outside scope.\n\n**3541 strict build jobs**, **61 public live tests**, no warnings or skips.\nAll 159 root-inclusive proof sources match private snapshot `9970e917`.\nSee the [public release report](docs/release-v0.5.14.en.md).\n\n## Earlier additions in v0.5.13\n\n[Ricart–Agrawala](knowledge/09_distributed_systems/DistributedRicartAgrawalaMutex.md)\nproves mutual exclusion on reachable states and eventual entry for each request\nunder explicit delivery, weak fairness and finite critical-section residence.\nThe [Simon conformance pilot](docs/statement-conformance.en.md) checks a pinned\nindependent contract and kernel-checked bridge; it is auxiliary tooling and adds\nno subject import. It is not a universal detector of vacuous statements.\n\n**3540 strict build jobs**, **60 public live tests**, no warnings or skips.\nAll 158 root-inclusive proof sources match private snapshot `09507001`.\nSee the [public release report](docs/release-v0.5.13.en.md).\n\n## Earlier additions in v0.5.12\n\n[Simon](knowledge/03_quantum_physics_and_optics/QuantumSimonsAlgorithm.md) derives\nthe complex two-register circuit and exact uniform weights on s-perp under the\nnonzero-period promise. The unique nonzero solution is recovered when the\northogonal observations span rank n-1 over F2. Sampling complexity and physical\nimplementation remain outside scope. See the [public release report](docs/release-v0.5.12.en.md)\nand [Reservoir readiness](docs/reservoir-readiness.en.md).\n\n**3537 strict build jobs**, **49 public live tests**, no warnings or skips.\n\n## Earlier additions in v0.5.11\n\n[Arbitrary-phase Grover](knowledge/03_quantum_physics_and_optics/QuantumGroverArbitraryPhase.md)\nproves complex unitarity and invariant-plane preservation for every real phase pair\nin dimension four with one marked item. For equal phases and the uniform input,\nP(phi)=1-3*(1+cos(phi))^2/16; exact success is equivalent to cos(phi)=-1.\nThe canonical bridge at pi includes a global minus sign. This case does not\nestablish a noncanonical fractional correction of overshoot.\nSee the [public release report](docs/release-v0.5.11.en.md). **3535 strict build jobs**, **48 public tests**, no warnings or skips.\n\n## Earlier additions in v0.5.10\n\n[Static-epoch AND deadlock detection](knowledge/09_distributed_systems/DistributedChandyMisraHaasDeadlock.md)\nproves probe provenance and detection soundness in a fixed wait graph, with\nprogress under explicit delivery assumptions and a dynamic phantom counterexample.\nSee the [public release report](docs/release-v0.5.10.en.md).\n\n## Earlier additions in v0.5.9\n\n[Two-participant 3PC](knowledge/09_distributed_systems/DistributedThreePhaseCommit.md)\nadds operational safety, recovery and conditional completion. Accurate membership,\nunique backup appointment and atomic epoch fencing are external contracts.\nEventual completion additionally requires a stable live view and weak action fairness.\nSee the [public release report](docs/release-v0.5.9.en.md).\n\n## Earlier additions in v0.5.8\n\n[Operational 2PC timeouts](knowledge/09_distributed_systems/DistributedTwoPhaseCommitTimeout.md)\nderives safe pre-vote abort, reachable-history indistinguishability and the unsafety\nof unilateral prepared decisions based only on a timeout. With both participants\nprepared and the coordinator stopped, blocking is characterized by absence of\nqueued decision packets. A decision in flight permits a delivery step; fairness,\nrecovery and completion of both participants are not established.\nSee the [public release report](docs/release-v0.5.8.en.md).\n\n## Earlier additions in v0.5.7\n\n[Raft commit application](knowledge/09_distributed_systems/DistributedRaftCommitApplication.md)\nderives commit-index provenance, prefix retention and ordered deterministic local\napplication from operational traces. The package includes a reachable 45-transition\nold-term-majority counterexample. Cross-node fold agreement requires equality of\nfull entries, including commands; no new global State Machine Safety is claimed.\nSee the [public release report](docs/release-v0.5.7.en.md).\n\n## Earlier additions in v0.5.6\n\n[QuantumDeutschJozsaGeneral](knowledge/03_quantum_physics_and_optics/QuantumDeutschJozsaGeneral.md)\nproves the n-qubit Hadamard transform, XOR-ancilla phase kickback, circuit-derived\namplitudes and zero-error classification under the constant-or-balanced promise.\nIt covers n=0, exact one-qubit compatibility and counterexamples outside the promise.\nPhysical implementation, gate synthesis and complexity bounds are not claimed.\nSee the [public release report](docs/release-v0.5.6.en.md).\n\n## Earlier additions in v0.5.5\n\n[QuantumGroverMultipleTargets](knowledge/03_quantum_physics_and_optics/QuantumGroverMultipleTargets.md)\nproves exact N=4 real-amplitude dynamics for every target subset and every natural\niteration count, arbitrary-state norm preservation, the invariant symmetric plane\nfor nonempty proper target sets and exact compatibility with the original singleton\nmodel. Two counterexamples delimit agreement with rank-one reflection.\nArbitrary N, oracle query complexity, fractional phase rotations, physical noise\nand hardware remain outside scope. Born-rule interpretation is external.\n\nSee the [public release report](docs/release-v0.5.5.en.md).\n\n## Earlier additions in v0.5.4\n\n[QuantumPhaseEstimation](knowledge/03_quantum_physics_and_optics/QuantumPhaseEstimation.md)\nproves controlled U/U² phase kickback, inverse Fourier cancellation and deterministic\nrecovery of the exact phases 0, 1/4, 1/2 and 3/4. The target operator preserves norm,\nand its normalized exact eigenstate is supplied as an input hypothesis.\nApproximate QPE, spectral leakage/error bounds, eigenstate preparation, noisy gates\nand physical quantum hardware are outside scope.\n\nSee the [public release report](docs/release-v0.5.4.en.md).\nThat report records source correspondence and regression coverage. The fresh strict build passed **3524 jobs** and all **41 public tests** passed without skips.\n\n## Earlier additions in v0.5.3\n\n[DistributedChandyLamportSnapshot](knowledge/09_distributed_systems/DistributedChandyLamportSnapshot.md)\nderives saved-cut consistency and exact completed-channel transit lists from\nexplicit two-process FIFO transitions. Partial recording has a separate theorem.\nTermination, failures and arbitrary network topologies are not proved.\n\nThe public module removes one unused broad tactic import to pass the enabled\nheader linter on a fresh build; definitions and proof bodies are unchanged.\nSee the [public release report](docs/release-v0.5.3.en.md).\nThat report records source correspondence. The fresh strict build passed **3523 jobs** and all **40 public tests** passed without skips.\n\n## Earlier additions in v0.5.2\n\n[NumericSQLGapBounds](knowledge/12_numeric_certificates/NumericSQLGapBounds.md)\nproves the affine enclosure of `G=A/I+B*I-2*sqrt(A*B)`, its exact-zero balance\ncriterion for positive parameters, canonical +0 and composition with real rounding.\nExact zero is distinct from a positive midpoint underflowing to +0.\nHistorical indeterminate records are retained alongside separate exact evidence.\n\nRationalization, exact cell-boundary comparison, the SimLab cell-search algorithm,\nPython, JSON/SHA-256 and external input-byte binding remain outside these proofs.\nThe strict build passed 3,522 jobs and all 39 public tests passed without skips.\nSee the [public release report](docs/release-v0.5.2.en.md).\n\n## Earlier additions in v0.5.1\n\nThis release adds exact binary rounding certificates, a real-input extension,\nconditional enclosures of `sqrt(hbar/(mass*frequency))`, and a conditional bridge\nthrough caller-supplied digest and parser functions. Three registry suites are\nimplemented by five Lean source files. The strict public build passed 3,521 tasks and all 38 public tests passed without skips. See the [release record](docs/release-v0.5.1.en.md).\n\nSHA-256 implementation, JSON/Python conformance, authenticated provenance and the\nseparate SimLab gap `A/I+B*I-2*sqrt(A*B)` remain outside these results. Historical\nindeterminate interval records are preserved; separate exact evidence does not\nrewrite them.\n\n## Earlier additions in v0.5.0\n\nThis release reaches **100 direct registry imports**, with three new domain\npackages and an acyclic milestone registry. It adds five Lean files in total.\n\n- [Time interval envelopes](knowledge/09_distributed_systems/DistributedMarzulloAlgorithm.md):\n  truth inclusion under an explicit fault bound; maximum-overlap localization is\n  refuted by a counterexample. No full NTP implementation is claimed.\n- [Elementary transcript forking](knowledge/07_cryptography/CryptoTranscriptForkingLemma.md):\n  finite matrix counting and scalar extraction, not the general multi-query\n  Bellare–Neven lemma or a ROM security proof.\n- [Beam splitter](knowledge/03_quantum_physics_and_optics/QuantumBeamSplitterTransform.md):\n  real mode and finite two-boson norm preservation, with an ideal balanced HOM zero;\n  complex phases, full Fock space, and physical detectors remain outside scope.\n- [Milestone registry](knowledge/11_meta_registry/MasterHundredRegistry.md):\n  selected existing guarantees assembled without changing hypotheses.\n  `MasterSuiteComponents` prevents cyclic imports and preserves component names.\n  The import count is not a count of independent domain results.\n\n## Earlier additions in v0.4.5\n\nThis release adds finite-field batch counting and conditional scalar noise\noptimization, bringing the registry to 96 direct imports.\n\n- [Schnorr batch verification](knowledge/07_cryptography/CryptoSchnorrBatchVerification.md)\n  proves completeness and exact accepting fractions `1/q` and `(1/q)^k` for\n  a fixed nonzero discrepancy over a prime field. The coefficient space contains\n  all vectors, including zeros. Uniform independent sampling is the interpretation\n  of the finite counting ratios, not an implemented sampler. EUF-CMA security,\n  CSPRNG correctness, and the BIP340 coefficient algorithm are outside scope.\n- [Conditional standard quantum limit](knowledge/03_quantum_physics_and_optics/QuantumStandardQuantumLimit.md)\n  proves the attained minimum `2*sqrt(A*B)`, balance, and unique positive optimizer\n  `sqrt(A/B)` of `A/I + B*I`. SQL-shaped bounds require explicit calibration.\n  The omitted noise correlation term is a modeling choice; no physical derivation\n  of calibration or detector certification is claimed.\n\n## Earlier additions in v0.4.4\n\nRelease v0.4.4 added two scalar algebraic models, bringing the registry to 94 direct imports.\n\n- [MuSig2-style aggregation](knowledge/07_cryptography/CryptoMuSig2Aggregation.md)\n  proves two-signer, two-nonce completeness and a restricted barrier to naive key\n  subtraction. Weights and challenges are supplied real scalars. Hash-based\n  rogue-key resistance, secp256k1, and the two-round network protocol are not proved.\n  Fixed weights admit a chosen target key; scalar public keys reveal their secrets.\n- [Interference visibility](knowledge/03_quantum_physics_and_optics/MithraicPhaseCollapse.md)\n  proves bounds, exact zero/unit contrast criteria, fixed-maximum monotonicity,\n  and threshold validity. Equality at the threshold is accepted. These results\n  do not establish quantum decoherence or physical dump-port control.\n\n## Earlier additions in v0.4.3\n\nThis release adds the Raft network induction and complete bridge, with eleven new\nLean files including supporting proofs. `reachable_global_log_matching` and\n`reachable_leader_completeness` follow from the unchanged operational transitions.\nCommitment is witnessed by an actual `Step.commit` in a finite execution, including\nthe majority replication evidence and current-term anchor.\n\nA node already holding the entire committed prefix retains it through later steps\nof that execution. Delayed acknowledgements, message loss, duplication, arbitrary\ndelivery order, and conflict-sensitive partial AppendEntries are covered.\nThe model has a fixed nonempty cluster and protocol-generated messages. Dynamic\nmembership, crash/recovery, Byzantine packet injection, and liveness are outside\nscope; this is not a certification of a deployed Raft implementation.\n\nSee the [complete bridge card](knowledge/09_distributed_systems/DistributedRaftCompleteBridge.md)\nand [validation record](knowledge/VERIFICATION.en.md).\n\n## Earlier additions in v0.4.2\n\nRelease v0.4.2 added scalar Feldman share verification, translation and rectangular\nplacement geometry, an exact 256-node placement certificate, and scalar\noptomechanical coupling. The concrete certificate is a separate registry module,\nbringing that release to 90 direct imports.\n\n- Feldman verification and reconstruction are algebraic statements over the reals.\n  The public scalar commitment reveals the secret as `A0/G`; hiding is not claimed.\n- The placement certificate checks 256 nodes in a 4000 by 4000 micrometre die,\n  positive dimensions, unique identifiers, and pairwise disjoint closed rectangles.\n  Bounds and nonintersection are separate statements. The packaged JSON and\n  deterministic converter permit an external provenance check; Lean does not\n  verify the JSON parser or SHA-256 implementation. No routes, optical losses, or\n  propagation delays are certified.\n- Optomechanics proves normalized scalar energy/force identities, affine frequency\n  shifts, and properties of prescribed damping rates and an exponential envelope.\n  The physical regime of `4*g^2/kappa` is documented, not derived in Lean. Neither\n  quantum cooling nor full device stability is proved.\n\n## What the proofs establish\n\nEach result applies to its formal definitions and hypotheses. This repository\ndoes not prove the Collatz or Riemann conjectures, resolve the Hopf problem, or\nestablish end-to-end security of the named protocols. Scalar commitment identities\ndo not prove cryptographic hiding or binding. Scientific priority of individual\nformalizations has not been established.\n\nEvery module has an English knowledge card with its result, scope, and source links.\n\n## Build and audit\n\nLean **4.33.1** and Mathlib **v4.33.1** are pinned. With elan installed:\n\n```bash\nlake build --wfail\nlake env lean -DwarningAsError=true Verification/AxiomAudit.lean\npython3 tools/verifier_skill.py verify-all\npython3 scripts/check_knowledge.py\n```\n\n`AxiomAudit.lean` checks the selected registry theorem's transitive axiom\ndependencies. `verify-all` checks all project modules and audits all project\ndeclarations in the imported environment. CI also runs an independent axiom audit.\n\n## Verification tooling\n\nThe [verifier CLI and Python API](docs/verifier-skill.en.md) support strict module\nverification, fresh axiom audits, integration using explicit recipes with source\nrollback, and draft English knowledge cards. The tool operates on trusted local\nprojects; it is not a sandbox for untrusted Lean or Lake code.\n\n[Contribution guide](knowledge/CONTRIBUTING.en.md) ·\n[Machine-readable catalog](knowledge/catalog.json) ·\n[Validation snapshot](tools/validation_snapshot.json)\n\n## License and releases\n\nLicensed under [Apache License 2.0](LICENSE). This repository is an independent\nEnglish-language source distribution with its own Git history and releases.\nSee [publication notes](docs/publication.en.md) for Reservoir requirements.\n\n[Operational 2PC timeouts](knowledge/09_distributed_systems/DistributedTwoPhaseCommitTimeout.md) separates safe pre-vote abort from unsafe unilateral prepared decisions, and characterizes blocking only with both participants prepared and a stopped coordinator. Delivery of an in-flight decision remains possible; fairness and recovery are not claimed.\n\n[Two-participant 3PC](knowledge/09_distributed_systems/DistributedThreePhaseCommit.md) proves operational safety and conditional completion using a kernel-checked finite invariant certificate. Accurate membership, unique backup appointment and atomic epoch fencing are explicit external contracts. Weak fairness is required for eventual completion; no partition tolerance or runtime implementation is claimed.\n\nSee the [quantum/hardware contract publication](docs/quantum-series-sync.en.md) for twelve additional scoped models and their explicit limits.\n\n## Provenance runtime and audit preparation\n\n[Source/export boundaries and test setup](docs/provenance-test-setup.en.md) · [SQLite adapter](tools/challenge_store/README.md) · [Runtime qualification](tools/challenge_store/RUNTIME.en.md). Native acceptance requires a separately qualified host; ordinary CI does not provide it.\n",1793400797532]