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{
"schemaVersion": 2,
"generatedBy": "anchor-gates-instill-subagent",
"observedAt": "2026-05-30",
"canonicalRule": "A theorem claim is active only when its runtime hook and validation command are present in GitHub. Lean proof status is scoped separately from runtime test status.",
"wiredGateCount": 35,
"claimedGateCount": 35,
"gapCount": 0,
"gapNote": "All 35 anchor formula gates now have TypeScript runtime files in packages/policy/src/gates/. 30 gates added in feat/policy-gates-instill-anchor-g1-g35. 4 gates are STAGED-ADVISORY where Lean proof has open sorries.",
"stagedAdvisoryGates": [
"A7-BekensteinBound",
"TH4-LambdaCategoryComposability",
"TH_L3-BekensteinSoundness",
"LiuHuiPi-axiom"
],
"testValidationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates.test.ts && npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"entries": [
{
"id": "RUNTIME-FALSE-POSITION",
"theorem": "Lutar.Calibration.FalsePosition.false_position_correct",
"formula": "FalsePosition",
"lineage": "Rhind Mathematical Papyrus problems 24-29 / false position",
"leanFile": "Lutar/Calibration/FalsePosition.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/falsePosition_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Runtime gate is tested; cite Lean proof status separately when making formal claims."
},
{
"id": "RUNTIME-MADHAVA-BOUND",
"theorem": "Lutar.PACBayes.MadhavaBound.madhavaRemainderBound_nonneg",
"formula": "MadhavaBound",
"lineage": "Madhava / Kerala school arctangent series",
"leanFile": "Lutar/PACBayes/MadhavaBound.lean",
"leanStatus": "theorem-with-tracked-sorries",
"runtimeFile": "packages/policy/src/gates/madhavaBound_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Full arctangent specialization still has tracked Lean sorries; runtime enforces numeric remainder threshold."
},
{
"id": "RUNTIME-LIU-HUI-PI",
"theorem": "Lutar.Banach.LiuHuiPi.sideSquared_bounds",
"formula": "LiuHuiPi",
"lineage": "Liu Hui polygon-doubling \u03c0 approximation",
"leanFile": "Lutar/Banach/LiuHuiPi.lean",
"leanStatus": "axiom-advisory",
"runtimeFile": "packages/policy/src/gates/liuHuiPi_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": true,
"caveat": "Convergence is axiom/tracked in Lean; runtime enforces approximation threshold. STAGED-ADVISORY by design."
},
{
"id": "RUNTIME-ADVERSARIAL-ROBUSTNESS",
"theorem": "Lutar.Composition.Robustness.robustness_preserved_by_composition",
"formula": "AdversarialRobustness",
"lineage": "Banach/Lipschitz robustness specialization",
"leanFile": "Lutar/Composition/AdversarialRobustness.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/adversarialRobustness_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Numeric gate is the Lipschitz special case, not the full abstract metric theorem."
},
{
"id": "RUNTIME-SUMMATION-INVARIANT",
"theorem": "Lutar.Khipu.SummationInvariant.khipuReceipt_checksum_invariant",
"formula": "SummationInvariant",
"lineage": "Inka khipu summation-cord accounting",
"leanFile": "Lutar/Khipu/SummationInvariant.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/summationInvariant_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Runtime checks additive receipt invariants."
},
{
"id": "RUNTIME-PARETO-STABILIZATION",
"theorem": "Lutar.Thesis.ParetoStabilization.th_v18_11_pareto_stabilization",
"formula": "ParetoStabilization",
"lineage": "Lynch 1996 Distributed Algorithms Ch.8; finite discrete Pareto frontier",
"leanFile": "Lutar/Thesis/TH_V18_11_ParetoFiniteStabilization.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/pareto_stabilization.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Pareto stabilization enforced in finite rounds; runtime iterates up to maxRounds."
},
{
"id": "RUNTIME-A1-SOUNDNESS-AXIOM",
"theorem": "soundnessAxiom",
"formula": "SoundnessAxiom",
"lineage": "SZL Doctrine v6 A1: conjunctive Lambda floor >=0.90",
"leanFile": "Lutar/Gate/SoundnessAxiom.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/soundnessAxiom_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Enforces conjunctive 9-axis Lambda floor; no open sorries in gate Lean file."
},
{
"id": "RUNTIME-A2-MORAL-GROUNDING-FLOOR",
"theorem": "moralGroundingFloor",
"formula": "MoralGroundingFloor",
"lineage": "SZL Doctrine v6 A2: moral grounding >= 0.95 with ORCID requirement",
"leanFile": "Lutar/Gate/MoralGrounding.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/moralGroundingFloor_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "ORCID absence collapses moral grounding score to 0."
},
{
"id": "RUNTIME-A3-MEASURABILITY-HONESTY-FLOOR",
"theorem": "measurabilityHonestyFloor",
"formula": "MeasurabilityHonestyFloor",
"lineage": "SZL Doctrine v6 A3: honesty floor with unsupported-claim penalty",
"leanFile": "Lutar/Gate/MeasurabilityHonesty.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/measurabilityHonestyFloor_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Each unsupported claim subtracts 0.05 from effective score."
},
{
"id": "RUNTIME-A4-DUAL-WITNESS-DISJOINTNESS",
"theorem": "dualWitnessDisjointness",
"formula": "DualWitnessDisjointness",
"lineage": "SZL Doctrine v6 A4: two witnesses must be distinct identities",
"leanFile": "Lutar/Gate/DualWitness.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/dualWitnessDisjointness_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Identity disjointness checked by string comparison of witness IDs."
},
{
"id": "RUNTIME-A5-DETERMINISTIC-REPLAY",
"theorem": "deterministicReplay",
"formula": "DeterministicReplay",
"lineage": "SZL Doctrine v6 A5: N replay runs must produce identical root hashes",
"leanFile": "Lutar/Gate/DeterministicReplay.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/deterministicReplay_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Replay determinism enforced over configurable number of runs."
},
{
"id": "RUNTIME-A6-HASH-CHAIN-INTEGRITY",
"theorem": "hashChainIntegrity",
"formula": "HashChainIntegrity",
"lineage": "SZL Doctrine v6 A6: SHA-256 hash chain over receipt sequence",
"leanFile": "Lutar/Gate/HashChainIntegrity.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/hashChainIntegrity_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "SHA-256 collision resistance is assumed (axiom), not Lean-proven."
},
{
"id": "STAGED-A7-BEKENSTEIN-BOUND",
"theorem": "bekensteinBound",
"formula": "BekensteinBound",
"lineage": "Bekenstein 1981 PRL47 information bound; TH6 DPI formally discharges",
"leanFile": "Lutar/Gate/BekensteinBound.lean",
"leanStatus": "conjectured",
"runtimeFile": "packages/policy/src/gates/bekensteinBound_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "staged-advisory",
"stagedAdvisory": true,
"caveat": "STAGED-ADVISORY. Lean proof pending; gate defaults to enforced:false, severity:warning."
},
{
"id": "RUNTIME-A8-INGEST-DISCIPLINE",
"theorem": "ingestDiscipline",
"formula": "IngestDiscipline",
"lineage": "SZL Doctrine v6 A8: bounded ingest queue with epoch timestamps",
"leanFile": "Lutar/Gate/IngestDiscipline.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/ingestDiscipline_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Ingest queue depth and epoch freshness enforced at gate boundary."
},
{
"id": "RUNTIME-A9-DOCTRINE-COMPLETENESS",
"theorem": "doctrineCompleteness",
"formula": "DoctrineCompleteness",
"lineage": "SZL Doctrine v6 A9: all required doctrine clauses present in receipt",
"leanFile": "Lutar/Gate/DoctrineCompleteness.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/doctrineCompleteness_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Checks presence of all required doctrine clause fields; no content validation."
},
{
"id": "RUNTIME-A10-TEMPORAL-CONSISTENCY",
"theorem": "temporalConsistency",
"formula": "TemporalConsistency",
"lineage": "SZL Doctrine v6 A10: receipt timestamps must be causally ordered",
"leanFile": "Lutar/Gate/TemporalConsistency.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/temporalConsistency_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Causal ordering enforced over receipt timestamp sequence."
},
{
"id": "RUNTIME-A11-CAUSAL-SEPARABILITY",
"theorem": "causalSeparability",
"formula": "CausalSeparability",
"lineage": "SZL Doctrine v6 A11: decisions may not carry unexplained causal loops",
"leanFile": "Lutar/Gate/CausalSeparability.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/causalSeparability_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Causal loop detection is structural (DAG check), not semantic."
},
{
"id": "RUNTIME-A12-CONSTRUCTIVE-TRANSPARENCY",
"theorem": "constructiveTransparency",
"formula": "ConstructiveTransparency",
"lineage": "SZL Doctrine v6 A12: every decision must cite a constructive evidence chain",
"leanFile": "Lutar/Gate/ConstructiveTransparency.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/constructiveTransparency_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Evidence chain field presence checked; content provenance is a separate concern."
},
{
"id": "RUNTIME-A14-ECONOMIC-GROUNDING",
"theorem": "economicGrounding",
"formula": "EconomicGrounding",
"lineage": "SZL Doctrine v6 A14: decision must have an economic cost receipt above floor",
"leanFile": "Lutar/Gate/EconomicGrounding.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/economicGrounding_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Economic cost floor enforced; currency normalization is caller responsibility."
},
{
"id": "RUNTIME-T1-RHO-CLOSURE-COMPOSITION",
"theorem": "rhoClosureComposition",
"formula": "RhoClosureComposition",
"lineage": "Category-theoretic rho-closure: composed organs inherit closure property",
"leanFile": "Lutar/Gate/RhoClosureComposition.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/rhoClosureComposition_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Closure composition checked over finite organ list."
},
{
"id": "RUNTIME-T2-LAMBDA-MONOTONICITY",
"theorem": "lambda_monotonicity",
"formula": "LambdaMonotonicity",
"lineage": "Lutar/Thesis/TH_V18_01_LambdaMonotonicity.lean; Lambda monotone in each argument",
"leanFile": "Lutar/Gate/LambdaMonotonicity.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/lambdaMonotonicity_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Pointwise vector comparison; geometric mean used as Lambda proxy."
},
{
"id": "RUNTIME-T3-MERKLE-DAG-BATCH",
"theorem": "merkleDagBatch",
"formula": "MerkleDagBatch",
"lineage": "Merkle/SCITT receipt DAG: acyclic batch hash chain",
"leanFile": "Lutar/Gate/MerkleDagBatch.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/merkleDagBatch_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "DAG acyclicity checked; full Merkle proof path verification is separate."
},
{
"id": "RUNTIME-T4-BEKENSTEIN-ENTROPY-MEASURE",
"theorem": "bekensteinEntropyMeasure",
"formula": "BekensteinEntropyMeasure",
"lineage": "Bekenstein 1973 PRD7 entropy-area proportionality; bounded by TH6 DPI",
"leanFile": "Lutar/Gate/BekensteinEntropyMeasure.lean",
"leanStatus": "conjectured",
"runtimeFile": "packages/policy/src/gates/bekensteinEntropyMeasure_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Lean proof conjectured; runtime numeric predicate is independently testable."
},
{
"id": "RUNTIME-T5-REPLAY-DETERMINISM",
"theorem": "replayDeterminism",
"formula": "ReplayDeterminism",
"lineage": "K10v2 PRNG replay: deterministic root produces identical receipt stream",
"leanFile": "Lutar/Gate/ReplayDeterminism.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/replayDeterminism_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Replay hash comparison; PRNG seed handling is caller responsibility."
},
{
"id": "RUNTIME-T6-CONJUNCTIVE-GATE-COUNTEREXAMPLE",
"theorem": "conjunctiveGateCounterexample",
"formula": "ConjunctiveGateCounterexample",
"lineage": "Logical gate composition: counterexample witness for non-trivial conjunctive failure",
"leanFile": "Lutar/Gate/ConjunctiveGate.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/conjunctiveGateCounterexample_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Counterexample witnesses are logged to receipt for audit."
},
{
"id": "RUNTIME-T7-PRIVACY-MASK",
"theorem": "privacyMask",
"formula": "PrivacyMask",
"lineage": "Lutar/DPI/SCITTMaskEntropy.lean: DPI H(mask(X)) <= H(X)",
"leanFile": "Lutar/Gate/PrivacyMask.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/privacyMask_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Redaction field masking enforced; entropy monotonicity is the formal backing."
},
{
"id": "RUNTIME-T8-SINGLE-WITNESS-EXCLUSION",
"theorem": "singleWitnessExclusion",
"formula": "SingleWitnessExclusion",
"lineage": "SZL Doctrine v6 T8: single witness insufficient for high-stakes decisions",
"leanFile": "Lutar/Gate/SingleWitnessExclusion.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/singleWitnessExclusion_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Minimum witness count enforced at gate boundary."
},
{
"id": "RUNTIME-T9-CROSS-REGION-POLICY",
"theorem": "crossRegionPolicy",
"formula": "CrossRegionPolicy",
"lineage": "SZL Doctrine v6 T9: decisions spanning regions require multi-region receipts",
"leanFile": "Lutar/Gate/CrossRegionPolicy.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/crossRegionPolicy_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Region tags checked for coverage; actual data residency is a separate enforcement."
},
{
"id": "RUNTIME-T10-DOCTRINE-ENFORCEMENT",
"theorem": "doctrineEnforcement",
"formula": "DoctrineEnforcement",
"lineage": "SZL Doctrine v6 T10: enforcement clauses must be flagged and receipt-anchored",
"leanFile": "Lutar/Gate/DoctrineEnforcement.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/doctrineEnforcement_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Enforcement clause flags checked; content of flags is caller responsibility."
},
{
"id": "RUNTIME-TH1-COMPOSABILITY",
"theorem": "composability",
"formula": "Composability",
"lineage": "Lutar/Composition/CompositionOverhead.lean: linear overhead bound for N composed systems",
"leanFile": "Lutar/Gate/Composability.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/composability_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Linear overhead bound enforced; asymptotic claim is the formal backing."
},
{
"id": "RUNTIME-TH2-REPLAY-DOI-DUALITY",
"theorem": "replayDoiDuality",
"formula": "ReplayDoiDuality",
"lineage": "SZL Doctrine v6 TH2: DOI citation and replay root must be paired",
"leanFile": "Lutar/Gate/ReplayDoiDuality.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/replayDoiDuality_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "DOI format and replay root presence checked; DOI resolution is not performed at gate time."
},
{
"id": "RUNTIME-TH3-ANATOMY-REDUCTION",
"theorem": "anatomyReduction",
"formula": "AnatomyReduction",
"lineage": "SZL Doctrine v6 TH3: 7-layer anatomy reduces to verifiable receipt chain",
"leanFile": "Lutar/Gate/AnatomyReduction.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/anatomyReduction_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Layer coverage checked; layer content validation is a separate concern."
},
{
"id": "STAGED-TH4-LAMBDA-CATEGORY-COMPOSABILITY",
"theorem": "lambdaCategoryComposability",
"formula": "LambdaCategoryComposability",
"lineage": "Pending Lutar/LaxFunctor.lean; lax functor property for Lambda over organ category",
"leanFile": "Lutar/Gate/LambdaCategoryComposability.lean",
"leanStatus": "conjectured",
"runtimeFile": "packages/policy/src/gates/lambdaCategoryComposability_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "staged-advisory",
"stagedAdvisory": true,
"caveat": "STAGED-ADVISORY. Pending LaxFunctor.lean formalization. Gate defaults to enforced:false."
},
{
"id": "RUNTIME-TH5-RECEIPT-CHAIN-CONFLUENCE",
"theorem": "receiptChainConfluence",
"formula": "ReceiptChainConfluence",
"lineage": "Church-Rosser confluence: concurrent receipt chains reduce to same root",
"leanFile": "Lutar/Gate/ReceiptChainConfluence.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/receiptChainConfluence_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Confluence enforced by deterministic hash ordering; formal confluence proof is the backing."
},
{
"id": "RUNTIME-TH6-BEKENSTEIN-ENTROPY-DPI",
"theorem": "bekensteinEntropyDpi",
"formula": "BekensteinEntropyDpi",
"lineage": "Cover-Thomas DPI: I(X;Z) <= I(X;Y); entropy non-increasing through masking",
"leanFile": "Lutar/DPI/DPIBound.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/bekensteinEntropyDpi_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Numeric DPI monotonicity enforced over discrete label distributions."
},
{
"id": "RUNTIME-TH7-CURRY-HOWARD-RECEIPT-CALCULUS",
"theorem": "curryHowardReceiptCalculus",
"formula": "CurryHowardReceiptCalculus",
"lineage": "Curry-Howard: receipt terms are proofs; proof terms are programs",
"leanFile": "Lutar/Gate/CurryHowardReceiptCalculus.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/policy/src/gates/curryHowardReceiptCalculus_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Receipt term structure checked; full type-theoretic correspondence is lineage."
},
{
"id": "CONJECTURE-THL1-LAMBDA-UNIQUENESS",
"theorem": "lambdaUniquenessConjecture",
"formula": "LambdaUniquenessConjecture",
"lineage": "Lutar/Thesis/TH_V18_12 Lambda uniqueness: only one Lambda satisfies A1-A4",
"leanFile": "Lutar/Uniqueness.lean",
"leanStatus": "conjecture-open",
"runtimeFile": "packages/policy/src/gates/lambdaUniquenessConjecture_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": true,
"caveat": "CONJECTURE \u2014 NOT a theorem. \u039b uniqueness is Conjecture 1 per Doctrine v11. Gate validates scoring consistency; formal uniqueness is unproven. Gate file renamed to lambdaUniquenessConjecture_gate.ts.",
"status": "CONJECTURE",
"proven": false,
"lambda_statement": "Conjecture 1 (NOT a theorem \u2014 LOCKED by Doctrine v11)"
},
{
"id": "RUNTIME-THL2-LAMBDA-MINMAX-BOUNDS",
"theorem": "lambdaMinMaxBounds",
"formula": "LambdaMinMaxBounds",
"lineage": "Lambda min/max bounds: floor <= Lambda(v) <= ceil for all valid v",
"leanFile": "Lutar/Gate/LambdaMinMaxBounds.lean",
"leanStatus": "theorem-with-2-tracked-sorries-in-wider-repo",
"runtimeFile": "packages/policy/src/gates/lambdaMinMaxBounds_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Gate Lean file has 0 sorries; 2 sorries exist elsewhere in lutar-lean (not in this gate's proof)."
},
{
"id": "STAGED-THL3-BEKENSTEIN-SOUNDNESS",
"theorem": "bekensteinSoundness",
"formula": "BekensteinSoundness",
"lineage": "Measured: 49.5% fire rate under uniform seed (ouroboros v6.3.0, n=8000); formal proof pending lutar-lean PR #12",
"leanFile": "Lutar/BekensteinSoundness.lean",
"leanStatus": "measured-conjectured-pending-PR12",
"runtimeFile": "packages/policy/src/gates/bekensteinSoundness_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "staged-advisory",
"stagedAdvisory": true,
"caveat": "STAGED-ADVISORY. Lean formal proof pending lutar-lean PR #12. Gate defaults to enforced:false."
},
{
"id": "RUNTIME-THL4-RHO-CLOSURE-PRODUCTION",
"theorem": "rhoClosureProduction",
"formula": "RhoClosureProduction",
"lineage": "Measured: 100% rho-closure rate over 8000 ouroboros v6.3.0 production calls",
"leanFile": "Lutar/Gate/RhoClosureProduction.lean",
"leanStatus": "measured-empirical",
"runtimeFile": "packages/policy/src/gates/rhoClosureProduction_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Empirically measured 100% closure; gate enforces minimum closure rate."
},
{
"id": "RUNTIME-THRESHOLD-POLICY-SEVERITY",
"theorem": "IQ-01 severity-indexed witness threshold gate",
"formula": "ThresholdPolicySeverity",
"lineage": "2-of-N / 3-of-N witness threshold invariant from cross-corpus doctrine synthesis",
"leanFile": null,
"runtimeFile": "packages/policy/src/gates/thresholdPolicySeverity_gate.ts",
"exportFile": "packages/policy/src/gates/index.ts",
"testFile": "packages/policy/src/gates/__tests__/policy_gates.test.ts",
"validationCommand": "npm run test:policy-gates",
"claimStatus": "verified-runtime",
"caveat": "TypeScript runtime gate is tested and emits a DSSE-shaped HMAC receipt on allow; Lean formalization is not claimed."
},
{
"id": "RUNTIME-QEC-LINEAGE",
"theorem": "Lutar.QEC.HammingFoundations / Shor / CSS / Kitaev runtime parity",
"formula": "QECLineage",
"lineage": "Hamming, Shor, CSS, Kitaev, Preskill QEC lineage",
"leanFile": "Lutar/QEC/*",
"leanStatus": "mixed-green-red",
"runtimeFile": "packages/qec-integrity/src/qec_lineage.ts",
"exportFile": "packages/qec-integrity/src/index.ts",
"testFile": "packages/qec-integrity/src/qec_lineage.test.ts",
"validationCommand": "npm run test:qec",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Runtime parity tests are real; do not claim full quantum threshold theorem. Kitaev/CSS Lean files fail lake build."
},
{
"id": "RUNTIME-RECEIPT-SUBSTRATE",
"theorem": "Operational receipt hash-chain integrity",
"formula": "ReceiptSubstrate",
"lineage": "Merkle/SCITT/DSSE-style receipt discipline",
"leanFile": "Lutar/DPI/* and Lutar/SBOMProvenance.lean",
"leanStatus": "theorem",
"runtimeFile": "packages/receipt-substrate/src/index.ts",
"exportFile": "packages/receipt-substrate/src/index.ts",
"testFile": "packages/receipt-substrate/src/receipt_substrate.test.ts",
"validationCommand": "npm test --prefix packages/receipt-substrate",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Local quorum labels are not external cryptographic signer verification."
},
{
"id": "RUNTIME-KNOWLEDGE-THEOREMS",
"theorem": "TH1-TH7 theorem lookup",
"formula": "KnowledgeGraph",
"lineage": "Ouroboros thesis theorem catalog",
"leanFile": "packages/a11oy-knowledge/src/theorems.ts",
"leanStatus": "theorem",
"runtimeFile": "packages/a11oy-knowledge/src/theorems.ts",
"exportFile": "packages/a11oy-knowledge/src/index.ts",
"testFile": "packages/a11oy-knowledge/src/theorems_lookup.test.ts",
"validationCommand": "npm run test:knowledge:lookup",
"claimStatus": "verified-runtime",
"stagedAdvisory": false,
"caveat": "Lookup reachability is runtime-verified; proof status remains per theorem."
},
{
"id": "STAGED-WHEELER-WINDOW",
"theorem": "Lutar.Wheeler.DelayedChoiceClosure",
"formula": "DelayedChoiceClosure",
"lineage": "Wheeler delayed-choice receipt closure",
"leanFile": "Lutar/Wheeler/DelayedChoiceClosure.lean",
"leanStatus": "lean-backed",
"runtimeFile": null,
"exportFile": null,
"testFile": null,
"validationCommand": null,
"claimStatus": "lean-backed-needs-runtime",
"stagedAdvisory": true,
"caveat": "Proof substrate exists; no A11oy TypeScript runtime gate wired yet. Not counted in the 35 anchor gates."
},
{
"id": "STAGED-FEYNMAN-KNOT",
"theorem": "Lutar.Feynman.PathIntegralAuditSum / Lutar.Feynman.FeynmanLineage",
"formula": "AuditReidemeister",
"lineage": "Feynman, Witten, Bar-Natan, Reidemeister, audit-knot calculus",
"leanFile": "Lutar/Feynman/* and Lutar/Knot/*",
"leanStatus": "conjectured",
"runtimeFile": null,
"exportFile": null,
"testFile": null,
"validationCommand": null,
"claimStatus": "historical-roadmap",
"stagedAdvisory": true,
"caveat": "Citation lineage is real; audit-Reidemeister invariance remains conjectural/tracked. Not counted in the 35 anchor gates."
}
]
}