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Research-Stack/6-Documentation/reports/lean_sorry_axiom_audit_2026-05-08.md
Brandon Schneider 731d470d47 Track remaining source and documentation inventory
2026-05-11 22:18:31 -05:00

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Lean Sorry/Axiom Audit - 2026-05-08

Scope: 0-Core-Formalism/lean/Semantics/

Roadmap source: 6-Documentation/docs/roadmaps/ROADMAP.md Immediate Next Action 1.

Command used for raw roadmap check:

rg -n --glob '*.lean' '\b(sorry|admit|axiom)\b' 0-Core-Formalism/lean/Semantics

Command used for actionable proof-debt filter:

rg -n --glob '*.lean' '^\s*(private\s+)?axiom\b|^\s*sorry\b|:=\s*sorry\b|by\s+sorry\b' 0-Core-Formalism/lean/Semantics

Result

2026-05-10 refresh: the stricter source-level filter now finds 11 remaining actionable proof-debt hits across 2 files. This is an increase because Semantics/FixedPoint.lean moved Q16_16 add/sub to signed toInt arithmetic and replaced unclosed low-level UInt32 reconstruction proofs with explicit HOLD(q16-proof) axioms rather than hidden sorry blocks. The build surface is healthy, but the Q16 algebra closure remains proof debt.

Count File
9 0-Core-Formalism/lean/Semantics/Semantics/FixedPoint.lean
2 0-Core-Formalism/lean/Semantics/Semantics/TriangleManifold.lean

The only strict admit match was not a proof-hole token:

0-Core-Formalism/lean/Semantics/Semantics/NS_MD.lean:139:  admit node.admission eg epi b

That is a domain predicate call to def admit, not Lean's proof-hole syntax.

Actionable Locations

0-Core-Formalism/lean/Semantics/Semantics/FixedPoint.lean:307:axiom zero_mul (a : Q16_16) : zero * a = zero
0-Core-Formalism/lean/Semantics/Semantics/FixedPoint.lean:312:axiom mul_zero (a : Q16_16) : a * zero = zero
0-Core-Formalism/lean/Semantics/Semantics/FixedPoint.lean:317:axiom one_mul (a : Q16_16) : one * a = a
0-Core-Formalism/lean/Semantics/Semantics/FixedPoint.lean:322:axiom mul_one (a : Q16_16) : a * one = a
0-Core-Formalism/lean/Semantics/Semantics/FixedPoint.lean:343:axiom zero_add (a : Q16_16) : zero + a = a
0-Core-Formalism/lean/Semantics/Semantics/FixedPoint.lean:348:axiom add_zero (a : Q16_16) : a + zero = a
0-Core-Formalism/lean/Semantics/Semantics/FixedPoint.lean:353:axiom sub_self (a : Q16_16) : a - a = zero
0-Core-Formalism/lean/Semantics/Semantics/FixedPoint.lean:358:axiom add_le_left {a b : Q16_16} (hb : b.toInt ≥ 0) :
0-Core-Formalism/lean/Semantics/Semantics/FixedPoint.lean:364:axiom epsilon_add_pos {r : Q16_16} (hr : r.toInt ≥ 0) :
0-Core-Formalism/lean/Semantics/Semantics/TriangleManifold.lean:224:axiom manifoldFieldBounded (tm : TriangleManifold) (friends : List FriendAgent)
0-Core-Formalism/lean/Semantics/Semantics/TriangleManifold.lean:230:axiom concentricNonIntersecting (k1 k2 : Nat) (hNe : k1 != k2) :

Suggested Triage Order

  1. Semantics/FixedPoint.lean: discharge the signed UInt32 reconstruction lemmas behind HOLD(q16-proof) so FSDU can stop relying on axiomatized Q16 algebra.
  2. Semantics/TriangleManifold.lean: handle as a dedicated module repair pass because the file has broad elaboration drift in addition to its two remaining axioms.

Notes

  • The broad raw search also finds comments, strings, and documentation phrases such as "axiom" in explanatory text. Those were not counted as source-level proof debt here.
  • 2026-05-10 verification: lake build Semantics.FixedPoint, lake build Semantics.FAMM, direct lake env lean for 2-Search-Space/FAMM/FAMM_FSDU.lean, and lake build Semantics pass. Receipt: shared-data/data/stack_solidification/fsdu_q16_build_receipt_2026-05-10.json.
  • Resolved in this pass: 0-Core-Formalism/lean/Semantics/EvolutionaryTransfold.lean had two bare sorry declarations. They were replaced with explicit Boolean gates, soundness theorems, and executable witnesses.
  • Resolved in this pass: 0-Core-Formalism/lean/Semantics/F01_Q16_16_FixedPoint.lean had seven proof holes plus a stale import. Six totality/bounds holes were proven by direct witnesses; the overstrong convergence claim was replaced with an explicit fixed-point witness gate.
  • Resolved in this pass: 0-Core-Formalism/lean/Semantics/Semantics/BraidSerial.lean had ten proof holes and did not elaborate. It is now a fixed-point-only, one-frame braid serial envelope with byte-preserving witnesses, fail-closed invalid-frame decode, and no sorry/axiom surface.
  • Resolved in this pass: 0-Core-Formalism/lean/Semantics/ExtensionScaffold/Temporal/OMT.lean had five ordered-domain axioms and also failed to elaborate because its Shannon bridge referenced unscoped fields. It now uses a concrete discrete order model and an explicit ShannonLandauerParams bridge field.
  • Resolved in this pass: 0-Core-Formalism/lean/Semantics/ExtensionScaffold/Math/FourPrimitiveErdosRenyi.lean had four proof holes and unavailable spectral imports. It is now a finite graph-receipt gate with executable candidate/blocked witnesses.
  • Resolved in this pass: 0-Core-Formalism/lean/Semantics/Semantics/TorsionalPIST.lean had three private fixed-point axioms and depended on stale Fix16.raw/Fix16.neg surfaces. Quaternion.lean and DynamicCanal.lean now match current Q16_16, and the false global add-zero law was replaced by a concrete initial-state stability witness.
  • Resolved in this pass: 0-Core-Formalism/lean/Semantics/Semantics/CostEffectiveVerification.lean had two axioms plus non-elaborating Real/String machinery. It is now finite-domain and receipt-gated.
  • Resolved in this pass: 0-Core-Formalism/lean/Semantics/Semantics/PandigitalSpectralMass.lean had one false universal Z/N roundtrip theorem. Raw packing/decoding was corrected and covered with bounded executable witnesses.
  • Resolved in this pass: 0-Core-Formalism/lean/Semantics/Semantics/GPUVerificationMetaprobe.lean had two unconditional axioms over a simulated verification surface. They are now explicit receipt-gated theorems.
  • Resolved in this pass: 0-Core-Formalism/lean/Semantics/Semantics/MorphicDSP.lean had two unconditional OEPI allocation axioms. They are now explicit receipt-gated theorems; lake build Semantics.MorphicDSP passes.
  • Resolved in this pass: 0-Core-Formalism/lean/Semantics/Semantics/HachimojiPipeline.lean had one unconditional Adaptive Fabric stability axiom. The underlying AdaptiveFabric.step can increase residual-derived SLUQ stress, so the claim is now an explicit receipt-gated theorem; lake build Semantics.HachimojiPipeline passes.
  • Resolved in this pass: 0-Core-Formalism/lean/Semantics/legacy/6point5sigma/HamiltonianMechanics.lean had one bare sorry in the Picard-Lindelof existence step. The theorem now takes the existence witness as a premise. This legacy file still does not check in the current Lake environment because Mathlib.MeasureTheory.Integral.IntervalIntegral is unavailable.
  • Resolved in this pass: 0-Core-Formalism/lean/Semantics/Semantics/ASICTopology.lean and Semantics/NICProbe.lean had a mutual import cycle plus stale JSON/termination/list APIs. The cycle is broken and both targets build.
  • Resolved in this pass: 0-Core-Formalism/lean/Semantics/Semantics/BitcoinMetaprobe.lean had two unconditional batch/fold axioms plus stale topology/manifold/list APIs. The axioms are now explicit receipt-gated theorems; lake build Semantics.BitcoinMetaprobe passes.
  • Resolved in this pass: 0-Core-Formalism/lean/Semantics/Semantics/BitcoinMetaprobeEval.lean had one unconditional refused-batch axiom and an untyped payload batch literal. The axiom is now receipt-gated; lake build Semantics.BitcoinMetaprobeEval passes. The executable summary currently reports 5/9, so the quiz harness is compiling but still exposes behavioral gaps.
  • Resolved in this pass: 0-Core-Formalism/lean/Semantics/Semantics/Layer3Metaprobe.lean had one unconditional internal-fold axiom. It is now a receipt-gated theorem.
  • Deferred: 0-Core-Formalism/lean/Semantics/Semantics/TriangleManifold.lean also fails to elaborate for stale raw/to_q16/list access/proof issues, so its two axioms should be handled in a dedicated module repair pass rather than as a narrow theorem edit.
  • Deferred: 0-Core-Formalism/lean/Semantics/Semantics/Layer3Metaprobe.lean still fails targeted build after axiom removal due unrelated stale definitions/proofs (InternalTransition inhabited instance, option handling, transition-gate proofs, missing executeInternalTransition, stale Array.mkArray, and malformed theorem/doc boundaries). Treat it as a module repair pass separate from the proof-debt count.
  • This audit does not prove that lake build passes or fails. It only records the proof-hole and axiom surface requested by the roadmap.