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mrwulf 02a45eae36 S5.4: THEOREM 3 COMPLETE — extractCons assembly + non-vacuity witness 
The paper's hardest theorem is fully kernel-checked. extractCons joins
the two proven halves: extractConsNode's collision (via consRecBinding,
steps 1-2) or the descent extractMTH D₀ (D₁.take n₀) (step 3, S4).

- extractCons_correct: acceptance ConsRec n₀ |D₁| C ⊤ (MTH D₀) =
  some (MTH D₀, MTH D₁) with D₀ ≠ D₁.take n₀ (and |D₀| = n₀ ≤ |D₁|,
  0 < n₀) ⇒ IsCollision of THIS function's output. Statement matches
  paper Thm 3 verbatim (the n₀ = 0 escape is vacuous there: [] is
  always the real prefix). Compiled on first attempt — the pre-verified
  skeleton held exactly.
- extractCons_nonvacuous (queued requirement honored): on a non-rewrite
  input the output is provably NOT a collision — choice-proof.

Cones: extractCons_correct [propext, Classical.choice, LTLAcc.sha256,
Quot.sound] — single hash axiom, no collision-resistance assumed
anywhere. 29 certs green. Fable statement-audit passed. LTL untouched
(12 leaves, bcd15f9d).

Corpus now holds kernel-checked: Lemma 1, Theorem 1, Theorem 2,
Theorem 3 (+ whole-tree Lemma 2). Remaining: Prop 1 (S6), fidelity
harness (S7), freeze (S8).

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-11 20:07:20 +02:00
verification S5.4: THEOREM 3 COMPLETE — extractCons assembly + non-vacuity witness 2026-07-11 20:07:20 +02:00
README.md S5.3: consRecBinding PROVEN — Theorem 3 steps 1-2 kernel-checked (the hardest object) 2026-07-11 19:18:26 +02:00

README.md

ltl-accumulator-verified

Lean 4 mechanization of the security analysis (§6) of the paper "The Lean Transparency Log" (https://ltl.zkdefi.org/paper): the Merkle accumulator's own correctness and soundness theorems, kernel-checked, in the same discipline as the four *-ed25519-verified subject corpora.

Status: layer scaffold (work in progress — honest ledger below)

layer content status
L1 bytes, hleaf/hnode, domain separation (Lemma 1) done (domsep: axiom-free)
L2 MTH, Root, ConsRec definitions + termination done (cones: propext, LTLAcc.sha256, Quot.sound)
L3 inclusion completeness (Theorem 1) done (incl_complete: propext, Classical.choice, LTLAcc.sha256, Quot.sound)
L4 frontier binding content (Lemma 2) inlined in the extractor walk (extractIncl); standalone receipt-uniqueness theorem queued for S4 restoration in extractor form
L5 inclusion soundness = EXPLICIT extractor extractIncl (Theorem 2) done, non-vacuous
L6a descent extractor extractMTH (Theorem 3 step 3 = Lemma 2, WHOLE-TREE instance) done, non-vacuous
— Lemma 2, PATH instance (receipt-uniqueness of Root): deleted with the vacuous root_binding in S3.5 and not yet restored; optional, not needed for Theorem 3
L6b ConsRec binding + Theorem 3 assembly (extractCons) in progress (S5): stage-1 arithmetic/list infrastructure done (kbelow_prefix_eq, take surgery); stage-1 infra + extractConsNode extractor DEFINED (faithful to ConsRec by inspection — NOT yet machine-checked); consRecBinding PROVEN (Theorem 3 steps 1-2, kernel-checked, no sorry); extractCons assembly (step 3 join) = S5.4
L6 pin-store state machine safety (Proposition 1) pending

Discipline (identical to the subject corpora)

  • verification/Proofs/ contains ZERO axiom declarations; the single sanctioned axiom site is verification/gen/ — here, one opaque function: SHA-256. The theorems are constructive collision extractors, so collision resistance is never assumed, only interpreted.
  • verification/check.sh is THE button: compiles every file through lean-guard (memory cap, core pinning, timeout, single-flight lock) and axiom-audits every certificate against its documented exact cone.
  • Expected boundary: propext, Classical.choice, Quot.sound plus LTLAcc.sha256 for hash-touching certificates — documented per certificate in check.sh, audited both directions.

The finished certificates are destined for the LTL itself as attestation leaves: the log carrying kernel-checked proofs of its own machinery.