saymrwulf/ltl-accumulator-verified
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ltl-accumulator-verified/README.md
mrwulf be232507cc S4: descent extractor extractMTH (Theorem 3 step 3 + F2 restoration), non-vacuous 
The 'descend' step of the paper's Theorem 3, built extractor-first per
the S3.5 lesson (never a bare '∨ collision'):

- extractMTH (D D'): total function that, given two equal-length leaf
  lists sharing a Merkle root, walks the common-shape tree to the first
  divergence and returns the concrete colliding preimage pair (a node
  pair, or a leaf pair at the bottom).
- extractMTH_correct: |D|=|D'| ∧ D≠D' ∧ MTH D = MTH D' →
  IsCollision (extractMTH D D'). Proven by functional induction on
  extractMTH; composite case uses MTH_split + append_inj (fixed-width
  Hash) to split node preimages or exhibit the node collision.
- extractMTH_nonvacuous: equal lists → output NOT a collision (pinned),
  so the conclusion is false for some inputs ⇒ choice-proof.

This also RESTORES, in explicit non-vacuous form, the receipt-uniqueness
content of Lemma 2 deleted in the S3.5 cleanup (re-audit F2): the honest
Merkle fold is injective up to a collision.

18 certs green. Fable statement-audit passed (matches paper Thm 3 step 3
verbatim). LTL untouched (12 leaves, bcd15f9d).

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-11 16:46:58 +02:00

2.1 KiB
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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; restored receipt-uniqueness of Lemma 2) done, non-vacuous
L6b ConsRec binding + Theorem 3 assembly (extractCons) pending (S5)
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.