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mrwulf eb3df7503f S3/L4-L5: root binding (Lemma 2, Path instance) + Theorem 2, constructive 
The crux layer — the statement whose HAND proof once carried the frontier
coverage bug is now kernel-checked.

- gen: hash outputs refactored to Hash = {l : List UInt8 // l.length = 32}.
  MECHANIZATION FINDING: the paper's pair-coincidence step ('equal hnode
  values of distinct argument pairs are a collision') is load-bearing on
  FIXED-WIDTH outputs — with unconstrained byte strings x++s = X++Y does
  not split. hnode_preimage_inj (cone: propext) makes this explicit via
  List.append_inj on equal-length components. Queued as a half-sentence
  for the paper's next cycle.
- HasCollision := ∃ x y, x ≠ y ∧ sha256 x = sha256 y — appears ONLY as a
  conclusion, never a hypothesis (no collision-resistance assumed).
- hnode_inj_or_collision / hleaf_inj_or_collision: the per-node dichotomy.
- root_binding: any accepting reconstruction from (v,P) to the honest root
  either IS the honest receipt (leaf hash AND full path P = Path m D — case
  (ii) pinning every consumed sibling) or exhibits a collision. Motive
  quantifies (v,P); induction on Path; k-fold discipline.
- incl_sound (Theorem 2, position binding): accepting a wrong leaf at m
  yields a collision. Cone [propext, Classical.choice, LTLAcc.sha256,
  Quot.sound] — the single hash axiom, pinned in check.sh. ALL GREEN.

Also: Root n=1 branch changed from list-match to decidable 'if P = []'
(well-founded unfolding generated a spurious exhaustiveness obligation);
Root_one_cons added. Fable-5 statement-audit passed. LTL untouched.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-11 13:21:17 +02:00
verification S3/L4-L5: root binding (Lemma 2, Path instance) + Theorem 2, constructive 2026-07-11 13:21:17 +02:00
README.md S3/L4-L5: root binding (Lemma 2, Path instance) + Theorem 2, constructive 2026-07-11 13:21:17 +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 root binding for inclusion (Lemma 2, Path instance) done (root_binding; boundary = single sha256 axiom)
L5 inclusion soundness = collision extractor (Theorem 2) done; consistency (Theorem 3) pending
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.