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: FROZEN for external review (corpus complete)

All paper-§10 mechanization targets are kernel-checked; the audit surface is defined and green (verification/check.sh, exit 0). See STATEMENT-MAP.md for the paper↔Lean review surface and KNOWN-GAPS.md for the honest scope ledger. Revised across four external review rounds (GPT-5.6 + a second Claude, adversarial; zero broken theorems in any round; both approved after round 4). The audit surface is an environment-derived inventory (Proofs/Inventory.lean + pinned allowlist — 222 constants, 61 human-reviewed cones, self-tested by selftest_audit.sh); the review kit is push-button reproducible (run_bare.sh, self-contained fidelity target); acceptIncl/acceptCons_sound route the theorems through the named acceptance predicates; fidelity = agreement over pinned families (230,271 + 230,016 baseline; 73,573 lied-size boundary cases with 3,867 expected one-sided divergences — KNOWN-GAPS gaps 14/15, not extensional equality). Doc counts are asserted by check.sh Phase 3c. The finished certificates' attestation into the LTL is a separate, explicitly-authorized operator decision, scoped per the runbook.

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) + named acceptance acceptIncl	done (incl_complete: propext, Classical.choice, LTLAcc.sha256, Quot.sound)
L4	frontier binding content (Lemma 2)	done as specializations — inlined in the extractor walk (extractIncl), whole-tree (extractMTH), ConsRec (consRecBinding); the standalone Root receipt-uniqueness instance was deleted with the vacuous root_binding in S3.5 and deliberately NOT restored (optional, unused — KNOWN-GAPS gap 3)
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
L6b	Theorem 3 (consistency soundness): consRecBinding (steps 1–2) + extractCons/extractCons_correct (+ _paper at the paper's exact quantifiers; acceptCons_sound routes it through the named acceptCons predicate, size bound derived from acceptance via consRec_some_le)	done, non-vacuous
L6c	pin-store state machine safety (Proposition 1): pinAccept_monotone, pin_prefix_correct, fork_distinct	done, non-vacuous (per-step; multi-step chain = gap 7)

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.
• Reviewers without the operator toolchain: verification/run_bare.sh compiles, axiom-audits, and inventory-gates the corpus with a plain public lean (version pinned in verification/lean-toolchain); the operator path is overridable via AENEAS_ENV.
• 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.