saymrwulf/ltl-accumulator-verified
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ltl-accumulator-verified/README.md
mrwulf 6a7d93ccb7 S5 stage 1: consistency infrastructure (kbelow prefix-split + list surgery) 
Theorem 3's binding (steps 1-2) turns on one non-obvious arithmetic fact,
isolated and proven here before the main proof:
- pow2_exp_unique / kbelow_eq_of_pow2_between: kbelow is pinned by its
  three defining inequalities (power-of-two, k<n≤2k), so a prefix that
  spills past the left subtree splits at the SAME point.
- kbelow_prefix_eq: with k=kbelow n, 2≤n, k<n₀≤n ⇒ kbelow n₀ = k (the
  fact the n₀>k recursion branch needs to align MTH(D₁.take n₀) with the
  fold).
- take_take_le, take_drop_prefix: the list-surgery identities relating
  (D.take n₀) to D.take k and (D.drop k).take (n₀-k).
Cones pinned; 21 certs green. Deliberate honest checkpoint — binding +
extractCons assembly is the next stage. LTL untouched.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-11 17:53:43 +02:00

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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 = 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); binding + assembly next
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.