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mrwulf 8795e82865 S5.3: consRecBinding PROVEN — Theorem 3 steps 1-2 kernel-checked (the hardest object) The single hardest proof in the corpus is complete, no sorry. Under the value-equality invariant y = MTH D₁, an accepting ConsRec fold either makes extractConsNode output a genuine collision or its first component is the honest prefix root MTH(D₁.take n₀). - ConsRec base changed from list-match to decidable if (if C=[] / if C.length=1) — same root-cause fix as Root, avoids WF-unfold exhaustiveness obligations; more faithful to the deployed Python. Whole chain (Basic..Consistency) rebuilt clean. - consRecBinding by ConsRec.induct (10 cases): 4 base/singleton, 3 rejection/none contradictions, 2 recursive (n₀≤k, n₀>k). The n₀>k none-branch is where all S5.1 infrastructure interlocks: kbelow_prefix_eq (prefix splits at same k) + take_take_le + take_drop_prefix assemble x = hnode s xx into MTH(D₁.take n₀). The collision branches use append_inj (fixed-width Hash) + MTH_split. - take_all helper (take-whole-list). Cone [propext, Classical.choice, LTLAcc.sha256, Quot.sound] — single hash axiom. 24 certs green. Fable statement-audit: matches paper Thm 3 steps 1-2. LTL untouched (12 leaves, bcd15f9d). Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>	2026-07-11 19:18:26 +02:00
verification	S5.3: consRecBinding PROVEN — Theorem 3 steps 1-2 kernel-checked (the hardest object)	2026-07-11 19:18:26 +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

mrwulf 8795e82865 S5.3: consRecBinding PROVEN — Theorem 3 steps 1-2 kernel-checked (the hardest object)

The single hardest proof in the corpus is complete, no sorry. Under the
value-equality invariant y = MTH D₁, an accepting ConsRec fold either
makes extractConsNode output a genuine collision or its first component
is the honest prefix root MTH(D₁.take n₀).

- ConsRec base changed from list-match to decidable if (if C=[] /
  if C.length=1) — same root-cause fix as Root, avoids WF-unfold
  exhaustiveness obligations; more faithful to the deployed Python.
  Whole chain (Basic..Consistency) rebuilt clean.
- consRecBinding by ConsRec.induct (10 cases): 4 base/singleton, 3
  rejection/none contradictions, 2 recursive (n₀≤k, n₀>k). The n₀>k
  none-branch is where all S5.1 infrastructure interlocks:
  kbelow_prefix_eq (prefix splits at same k) + take_take_le +
  take_drop_prefix assemble x = hnode s xx into MTH(D₁.take n₀). The
  collision branches use append_inj (fixed-width Hash) + MTH_split.
- take_all helper (take-whole-list).

Cone [propext, Classical.choice, LTLAcc.sha256, Quot.sound] — single hash
axiom. 24 certs green. Fable statement-audit: matches paper Thm 3
steps 1-2. LTL untouched (12 leaves, bcd15f9d).

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

2026-07-11 19:18:26 +02:00

verification

S5.3: consRecBinding PROVEN — Theorem 3 steps 1-2 kernel-checked (the hardest object)

2026-07-11 19:18:26 +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.