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mrwulf
6a7d93ccb7
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>
36 lines
2.4 KiB
Markdown
36 lines
2.4 KiB
Markdown
# ltl-accumulator-verified
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Lean 4 mechanization of the security analysis (§6) of the paper
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"The Lean Transparency Log" (https://ltl.zkdefi.org/paper): the Merkle
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accumulator's own correctness and soundness theorems, kernel-checked, in
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the same discipline as the four `*-ed25519-verified` subject corpora.
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## Status: layer scaffold (work in progress — honest ledger below)
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| layer | content | status |
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| L1 | bytes, hleaf/hnode, domain separation (Lemma 1) | **done** (domsep: axiom-free) |
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| L2 | MTH, Root, ConsRec definitions + termination | **done** (cones: propext, LTLAcc.sha256, Quot.sound) |
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| L3 | inclusion completeness (Theorem 1) | **done** (incl_complete: propext, Classical.choice, LTLAcc.sha256, Quot.sound) |
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| L4 | frontier binding content (Lemma 2) | **inlined in the extractor walk** (extractIncl); standalone receipt-uniqueness theorem queued for S4 restoration in extractor form |
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| L5 | inclusion soundness = EXPLICIT extractor `extractIncl` (Theorem 2) **done, non-vacuous** |
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| L6a | descent extractor `extractMTH` (Theorem 3 step 3 = Lemma 2, WHOLE-TREE instance) **done, non-vacuous** |
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| — | 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 |
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| L6b | ConsRec binding + Theorem 3 assembly (extractCons) | in progress (S5): stage-1 arithmetic/list infrastructure done (kbelow_prefix_eq, take surgery); binding + assembly next |
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| L6 | pin-store state machine safety (Proposition 1) | pending |
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## Discipline (identical to the subject corpora)
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- `verification/Proofs/` contains ZERO `axiom` declarations; the single
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sanctioned axiom site is `verification/gen/` — here, one opaque
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function: SHA-256. The theorems are constructive collision extractors,
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so collision resistance is never assumed, only interpreted.
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- `verification/check.sh` is THE button: compiles every file through
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`lean-guard` (memory cap, core pinning, timeout, single-flight lock)
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and axiom-audits every certificate against its documented exact cone.
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- Expected boundary: `propext, Classical.choice, Quot.sound` plus
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`LTLAcc.sha256` for hash-touching certificates — documented per
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certificate in `check.sh`, audited both directions.
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The finished certificates are destined for the LTL itself as attestation
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leaves: the log carrying kernel-checked proofs of its own machinery.
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