Re-auditing the prior (Opus-produced) depth pass adversarially found and
fixed three genuine issues:
1. OVERCLAIM (serious): §5.3 said the consistency verifier was
differential-tested 'on all (n0,n1) with n1<=256' but the script only
SAMPLED sizes (5,508 cases). Ran the genuinely exhaustive test — all
1<=n0<=n1<=256, honest + 4 mutations — 164,224 invocations, and the
inclusion verifier likewise (164,479). Paper now states the true scope
and counts; both are pinned in a new CI test (test_paper_verifiers.py,
104 tests) so the numbers cannot rot.
2. PROOF IMPRECISION: Lemma 2 (Root binding) was applied to ConsRec's
first component, which PASSES THROUGH (no hnode) at some levels and so
is not the hash-fold the lemma needs. Reworked: Lemma 2 now defined
over 'hash-folds' only; Theorem 3 restructured into 3 clean steps that
put only the full-hashing second component through the lemma, then
argue algebraically + one honest-tree collision. Also hoisted Lemma 2
above Theorem 2 and made Theorem 2 invoke it (was inlined), so the
'two theorems share the lemma' remark is now true; deduped the remark.
3. MISLABELED TABLE: Table 1's 'files vs upstream' column actually held
line-diffs against different baselines. Dropped it for clean comparable
columns (files / apex axioms / SHA-512 shape); the diff story stays in
the portability paragraph where each baseline is named.
17 pages, all refs resolve, 104 tests green.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
