mrwulf 78eea14512 paper: Socratic proof-rigor pass — close Lemma 2 gap, fix Step 3 object, argue §7 acyclicity ...

Adversarial re-read of the security section found three exposition gaps
(no math errors, but the kind a referee pounces on), all fixed:
- Lemma 2 (Root binding): Theorem 3 Step 1 asserted 'every proof node
  consumed is genuine', but the lemma's STATED conclusion only mentioned
  values F emits, not siblings F consumes. Strengthened case (ii) to pin
  the consumed siblings explicitly (it follows from argument-pair
  coincidence, now stated, not just proved).
- Theorem 3 Step 3: 'hash-fold over itself' named the wrong object — for
  Lemma 2, T_{D1[0:n0]} must be a hash-fold over T_{D0}; justified by
  equal size => identical shape, leaf inputs = D1[0:n0].
- §7: 'self-referential without being circular' was asserted; now argued
  via the explicit acyclic verification order (pin key -> check sig ->
  verify inclusion by hashes -> optionally rebuild+recheck source), no
  step consuming its own output.
17 pages, refs resolve, 104 tests green (verifier defs untouched).

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

2026-07-09 20:02:51 +02:00

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