[JosieElliston]

This is a separately written audit of #1624 (an664 / Andrey Mas, head 712a9b9a). #1624 proves that PR1020's fixed 26-line puncture with designated pair (48, 0) has an eight-term separate-COPY minimum of 62, with 256 optimal classes and a sharp branch bound of 67. #1624 itself notes two limits on its evidence: both of its checkers came from one session, and its 69 baseline was replayed from transcribed data rather than with PR1020's program.

Result: corroborated, no gap found. Only research/paired26-independent-audit/ is added. The selected frontier and κ are unchanged.

What it checks

• Finite premises. verify.py was written from proof.md's prose only; Research: fixed paired26 completion minimum 62 with exact certificates #1624's verify.py, audit.py and certificate were not read. It recomputes every finite premise of §§2, 4–6, 8 and 9 with exact integer and Fraction arithmetic:
  • the label basis and the 14,400-entry bilinear identity;
  • the −256 minor;
  • 511 kernels: 482 of rank 8, 29 of rank 7, on 27 lines P ∪ {30}, cross-checked mod p, with no rank ≤ 6;
  • the §5 table row for row, with each annihilator also found by enumeration;
  • the 13 + 1 perp candidates and the c·r_j list;
  • the 62 witness on all 8,836 entries, and the §8 table;
  • 256 independent seven-sets, matching the structural formula.
• Beyond Research: fixed paired26 completion minimum 62 with exact certificates #1624.
  • Each of the 256 optimal classes is expanded entrywise; all cost 62. Research: fixed paired26 completion minimum 62 with exact certificates #1624 left these unexpanded.
  • A branch-67 witness is built here rather than taken from Research: fixed paired26 completion minimum 62 with exact certificates #1624.
  • The §10 complex example is checked over Q(i): cost 63, and the real look-alike has the same 16 supports.
• Binding to PR1020. Merged PR1020's own decoder_check prices its decoder at 69 and Research: fixed paired26 completion minimum 62 with exact certificates #1624's witness at 62. PR1020's root indexing, pairing and puncture equal Research: fixed paired26 completion minimum 62 with exact certificates #1624's spec. This stage imports predecessor code on purpose and is labelled as binding, not independence.
• Written audit. The README reviews the §3 normal form, the §4 reduction over C, the (2.1) bound, both §7 cases and the §9 converse step by step. No missing implication was found.

Commands

All run on macOS arm64, about 30 s each. Seven rejection controls run in normal and -O modes.

python3.12 scripts/research_package.py --package research/paired26-independent-audit   # PASS_REGISTERED_RESEARCH_PACKAGE
python3.12 -B research/paired26-independent-audit/verify.py      # also 3.10, 3.14, and -O
python3 scripts/research_package.py --package research/paired26-independent-audit --check-only
python3 -B -m unittest discover -s tests -p 'test_research_*.py' # 20 tests OK

A read-only OpenAI Codex adversarial review found no problem in the mathematics or the main gates. It flagged two tautological controls, an unchecked support premise in the §10 control, and an overbroad independence claim. All four are fixed in 99a8cd75.

Limits

• The spec (P, J_label, tables, matrices) is transcribed from Research: fixed paired26 completion minimum 62 with exact certificates #1624's proof.md and compared against recomputation.
• One Claude session wrote this audit. It is not a human review and not a proof-assistant proof.
• Not checked: Research: fixed paired26 completion minimum 62 with exact certificates #1624's own certificate bytes, its 14 controls, and its external GPT-6 Pro review. None of these is needed for the theorem as written.
• The theorem's scope is unchanged: one puncture, one ordered pair, COPY-only. No physical decoder, moment or κ.

Task and overlap

• Chooser nonce 37b2c62ff85db7b743acb46efb8fc1d1: track independent-verification, card formal-interface-lemma, priority revision 3.
• The scope is changed to this audit. The reason is recorded in TASK.json.
• independent-moment, the other card offered, is saturated for the selected record.
• Base: main a73173f7.
• Claim: 1570 comment.
• Overlap refresh at 05:41 UTC covered 535 open PRs and 306 discussion records, with complete pagination. The only matches were Research: fixed paired26 completion minimum 62 with exact certificates #1624, its discussion, and this claim.

Credit

• an664 / Andrey Mas with GPT-6 Pro (Research: fixed paired26 completion minimum 62 with exact certificates #1624): the theorem and proof.
• woklerx (PR1020): the puncture, the cost-six pair, and the 69 decoder.
• themilkman216 (PR968) and DreamingOfClouds (PR717): the model.
• Hanson Sun / bbMisk (PR1521): the question that Research: fixed paired26 completion minimum 62 with exact certificates #1624 answered.

Prepared in JosieElliston's donated Claude Code session, with substantial AI assistance. Apache-2.0.

Workflow feedback: independent-moment was again offered although it is saturated for the selected record. The feedback request in 1200 for a per-card "existing checks" field still applies.

🤖 Generated with Claude Code

[Mister-Meeseeks]

Batch review at 99a8cd75db82802994a9e9d8fb6efb5cfa3109b7.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Independent exact audit of PR1624 paired26 minimum62 and all256 optimal classes, with PR1020 code binding, independent67-branch witness and Q(i) controls. Corroborates the fixed pair/puncture theorem without claiming supplier admission.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.