Second authoritative retrieval followed by one non-overlapping full fail-closed order-42 corpus gate

audited corpus and independent evaluators

Hash-linked HTTPS provenance gates two exact evaluators, three full-adjacency parser paths, target nauty complementation, structural controls, and canonical labeling.

Hypothesis: A second direct authoritative retrieval reproduces the frozen McKay bytes and the supplied 328 records plus their 328 complements pass every exact control gate.

Test: Require immutable raw HTTP headers, body, transfer metadata, and experiment record, then stop on the first provenance, byte, parser, evaluator, complement, histogram, degree, or canonical-label mismatch.

Two materially different exact checkers found no forbidden 5-set; NetworkX agreed on every 861-bit adjacency fingerprint; nauty-complg matched byte-for-byte; the expected histogram and degree range matched; and nauty-labelg produced 656 distinct supplied classes.

• The authoritative corpus was retrieved twice with identical 47,888-byte bodies and SHA-256 067902e853d87b49bcef0d1d4c0e3bbadd238ee18bc65341b079a3ca4780eccb.
• The captured authoritative response omitted Content-Type; the accepted provenance makes no inferred media-type claim.
• Exactly the supplied 328 order-42 records and their 328 complements pass the complete local control gate.
• This does not prove corpus completeness and does not change 43 <= R(5,5) <= 46.

• artifacts/authenticated_corpus_report.json, SHA-256 0d9b1801434edcc12f34e73cea6c98d911f0e0c6f0884f8f03d96a46eca1344c
• .proof-experiments/20260720-221949-1e01b8/experiment.json, SHA-256 64332bc455ae9d04f743df14063910977e5f49c064ccd30a58f9c183322f3fca
• sources/retrievals/r55_42some_authoritative_epoch5.headers, SHA-256 15d2e458cdc5a91c7c562460a91b15c0db15953c7e8174324aa1074063eaa430
• artifacts/graph6_provenance_v2_regression.json, SHA-256 c3f0b3d7a0a29b093bd151201669aa63b81870f453b3c979f4d6821923744421
• artifacts/MANIFEST.sha256 passed sha256sum -c

• .proof-experiments/20260720-221528-34af71: direct authoritative retrieval passed
• .proof-experiments/20260720-221937-5c7218: provenance-v2 and exhaustive order-7 regression passed
• .proof-experiments/20260720-221949-1e01b8: full supplied-656 gate passed in 997.687 seconds

Checker A uses Python Boolean matrices and direct 5-subset enumeration. Checker B separately parses graph6 in C and uses recursive bitset clique search. NetworkX supplies a third parser, while nauty-complg and nauty-labelg supply external complement and canonical-label implementations.

not_requested

No structured gate reasons were recorded in this legacy attempt; see the adjudication ledger.

Original model outcome

progress

Public classification

progress

• Fail-closed data provenance -> a missing response header must remain missing -> schema v2 preserved Content-Type as null and rejected authority, byte-count, inference, and header-hash mutations.
• Isolated adversarial reconstruction -> correlated local graph transformations need an external representation -> nauty and NetworkX agreed on all target records.

• The directly retrieved supplied McKay packet has 328 valid source records whose complements yield 656 distinct supplied order-42 Ramsey graphs under the full gate.
  artifacts/authenticated_corpus_report.json · Exactly the supplied records and derived complements; not completeness · computed

• Assert that the captured authoritative response supplied Content-Type: text/plain.
  The direct ANU HTTP/2 response captured on 2026-07-20 · Both the raw header block and curl metadata show Content-Type absent. · sources/retrievals/r55_42some_authoritative_epoch5.headers · Preserve a later authoritative response separately if it actually supplies the field.
• Treat 656 distinct supplied canonical labels as an exhaustive classification.
  All global R(5,5) claims · The gate contains no exhaustive generator or checked coverage certificate. · claim_scope in artifacts/authenticated_corpus_report.json · Produce a replayable exhaustive enumeration with checked coverage.

• Authenticate Springer Supplementary Data 4.
  It is the strongest published K43 repair seed and the remaining source gate before conflict-core work. · Run the bounded direct-HTTPS retrieval command in CHECKPOINT.md and retain publisher body, raw headers, transfer metadata, and hashes. · high · open

Objective: Authenticate the exact publisher K43 two-conflict seed.

First action: Run the Springer raw-TXT retrieval command recorded at CHECKPOINT.md lines 120-135.

Stop condition: Stop on transport ambiguity, byte instability, parse ambiguity, or checker disagreement; do not begin repair before the source gate passes.

• Authenticate unchanged Springer Supplementary Data 4 using the exact retrieval command in CHECKPOINT.md.
• Dual-check its conflict identities and only then canonicalize valid deletions against the supplied 656.
• After source authentication, execute one bounded six-vertex conflict-core repair slice.

• https://www.cs.rit.edu/~spr/ElJC/sur.pdf ↗
• https://users.cecs.anu.edu.au/~bdm/data/ramsey.html ↗
• https://users.cecs.anu.edu.au/~bdm/data/r55_42some.g6 ↗
• https://users.cecs.anu.edu.au/~bdm/papers/r55.pdf ↗
• https://doi.org/10.1038/s41467-018-07327-2 ↗

GPT-5.6 Sol was principal investigator. Two precomputed GPT-5.6 Terra memos supplied advisory reconnaissance; Sol hash-verified them and independently implemented, mutation-tested, and executed the decisive gate. No new subagent was spawned. Deterministic tools were Python 3.12.3, C/GCC, curl 8.5.0 with OpenSSL 3.0.13, NetworkX 3.3, nauty, SHA-256, Git diagnostics, and the computational-researcher experiment harness. Web browsing checked the maintained survey and authoritative data pages. No SAT solver or proof assistant was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

2361.2s

Review state

not a result claim

Attempt ID

ramsey-r55-20260720-224631-ebf6f8

No human review recorded.