Fail-closed authentication and independent validation of the R(5,5) order-42 control corpus and provisional two-conflict K43 seed

audited corpus and independent evaluators

Freeze exact source-byte discriminators, require them before computation, compare independent Python/direct-combination and C/recursive-bitset evaluators, and cross-check graph6 plumbing with nauty and NetworkX

Hypothesis: The authoritative McKay corpus is locally available with the frozen 47,888-byte SHA-256 discriminator and can then reproduce 656 valid, canonically distinct controls under two independent exact checkers.

Test: Require the local corpus to have SHA-256 067902e853d87b49bcef0d1d4c0e3bbadd238ee18bc65341b079a3ca4780eccb, size 47,888, and 328 records before running any graph check; otherwise record source_preflight_failed with downstream_checks_run=false.

The epoch produced independently replayable control infrastructure and eliminated parser/complement behavior as an immediate ambiguity, while respecting the source-authentication stop condition. Missing authoritative bytes prevent promotion beyond internal progress.

• For the exact unauthenticated transcription with SHA-256 3beebde4f3120337029bb24de1f737f72eab567cbe92c77f79e7206ce4c304e9, two independent checkers agree that graph2 has exactly the K5s {0,15,22,28,39} and {0,15,24,28,39}; deleting 0, 15, 28, or 39 yields a valid order-42 graph.
• Across one representative of every 1,044 unlabeled simple graph class on seven vertices, the two graph6 checkers agree exactly, NetworkX agrees on graph signatures, and the complement encoding agrees byte-for-byte with nauty-complg.
• The authoritative order-42 corpus was absent locally, so zero corpus or complement instances were checked this epoch.

• artifacts/provisional_k43_control_report.json, SHA-256 f854b8e8b69c9006fca6e797952eeac5c3540a452105420878b7e4d356df69e5
• artifacts/graph6_plumbing_report.json, SHA-256 b217efb5a2393c62d0ffde250fac4e419d30bb8e431c15b61e3232ff51eb1812
• artifacts/corpus_source_preflight_report.json, SHA-256 db893987f58b718712ebd39f6e8338df2c79d32f0fe2dfdc62f7c051011e7fb4
• artifacts/MANIFEST.sha256 passes sha256sum -c
• CHECKPOINT.md contains exact replay command, hashes, scope limits, and stop conditions

• .proof-experiments/20260720-193914-fbe251: provisional K43 dual control passed in 19.857 seconds
• .proof-experiments/20260720-194142-be8455: all 1,044 order-7 graph6 classes passed independent plumbing checks in 1.194 seconds
• .proof-experiments/20260720-193953-b4e5bd: corpus preflight returned code 2 because the authoritative file was absent; downstream_checks_run=false

Checker A is Python using a separately written matrix/graph6 parser and literal combination enumeration. Checker B is C using separate parsers and recursive bitset clique enumeration in the graph and complement. Nauty 2.8.8+ds-5 independently checked complement bytes, and NetworkX 2.8.8 independently checked parsed signatures.

not_requested

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

Original model outcome

progress

Public classification

progress

• Isolated adversarial reconstruction -> independent graph representations should expose shared parser mistakes -> exact agreement was observed across all 1,044 order-7 isomorphism classes.
• Fail-closed source authentication -> missing or altered bytes must prevent downstream mathematical claims -> the absent corpus produced an explicit preflight failure with no graph checks.

• The maintained published range remains 43 <= R(5,5) <= 46.
  2026 Dynamic Survey and Angeltveit-McKay journal publication · Published global R(5,5) bounds as checked on 2026-07-20 · proved
• The custom short-graph6 parsing and complement plumbing agrees with nauty and NetworkX on every unlabeled order-7 graph class.
  artifacts/graph6_plumbing_report.json · The 1,044 unlabeled simple graph isomorphism classes at order 7 · computed
• The two exact checkers agree on the violation identities and four valid deletions in the provisional K43 transcription.
  artifacts/provisional_k43_control_report.json · Only input SHA-256 3beebde4f3120337029bb24de1f737f72eab567cbe92c77f79e7206ce4c304e9; publisher equivalence unverified · conditional

• Treat the visible third-party K43 transcription as the authenticated Springer supplementary seed.
  The current local input artifact · Checker agreement proves properties of supplied bytes but not their publisher provenance. · publisher_authentication=false in artifacts/provisional_k43_control_report.json · Recover unchanged Springer Supplementary Data 4 and establish an exact transformation or byte correspondence.
• Start novel-42 or K43 repair search from the current control packet.
  This epoch and any continuation lacking the raw corpus · The required source preflight failed before any corpus validation or canonical comparison. · artifacts/corpus_source_preflight_report.json · The authoritative corpus passes the complete dual-check, complement, histogram, degree, and canonical-label gate.

• Authenticate the 328 McKay source records and their complements.
  Every novelty and canonical-comparison claim depends on this immutable control set. · Place unchanged bytes at sources/r55_42some.g6 and run the authenticated-corpus command in CHECKPOINT.md. · high · open
• Authenticate Springer Supplementary Data 4.
  It is the strongest published K43 repair seed, but the current transcription cannot establish publisher provenance. · Retrieve the unchanged supplementary TXT, hash it, determine its color convention, and compare exact violation identities under both checkers. · high · open
• Enter the unknown-order-42 basin only after controls pass.
  Every deletion of a hypothetical K43 witness must lie outside the historically supplied 656. · Canonicalize authenticated seed deletions against the 656, then execute a bounded nonlocal destroy-and-repair discriminator. · high · open

Objective: Close the authoritative order-42 corpus control gate.

First action: Acquire sources/r55_42some.g6 unchanged, then execute the r55-authenticated-corpus-gate command recorded verbatim in CHECKPOINT.md.

Stop condition: Stop at any source hash, record count, parser output, forbidden-set identity, histogram, degree, complement, or canonical-label mismatch; otherwise proceed to the Springer source gate.

• Acquire unchanged McKay bytes at sources/r55_42some.g6 while recording timestamp, headers, final URL, byte count, and hash.
• If and only if the frozen byte discriminator matches, run the exact authenticated-corpus experiment command recorded in CHECKPOINT.md.
• After that gate passes, acquire and authenticate Springer Supplementary Data 4, then canonicalize the four valid deletion controls against the supplied 656.
• Do not begin unknown-42 or K43 repair search until both raw-source gates pass.

• https://www.combinatorics.org/ojs/index.php/eljc/article/download/DS1/pdf/0 ↗
• https://onlinelibrary.wiley.com/doi/full/10.1002/jgt.70029 ↗
• https://users.cecs.anu.edu.au/~bdm/data/ramsey.html ↗
• https://users.cecs.anu.edu.au/~bdm/data/r55_42some.g6 ↗
• https://doi.org/10.1038/s41467-018-07327-2 ↗
• https://huggingface.co/datasets/linxy/RamseyGraph/blob/main/data/r55_42some.g6 ↗

GPT-5.6 Sol served as principal investigator. Two pairs of GPT-5.6 Terra delegate memos supplied advisory pre-epoch reconnaissance; Sol independently replayed every local claim used. Deterministic tools were Python 3.12.3, C/GCC 13.3.0, nauty 2.8.8+ds-5, NetworkX 2.8.8, SHA-256, the computational-researcher experiment harness, shell diagnostics, web search, and read-only GitHub search/fetch. No SAT solver, proof assistant, new delegate, or frontier search was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1247.3s

Review state

not a result claim

Attempt ID

ramsey-r55-20260720-194611-f14832

No human review recorded.