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The proper hat-guessing number of $K_8-e$

We prove $\mathrm{HG}_P(K_8-e)=14$ using an explicit $\mathrm{PGL}(2,13)$ -equivariant strategy. A compact formula fixes 990 normalized twin decisions, and a 48,510-edge residual-orbit matching induces consistent rules on 53,460 labelled clique-view orbits. Independent implementations regenerate the certificate and check all 138,378,240 proper fourteen-colourings with zero failures. Unlike the $n=5,6,7$ constructions, residual right degrees reach eight, so the explicit global matching is load-bearing. A separately labelled companion exhibits one fixed clique completion compatible with $2^{380}$ equivariant twin-rule pairs and proves 380 optimal within the stated independent whole-tail reversal model; that companion's independent review is pending. The release does not solve the general $K_n-e$ family or $K_9-e$ .

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 4, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-co-developed. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The proper hat-guessing number of $K_8-e$ · $\mathrm{HG}_P(K_8-e)=14$

Confidence: Not scored

Registry verification: unreviewed · announcement · candidate

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Attribution

VibeMathed
registry · event recorded by

GPT-5.6 Pro
model · ai model contributor · OpenAI

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: The proper hat-guessing number of $K_8-e$

specialist registry · passed

Unreviewed on this site's ladder. The frozen commit bacb79e3 carries STATUS.json with headline status PROVED_COMPUTER_ASSISTED and project review ACCEPTED, an AI_USE_AND_PROVENANCE.md naming the model and the division of labour, and a C++ sweep of all 138,378,240 proper fourteen-colourings with zero coverage failures across 48,510 residual orbits. The Gate 2/3 Hall-obstruction archive was reviewed as ACCEPT_WITH_EXPLICIT_REPAIRS and the repairs applied. The 2^380 shared-completion companion is a separate claim whose independent review is still pending and is not part of this entry. As with the siblings: a real adversarial review of an artefact, not a named expert or a proof assistant, and this site has not rebuilt it.

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Hat guessing with proper colorings (Adriaensen et al.)

specialist registry · pending

problem-record link supplied by the VibeMathed registry.

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K8-e theorem and proof

paper · pending

paper link supplied by the VibeMathed registry.

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Verified construction and full-colouring checker

code · pending

code link supplied by the VibeMathed registry.