VibeMathed reports this item as candidate. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise statement
Determine the exact proper hat-guessing number of the complete graph on eight vertices with one edge removed. The general bounds leave $\mathrm{HG}_P(K_8-e)\in\{13,14\}$.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement
fidelity, correctness, priority, or novelty.
What AI did
GPT-5.6 Pro
OpenAI GPT-5.6 Pro contributed substantively to literature search, target selection, construction search, proof development, code generation, exact verification, adversarial critique, certificate design, and manuscript and release preparation. The equivariant construction, residual-matching proof, Hall-obstruction analysis, and shared-completion family were developed in a human-directed model-assisted research process. Matthew Protti selected and framed the target, directed and evaluated the work, commissioned review, required exact checks, approved the public scope, and accepts responsibility.
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.
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 $K_9-e$.
Known method families
computation (source-reported)
Source-reported tools: computation.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
The source status is candidate and must not be represented as solved.
VibeMath has not independently verified the mathematical claim.
AI-attempt independence and training-data exposure are unknown unless explicitly documented.
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.