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The proper hat-guessing number of K5−eK_5-e

The exact value is HGP(K5−e)=8\mathrm{HG}_P(K_5-e)=8. The lower bound uses explicit legal twin-player rules over F23\mathbb F_2^3. After those rules cover 3,024 of the 8,400 proper colorings, the residual-coloring/local-view incidence graph has left degree three and right degree at most three; Hall's theorem supplies consistent guesses for the three clique players. The release also proves a general sufficient twin-completion lemma for Kn−eK_n-e. It does not solve the full Kn−eK_n-e family or determine HGP(C5)\mathrm{HG}_P(C_5).

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 2, 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 $K_5-e$ · $\mathrm{HG}_P(K_5-e)=8$

Confidence: Not scored

Registry verification: unreviewed · announcement · candidate

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VibeMathed
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GPT-5.6 Pro
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This event attributed to GPT-5.6 Pro

Tagged v0.1 release (ZIP and PDF) evidence for this event

The proper hat-guessing number of K5−eK_5-e parent of this event

The proper hat-guessing number of K5−eK_5-e evidence for this event

VibeMathed record: The proper hat-guessing number of K5−eK_5-e evidence for this event

The exact value is HGP(K5−e)=8\mathrm{HG}_P(K_5-e)=8. The lower bound uses explicit legal twin-player rules over F23\mathbb F_2^3. After those rules cover 3,024 of the 8,400 proper colorings, the residual-coloring/local-view incidence graph has left degree three and right degree at most three; Hall's theorem supplies consistent guesses for the three clique players. The release also proves a general sufficient twin-completion lemma for Kn−eK_n-e. It does not solve the full Kn−eK_n-e family or determine HGP(C5)\mathrm{HG}_P(C_5). parent of this event

Hat guessing with proper colorings (Adriaensen et al.) evidence for this event

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The proper hat-guessing number of $K_5-e$ — Mathematical Frontier Network