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The proper hat-guessing number of
We prove . One lower-bound proof uses two explicit block-disjoint Witt designs. A second uses orbit maps from an explicitly regenerated sharply five-transitive twelve-point permutation group, combining one set-symmetric and one order-sensitive rule. Both satisfy a general coordinate-line twin-completion criterion, and Hall's theorem completes the clique strategy. The release also proves a disjoint completion-design theorem, an even- obstruction scoped to set-symmetric line-permutation twins in this sufficient framework, and a prime-admissibility theorem for the design parameters. It does not solve the general problem or .
Exact FrontierDelta
Prior state unknown→proved
Scope and record
Occurred: Sep 3, 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 $K_7-e$ · $\mathrm{HG}_P(K_7-e)=12$
Confidence: Not scored
Registry verification: unreviewed · announcement · candidate
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This event attributed to GPT-5.6 Pro
Public draft PR #2 and release record evidence for this event
We prove . One lower-bound proof uses two explicit block-disjoint Witt designs. A second uses orbit maps from an explicitly regenerated sharply five-transitive twelve-point permutation group, combining one set-symmetric and one order-sensitive rule. Both satisfy a general coordinate-line twin-completion criterion, and Hall's theorem completes the clique strategy. The release also proves a disjoint completion-design theorem, an even- obstruction scoped to set-symmetric line-permutation twins in this sufficient framework, and a prime-admissibility theorem for the design parameters. It does not solve the general problem or . parent of this event
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The proper hat-guessing number of parent of this event
VibeMathed record: The proper hat-guessing number of evidence for this event
The proper hat-guessing number of evidence for this event
Four-page K7-e preprint source evidence for this event
Hat guessing with proper colorings (Adriaensen et al.) evidence for this event
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