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Around the Kemeny median problem, which stays open for $m=3$ and $m=5$ voters, the paper refutes three conjectures on tournament inducibility: both conjectures of Milosz, Hamel and Pierrot (the 3-cycle extension for odd $m\ge5$, and $\mathrm{FAS}=\mathrm{HS}_3$ at $n=11$), and Shepard's threshold conjecture.
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The authors report using Claude for exploratory reasoning, implementation assistance, drafting and editing. Exploration and implementation are mathematical work; drafting and editing are not, and the disclosure does not separate them, so the lowest tier applies.
Provider: Anthropic · Prompt public: unknown · Independence: unknown
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VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
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VibeMath has not independently audited the mathematical statement, proof, or novelty claim.