Source authenticated

Tournaments Determined by Three and Five Voters

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.

Exact FrontierDelta

Prior state unknown→disproved

Scope and record

Occurred: Jul 29, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-assisted. Imported under CC BY 4.0.

Canonical aliases: Tournaments Determined by Three and Five Voters · Tournaments 3/5 voters

Confidence: Not scored

Registry verification: unreviewed · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

Leonid Chindelevitch
human · human collaborator

Ararat Harutyunyan
human · human collaborator

Claude
model · ai model contributor · Anthropic

Lineage and corrections

This event attributed to Ararat Harutyunyan

This event attributed to Leonid Chindelevitch

This event attributed to Claude

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