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Feige's Hypergraph Moore-Bound Conjecture

Combinatorics · posed by Uriel Feige, 2008 · solved

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Statement

At the conjectured density, must every kk-uniform hypergraph contain a short nontrivial even cover - a set of hyperedges covering each vertex an even number of times - with no superfluous polylogarithmic factors? Known up to polylog factors since 2022; now proved exactly for every k≥3k \ge 3.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    GPT-5.6 Sol, GPT-5.5 Pro, Claude Opus 4.8, Claude Fable 5

    No person is named on this work: the record names only the tool it came from, and no ProbXiv account is credited for it.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    The colored-walk polynomial-interpolation argument over Kikuchi graphs was developed across several frontier models and written up by a five-author team, with an independent spectral proof alongside.

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open in Claude →open in ChatGPT →

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