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The Equality Case of Ehrhart's Volume Conjecture

Geometry & topology · posed by Eugene Ehrhart, 1964 · solved

1 comment

Statement

Ehrhart conjectured that a full-dimensional compact convex body in Rn\mathbb{R}^n whose barycenter is its unique interior lattice point has volume at most (n+1)n/n!(n+1)^n/n!. With the inequality itself settled, the remaining question was which bodies attain it. Every such body is a unimodular image of the simplex (n+1)Δn−(1,…,1)(n+1)\Delta_n - (1,\dots,1).

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

  1. proof attempt · #1

    Jihao Liu, using GPT-5.6 Sol, Fable 5, Danus

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

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

    The paper states the main result was obtained by generative AI, naming GPT-5.6-sol, Fable 5 and the Danus system, and its comment records essential human strategic input followed by human verification.

    the equality case; the inequality was settled separately and is tracked on its own entry

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