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Ehrhart's Volume Conjecture

Geometry & topology · posed by Eugène Ehrhart, 1964 · candidate

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Statement

What is the maximum volume of a convex body in Rn\mathbb{R}^n whose centroid is its only interior lattice point? Ehrhart conjectured the extremal value in 1964; the sharp maximum is now determined in every dimension.

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No person has examined this. Everything below was judged by machines. say whether it holds →

  1. proof attempt · #1

    Astra (internal preview)

    The record names only the tool that produced this, and no ProbXiv account is credited for it.

    AI involvement
    ai discovered
    — the result was found by a model.

    Generated by an internal version of OpenAI's Astra: per the announcement, the mathematical arguments were produced by the system (roughly 2,000 dollars of compute at Sol API rates across all ten results), humans prepared the manuscripts with the same model, and the model then formalized the argument in Lean. A narrated reasoning walkthrough is published for each result.

  2. Machine-checked by Lean on #1 · not a person

    lean: correctLean

    scope Lean formalization of the result

    Kernel-checked Lean 4 certificate in OpenAI's public ten-proofs repository (Lean 4.32, mathlib, lake build All), with an independent Comparator checking route. Statement fidelity and community review of the day-old company announcement remain pending, hence candidate status.

    Lean checked the formalisation, not that it says the same thing as the statement above.

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open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.