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Makeev's conjecture on universal cover

Geometry & topology · posed by V. V. Makeev, 1994 · disproved

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Statement

Let Un⊂RnU_n\subset\mathbb R^n be the difference polytope of a regular nn-simplex such that UnU_n circumscribes a sphere of diameter 1. Then every set of diameter 1 in Rn\mathbb R^n is covered by a rotated copy of UnU_n.

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

  1. construction · #1

    ChatGPT 5.6 Pro

    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.

    AI found the counterexample in dimensions 4 and 5 and wrote the paper and code without human mathematical input.

    Makeev conjectured it to be true for all dimensions. This result disproves it for dimensions 4 and 5. Dimensions 6 and above remain open.

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