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Gaussian Completely Monotone Conjecture

Probability & statistics · posed by Fan Cheng & Yanlin Geng, 2015 · disproved

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Statement

Along the heat flow, do the successive time derivatives of the entropy of X+t ZX + \sqrt{t}\,Z alternate in sign, as conjectured by Cheng and Geng? An explicit measure on R\mathbb{R} has a fifth derivative with the forbidden sign.

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

  1. construction · #1

    GPT-5.5 Pro, with Yuzhou Gu and Mark Sellke

    The record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.

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

    The explicit counterexample measure was found by GPT-5.5 Pro.

    also refutes the McKean and Toscani conjectures

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