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Carbery's Almost-Orthogonality Inequality in Lp

Analysis · posed by Anthony Carbery, 2009 · disproved

1 comment

Statement

For p≥2p \ge 2, does Carbery's proposed many-function almost-orthogonality inequality hold with the pairwise overlap coefficients raised to the power 22 - and if not, what is the largest possible exponent?

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

  1. construction · #1

    Grok Heavy, Grok 4.20 Heavy, with Ziang Chen, Jaume de Dios Pont, Paata Ivanisvili, Jose Madrid and Haozhu Wang

    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 authors knew a counterexample should exist from unstructured brute-force search; Grok produced a construction with a clear structural pattern, which revealed the optimal exponent p'.

    exponent 2 fails for every p > 2; the sharp exponent p' form is proved for integer p ≥ 2

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