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Ben Green's Open Problem 57

Analysis · posed by Ben Green, 2024 · disproved

2 comments

Statement

For a finite abelian group GG, let Φ(G)\Phi(G) be the absolutely convex hull of the specified trilinear kernels and Φ′(G)\Phi'(G) its restriction where the third factor depends only on x1+x2x_1 + x_2. Is Φ(G)=Φ′(G)\Phi(G) = \Phi'(G)? A counterexample over Z/3Z\mathbb{Z}/3\mathbb{Z} separates the hulls.

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

  1. construction · #1

    AlphaProof Nexus

    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.

    Solved autonomously by AlphaProof Nexus, with the proof formally verified in Lean.

    intended complex form disproved, with a certified strict support-function gap

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

    lean: correctLean

    scope Lean formalization of the result

    Lean-checked; formal proofs published with DeepMind's AlphaProof Nexus report (arXiv:2605.22763) and its accompanying repository.

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

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