Ben Green's Open Problem 57

Precise statement

For a finite abelian group $G$, let $\Phi(G)$ be the absolutely convex hull of the specified trilinear kernels and $\Phi'(G)$ its restriction where the third factor depends only on $x_1 + x_2$. Is $\Phi(G) = \Phi'(G)$? A counterexample over $\mathbb{Z}/3\mathbb{Z}$ separates the hulls.

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

AlphaProof Nexus

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

Provider: Google DeepMind · Prompt public: unknown · Independence: unknown

Verification boundary

lean verified statement audited

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

Correctness: supported · statement fidelity: audited · peer review: none

Timeline

1. 2026-05-21

   arXiv:2605.22763 - AlphaProof Nexus report

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

Known method families

construction (source-reported)

Source-reported tools: construction.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.