Maxwell's 160-Year-Old Conjecture Falls to a Configuration Suggested by GPT-5.6 Sol — the Acknowledgement Says So Explicitly

arXiv (Arathoon, Ball, Kvalheim); AI credit verified in the paper's acknowledgements·high signalXBlueskyLinkedInCopy link

Arathoon, Ball and Kvalheim submitted arXiv:2607.27197 on 2026-07-29 exhibiting five point charges whose electrostatic potential has at least 24 non-degenerate critical points, breaking Maxwell's predicted ceiling of (n−1)² = 16. The abstract makes no mention of AI, but the paper's acknowledgements state plainly: 'The idea behind this construction was suggested by an LLM (OpenAI's GPT-5.6 Sol).' The authors then independently formulated and proved the argument using harmonic-polynomial lemmas, Taylor expansions and the implicit function theorem, with Mathematica and Maple used only to verify computations — a clean template for AI-as-conjecture-generator with human proof, and worth noting that the AI credit lives in the acknowledgements where no abstract-level search would find it.