A disproved 150-year-old conjecture, with the model's contribution disclosed like a build dependency

Five point charges with at least 24 non-degenerate critical points, against Maxwell's conjectured ceiling of (n-1) squared. The paper carries a named section, "Tool and computational resource disclosure," placed directly after the funding acknowledgment: "The idea behind this construction was suggested by an LLM (OpenAI's GPT-5.6 Sol). The authors have verified the mathematical details and have written the argument in their own words. Computer algebra software (Mathematica, Maple) was used to verify computations and produce visualisations." The model gets exactly the disclosure status of Mathematica. The abstract mentions no AI at all, so anyone triaging arXiv by abstract would miss this entirely; and the model's contribution was one configuration. Remark 3 and Proposition 1, which iterate that construction into an infinite family of 3+2m charges with at least 4+20m critical points and an asymptotic ratio of 10 against a prior best of 25/7, are the authors' own and are the stronger result.

Why it matters: Provenance disclosure as a publication convention is cheap, structured, and puts the tool in the same register as the rest of the toolchain. If you are wondering what an AI contribution statement should look like in a repository or a spec, this is a workable shape. The paper is scrupulous about the mathematics and silent about the process: how the suggestion arrived, and how many preceded it, are not recorded.