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Maxwell's Conjecture on Point-Charge Equilibria

Mathematical physics · posed by James Clerk Maxwell, 2004 · disproved

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Statement

Do nn point charges whose electrostatic potential has only non-degenerate critical points always have at most (n−1)2(n-1)^2 of them? A configuration of five charges - three at the vertices of an equilateral triangle plus two small central charges pulled apart into a shallow bipyramid - has at least 24>1624 > 16 non-degenerate critical points, so the conjecture is false.

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

  1. construction · #1

    Philip Arathoon, Gavin Ball and Matthew D. Kvalheim, using GPT-5.6 Sol

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    The idea behind the counterexample construction was suggested by the model; the authors verified all mathematical details and wrote the note.

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