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arXiv:2607.27197physics.class-ph

The Maxwell Conjecture is False

Philip Arathoon, Gavin Ball, Matthew D. Kvalheim

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Abstract

We exhibit a configuration of five point charges in Euclidean space whose electrostatic potential admits at least 24 critical points all of which are non-degenerate. Maxwell's conjecture that the field of \(n\) point charges has at most \((n-1)^2\) critical points which are all non-degenerate is therefore false.

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physics.class-phClassical Physics math-phMathematical Physics

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Linked by 1 identifiable commenter in 1 comment across 1 thread, from Jul 2026 to Jul 2026. Found in 1 HN submission from Jul 2026 to Jul 2026. Open submission discussions.

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  1. The Maxwell conjecture is false. Counterexample found by AI (GPT-5.6 Sol) 1 comment

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