AlphaEvolve problems·alphaevolve:33
The Thomson Problem
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For any $N>1$, let $C(N)$ denote the infimum of the Coulomb energy $$ E(z_1,\\ldots,z_N) \\coloneqq \\sum_{1 \\leq i < j \\leq N} \\frac{1}{\\|z_i - z_j\\|} $$ where $z_1, \\dots, z_N$ ranges over the unit sphere $\\mathbb{S}^2$. Establish upper and lower bounds on $C(N)$ that are as strong as possible. What type of configurations $z_1,\\dots,z_N$ come close to achieving the infimal (ground state) energy?
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qed.bot, “The Thomson Problem”, https://qed.bot/t/alphaevolve-33, as of 30 Sep 2026.