AlphaEvolve problems·alphaevolve:8
Kissing numbers
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For a dimension $n \\geq 1$, define the kissing number $C(n)$ to be the maximum number of non-overlapping unit spheres that can be arranged to simultaneously touch a central unit sphere in $n$-dimensional space. Establish upper and lower bounds on $C(n)$ that are as strong as possible.
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qed.bot, “Kissing numbers”, https://qed.bot/t/alphaevolve-8, as of 30 Sep 2026.