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A note on five dimensional kissing arrangements
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abstract
The kissing number $\tau(d)$ is the maximum number of pairwise non-overlapping unit spheres each touching a central unit sphere in the $d$-dimensional Euclidean space. In this note we report on how we discovered a new, previously unknown arrangement of $40$ unit spheres in dimension $5$. Our arrangement saturates the best known lower bound on $\tau(5)$, and refutes a `belief' of Cohn--Jiao--Kumar--Torquato.
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Finding Kissing Numbers with Game-theoretic Reinforcement Learning
A Gram-matrix completion game played by two reinforcement-learning agents produces new kissing-number lower bounds in dimensions 25–31 and new rational and generalized spherical-code records.
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