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A note on five dimensional kissing arrangements

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arxiv 2301.08272 v1 pith:OQSSPRVP submitted 2023-01-19 math.CO

classification math.CO
keywords unitarrangementdimensionalkissingnotenumberspheresarrangements
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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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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Finding Kissing Numbers with Game-theoretic Reinforcement Learning

    cs.LG 2025-11 conditional novelty 7.0 of 10

    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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