Computability questions in the sphere packing problem

Yuri Manin; Matilde Marcolli

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arXiv · 2212.05119

Computability questions in the sphere packing problem

Yuri Manin·Matilde Marcolli

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Abstract

We consider the sets of dimensions for which there is an optimal sphere packing with special regularity properties (respectively, a lattice, or a periodic set with a given bound on the number of translations, or an arbitrary periodic set). We show that all these sets are oracle-computable, given an oracle that orders an associated set of spherical codes by increasing Kolmogorov complexity.

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Yuri Manin, Matilde Marcolli. 2022-12-09. Computability questions in the sphere packing problem. https://arxiv.org/abs/2212.05119

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