Computability questions in the sphere packing problem
Information Theory
2022-12-13 v1 math.IT
Logic
Metric Geometry
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.
Cite
@article{arxiv.2212.05119,
title = {Computability questions in the sphere packing problem},
author = {Yuri Manin and Matilde Marcolli},
journal= {arXiv preprint arXiv:2212.05119},
year = {2022}
}
Comments
24 pages, LaTeX