A single-lattice covering bound of order n log n
Every convex body in ℝ n , n ≥ 2, admits a covering by translates along one full-rank lattice with density at most $Cn\log n$, for an absolute constant C . No symmetry or boundary regularity is assumed.
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Updates: Sharing AI progress on mathematics (amazing!); and my lecture plansCombinatorics and moreOct 7, 2026
OpenAI announces a universal lattice-covering bound and matching examples even for unrestricted translative coverings , determining the worst-case order over convex bodies. Distinct distances and unit distances. These problems featured in János Pach’s guest post on Guth and Katz and in my earlier…