Preprint in the OpenAI Math release

A power saving for planar unit distances

OpenAI

Abstract

We prove a power saving for the planar unit-distance problem: for some absolute $β < 4/3$ , every set of n points in the Euclidean plane determines $O (n^{β})$ unordered pairs at unit distance.

open until 1 Jan 2028

est. 50% chance this result is independently verified by the end of 2027.

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est. 50% chance this result is independently verified by the end of 2027.

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