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Claim. Jonathan Reed, The Hadwiger-Nelson Problem: Formal Verification of the 7-Color Chromatic Number of the Plane via Toroidal Projection and the Irrationality of $2\pi$, a public manuscript in a GitHub repository first posted on 13 May 2026; the version of 14 May 2026 is the one linked above and the one the release preprint of OpenAI's claim discusses. The manuscript announces that the chromatic number of the plane asked for by Problem 508 is $\chi(\mathbb R^2)=7$. Its argument projects a unit-distance path onto a circle and asserts that, because the circumference $2\pi$ is irrational relative to the unit chord, every unit-independent subset of the circle (a set with no two points at distance one) has angular measure strictly less than $\pi/3$; six color classes would then have total measure below $2\pi$ and could not cover the circle, and the de Bruijn–Erdős compactness theorem is invoked to carry the exclusion of six colors to the plane. A value of $\chi(\mathbb R^2)$ answers the question the problem asks, so the claim is full and its value answered.

Rejection. The release preprint records, in a footnote to its introduction, that the proposed strict bound fails: the half-open arc $\{e^{it}:0\le t<\pi/3\}$ of the unit circle has angular measure exactly $\pi/3$ and contains no unit pair, since a unit chord of the unit circle subtends the angle $\pi/3$. The manuscript's displayed formal theorem, coloring_collision, takes that density bound (SafeDensity, the color measure below $\pi/3$) as a hypothesis for each color rather than proving it, so the Lean text verifies only that six measures each below $\pi/3$ sum to less than $2\pi$, and the argument does not establish the announced equality. The claim is recorded as rejected on that record. The accepted bounds $6\le\chi(\mathbb R^2)\le7$ on OpenAI's claim page leave seven possible, so the objection concerns the argument and not the value.

Depends on. No page of this wiki.

Acceptance. None recorded. The manuscript has no journal or arXiv record; it is deposited on Zenodo as version 1.0 of 13 May 2026 (DOI 10.5281/zenodo.20149767), which the repository's README cites; the site's page labels the problem OPEN, last edited on 22 January 2026, with the bounds $5\le\chi\le7$ in its remarks and no mention of the manuscript, and its proof-claims thread listed no claim on 6 October 2026. The release's footnote is the only outside examination of the manuscript recorded here.