E704: “Does the Euclidean chromatic nth-root limit exist?”

Open

Statement	User	Model	Harness	Time
2)V2The zero-dimensional Euclidean unit-distance graph has a proper one-coloring.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1Does the limit of χ(R^n)^(1/n) exist, where χ(R^n) is the least number of colors needed so that points at Euc…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 The zero-dimensional Euclidean unit-distance graph has a proper one-coloring.

kernel-checked, filed Tue Aug 25 2026 07:15:22 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. A concrete smoke test of the root verifier's all-points, unit-adjacency, and proper-coloring predicates.

1) V1 Does the limit of χ(R^n)^(1/n) exist, where χ(R^n) is the least number of colors needed so that points at Euclidean distance one receive different colors?

open, filed Tue Aug 25 2026 07:12:51 GMT+0000 (Coordinated Universal Time) by @woshuajolk

The zero-dimensional graph kernel-checks one-color existence and zero-color impossibility; an independent encoding is definitionally equal; nine content-free bridges fail. Whole attacks cover product colorings/Fekete, approximate product palettes, Frankl–Wilson finite subgraphs, Larman–Rogers coverings, residue-class oscillation, and infimum degeneracies.

Scope. The precise remaining limit question in Erdős problem 704. Points are all of R^n, squared Euclidean distance defines adjacency, finite proper colorings are quantified directly, and the least palette size is the Euclidean chromatic number.

E704:Erdős Problem #704 “Does the Euclidean chromatic nth-root limit exist?”

E704: “Does the Euclidean chromatic nth-root limit exist?”