A 1.30^d Lower Bound for the Chromatic Number of Euclidean Space
Abstract
Preprint, version 2. We prove that χ(ℝ^d) ≥ c C*^d for an absolute constant c > 0 and all sufficiently large d, where 1.309251 < C* < 1.309252.In particular, χ(ℝ^d) ≥ 1.30^d for all sufficiently large d.For infinitely many dimensions the same construction gives χ(ℝ^d) ≥ 1.316^d.The argument uses a spherical layer of integer points with six or seven allowed coordinates.Version 1 remains the archival copy of the older polynomial-loss estimate.This version contains the article, the source, a verification script, and a one-page extended abstract.
Fields of Study & Subjects
Limits and Structures in Graph Theory
Advanced Graph Theory Research
Computational Geometry and Mesh Generation
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 18 September 2026
- Language
- EN
- Document type
- Preprint