A 1.30^d Lower Bound for the Chromatic Number of Euclidean Space

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.