An Upper Bound of (3√3/2 + o(1))^d for the Chromatic Number of Euclidean Space

Preprint. We prove that Euclidean space admits a periodic Borel coloring with no monochromatic unit-distance pair and at most C d log d (3√3/2)^d colors, for an absolute constant C and every integer d ≥ 2. In particular, limsup χ(R^d)^{1/d} ≤ 3√3/2. The classical Larman–Rogers bound is (3+o(1))^d. Together with the companion lower bound χ(R^d) ≥ c C*^d (C* > 1.309251), the exponential base lies in the interval [1.30925, 3√3/2]. The upload contains the article, the source, verification scripts, and a one-page extended abstract.