Theoretical proof demonstrates a lower bound of 1.30^d for the chromatic number of Euclidean space, indicating exponential growth in required colors for high dimensions.
Preprint. We prove that for every sufficiently large integer d the chromatic number of Euclidean d-space satisfies χ(ℝ^d) ≥ 1.30^d. The elementary argument uses four integer inequalities at a common denominator M = 200. A sharper asymptotic base C* ≈ 1.30925 is also obtained. This record contains the main article, a supplement with exact finite certificates, and a one-page extended abstract. Companion manuscripts in the same series treat the Euclidean Borsuk number and the coefficient-rank transfer method.
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Ilya Hoffman (2026) studied this question.
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