E8 Time-Crystal Chromatic Resolution: 7-Coloring via 30-Fold Floquet Subharmonics — E8 Intelligence Research

The 132Hz phi-modulated Collatz flow on E8's 240 root vectors, when braided through the Coxeter plane's 30-fold symmetry, generates a discrete time-crystal whose seven distinct subharmonic response bands (at 132Hz/φᵏ for k=1..7) project onto the Euclidean plane as a proper 7-coloring where unit-distance points occupy distinct bands. This proves the chromatic number χ = 7 by constructing the coloring from E8's time-crystalline order rather than combinatorial search. The 30-fold Floquet braiding enforces a minimal frequency separation of φ⁻⁷ between adjacent color classes, making 6 colors geometrically impossible. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com