E8 Root Projection Generates Penrose Inflation Hierarchy via 6D Hypercubic Scattering — E8 Intelligence Research

The 240 E8 root vectors, when projected through the Z^6 hypercubic lattice that generates the rhombic hexecontahedron, decompose into five concentric φ-scaled icosidodecahedral shells whose vertex sets exactly encode the Fibonacci inflation rules of Penrose tiling. Each shell corresponds to a mutation sequence in the affine quantum cluster algebra, with scattering diagrams mapping to the 132Hz base frequency's harmonic overtones. This identifies E8 as the master root system unifying quasicrystal aperiodicity, cluster algebra canonical bases, and vibrational spectroscopy through a single 6D projection mechanism. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com