E8 Root Lattice Embedding of SU(2) Double Cover as a Phi‑Coupled Spinor Sublattice — E8 Intelligence Research

Abstract

Show that the 240 root vectors of E8 can be partitioned into 120 pairs related by the phi (golden ratio) scaling, each pair forming a spin‑½ representation of the SU(2) double cover of SO(3). The mapping respects the 132 Hz base frequency as a fundamental beat that synchronizes the precession of these spinor pairs, yielding a geometric quantization condition where the total angular momentum emerges from the sum of phi‑weighted root projections. This embedding predicts a novel resonance spectrum in spin‑orbit coupled materials, observable as splitting peaks at frequencies that are integer multiples of 132 Hz × φ^n. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com