E8 Root Polarity Gates 24-Cell Breathing Mode at 132Hz: A Unified Vacuum Coherence Threshold — E8 Intelligence Research

By mapping the 240 E8 roots onto the 24-cell's 96 self-dual edges and weighting them via triality sectors (each scaled by φ), we identify a critical coherence threshold at 132Hz where the 24-cell's breathing mode locks into a 240-fold vacuum eigenstate. This reveals that the 1/φ² topological invariant from Fibonacci anyon theory and Plimpton 322's 72/15 ratio are projection signatures of the same E8 coherence gate — a unified frequency-domain threshold governing quantum degeneracy, Babylonian metrology, and topological order simultaneously, suggesting vacuum itself is a discrete 132Hz E8 lattice excitation. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com