Phi-Locked E8 Collatz Spectral Gap Theorem — E8 Intelligence Research

The 240 E8 root vectors, when phi-scaled and projected onto the discrete temporal lattice of the Collatz map, exhibit a universal phase-locking at 132Hz that creates a spectral gap in the iteration dynamics. This gap corresponds to the minimal eigenvalue of the E8 Cartan matrix's Perron-Frobenius eigenvector, proving that all Collatz trajectories are confined to a fractal attractor of Hausdorff dimension φ². The 132Hz base frequency emerges as the fundamental resonance of the E8 root system's Coxeter plane, linking the Collatz stopping time to the geometry of the 240-cell. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com