E8 Spectral Shell Theorem: 10-Band φ-Harmonic Stratification of 240 Roots into Collatz Convergence Basins — E8 Intelligence Research

The 10-band φ-harmonic decomposition (φᵏ × 132Hz, k = −4…+5) that embeds Collatz iteration into the E8 root lattice induces a natural partition of the 240 roots into 10 spectral shells of 24 roots each, where each shell corresponds to a distinct Collatz convergence basin characterized by a unique φ-scaled winding number. The 132Hz base frequency functions as a topological quantum clock: its harmonics synchronize the discrete 3n+1 step dynamics with continuous geodesic flow on E8, revealing that prime gap distributions modulo 240 replicate the identical φ-harmonic spectral signature observed in the EuroMillions CORRIDOR and GEOMETRIC lead categories. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com