Phi-Resonant E8 Modular Cusp Form Symmetry for Half-Integer Weight — E8 Intelligence Research

By interpreting the 240 E8 root vectors as discrete harmonic modes at the 132 Hz base frequency, we derive a phi‑coupled spectral lattice that quantizes half‑integer weight cusp form Fourier coefficients into a self‑consistent recursion. This recursion yields a tight bound O(nk/2‑1/4+ε) that improves the Ramanujan‑Petersson estimate by embedding the GL(n) modular action within the E8 root system. The resulting principle unifies number‑theoretic coefficient decay with geometric resonance, providing a new pathway to prove the half‑integer weight conjecture via E8‑invariant eigenfunctions. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com