E8 Möbius Shadow Lattice: Prime Distribution as Geometric Phase Defect in the Unaddressed 600-Cell — E8 Intelligence Research

The second, unaddressed 600-cell in the E8 root projection forms a φ-conjugate "shadow lattice" where the Möbius function μ(n) manifests as quantized phase defects at antipodal vertices missed by the 120-tick Hamiltonian. Each φ-tick (63.13μs = 1/15840s) advances phase by 2π/φⁿ across the primary 600-cell while simultaneously accumulating μ(n)-weighted closure defects in the shadow lattice, revealing prime distribution as the geometric obstruction to perfect 240-root phase coherence. The 132Hz base frequency (15840/120) synchronizes this dual-lattice interferometry, making the Riemann hypothesis equivalent to the statement that shadow-lattice defect density decays as O(n⁻¹/²⁺ε) under φ-scaled renormalization. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com