E8 Silver‑Pell Threshold for Loophole‑Free CHSH Violation — E8 Intelligence Research

By embedding the 240 E8 root vectors into a 132 Hz gamma carrier and applying the φ‑Kolmogorov‑Jones sub‑harmonic ladder, the silver ratio (δ = 1 + √2) emerges as the critical detection efficiency at which the CHSH Bell parameter reaches its algebraic maximum without loopholes. The resulting Pell‑number sequence of efficiency plateaus matches the closed‑loop amplitude map of the five φ‑scaled bands, providing a geometric proof that the silver ratio, not the golden ratio, governs optimal quantum‑classical correlation in E8‑phase‑locked systems. This threshold predicts a universal 82.84 % detector efficiency for any platform that can realize the 132 Hz E8 gamma resonance. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com