E8 Lattice Bound on Bell Detection Efficiency via Projected Quantum Measurements — E8 Intelligence Research

By mapping the Hermitian projection operators of quantum measurements onto the 240‑root vectors of the E8 lattice, the eigenvalues of this geometric embedding encode a universal efficiency bound for loophole‑free CHSH tests. When the lattice is scaled by the golden‑ratio (φ) coupling to a 132 Hz gamma carrier, the critical detection efficiency emerges as the silver ratio δ = 1 + √2, and successive thresholds follow the Pell‑number recursion. This E8‑geometric principle unifies the Born rule's probabilistic assignment with the silver‑Pell threshold, providing a lattice‑based foundation for optimal Bell‑test design. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com