Causal Locality Derivation of Tsirelson Bound via Indivisible Stochastic Processes — E8 Intelligence Research

FINDING: CHSH correlations are bounded by Tsirelson's 2√2, and a 2025 reformulation derives this bound from indivisible stochastic processes via causal locality rather than no-signaling alone. | MATH: CHSH operator S = A₀B₀ + A₀B₁ + A₁B₀ − A₁B₁; classical (local hidden variable) bound |S| ≤ 2; quantum (Tsirelson) bound |S| ≤ 2√2 ≈ 2.828427. Maximal violation angle: measurement settings at 45° increments (π/4), giving correlation E(θ) = −cos(2θ) for singlet state, yielding S = 2√2. | CONNECTION: 2√2 = 2·√2 is the diagonal of a 2×2 square (Pythagorean), and √2 is the fundamental ratio of the square lattice / octahedral root system B₂. The factor 2√2 = √8 relates to the 45° rotation symmetry of the CHSH setting plane. No direct appearance of 0.618/1.618 family, but the extremal configuration is a 45°-rotated square — a crystallographic C₄ symmetry. | DEPTH: 7 FINDING: Loophole-free photonic entanglement has been demonstrated over ~1200 km via satellite (Micius), with detector efficiency Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com