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

FINDING: CHSH correlations are bounded by Tsirelson's 2√2, and a 2025 preprint re-derives this bound from indivisible stochastic processes via Barandes's stochastic-quantum correspondence, replacing the no-signaling axiom with causal locality. | MATH: CHSH operator S = E(a,b) − E(a,b′) + E(a′,b) + E(a′,b′); classical (local hidden variable) bound |S| ≤ 2; quantum bound |S| ≤ 2√2 ≈ 2.828427; quantum value for maximally entangled qubits at optimal angles = 2√2. Optimal measurement angles: a=0, a′=π/2, b=π/4, b′=−π/4 (mod π/2). Maximal violation ratio: 2√2/2 = √2 ≈ 1.414214. | CONNECTION: 2√2 = 2·√2 is the diagonal of a unit square scaled by 2, i.e. the length of the space diagonal of a 2×2 square lattice cell — a √2-scaling, not a φ-scaling. √2 is the fundamental ratio of the square lattice / BCC root system (A₁⊕A₁, B₂). No direct φ (1.618), 0.618, or 0.382 relation appears in the CHSH bound itself. The optimal angles π/4, π/2 are base-4 / base-8 (octonionic) divisions of the circle, con Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com