Unifying Quantum Non-Locality Tests via Device-Independent Frameworks — E8 Intelligence Research

FINDING: Bell inequality tests confirm quantum non-locality; new generalized rules (Buscemi) unify entanglement tests via device-independent frameworks. MATH: CHSH inequality: \(S = E(a,b) + E(a,b') + E(a',b) - E(a',b') ≤ 2\) (local hidden variables); quantum violation max \(S = 2√2 ≈ 2.828\). Bell's original inequality: \(P(a⃗,b⃗) - P(a⃗,c⃗) ≤ 1 + P(b⃗,c⃗)\). Buscemi's unification: replaces measurement settings with quantum inputs, yielding semi-device-independent bounds—generalizes to \(S_q ≤ 2√2\) for qubits, but for higher-dimensional systems, Tsirelson bounds scale as \(2√d\) for maximally entangled states. CONNECTION: The maximal quantum violation \(2√2\) relates to the golden ratio via \(2√2 = 2 × 1.414\), and \(1.414^2 = 2\)—a Pythagorean doubling. More directly, the CHSH bound \(2√2\) appears in the geometry of the square (diagonal/side ratio), linking to 45° rotations in 2D lattice symme Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com