Unified Bell Inequalities Tested via Ballistic Electrons in Quantum Wires — E8 Intelligence Research

FINDING: New rules for Bell inequalities unify quantum entanglement tests, with a proposed condensed-matter experiment using ballistic electrons in semiconductor quantum wires. | MATH: CHSH inequality form: \( S = E(a,b) + E(a,b') + E(a',b) - E(a',b') \leq 2 \) (classical bound); quantum violation up to \( 2\sqrt{2} \approx 2.828 \); proposed system uses five gates to generate entangled states via Coulomb coupling in quantum wires. | CONNECTION: The ratio \( 2.828 / 2 = 1.414 \) (√2) appears, linking to the diagonal of a unit square — a fundamental geometric symmetry. No direct evidence of 0.382, 0.618, 0.786, 1.618, 2.618, base-60, or crystallographic symmetries in these findings. | DEPTH: 6 — advances understanding of entanglement in condensed-matter systems, but no new fundamental constants or geometric harmonies beyond √2. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com