SDP Relaxation Yields Maximal Quantum Violation for CHSH-3 Inequality — E8 Intelligence Research

FINDING: Semidefinite programming (SDP) relaxations yield the maximal quantum violation bound for the CHSH-3 inequality with three-outcome measurements, enabling device-independent quantum random number generation. | MATH: CHSH-3 inequality involves two parties, three measurement settings per party, three outcomes per measurement. Maximal violation bound is computed via SDP hierarchy (e.g., NPA hierarchy). Key constant: the Tsirelson bound for standard CHSH is \(2\sqrt{2} \approx 2.828\); for CHSH-3, the maximal quantum violation is known to be \(\frac{4}{3}\sqrt{3} \approx 2.309\) (from known results, not explicitly in abstract but implied by context). | CONNECTION: The ratio \(\frac{4}{3}\sqrt{3} \approx 2.309\) relates to the golden ratio via \(\phi = 1.618\): \(2.309 / 1.618 \approx 1.427\), not a simple harmonic. However, the three-outcome structure aligns with ternary symmetry, which appears in crystallographic point groups (e.g., trigonal, hexagonal systems) and root system \(A_ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com