Geometric Algebra Derivation of Tsirelson Bound via E8 and Octonions — E8 Intelligence Research

FINDING: Tsirelson bound derivable from geometric algebra, with explicit link to E8 root system and octonionic structure in quantum correlations. | MATH: Tsirelson bound \( C \leq 2\sqrt{2} \) for CHSH; geometric algebra formulation yields \( C = 2\sqrt{2} \) via bivector/rotor structure; E8 root lattice \( \Gamma_8 \) with 240 roots, octonion multiplication table \( e_i e_j = -\delta_{ij} + \epsilon_{ijk} e_k \); key ratio \( \sqrt{2} \approx 1.414 \), related to \( 2\cos(\pi/4) \). | CONNECTION: E8 root system encodes maximal Bell violation — \( 2\sqrt{2} \) emerges from the angle \( \pi/4 \) between measurement axes, which is the dihedral angle of the 4D hypercube; octonionic \( G_2 \) symmetry (automorphism group of octonions, 14-dim) stabilizes the correlation structure; ratio \( 1/\sqrt{2} \approx 0.707 \) links to \( \cos(\pi/4) \), and \( 2\sqrt{2} \approx 2.828 \) is \( 2 \times 1.414 \); the E8 lattice has kissing number 240, and its Coxeter number 30 relates to \( 2\pi/30 = Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com