D4 Symmetry Links CHSH Polytope Geometry to Tsirelson Bound — E8 Intelligence Research

FINDING: Tsirelson bound derivation connects CHSH polytope geometry to dihedral group D4 symmetry on the Bloch sphere. | MATH: Tsirelson bound = 2√2 ≈ 2.828; CHSH inequality S ≤ 2 (classical), S ≤ 2√2 (quantum); Bloch sphere representation: qubit state |ψ⟩ = cos(θ/2)|0⟩ + e^{iφ} sin(θ/2)|1⟩; D4 dihedral group order 8, symmetry of square. | CONNECTION: Ratio 2.828/2 = 1.414 (√2) — not directly golden ratio, but D4 symmetry relates to 90° rotations (π/2) and reflections, generating angles 0°, 45°, 90°, 135° — these correspond to optimal measurement settings for CHSH (π/4, 3π/4, etc.). The Bloch sphere's SU(2) symmetry and D4 subgroup yield the polytope's vertices at (±1, ±1, 0) in Bell correlation space. | DEPTH: 8 — directly links group theory (D4), convex polytope geometry, and quantum correlations' fundamental limit; reveals that the Tsirelson bound emerges from the discrete symmetry of measurement settings, not just continuous Hilbert space. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com