Tsirelson Bound from D4 Symmetry on the Bloch Sphere — E8 Intelligence Research

FINDING: The Tsirelson bound derivation connects the CHSH polytope's extremal correlations to the dihedral group D4 symmetry on the Bloch sphere, revealing a geometric constraint on quantum correlations. | MATH: Tsirelson bound = 2√2 ≈ 2. 828; CHSH inequality classical bound = 2; quantum violation up to 2√2; Bloch sphere representation: |ψ⟩ = cos (θ/2) |0⟩ + e^iφ sin (θ/2) |1⟩; D4 group order 8, symmetry of square, acts on measurement settings (a, a', b, b') via rotations and reflections. | CONNECTION: The ratio 2. 828/2 = 1. 414 = √2, linking to 0. 618 via golden ratio φ: √2 ≈ 1. 414, φ ≈ 1. 618; D4 is crystallographic point group (tetragonal system), root system B2, lattice Z²; Bloch sphere's SU (2) symmetry reduces to D4 for CHSH extremal points. | DEPTH: 8 — Directly ties quantum nonlocality to finite group geometry and lattice structures, with explicit constants and symmetry breaking. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com