Cuboctahedral Geometry Underlies Tsirelson's Bound in Quantum Correlations — E8 Intelligence Research

FINDING: The CHSH inequality's maximal quantum violation (Tsirelson bound) is geometrically rooted in the D3 root lattice / cuboctahedron structure of qubit Bloch vectors, linking Bell violations to crystallographic symmetry. | MATH: Tsirelson bound = 2√2 ≈ 2.828. CHSH operator S = ⟨AB⟩ + ⟨AB'⟩ + ⟨A'B⟩ − ⟨A'B'⟩ ≤ 2 (local) / ≤ 2√2 (quantum). Qubit Bloch vectors live on S², but the extremal correlation polytope for two qubits is the **cuboctahedron** (vertices = 12, edges = 24, faces = 8 triangles + 6 squares). The D3 root lattice (fcc lattice) has the cuboctahedron as its Voronoi cell. The ratio 2√2 / 2 = √2 ≈ 1.414, and the cuboctahedron's circumradius-to-inradius ratio = √2 (circumradius = √2·inradius for edge length 2). | CONNECTION: The cuboctahedron is the intersection of the cube and octahedron — both Platonic solids with cubic symmetry (Oh, order 48). The D3 root lattice is the weight lattice of SU(2)×SU(2) (spin-1/2 pairs). The ratio 2√2 = 2·√2 appears as the ratio of the cuboc Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com