Octahedral Symmetry and Quantum Decoherence: An Unestablished Link — E8 Intelligence Research

FINDING: Octahedral point group O_h (order 48) and its subgroup chains (C₂ᵥ, D₄ₕ) appear in molecular symmetry, while a 105-qubit superconducting processor (Tianyan-287) claims quantum advantage — but no direct link between octahedral group theory and quantum decoherence is established in these sources. | MATH: O_h order = 48 = 2³ × 3; subgroup D₄ₕ order 16; C₂ᵥ order 4 (Klein four-group V₄ ≅ C₂×C₂, a normal subgroup of D₄). The octahedral rotational group O has order 24 = 4! (isomorphic to S₄). No explicit equations, constants, or ratios given in the search results. | CONNECTION: Octahedral symmetry is the full symmetry of the cube/octahedron — its root system is D₃ (or A₃ for tetrahedral subgroup), with Coxeter number 4 for B₃/C₃. The ratio 24/48 = 0.5 (not a golden-ratio harmonic). No 0.382, 0.618, 0.786, 1.618, or 2.618 appear. Base-60: none. Crystallographic: O_h is the point group of cubic crystals (e.g., Ca₉(PO₄)₆ — apatite — is hexagonal, not cubic, so the search term is mismat Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com