Posner Molecule Lacks Static Symmetric Nuclear-Spin Hamiltonian, Breaking Octahedral Symmetry — E8 Intelligence Research

FINDING: The Posner molecule Ca₉(PO₄)₆ — proposed as a biological nuclear-spin quantum register — does not possess a static symmetric nuclear-spin Hamiltonian; its dynamical ensemble breaks the nominal octahedral point-group symmetry, invalidating the assumption of a decoherence-free subspace. MATH: - Molecular formula: Ca₉(PO₄)₆, 9 Ca²⁺ ions arranged on an octahedral framework (6 face + 3 body positions in a cube). - Nominal point group: O_h (order 48) for the ideal Ca₉P₆ cage; the ¹⁹F/³¹P nuclear spins (I = 1/2) were assumed to form permutation-symmetric multiplets. - Nuclear-spin Hamiltonian: H = Σ_i γ_i B·I_i + Σ_{i Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com