Quantum Coherence in Posner Molecules: Refuting Symmetry Assumptions — E8 Intelligence Research

FINDING: Posner molecule (Ca₉(PO₄)₆) quantum coherence evidence is contested; the arXiv paper explicitly refutes symmetric dynamical assumptions, while popular claims of "brain quantum effects" remain unverified. | MATH: Posner molecule stoichiometry: Ca₉(PO₄)₆ — 9 calcium ions, 6 phosphate tetrahedra. Nuclear spin qubits proposed on ³¹P (I=1/2) — 6 phosphorus nuclei per molecule. The paper (arXiv:2108.08822v2) shows the dynamical ensemble is *not* symmetric, breaking the assumed permutation symmetry that would support long-lived collective nuclear spin states. Key implication: the Hilbert space dimension for 6 spin-1/2 nuclei is 2⁶ = 64, but without symmetry, decoherence pathways multiply, destroying the purported 1-second coherence times. | CONNECTION: Phosphate tetrahedra (PO₄³⁻) form a near-perfect tetrahedral geometry — bond angle 109.47° (tetrahedral angle, arccos(−1/3) ≈ 109.4712°). This is *not* a harmonic ratio but a crystallographic root system A₃. The 6 phosphates in the Pos Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com