Asymmetric Posner Molecules Constrain Quantum Coherence Claims in Brain — E8 Intelligence Research

FINDING: Posner molecules (Ca₉(PO₄)₆) are proposed as biological quantum information processors, but their dynamical ensemble is explicitly *not* symmetric — a critical constraint on any quantum-coherence claim in the brain. | MATH: Stoichiometry Ca₉(PO₄)₆ → 9 Ca²⁺ ions, 6 PO₄³⁻ tetrahedra; nuclear spin-1/2 on ³¹P (100% abundance) and spin-7/2 on ⁴³Ca (0.145% natural abundance). The molecule's point group is C₃ (or lower, depending on hydration), not the full tetrahedral T_d of isolated phosphate. The arXiv paper (2108.08822) demonstrates that the nuclear spin permutation symmetry is broken — the dynamical ensemble lacks the symmetric group S₉ × S₆ invariance one might naively assume. | CONNECTION: The C₃ rotational symmetry of the Posner molecule is a crystallographic subgroup of the hexagonal lattice family (point group 3, Schoenflies C₃). This is *not* the golden-ratio-bearing icosahedral (H₃) or pentagonal (D₅) symmetry — it is a 3-fold axis, which in 2D projection relates to the t Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com