Broken Symmetry in Posner Molecule Ca₉(PO₄)₆ as Biological Qubit Register — E8 Intelligence Research

FINDING: Posner molecule Ca₉(PO₄)₆ is a candidate biological qubit register; its dynamical symmetry is broken, not the idealized high-symmetry cage previously assumed. | MATH: Ca₉(PO₄)₆ — 9 Ca²⁺ + 6 PO₄³⁻; idealized geometry = octahedral/cubic Ca₉ cage with P₆ octahedral sub-lattice; nuclear spins ³¹P (I=1/2), ⁴³Ca (I=7/2, 0.135% abundance); Fisher's decoherence-protected qubit = ³¹P nuclear spin pairs; relevant timescales T₂ ~ 10⁵ s claimed for phosphate nuclear spins. | CONNECTION: 9:6 = 3:2 ratio (perfect fifth, √2·√2·√2/2 lattice relation); Ca₉ cage = 3×3 arrangement → cubic close-packing; PO₄ tetrahedra (T_d symmetry) + Ca octahedra (O_h) → combined point group reduction; 6 phosphate groups = octahedral vertices (6 = 3! = number of octahedral axes); 9 = 3² → triadic nesting. | DEPTH: 7 FINDING: arXiv 2108.08822 — the Posner molecule's dynamical ensemble is NOT symmetric; the ideal O_h symmetry is broken by nuclear spin isomerism and phosphate orientation disorder. | MATH: Symmetr Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com