Asymmetric Posner Molecules: A 8.6-Billion-State Quantum Information Processor — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 5, 2026• 0 citations

Abstract

FINDING: The Posner molecule (Ca₉(PO₄)₆) is proposed as a biological quantum information processor, but its dynamical ensemble is explicitly **not symmetric** — breaking naive crystallographic or Platonic assumptions. | MATH: Stoichiometry: Ca₉(PO₄)₆ → 9 Ca²⁺ + 6 PO₄³⁻. Nuclear spin count: ⁴³Ca (I=7/2) and ³¹P (I=1/2) — total spin Hilbert space dimension = (2·7/2+1)⁹ × (2·1/2+1)⁶ = 8⁹ × 2⁶ = 134,217,728 × 64 = 8,589,934,592 states. The paper (arXiv:2108.08822) shows the dynamical ensemble (density matrix averaged over molecular orientations) lacks the full octahedral (Oₕ) symmetry one might naively assign to the phosphate cage. | CONNECTION: The phosphate tetrahedra (PO₄³⁻) form a near-regular tetrahedral lattice (Tₕ point group), but the Ca²⁺ ions sit in non-equivalent sites — the ratio of Ca–O bond lengths deviates from ideal 1.000, introducing a **broken symmetry** that maps to a distortion from perfect tetrahedral angle (109.47°) toward ~107–110° depending on site. This is a crysta Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.23152228

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