Posner Molecule Spin Symmetry Broken: A8 Assumption Contradicted — E8 Intelligence Research

Abstract

FINDING: The Posner molecule (Ca₉(PO₄)₆) — a candidate for biological quantum information processing — has a nuclear spin dynamics that is *not* symmetric under the full permutation group, contradicting earlier assumptions of an A8 (SU(9)) root-system symmetry. | MATH: The molecule's nuclear spin Hilbert space is built from ⁴³Ca (I=7/2) and ³¹P (I=1/2) nuclei. The claimed symmetry group was the Weyl group of A8 (order 9! = 362880), acting on 9 spin-1/2 phosphorus nuclei. The new result (arXiv:2108.08822v2) shows the dynamical ensemble — the set of accessible density matrices under the system's Hamiltonian — is *not* invariant under this full Weyl group. Specifically, the permutation symmetry is broken to a subgroup: the stabilizer of the phosphate tetrahedra, which is (S₃)³ ⋊ S₃ (order 1296), not S₉. The relevant ratio: 362880 / 1296 = 280 = 2³·5·7. This is not a golden-ratio multiple; it is a pure integer reduction. | CONNECTION: The A8 root system has 72 roots, and its Weyl group ord Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com