Posner Molecule's Symmetry Assumption Fails, Undermining Quantum Spin-Protection Model — E8 Intelligence Research

FINDING: The Posner molecule (Ca₉(PO₄)₆) — proposed as a quantum biological information processor via long-lived nuclear spins — is shown to lack the symmetric dynamical ensemble previously assumed, undermining the simplest A₃/Weyl-group-based singlet-protection model. | MATH: Posner molecule stoichiometry: Ca₉(PO₄)₆ → 9 Ca²⁺, 6 PO₄³⁻. Nuclear spin-1/2 on ³¹P (6 P atoms) → Hilbert space dimension 2⁶ = 64. Singlet subspace for 6 spins: dimension = (6 choose 3) − (6 choose 2) = 20 − 15 = 5 (for S=0, using Young tableau / SU(2) branching). The A₃ root system (rank 3, 12 roots) corresponds to SU(4) ⊃ SU(2)⁴; the Weyl group |W(A₃)| = 4! = 24. The paper (arXiv:2108.08822) shows the dynamical ensemble (time-averaged density matrix under nuclear spin Hamiltonian) is *not* symmetric under the full permutation group S₆ (nor under the tetrahedral subgroup T_d of the A₃ Weyl group), breaking the assumed high symmetry. | CONNECTION: The tetrahedron (A₃ root system) is the natural geometric frame fo Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com