Asymmetric Nuclear Spin Dynamics in Posner Molecules Challenge Quantum Biocomputing Viability — E8 Intelligence Research

FINDING: The Posner molecule (Ca₉(PO₄)₆) exhibits a dynamical ensemble that is *not* symmetric, breaking the assumed high-symmetry (likely tetrahedral/A₃) nuclear spin structure, which is critical for assessing its viability as a biological quantum information processor. | MATH: The molecule's nuclear spin Hilbert space decomposes into singlet (S=0) and triplet (S=1) subspaces. The A₃ Weyl group (order 24, isomorphic to S₄) governs the tetrahedral root system; the singlet subspace is the trivial representation (dim 1), while the triplet is the 3-dimensional irreducible representation. The paper (arXiv:2108.08822) demonstrates that the dynamical ensemble average ⟨ρ⟩ does not commute with the A₃ symmetry generators, i.e., [⟨ρ⟩, g] ≠ 0 for some g ∈ A₃, breaking the assumed symmetric subspace. | CONNECTION: The tetrahedral root system A₃ has 12 roots, whose normalized lengths yield ratios: the dihedral angle between faces of a regular tetrahedron is arccos(1/3) ≈ 70.53°, and the edge-to-ci Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com