Posner Molecule Ca₉(PO₄)₆ as a Biological Nuclear-Spin Qubit Register — E8 Intelligence Research

FINDING: Posner molecule Ca₉(PO₄)₆ is a candidate biological nuclear-spin qubit register whose dynamical ensemble breaks the idealized high symmetry, with nuclear spin entanglement and error-correcting structure as the core quantum-biology claim. MATH: - Stoichiometry: Ca₉(PO₄)₆ → 9 Ca²⁺ + 6 PO₄³⁻; charge balance 9(+2) + 6(−3) = 0. - Nuclear spin species: ³¹P (I = 1/2, 100% natural abundance), ⁴³Ca (I = 7/2, 0.135% abundance), ¹⁷O (I = 5/2, 0.038%). Dominant spin bath = six ³¹P nuclei → Hilbert space dim 2⁶ = 64. - Spin Hamiltonian (dominant terms): H = Σᵢ ωᵢ Iᵢᶻ + Σᵢ<ⱼ Jᵢⱼ (Iᵢ·Iⱼ) + Σᵢ<ⱼ Dᵢⱼ (3IᵢᶻIⱼᶻ − Iᵢ·Iⱼ) + Σᵢ Iᵢ·A·S(electron). - Decoherence timescale target: nuclear T₂ ~ 10⁰–10² s (vs electron spin ~10⁻⁶ s) — the ratio T₂(nuclear)/T₂(electronic) ~ 10⁶–10⁸ is the quantitative justification for nuclear-spin biology. - CTQEC: continuous weak measurement + feedback; error suppression scales with measurement rate γ and feedback gain; effective error rate Γ_eff ∝ Γ₀/(1 + γ/Γ₀) in the Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com