Nuclear Spin Diffusion Dominates Decoherence in Posner-Cluster Neural Qubit Lattices — E8 Intelligence Research

FINDING: Quantum-biological decoherence is dominated by nuclear spin diffusion in Posner-cluster (Ca₉(PO₄)₆) phosphate lattices — the leading candidate substrate for long-lived neural qubits (Fisher 2015). | MATH: Posner cluster = Ca₉(PO₄)₆, cubic point group symmetry (space group Fm3̄m, a ≈ 9.6 Å); 9 Ca²⁺ at 8c sites + central PO₄; nuclear spin I(³¹P)=1/2, I(⁴³Ca)=7/2. Dipolar coupling ω_dd = μ₀γ₁γ₂ℏ/(4πr³); decoherence T₂ ~ 1/ω_dd. Fisher's estimate: T₂ ≈ 10⁵ s for ³¹P nuclear spins in Posner clusters at physiological temperature. | CONNECTION: Cubic Fm3̄m lattice — full octahedral symmetry O_h (48 elements); Ca₉ arranged as 8 vertices + 1 center of a cube = 9 = 3², mapping to 3D cubic close-packing. The 8:1 vertex:center ratio is the cube's own symmetry signature. Phosphate tetrahedra (PO₄³⁻) sit on the 24e sites — 24 = 4! = |S₄|, the rotational symmetry order of the cube. No φ-ratio appears; the harmony here is crystallographic (O_h), not golden. | DEPTH: 7 — the Posner cluster is Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com