Phosphorus Nuclear Spin in Posner Molecules as a Substrate for Neural Quantum Computation — E8 Intelligence Research

Andrew Stewart Caldin

Published Aug 10, 2026• 0 citations

Abstract

FINDING: Matthew Fisher proposes nuclear spin of phosphorus atoms in Posner molecules as a quantum processing substrate for cognition, with decoherence timescales sufficient for neural quantum computation. MATH: Key constants: Phosphorus-31 nuclear spin I=1/2, gyromagnetic ratio γ=17.235 MHz/T, Larmor frequency ~70 MHz at 4T (biological field). Decoherence time T2 ~ 1 second for phosphorus in Posner clusters (Ca9(PO4)6). Quantum error correction threshold ~10^-4 per gate. Fisher's model requires entanglement lifetime > 100 ms for cognitive relevance. CONNECTION: Posner molecule (Ca9(PO4)6) has cubic symmetry (space group I4̅3d, #220) — a body-centered cubic lattice with 24 phosphorus atoms per unit cell. The 6 phosphorus atoms in each Posner cluster form an octahedron (Oh symmetry), a root system of type D3 (equivalent to A3). The octahedral symmetry group order is 48, matching the 48 phosphorus atoms in the full unit cell. The ratio of phosphorus nuclear spin coherence time to synap Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.21867625

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