Phosphorus Nuclear Spins in Posner Molecules: A Quantum Cognition Substrate with 10^5-Second Coherence — E8 Intelligence Research

Andrew Stewart Caldin

Published Jul 28, 2026• 0 citations

Abstract

FINDING: Matthew Fisher proposes phosphorus nuclear spins in Posner molecules as a quantum processing substrate for cognition, with decoherence times up to ~10^5 seconds. | MATH: Key constants: phosphorus-31 nuclear spin I=1/2, gyromagnetic ratio γ=17.235 MHz/T, Larmor frequency ω_L = γB (e.g., ~1.2 kHz at Earth's field ~0.07 mT). Decoherence time T₂ ~ 10^5 s implies Q = ω_L T₂ ~ 10^8. Fisher's model uses spin-spin coupling J ~ 10-100 Hz between adjacent phosphorus nuclei in Ca₉(PO₄)₆ clusters (Posner molecules). The quantum error threshold for fault-tolerant computation is ~10⁻⁴ per gate; Fisher's estimated gate fidelity from dipolar coupling is ~10⁻³. | CONNECTION: Weak — no explicit geometric ratios (0.382, 0.618, 0.786, 1.618, 2.618) or base-60 appear. However, Posner molecule symmetry (Ca₉(PO₄)₆) has approximate octahedral (O_h) crystallographic symmetry, with 6 phosphate tetrahedra arranged around a central calcium ion — a structure related to the root system of F₄ (24 roots) and Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.21637025

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