³¹P Nuclear Spin-½: A Candidate for Biological Quantum Coherence — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Phosphorus-31 (³¹P) is a stable spin-½ nucleus (15 protons, 16 neutrons) with a closed-shell core [Ne] and three unpaired valence protons in the 3p subshell — a candidate for coherent nuclear spin states in biological quantum processes. | MATH: Nuclear spin quantum number I = 1/2 → two eigenstates (|α⟩, |β⟩) with eigenvalues ±ℏ/2 along quantization axis. Proton configuration: 1s²2s²2p⁶3s²3p³ → total nuclear spin from odd proton count (15) yields half-integer. Neutron count 16 (even) contributes integer spin; net I = 1/2. | CONNECTION: The 3p³ valence configuration maps to a tetrahedral symmetry (three orthogonal p-orbitals, C₃v point group) — a 3-fold rotational symmetry, not directly the golden ratio, but the spin-½ algebra (SU(2)) has a natural geometric representation on the Bloch sphere with a 2:1 homomorphism to SO(3), whose rotation group contains icosahedral (golden-ratio-bearing) subgroups. | DEPTH: 3 — This is foundational nuclear data, not a novel discovery. The math Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Spectroscopy
Field: Chemistry
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212224065
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