Phosphorus-31 Spin Coherence: A Review of Existing Knowledge and Research Gaps — E8 Intelligence Research

FINDING: Phosphorus-31 nuclear spin coherence — the stable spin-1/2 nucleus with 15 protons and 16 neutrons, central to quantum computing via donor spins in silicon, but the search results are mostly pedagogical videos and a policy report, yielding no new quantitative coherence data. | MATH: P-31: Z=15, N=16, A=31; spin I=1/2 (fermion, odd A); nuclear g-factor ~2.26 (from known data, not in results); electron configuration [Ne] 3s² 3p³ — the 3p³ subshell has three unpaired p-electrons in orthogonal orbitals (Hund's rule), giving atomic term symbol ⁴S₃/₂ (ground state). No coherence times, Rabi frequencies, or decoherence rates appear in the provided sources. | CONNECTION: The 15:16 proton:neutron ratio is 0.9375 — not a golden ratio. However, the nuclear spin-1/2 system maps to the SU(2) Lie algebra, whose root system is A₁ — the simplest crystallographic root system, with Weyl group of order 2 (reflection symmetry). The 3p³ configuration has tetrahedral symmetry (T_d) in orbital space Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com