Electrical Detection of Phosphorus-31 Spin Coherence in Silicon for Quantum Control — E8 Intelligence Research

FINDING: Phosphorus-31 nuclear spin coherence in silicon enables precise quantum control via electrical detection and low-field magnetic resonance. | MATH: Nuclear spin I=1/2; stable isotope with 15 protons, 16 neutrons; gyromagnetic ratio γ(31P) ≈ 108.394 MHz/T; hyperfine coupling constant A ≈ 117 MHz for P donors in Si; Zeeman splitting ΔE = ħγB; spin coherence time T₂ up to ~0.5 s in isotopically purified ²⁸Si. | CONNECTION: The 1/2 spin symmetry corresponds to the simplest non-trivial representation of SU(2) — a double cover of SO(3) rotation group. The 15:16 neutron-proton ratio (0.9375) is close to 0.939 (≈ 1/√π), but no direct golden ratio or base-60 link. The hyperfine constant 117 MHz yields a dimensionless ratio A/γ ≈ 1.08, near unity. | DEPTH: 6 — The findings are experimentally robust and foundational for quantum computing (spin qubits), but the mathematical structure is standard SU(2) algebra without novel geometric constants. The coherence times and detection methods are Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com