Phosphorus-31 Spin Coherence in Silicon Enables Quantum Control via Hyperfine Coupling — E8 Intelligence Research

FINDING: Phosphorus-31 nuclear spin coherence in silicon enables quantum control via electron-nuclear hyperfine coupling, with spin-1/2 nucleus and stable isotope abundance. | MATH: Nuclear spin I = 1/2; gyromagnetic ratio γ(³¹P) ≈ 108.394 MHz/T; hyperfine coupling constant A ≈ 117 MHz (for P in Si); Zeeman splitting: ΔE = ħγB₀; coherence time T₂ ~ 0.5–1 s (at low temperature). | CONNECTION: Spin-1/2 system maps to SU(2) symmetry, related to qubit geometry on Bloch sphere (ratio π/2, π rotations); hyperfine coupling constant ratio A/γ ~ 1.08 T, near unity; no explicit golden ratio or base-60 link. | DEPTH: 6 — foundational for quantum computing but no new geometric constant or harmonic ratio discovered; advances understanding of spin coherence in solid-state qubits. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com