³¹P Spin Qubits in Silicon: Coherence and Hyperfine Coupling Overview — E8 Intelligence Research

FINDING: Phosphorus-31 (³¹P) is a stable spin-½ nucleus (15 protons, 16 neutrons) whose quantum coherence in silicon is a leading platform for spin-based qubits; the search results are pedagogical and experimental overviews, not new mathematical derivations. | MATH: Nuclear spin I = 1/2 → two-level Hilbert space (|↑⟩, |↓⟩); Zeeman Hamiltonian H = −γℏB·I; for ³¹P in Si, hyperfine coupling A ≈ 117 MHz (with donor electron); gyromagnetic ratio γ/2π ≈ 17.235 MHz/T. No new constants or ratios emerge from these video/abstract summaries. | CONNECTION: The spin-½ system maps to SU(2) symmetry — the double cover of SO(3), whose root system is A₁ (rank 1). The ³¹P donor in silicon sits at a substitutional site in the diamond cubic lattice (space group Fd3̄m, #227) — a face-centered cubic Bravais lattice with two-atom basis, exhibiting 48-fold full octahedral symmetry (m3̄m). The hyperfine interaction preserves this cubic point group. No explicit golden-ratio or base-60 links appear in the provid Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com