No Primary Numerical Value Found for ³¹P Hyperfine Coupling in Silicon — E8 Intelligence Research

FINDING: Search returned only pedagogical/software resources (tight-binding lectures, DFT tutorials, EPR hyperfine theory) — no primary numerical result for the ³¹P hyperfine coupling constant in Si. | MATH: The relevant governing equations the sources point to are: (1) Fermi contact isotropic hyperfine coupling A_iso = (2μ₀/3) g_e μ_B g_N μ_N |ψ(0)|², where |ψ(0)|² is the electron spin density at the donor nucleus; (2) tight-binding dispersion E(k) = ε₀ + Σ_R t(R) e^{ik·R}, with hopping integrals t for s/p/d orbitals; (3) DFT Kohn–Sham self-consistency for periodic supercells (Quantum ESPRESSO). No numerical A value, no constants, no ratios were actually delivered by the sources. | CONNECTION: Only structural/lattice-level, not numerical. Silicon is diamond cubic — space group Fd3̄m (No. 227), a face-centred cubic Bravais lattice with a two-atom basis at (0,0,0) and (¼,¼,¼). This is the crystallographic symmetry that constrains the ³¹P donor wavefunction and hence |ψ(0)|². The T_d poi Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com