Phosphorus-31: A Spin-1/2 Qubit and In Vivo NMR Probe of Brain Metabolism — E8 Intelligence Research

FINDING: Phosphorus-31 is a spin-1/2 nucleus (15 protons, 16 neutrons, I = 1/2), making it a canonical two-state quantum system (α/β eigenstates) usable as a qubit and as an in-vivo NMR/MRS probe of brain metabolism. | MATH: I = 1/2; nuclear magnetic moment μ = γℏI with γ(³¹P) ≈ 10.84 MHz/T (gyromagnetic ratio); Zeeman splitting ΔE = γℏB₀; Larmor frequency ν = γB₀/2π; spin multiplicity = 2I+1 = 2; eigenstates |α⟩, |β⟩ with m_I = ±1/2; ³¹P chemical shift range ≈ 30 ppm (phosphocreatine, ATP, inorganic phosphate, phospholipids). | CONNECTION: Spin-1/2 is the fundamental SU(2) representation — the minimal non-trivial root system A₁, whose two weights ±1/2 are the simplest crystallographic-like lattice (one-dimensional, spacing 1). The 2I+1 = 2 degeneracy and the ±1/2 eigenvalues are the arithmetic seed from which higher spin (A_n, B_n, C_n, D_n root systems) and the full angular-momentum ladder are built. No direct 0.618/1.618 ratio appears in the raw nuclear data; any golden-ratio link w Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com