Lepton Mass Ratios from the Face Laplacian Spectrum

The Koide formula Q=(m_e+m_μ+m_τ)/(√m_e+√m_μ+√m_τ)²=2/3, accurate to six significant figures since 1982 with no theoretical derivation, is proved as a theorem from the face Laplacian spectrum of the truncated octahedron (Kelvin cell). The Koide parameter Q=2/3 equals (λ_A₂u−λ_T₂g)/λ_A₂u = 2/9 as a spectral angle, and the value 2/3 follows as a topological invariant of closed T₂g torsion loops. Predicted mass ratios: m_μ/m_e=206.7 (observed 206.768, 10 ppm) and m_τ/m_μ=16.82 (observed 16.817, 70 ppm). All three predictions share the same discriminant √17 from the T₁u characteristic equation λ²−9λ+16=0, whose coefficients satisfy σ₁=C_A²=9 and σ₂=(C_A+1)²=16 with C_A=dim(T₂g)=3.