Mass Ratios from the Face Laplacian Spectrum of the Truncated Octahedron

The Koide identity Q = 2/3 derived from ε = √(dim T₂g − 1) = √2. The Koide angle θ = 2/9 derived from (λ_A₂u − λ_T₂g)/λ_A₂u = (9−7)/9. Lepton mass ratios m_μ/m_e and m_τ/m_μ predicted to 10–70 ppm with zero free parameters. Both parameters derived from the face Laplacian spectrum of the truncated octahedron.