SM-3: K3 Spectral Theorem and the Koide Formula

Abstract: The Koide relation K = 2/3 for the three charged lepton masses is proved from the adjacency spectrum of the colour cage base graph K3 (the equilateral triangle of the tetrahedral cage). The eigenvalue ratio λ_max/|λ_min| = 2 forces the Lorentz modulation depth ρ = √2, from which K = (1 + ρ²/2)/3 = 2/3 follows exactly. The result is specific to K3: only the three-colour cage (N = 3) gives K = 2/3.