This paper provides the complete spectral analysis of the 600-cell adjacency matrix — the foundational computational result on which much of Pentagon Physics rests. The 600-cell has 120 vertices, each connected to 12 neighbours. Its adjacency matrix has nine distinct real eigenvalues, all in ℚ(√5): {30, 12, 6φ, 6/φ, 2+√5, 2−√5, −2+√5, −2−√5, −6}. The Galois automorphism √5 → −√5 maps each eigenvalue to its conjugate. The discriminant selection rule Δ = φ² − λ/3 divides them into propagating (λ > 3φ²) and frozen (λ < 3φ²) modes. All subsequent derivations in Pentagon Physics use this spectral data.