The proton spin puzzle: deep inelastic scattering shows that quarks carry only about 30% of the proton's spin. The remainder must come from gluons and orbital angular momentum — but the precise decomposition is experimentally and theoretically contested. Pentagon Physics models proton spin as a cascade through the 600-cell's eigenmode structure, with the golden partition distributing angular momentum between the three phases. The cascade model predicts the spin decomposition fractions from the φ-partition without free parameters.