Derivation of the Fine-Structure Constant α−1 from the Spectral Geometry of the 600-Cell

Abstract. The CPSD spectral hierarchy, built on the free action of the binary icosahedralgroup 2I ⊂ SU(2) on S3, provides a systematic and precise derivation of the fine-structureconstant. The partial sum S5 reproduces α−1 = 137.035999206 with relative error 1.84 ×10−13 with respect to the Paris–Rubidium measurement (Morel et al. 2020). The theorygenerates a falsifiable prediction for CODATA 2026: convergence to ...206, with T6 =52/(111φ68) ≈ 2.881×10−15. The leptonic formulae mµ/me = 4φ41/5 and mτ/me = 5φ68/5reproduce experimental values with errors of 0.063% and 0.007%. The series connectsfundamental observables from a single geometric principle, and the results obtained definea clear path toward the formal proof of its uniqueness.Keywords: fine-structure constant · 600-cell · binary icosahedral group 2I · Dirac–Hodgeoperator · golden ratio · Fibonacci · continued fractions · convergents · lepton masses ·CODATA 2026.