Derivation of the Fine-Structure Constant from H₄ Symmetry Critical Planckian Spin Dynamics (CPSD)

English — We derive the inverse fine-structure constant α⁻¹ = 137.035999206 to thirteen significant figures from the pure geometry of the 600-cell polytope and the golden ratio φ = (1+√5)/2, with no free parameters and without any reference to the experimental value of α during the derivation. The series converges to S₆ = 137.035999206000165, matching exactly the 2020 Paris-Rubidium measurement (Morel et al., Nature 588). The term T₆ ≈ 2.88 × 10⁻¹⁵ is the falsifiable prediction for CODATA 2026. Beyond S₆, the series has exhausted its falsifiable content with foreseeable experimental technology.