A Zero-Parameter Geometric Expression for the Fine-Structure Constant Derived from Three-Sphere Topology

This paper reports a pure mathematical expression for the fine-structure constant α. Based on a geometric scaling model of the three-sphere (S³) and considering its spin structure (Spin(4)) corresponding to the double-covering space, we derive α⁻¹ = 4π³ + π² + π (see Eq.~(1)). Its numerical value is $137.0362697759$, which differs from the CODATA 2023 recommended value $137.035999084(21)$ by Δ = +2.7069 × 10⁻⁴, corresponding to a relative deviation δ = +1.98 × 10⁻⁶ ($+1.98$ ppm). This expression contains no free parameters and provides a concrete, computable mathematical model for the geometric origin of fundamental physical constants.