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. 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 ^-1 = 4³ + ² + (see Eq. ~ (1) ). Its numerical value is 137. 0362697759, which differs from the CODATA 2023 recommended value 137. 035999084 (21) by = +2. 7069 10^-4, corresponding to a relative deviation = +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.