December 2, 2025Open Access

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

Key Points

The derived fine-structure constant equals 137.0362697759, differing from CODATA's value by a small margin.
Convergence between the expression's numerical value and standard values highlights its significance in physics.
Analysis built upon the geometry of a three-sphere and explores its spin structure through advanced mathematical modeling.
The model's zero-parameter approach calls for further verification and may reshape ties between geometry and physical constants.

Abstract

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.

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Liu Yi

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

Key Points

Abstract

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