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This study aims to derive closed-form expressions for the fine-structure constant and electron charge using core-decomposition.

May 25, 2026Open Access

Core-Decomposition Derivation of the Fine-Structure Constant and the Electron Charge

Key Points

This study aims to derive closed-form expressions for the fine-structure constant and electron charge using core-decomposition.
Defined the core constant based on a recurrence relation and natural logarithm.
Deduced expressions for the fine-structure constant and electron charge involving the first five primes.
Performed numerical evaluations to compare results with experimental values.
Numerical evaluation yields 1/α≈137.036, closely matching the experimental value of 137.035999084.
Expressions proposed do not include free parameters and depend solely on fundamental primes.
Results are conjectural and derived heuristically within the core-decomposition framework.

Abstract

Based on the core-decomposition recurrence (ak−2) ak+1=k (ak−2) ak+1=k and its continuum limit, we define the core constant p=ln⁡43+125⋅7⋅11p=ln34+25⋅7⋅111. We then propose the conjectural closed-form expressions α=p/ (4π2) α=p/ (4π2) for the fine-structure constant and e=p/πε0ℏce=p/πε0ℏc for the electron charge. These expressions contain no free parameters and depend only on the first five primes 2, 3, 5, 7, 112, 3, 5, 7, 11 and the natural logarithm. Numerical evaluation gives 1/α≈137. 0361/α≈137. 036, close to the experimental value 137. 035999084137. 035999084. The derivation is heuristic; the results are presented as conjectures within the core-decomposition framework

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