A Unified Moment Condition for Closed Surfaces: Explaining the Fixed Sizes of Electrons and Nuclei

This work establishes a universal principle for the determination of particle sizes based on closed-surface geometry. By uniting the mass–frequency relation m= , the tangential velocity condition rω=c , and the invariant surface moment mr=ℏ/c, we show that electrons, protons, and neutrons possess fixed, non-arbitrary sizes. The Bohr radius emerges as the Compton length scaled by the fine-structure constant, while nuclear radii follow from collective closed-surface scaling with R(A)≈R(A)≈. This framework replaces the empirical treatment of particle sizes with a necessary geometrical balance law, offering a unified explanation for atomic and nuclear scales.