The Surface-Tension Origin of Proton‒Electron Structure: A Closed Surface Model of Charge, Curvature, and Stability

This paper develops a geometric model of the proton–electron system based on closed-surface tension. The proton is interpreted as a maximal-tension closed surface defined by its minimal radius and maximal curvature, yielding intrinsic stability. The electron is described as a flexible closed surface with moderate tension, enabling deformation and chemical reactivity. Surface tension is identified with curvature q/rq/rq/r, and the square of this quantity yields Coulomb interaction. This framework explains why all physical objects are enclosed by closed surfaces, why electromagnetic interaction arises as curvature tension, and why substances such as mercury exhibit extremely high surface tension due to dense continuous electronic surfaces. The theory provides a unified surface-based ontology of matter, replacing point-particle assumptions with geometrically grounded structures.