Vortex rings and knots have long been proposed as classical analogues of elementary particles. This paper demonstrates that the physical characteristics of the electron emerge naturally from a leapfrogging pair of vortex rings encased in a motion-induced sheath, a configuration which demonstrates a formal correspondence with topological soliton solutions found in gauge field theories. The model provides exact derivations for the fine structure constant, the Bohr magneton, and related magnetic formulae. Furthermore, Coulomb’s law is recovered as a formal isomorphism, utilising the same physical parameters and inverse square scaling as classical electrostatics. By reframing the particle as a topologically protected flow in a superfluid vacuum, the historical objection of the Larmor radiation catastrophe is resolved as this category of model is known to retain an energetic state which remains in equilibrium. The model provides a rigorous mechanical reproduction of the electron’s fundamental properties through purely geometric constraints utilising the standard inputs of the Compton frequency and speed of light. These results are not in contradiction to quantum physics, QFT, and the Standard Model.