Topological Evolution of the Natural Constant e and the Structure Theory of Lepton Free Fields

This paper establishes a unified topological theory between the natural constant e and the structure of lepton free fields, perfecting the mathematical-physical dual system of e and π. It provides a topological explanation for the structure and evolution of elementary particles, which is fully compatible with Quantum Electrodynamics (QED) and the Standard Model. The study reveals that e, as the core transcendental number describing continuous and self-driven evolutionary systems, corresponds to the open, non-compact, and irreversible topological evolution of leptons. In contrast, π corresponds to the closed, compact, and conserved topological structure of hadrons, forming the fundamental "change vs. non-change" duality in the universe. Four categories of experimentally testable paths are proposed, verifying the exponential decay law of muons and tauons, and the exponential form of the lepton wave function. This theory supplements the topological origin explanation for the existing Standard Model without modification, clarifying the topological root of lepton non-confinement and decay.