The Electron is a Topological Soliton: Discrete Graph Origin of Dirac–Maxwell Theory and Beyond

We show that the electron can be described not as a fundamental point particle, but as a stable topological soliton—a knot-like defect in a discrete ribbon graph. The graph has seven vertices, twelve edges, and a binary edge-coloring; its vertices carry labels from the binary icosahedral group. A single local rewrite rule governs the dynamics. After coarse-graining, the emergent large-scale behavior is exactly Dirac–Maxwell theory: a spin-½ fermion with the correct charge, a topological mass, and the Schwinger magnetic moment ae=α/2πae=α/2π. The model further predicts the Weinberg mixing angle from edge-flip combinatorics, a discrete Standard Model particle spectrum as topological excitations, and a naturally vanishing cosmological constant via a discrete BF extension. A working prototype verifies topological stability, continuum convergence, emergent gauge coupling, and the 4D Dirac spectrum. No continuous parameters are introduced beyond a single universal scale. The construction is purely algebraic and points toward a third paradigm of computation—topological—distinct from both classical and quantum.