Geometric Derivation of the Schwinger Anomaly (g − 2) and Finite Electron Self-Energy: A 10D Helical Model with Heterotic String Winding Corrections

Abstract The divergent self-energy of the point-particle electron in quantum electrodynamics (QED) remains unresolved through renormalization alone. We present spectral graph-theoretic evidence that the electron possesses an intrinsic toroidal topology with helical internal flows across compactified dimensions. Simulations spanning 2D–10D (N = 64–729 nodes) reveal five fundamental results: Golden-ratio emergence: Static toroidal graphs at N = 100 naturally optimize to the Golden Ratio (λ₂ = 1/ϕ², E = 100ϕ²). Helical stability enhancement: Double-helix topologies achieve stability factors E = 9–81 in 6D, representing a 3–9× improvement over classical point-electron models. Experimental compatibility: The inferred toroidal radius remains consistent with experimental bounds (r < 10⁻²² m). High-dimensional refinement: Extension to 10D yields a baseline anomalous magnetic moment aₑ = 0.001160966, corresponding to a 0.113% deviation from the experimental value. Gauge-flux correction: Introducing a U(1) gauge flux with heterotic string winding correction κ = 1 + 1/30 achieves 0.001% precision (aₑ = 0.001159664), effectively eliminating radiative loop corrections. The factor 1/30 emerges from the rank-30 effective degrees of freedom in SO(32) heterotic string theory, establishing a direct topological link between the Schwinger anomaly and vacuum winding structure.