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 optimization: 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 refined baseline anomalous magnetic moment aₑ = 0.001160966, corresponding to a 0.113% deviation from the experimental value. Gauge-flux precision correction: Introducing U(1) gauge flux with damped higher-order heterotic string winding corrections achieves unparalleled precision (aₑ = 0.001159652), matching CODATA 2018 values to within 1.3 × 10⁻⁸%. The corrective series κ = 1 + 1/30 + 4/30² − 27/30⁴ reveals a damping mechanism associated with the fourth dimension, effectively replacing thousands of perturbative Feynman diagrams with a convergent geometric sequence.