P-13: The Geometric Origin of Lepton Anomalous Magnetic Moments — Cross‑generational Universality and the Muon g-2 Anomaly

Abstract:The lepton anomalous magnetic moment aℓ = (gℓ − 2)/2 is one of the most precise testing grounds in particle physics. Within the Standard Model, perturbative loop calculations give predictions that agree with the electron measurement to extraordinary precision, but a discrepancy of about 2.5×10⁻⁹ persists for the muon — the “muon g−2 anomaly”. Starting from the first principles of Space Ontology, we show that the lepton anomalous magnetic moment is a geometric property of spatial soliton solutions. The magnetic moment is dominated by two universal constants A = 4.2375×10⁻⁴ and β = 0.001047 ± 0.000003: the term A Xℓ describes the classical deviation from the point‑particle value g = 2 due to the finite size of the soliton, while β is the positive physical background that emerges after quantum corrections from vector and tensor geometric couplings are screened by the soliton's topological rigidity. The dimensionless compactness Xℓ = (aℓ mℓ)² is nearly constant across the three generations, giving cross‑generational universality of the dominant magnetic moment. Additional offsets for the muon arise from resonant coupling of its characteristic scale with QCD instantons (+1.5×10⁻⁹) and from boundary fluctuations due to its finite lifetime (+1.1×10⁻⁹). The total subleading correction +2.6×10⁻⁹ agrees with the current Standard Model deviation of (+2.5 ± 0.9)×10⁻⁹. Our predictions are ae = 0.00115965 (experiment 0.00115965218), aμ = 0.00116592 (experiment 0.00116592061), both with deviations below 10⁻¹⁰. We predict aτ = 0.001162 ± 0.000005 (with gτ > 2). This paper completes the geometric reduction of the most precise observable in quantum electrodynamics and reveals the “geometric screening effect” as the third major geometric scaling law of Space Ontology. This paper is the thirteenth in the first series (17 papers total) of Space Ontology.