Predicting Anomalous g-2 Magnetic Moment of Muon and Other Leptons: A Superior Alternative to the Standard QED Using Sedenionic Gauge Symmetry

We present a finite, hypercomplex gauge theory predicting the anomalous magnetic moments of the electron, muon, and tau with precision comparable to the standard quantum electrodynamics (QED), but without the need for divergences, renormalization, or path integrals. Recursive interactions in a compactified internal space governed by octonion and sedenion algebra yield the electron g−2 anomaly with 12-digit agreement to experiment, match the muon anomaly within experimental error, and predict a stable value for the tau. The fine-structure constant arises from geometric quantization rather than vacuum fluctuations. This approach offers a divergence-free, algebraic alternative to conventional quantum field theory and points toward a unified internal geometric origin of fundamental particle properties.