Geometric Origin of the Muon Anomalous Magnetic Moment in the Zhang Effective Metric

The anomalous magnetic moment of the muon (g-2) has been measured with unprecedented precision by Fermilab, but the Standard Model (SM) prediction remains subject to theoretical debate between data-driven and lattice QCD approaches. In this paper, we demonstrate that the rotational-order geometric unification framework provides a geometric contribution that can account for the historical tension under the data-driven SM baseline. Using the Zhang Effective Metric, we show that zero-point fluctuations of the internal S³ orientation field generate an effective geometric loop correction to the muon's magnetic moment. For a characteristic correlation length r_c ~ 10⁻¹⁸ m (comparable to the electroweak length scale), the predicted deviation Δa_μ accounts for the historical 2.5×10⁻⁹ tension under the data-driven SM baseline, while providing a falsifiable prediction for the lattice QCD baseline. This geometric explanation unifies flavor anomalies with the framework's cosmological and gravitational scales, requiring no new fundamental particles.