Geometric Closure of Lepton Magnetic Anomalies and the Running of $\alpha(q^2)$ in Quantum Measurement Units

This manuscript presents a Quantum Measurement Units (QMU) program for describing lepton magnetic anomalies and the running electromagnetic coupling in the Aether Physics Model (APM). The organizing idea is that the lepton anomalous magnetic moment can be decomposed into a baseline geometric holonomy term and a species-dependent torsion-mismatch correction. The lepton anomaly is defined by\[a_\ell \equiv \frac{g_\ell - 2}{2}.\]In the APM/QMU ledger-first approach, the torsion-mismatch component is proposed to close as a parameter-free, mass-ratio scaling law,\[\Delta a_\ell = \frac{\alpha^2}{32\pi}\frac{m_e}{m_\ell},\]interpreted as an inertial-loading leakage for a lepton occupying a common electron-anchored spin-seat with different mass loading. The electron is treated separately as the sector that fixes the baseline normalization and the fine-structure geometry selector. The paper also gives a ledger-consistent interpretation of the conventional running coupling,\[\alpha(q^2) = \frac{\alpha(0)}{1 - \Delta\alpha(q^2)},\]as an Aether screening response: the scale dependence is modeled as a dimensionless projector acting on the charge-sector geometry while preserving the APM closure constraints. This motivates experimental discriminators based on (i) lepton-hierarchy scaling tests (notably future global constraints on the tau anomaly), and (ii) spacelike extractions of \Delta\alpha(t) from muon--electron scattering as a direct probe of screening consistency across momentum transfer. All primary relations are stated in QMU terms, with SI used only as a final-stage numerical bridge where required for comparison with the literature.