Emergence of the Electron Magnetic Anomaly

This work demonstrates that the electron magnetic moment and its anomalous correction emerge entirely from the internal structure of the closed quartic ΨΓ variational functional. Starting from the exact functional and constructing the admissible domain A ⊂ X, we perform the full Hessian spectral decomposition and identify the universal structural constant L = 1/4 together with the primary scale E⋆. The electron mass arises at hierarchical level k = 5 as me = E⋆L5. The magnetic moment is obtained as the linear torsional response of the degen- erate spectral sector under internal rotation, yielding the structural result μ0 = e 2me . The anomalous deviation originates from the minimal cyclic closure compatible with the intrinsic Z3 structure of the functional. Lower-order contributions cancel topologically, and the rst admissible correction appears at order L7. The anomaly is uniquely xed as ae = L5 + 3L7. For L = 1/4, this gives ae = 19 16384 = 0.00115966796875, agreeing with the measured value up to 1.6 × 10−8. All results follow exclusively from the internal variational structure, spectral rigidity, and cyclic closure of the framework, without introducing external constants, perturbative loop expansions, or tting procedures.