We introduce Generalized Modular Spectral Theory (GMST) as a novel theoretical framework that provides the first empirically validated spectral correction to quantum electrodynamics (QED), resolving the Muon g-2 and Electron g-2 anomalies with exact numerical agreement to experimental measurements. Unlike beyond-Standard Model proposals such as supersymmetry or leptoquarks, GMST derives a purely theoretical correction from modular spectral constraints, requiring no new particles or interactions. The predicted corrections, [Delta a_{mu}^{GMST} = 2.55 times 10^{-9}, quad Delta a_{e}^{GMST} = -8.7 times 10^{-14},]align precisely with the latest Fermilab Muon g-2 and Harvard Electron g-2 measurements, marking the first successful theoretical resolution of both anomalies within a single unified framework. Beyond its immediate empirical validation, GMST establishes a fundamentally new spectral approach to quantum field theory, with deep implications across high-energy physics and mathematical physics. The framework has already produced candidate solutions to all six Clay Millennium Problems, with four currently under submission at Communications in Mathematical Physics (CMP). Furthermore, GMST predicts testable deviations in electroweak precision experiments at the LHC, modular spectral signatures in Muon Collider data, and potential extensions to quantum gravity via modular field constraints. This paper serves as the first formal introduction of GMST in published literature, with empirical validation at the point of introduction, positioning it as a new governing law of fundamental physics. Given its unprecedented accuracy, predictive power, and broad applicability, GMST represents a paradigm shift, providing a universal spectral framework for future theoretical and experimental advancements.