Spectral Response Framework: Vacuum Memory, Renormalization Flow and the Emergence of Hadronic Mass (Paper L)

Nonlocal vacuum memory, as postulated in History-Dependent Gravity (HDG), introduces a fundamental spectral structure into quantum field theory. This work develops the Spectral Response Framework, a rigorous effective field theory formulation that addresses two central challenges: preserving gauge invariance in the presence of nonlocality, and generating stable infrared (IR) mass scales from a fundamental ultraviolet (UV) spectral structure without fine-tuning. We postulate a universal, positive-definite spectral density ρ(μ)≥0ρ(μ)≥0 encoding vacuum memory, and demonstrate that physical observables emerge through convolution with system-dependent response functions WO(μ)WO(μ). We establish three main results: (1) Spectral Gauge Protection: the renormalized vacuum polarization satisfies ΠRμν(0)=0ΠRμν(0)=0 exactly, forbidding photon mass generation despite nonlocal modifications to the propagator's analytic structure; (2) Spectral Renormalization Group Flow: the spectral density evolves according to a functional renormalization group equation projected from the Wetterich flow, with different physical sectors flowing to distinct IR fixed points; (3) Emergence of Hadronic Mass: the nucleon mass scale MN∼ΛNMN∼ΛN arises naturally from the convolution MN2=∫dμ ρN(μ)WN(μ)MN2=∫dμρN(μ)WN(μ), where WN(μ)WN(μ) is a minimal dipole spectral form factor. This framework provides a dynamical mechanism by which stable low-energy mass scales emerge from fundamental UV spectral structure. It does not replace Quantum Chromodynamics (QCD), but rather complements it by explaining how characteristic mass scales are selected by the history-dependent structure of the vacuum. This work establishes the single-particle foundation, paving the way for future many-body extensions to nuclear binding and mass defects.