Spectral Evolution in History-Dependent Gravity: Conservative Flow and Linear Response

We study the spectral evolution of tensor perturbations in history-dependent gravity (HDG), where nonlocal memory terms arise from functional renormalization group (FRG) flow. The spectral density obeys a conservative Boltzmann-type kinetic equation with exact norm and first moment preservation. Numerical integration reveals a universal attractor and linear response n_T ∝ ξ, establishing a theoretically controlled framework for memory-induced spectral redistribution.