Gravity with Memory: Non-Markovian Vacuum Response and Galactic Infrared Closure

The main text investigates the structural consequences of replacing the memoryless assumption of standard gravity with a causal, non-Markovian vacuum response. Motivated by finite information capacity and fluctuation-dissipation scaling, a minimal constitutive relaxation equation is formulated. The framework establishes that standard local Newtonian dynamics and the empirical radial acceleration relation observed in galaxies emerge as the exact high-frequency (frozen-memory) and low-frequency (infrared equilibrium) asymptotic regimes of the same constitutive law. The Supplemental Material formalises the epistemological structure of the framework. It strictly delineates exact mathematical derivations from minimal thermodynamic assumptions, formulates the dataset-observable correspondence principle, establishes explicit channels for empirical falsification, and outlines required formal extensions. A separate companion record provides the observational audit package (SPARC dataset analysis) and is linked via related identifiers. Keywords: Non-Markovian dynamics, gravitational memory, linear response, vacuum susceptibility, galactic kinematics, foundations of gravity.