Finite-Relaxation Geometry (FRG): Spacetime with Memory as a Unified Framework for Gravity, the Dark Sector, and the Arrow of Time

This work presents Finite-Relaxation Geometry (FRG), an interpretational cosmological framework in which spacetime geometry is characterized by a finite relaxation time and therefore retains long-lived memory of past curvature perturbations. Within this framework, phenomena conventionally attributed to dark matter emerge as manifestations of incomplete local relaxation of geometric memory, while dark energy corresponds to a homogeneous global relaxation mode of the same underlying geometry. FRG preserves the Einstein field equations without modification, introduces no new particles or fields, and offers a natural geometric origin for the cosmological arrow of time. We further present a consistent interpretation of black holes as maximal excitations of geometric memory and discuss a possible cosmological origin of spacetime through gravitational collapse. The framework is shown to be consistent with current cosmological observations while remaining falsifiable at macroscopic scales.