Global Realization Sectors, Gravitational Memory, and Lensing Offsets

This work provides the empirical closure of a theoretical framework in which gravitation admits a separation between local force-based dynamics and a single global realization degree of freedom. Building on a variational formulation with a global realization constraint, we show that gravitational observables sensitive to time-integrated structure encode relaxation of this global sector following major structural rearrangements. Observations of dissociative galaxy cluster mergers reveal that offsets between gravitational lensing peaks and baryonic tracers decay systematically with time since core passage and are empirically overconstrained by a single relaxation timescale. We demonstrate that this behavior is naturally interpreted as gravitational memory: the relaxation of a non-force global realization sector that does not contribute to local acceleration or curvature and therefore requires no additional local mass components. The framework yields testable predictions, including the universality of the relaxation timescale, the absence of persistent offsets at late times, and the preferential sensitivity of time-integrated observables. Independent evidence for a slow, coherent drift with characteristic frequency Ω ≈ 31 nHz in realized systems is identified as a complementary empirical signature of global temporal organization. This frequency is not identified with the realization parameter itself, but with the observable rate at which changes in the global realization state manifest. Taken together, the results define a closed and minimal theoretical structure: local gravitational behavior is exhausted by the temporal gradient, while global gravitational memory and temporal organization are governed by a single realization sector. Further work may extend or test the framework, but no additional degrees of freedom are required to account for the class of phenomena considered here.