The Spacetime Relaxation Chronometer (SRC): Definition and Tier-1 Calibration in Dissociative Galaxy-Cluster Mergers

Dissociative galaxy–cluster mergers provide a unique laboratory for probing the dynamical response of gravity to rapid rearrangements of baryonic matter. In such systems, the hot intracluster gas traced by X-ray emission becomes spatially separated from the gravitational potential inferred from weak lensing. While these offsets are often discussed in static terms, their time evolution has not been systematically calibrated. This work introduces the Spacetime Relaxation Chronometer (SRC), a dimensionless observable defined as the projected system-level separation between the gas and the gravitational potential, normalized by the halo scale radius. A reproducible measurement protocol is specified, and a clean Tier-1 calibration sample of five dissociative mergers is constructed, each with independently constrained time brackets since first core passage. The temporal evolution of the SRC observable is modeled using a simple exponential relaxation law under conservative assumptions about cluster-to-cluster scatter. For the Tier-1 sample, a characteristic relaxation timescale of order one tenth of a gigayear is inferred, and a no-relaxation null is disfavored under the adopted uncertainty model. This release establishes the SRC as an empirical chronometer for post-merger evolution in dynamically young galaxy clusters. The framework is agnostic to the underlying physical interpretation and is intended as a foundation for future extensions to larger samples and for testing models of time-dependent gravitational response.