Turning Galaxy Rotation Curves into Radial Cosmic Chronometers: A Nexus Paradigm Approach

We present a novel method for deriving radially resolved dynamical chronometers from galaxy rotation curves, allowing galaxy assembly histories to be reconstructed directly from kinematic data. In the Nexus Paradigm, the baryonic Tully–Fisher relation is used to estimate the dynamical mass profile. We compare this profile with independently derived intrinsic baryonic mass distributions obtained from stellar Sérsic fits and gas surface-density measurement yields. This yields a radial ratio that maps to formation redshift with radial resolution. Inverting this ratio within a standard cosmological framework produces a radial lookback-time profile, representing the time since each radial shell last experienced dynamical reconfiguration. Applying the method to a pilot sample of seven SPARC galaxies, including both high- and low-surface-brightness systems as well as the Milky Way, reveals diverse age structures: stratified profiles associated with inside-out growth and flatter profiles consistent with coherent disk assembly. The method requires no dark-matter halo fitting and offers a kinematic chronometer that complements stellar population and chemical evolution approaches. The NP rotation-curve parameters were determined by minimizing the chi-squared statistic between the observed and predicted velocities using a two-stage optimization consisting of a global differential-evolution search followed by nonlinear least-squares refinement. Observational uncertainties were taken from the published rotation-curve data, supplemented by a 5 km s−1 systematic error floor added in quadrature to account for non-circular motions and other unresolved systematics. We also show that the governing dynamical equation admits a gravitoelectromagnetic interpretation, in which a velocity-dependent term generates disk-wide torques that regulate angular momentum transport. This leads to a unified stability framework in which galaxy morphology emerges from a single parameter regime: balanced conditions favor a coherent spiral structure, whereas dynamically hot regimes naturally produce diffuse and ultra-faint systems. The cosmological scaling of the effective gravitomagnetic field further suggests that the spiral structure is partly regulated by cosmic time. Although the inferred ages depend on the accuracy of the baryonic mass reconstruction and on the local validity of the evolving baryonic Tully–Fisher relation, our results show that rotation curves encode time-resolved dynamical information. This establishes the radial dynamical chronometer as a new observable for studying galaxy evolution and testing gravitational frameworks.