Four Distinct Dynamical Families in Galactic Rotation Curves: A Data-Driven Discovery

We report a direct empirical discovery from the analysis of 149 galaxies in the SPARC database. Through a purely data-driven computational approach, we find that galactic rotation curves naturally organize themselves into four statistically distinct dynamical families, with hierarchical substructure revealing seven finer-grained families. Two families exhibit exceptional regularity, with 100% success in basic kinematic modeling. This classification emerges objectively from the data structure itself, without any theoretical assumptions about dark matter or galaxy formation. Extensive validation including PCA analysis (shape parameters dominate over scale), cross-validation (85.2% agreement), bootstrap uncertainty (mean probability 0.654), and comparison with previous morphological classifications shows only 16.7% agreement, confirming that this is a fundamentally new classification scheme based purely on kinematics. Physical properties reveal systematic differences across families: Family 3 (Rising) has the highest mass (log M = 9.75), largest radius (14.5 kpc), and highest baryonic fraction (31.2), while Family 0 (Flat) has the lowest mass and smallest radius. We present these families as a new phenomenological framework for understanding galactic dynamics, independent of morphological considerations.