Morphology-Conditioned Occupancy States in SPARC Rotation Curves

We investigate whether late-type galaxy rotation curves in the SPARC sample exhibit reproducible higher-order organization beyond conventional one-parameter descriptions such as global velocity or acceleration-based relations. Rather than treating rotation curves solely as a fitting problem, we examine whether the observed behavior can be organized within a morphology-conditioned state space constructed from rotation-curve-derived structural observables. Using measures of compactness, coherence, concentration, outer growth, and residual structure, we construct a two-dimensional occupancy space characterized by condensation capacity and growth activation. The resulting occupancy geometry separates 143 SPARC galaxies into four distinct states, termed fragmented, compact condensed, growth condensed, and growth overextended. Occupancy-state assignments are derived directly from rotation-curve morphology and are not constructed using the validation observables subsequently examined. A notable result is the emergence of a compact condensed population characterized by strong internal structural organization but suppressed outward growth activation. This behavior suggests that structural organization and large-scale rotational growth may represent partially independent dimensions of rotation-curve phenomenology rather than a single progression along a common organizational axis. The resulting occupancy hierarchy systematically organizes multiple validation observables, including recovery behavior, residual-amplitude diagnostics, coherence measures, outer-underfit indicators, and MOND-related residual diagnostics. Statistically significant separation is observed across all principal validation quantities. The hierarchy remains stable under randomized-control tests, threshold perturbations, normalization variations, coefficient-perturbation analyses, and state-weight permutation tests. The present work is intentionally phenomenological and does not propose a modified-gravity framework, dark-matter alternative, or microscopic physical mechanism. Instead, it provides evidence that SPARC rotation curves contain a reproducible morphology-conditioned state structure that organizes higher-order residual and structural behavior beyond conventional one-parameter descriptions.