Comprehensive analysis of 175 SPARC galaxies demonstrating regime-dependent validity in rotation curve modeling

We present a comprehensive analysis of 175 galaxies from the Spitzer Photometry and Accurate Rotation Curves (SPARC) database, extending our pilot N=20 study that introduced the Energy-Flow Cosmology Regime Framework (EFC-R). Using an ultra-phenomenological fitting model, we demonstrate robust evidence for regime-dependent validity in galaxy rotation curve modeling. The analysis reveals three distinct regimes: (1) FLOW regime (62 galaxies, 35% of sample) where models achieve 100% success rate with mean reduced chi-squared of 2.05, characterized by low structural complexity; (2) TRANSITION regime (86 galaxies, 49%) showing mixed dynamics with neither model clearly dominating; and (3) LATENT regime (27 galaxies, 15%) where models systematically fail with mean reduced chi-squared of 297.83, characterized by high structural complexity from bars, tides, and warps. Statistical testing confirms the regime separation is highly significant: Mann-Whitney U test comparing FLOW and LATENT regimes yields p < 0.0001. The latent proxy (L), a composite metric quantifying structural complexity, shows mean values of L=0.290±0.143 for FLOW versus L=0.500±0.111 for LATENT, demonstrating clear stratification. These findings validate the core prediction of EFC-R: gravitational dynamics exhibit distinct domains of validity defined by system complexity, rather than continuous applicability across all scales. The pattern aligns with independent findings from FIRE simulations (bursty star formation creating regime transitions) and resolves long-standing "problems" in galactic astrophysics (cusp-core, diversity) by reframing them as regime boundary signatures. We provide complete reproducible methodology with all data files, analysis scripts, and diagnostic tools. This work establishes the empirical foundation for the EFC-R meta-framework while explicitly distinguishing phenomenological modeling from physical theory. The regime structure observed in N=175 robustly replicates the N=20 pilot findings, confirming this is not a small-sample artifact but a fundamental feature of galactic dynamics.