Self-Interacting Fuzzy Dark Matter and the SPARC Galaxy Catalog: Statistical Validation of the Guerrero si-FDM Framework Across 135 Disk Galaxies

We present a systematic statistical validation of the self-interacting fuzzy dark matter (si-FDM) framework—the Guerrero model—against the SPARC galaxy catalog (Lelli, McGaugh & Schombert 2016). The model utilizes globally fixed physical parameters: a scalar boson mass m22 = 8, a dimensionless quartic self-coupling g_NL = 0.00597 (derived from a one-loop renormalization group flow), and a fixed soliton core radius r_c = 1.5 kpc. A central structural prediction, the Rigidity Filter, classifies halos beforehand into two sharp regimes based on a critical mass threshold of M_crit = 1.105x10^10 M_sun, separating stable soliton-hosting cores from diffuse dark matter configurations. Applying analytical rotation curves to the 135 disk galaxies in the catalog that possess a measured asymptotic flat velocity (V_flat), we optimize three free parameters per galaxy: halo mass (M_halo), NFW concentration (c), and the stellar mass-to-light ratio (Upsilon_disk). The framework achieves a remarkable median fractional deviation in V_flat of just 1.50%, with a good-fit fraction (error < 10%) of 91.1% across the entire sample. Furthermore, a halo Tully-Fisher relation with a slope of 3.97 emerges naturally from independent per-galaxy optimizations. We report and discuss known systematic limitations of the V_flat analytical method, specifically the Upsilon_disk boundary clustering and elevated concentration parameters in diffuse galaxies, establishing a clear baseline for forthcoming full rotation curve shape analysis.