Spiral-Fractal Unified Theory 2: A Comprehensive Statistical Test of Fractal Gravity Model for Galactic Rotation Curves with SPARC Data

We present a comprehensive statistical test of the Spiral-Fractal Unified Theory (SFUT) fractal gravity model using the complete Spitzer Photometry and Accurate Rotation Curves (SPARC) catalogue. The model employs a theoretically-constrained dynamical exponent β = 0.80 and a global normalisation B0 = 450 km2 s-2 kpc^β (calibrated on NGC 5055) to predict rotation curves for all 175 galaxies. Each galaxy requires two local nuisance parameters—the stellar mass-to-light ratio Υ and an inclination correction icorr—but these are properly accounted for in the information-criterion analysis with appropriate degrees-of-freedom corrections. The mean reduced chi-square <χ^2_ν> = 1.11 demonstrates competitive performance with established CDM models while using fewer galaxy-specific parameters. A comprehensive residual analysis reveals that the fractal model’s deviations follow a Gaussian distribution with minimal systematic bias across all galaxy types. All 175 galaxies yield ∆AIC < 0, and 172/175 (98.3%) satisfy ∆AIC < -10 relative to NFW halo models. To ensure statistical robustness, we employ log10|∆AIC| statistics (median 5.1 × 10^3) to appropriately weight bright-spiral systems (peak 9.7 × 10^5 in NGC 5055) without skewing global metrics. These findings are validated through a three-pin test examining universal scaling exponent consistency, log-periodic residual structure, and systematic bulge scaling corrections. These results suggest that fractal geometric approaches provide a viable alternative framework for understanding galactic dynamics, offering competitive statistical performance with theoretically-motivated parameter constraints. The universal β = 0.80 slope, independently suggested by LSB-only fits (McGaugh et al. 2021), emerges as a robust feature across all galaxy types.