Evidence for Asymptotic Quarter-Law Scaling in the Deep Low-Acceleration Regime of Galaxies

This work presents a model-independent analysis of galaxy rotation curves using the SPARC database, focusing on the asymptotic behavior in the deep low-acceleration regime. We reconstruct the logarithmic slope α = d log g_obs / d log g_bar and demonstrate a systematic convergence toward a quarter-law scaling (p → 1/4) as baryonic acceleration decreases. The analysis combines global fitting, bootstrap resampling, and a progressive low-acceleration cut, providing strong empirical evidence that the asymptotic scaling differs from the commonly assumed square-root behavior (p = 1/2). This dataset includes the full paper and figures supporting the analysis.