A Derived Screening-Kernel Model for SPARC Galaxy Rotation Curves in the Space–Matter–Motion (RMB) Framework

This work presents a numerical test of the Space–Matter–Motion (RMB) framework on SPARC galaxy rotation curves. Building on a previously published RMB effective field-theoretic formulation, an earlier empirical shape parameter is replaced by a derived effective screening scale obtained from the disk-convolved RMB field response. The resulting model contains three fitted parameters: a coupling strength α, a base screening scale ℓ₀, and a stellar mass-to-light ratio Υ_disk. The photometric disk scale length r_d is taken directly from SPARC photometry and is not treated as a free parameter. The model is tested on 170 SPARC galaxies using a reproducible Python pipeline with a 2% systematic velocity floor. The derived three-parameter model achieves a median reduced chi-square of χ²_red = 0.62 and a mean of 1.38. Approximately 66.5% of galaxies satisfy χ²_red < 1, and 82.9% satisfy χ²_red < 2. The fraction of boundary-limit cases for the primary coupling parameter α decreases from 12% in the four-parameter baseline to 2.4% in the derived model, indicating improved physical constraint. Remaining tensions are confined to a compact subset of galaxies and are interpreted as diagnostic limits of the present kernel formulation. A supplementary ZIP archive is provided, containing all Python scripts, batch summary tables, per-galaxy fit outputs, and a README file with full reproduction instructions. The analysis is reproducible using the provided scripts and publicly available SPARC data. Minor platform-dependent numerical differences (<0.1%) may occur due to floating-point rounding.