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 Υdisk. The photometric disk scale length rd 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 χ²ᵣed = 0. 62 and a mean of 1. 38. Approximately 66. 5% of galaxies satisfy χ²ᵣed < 1, and 82. 9% satisfy χ²ᵣed < 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.