HGD–GSR: A Structural Residual Test of Galaxy Dynamics

Abstract

HGD–GSR is a locked-definition, zero-free-parameter structural residual analysis of galaxy rotation-curve data using the SPARC subset of the Unified Galaxy Rotation Curve Corpus v7.0. The study tests whether Q_bar, a compact descriptor of the radial baryonic hierarchy, retains measurable information about residual galaxy dynamics after published baryonic contributions are applied without refitting mass-to-light ratios, inclination, distance, or other galaxy parameters. The analysis proceeds through multiple validation phases including correlation analysis, machine-learning audit, partial regression, feature importance, Monte Carlo uncertainty propagation, target replacement, ablation, hold-out validation, nested cross-validation, randomized controls, and sensitivity to alternative definitions of Q. A central methodological result is that the mean GSR residual is algebraically coupled to Q_bar through mean(GSR) ≈ 1 − Q_bar and therefore cannot be treated as independent predictive evidence. More informative non-equivalent residual statistics show that Q_bar retains substantial association with maximum residual structure and outer-disc residual structure, but little or no association with residual dispersion or the pure inner residual. The conclusions are restricted to the SPARC sample and do not claim a new gravitational theory, a modification of General Relativity, a replacement for dark matter, or a universal law.