HGD–GSR: A Structural Residual Test of Galaxy Dynamics

Hierarchical Gravitational Dynamics – Galaxy Structural Residual (HGD–GSR) is presented as a falsifiable observational framework designed to test whether structural information extracted from galaxy organization contributes measurable predictive value beyond conventional baryonic and halo-based descriptors. Rather than proposing a modification of gravity, a dark matter alternative, or a new fundamental interaction, HGD–GSR is formulated as a residual-information hypothesis. The central question is whether hierarchy-related observables contain statistically significant information about galaxy rotation behavior after controlling for standard astrophysical variables. Using the SPARC database of 175 disk galaxies and 3,389 rotation-curve measurements, the framework evaluates several structural descriptors, including Qlocal, QSB, and Qbar. Results indicate that Qbar provides the strongest predictive contribution, improving explanatory performance relative to baryonic-only baselines while remaining substantially weaker after halo controls are introduced. The framework therefore does not claim evidence for new physics. Instead, it investigates whether structural organization retains residual predictive information that may complement existing galaxy-dynamics models. The work includes falsification criteria, bootstrap validation, cross-validation tests, model-comparison metrics (AIC/BIC), and an explicit operational framework for future replication across independent surveys including THINGS, LITTLE THINGS, and WALLABY. Keywords: galaxy dynamics, rotation curves, SPARC, structural hierarchy, residual information, dark matter, galaxy structure, statistical astrophysics, HGD, GSR.