HGD–GSR: A Structural Residual Test of Galaxy Dynamics — Locked Definitions, Multi-Phase Robustness Audit, and SPARC-Internal Validation

Abstract

The HGD–GSR program investigates a residual-information question in galaxy dynamics: after published baryonic contributions are subtracted under a locked mass-to-light prescription, does a compact descriptor of radial baryonic organization retain measurable information about dynamical residual structure? The analysis uses 175 SPARC galaxies with full published baryonic decompositions. The point-wise residual is defined as GSR_i = (V_obs,i² − V_bar,i²)/V_obs,i², while the baryonic hierarchy descriptor Q_bar is the mean of V_bar,i²/V_obs,i² over the same valid radial points. The analysis explicitly recognizes that the mean residual is algebraically coupled to Q_bar, with mean(GSR) ≈ 1 − Q_bar under the locked implementation. Consequently, the near-perfect predictive performance for the mean residual is treated as an algebraic consistency diagnostic rather than independent predictive evidence. More informative non-equivalent residual statistics show a target-dependent pattern. Q_bar is substantially associated with the outer 30% residual structure (R² = 0.697 ± 0.059) and maximum residual structure (R² = 0.627 ± 0.117), while showing little or no predictive utility for the pure inner residual (R² = 0.094 ± 0.124) or residual dispersion (R² = −0.113 ± 0.097). The results support a reproducible SPARC-internal structural residual pattern under locked definitions. They do not constitute evidence for a new gravitational mechanism, a modification of General Relativity, a replacement for dark matter, or a survey-independent universal law.