Corrected Structured a0 Law Results for the N=45 High-Quality Galaxy Subset

This release provides the corrected results for the N=45 high-quality subset analysis of structured galaxy-to-galaxy variation in fitted a0. A code-level bug in the handling of the SPARC morphological type T was identified in several phase scripts. Specifically, a fallback written as T || 5 incorrectly replaced valid T = 0 values with 5. The affected logic has now been corrected to T ?? 5, all impacted scripts have been rerun, and the final reported coefficients and validation metrics have been updated accordingly. The correction does not remove the structured-law signal. However, it reduces the apparent independent contribution of the orthogonalized stellar-structure term Ups_perp and correspondingly reduces the performance gap between the extended 5-variable model and the compressed 3-variable model. Corrected main results: Extended model M5: logA0 = 5.016 - 0.235 logMHI - 0.175 logMhost + 0.146 logSigma0 + 0.447 logMeanRun + 0.372 Ups_perp Leave-one-out gap closure: 46.6% Leave-one-out RMS: 0.189 dex In-sample R²: 0.588 Confounder regression R² for Ups_perp construction: 73.3% Compressed model M3: logA0 = 5.182 - 0.198 logMHI - 0.155 logMhost + 0.459 logMeanRun Leave-one-out gap closure: 44.1% Leave-one-out RMS: 0.193 dex Retains about 95% of the predictive signal of M5 Validation results after correction: Nested CV gap closure: 37.8% Permutation test: p < 0.001 Falsifiable predictions: 24/26 Matched pairs: 22/25 Bootstrap sign stability: all coefficient signs stable Residual frontier: approximately Gaussian with 0.189 dex scatter Interpretation: The corrected results continue to support a structured, non-universal description of fitted a0 on the N=45 high-quality subset. However, the corrected hierarchy is now clearer: the compressed 3-axis state law M3 captures nearly all of the predictive content of the extended model, while the additional stellar-structure information in M5 provides only a modest refinement. Important note on units: In this project, logA0 is stored in log10[(km/s)²/kpc], not log10(m/s²). Any older documentation stating SI-log units for the stored target variable should be considered outdated. This release supersedes earlier posted values in which Ups_perp was overstated, M5 gap closure was reported near 51%, and M3 retention relative to M5 was understated. Changelog: Fixed morphT fallback bug in affected phase scripts Reran impacted analysis chain Updated M5 coefficients and validation metrics Reduced Ups_perp coefficient from 0.658 to 0.372 Updated M5 LOO gap closure from about 50.9% to 46.6% Updated M3 retention relative to M5 from about 86% to about 95% Clarified stored logA0 units as log10[(km/s)²/kpc]