A Robust Geometric Scaling Relation from Higher-Dimensional Projection: Evidence from the SPARC Galaxy Sample

We confront a geometric dark matter toy model with the SPARC sample of 175 late-type disk galaxies. Fitting 171 galaxies yields a robust power-law scaling relation between the geometric normalization parameter α and the outer flat rotation velocity: α ∝ v_flat^n, n = 2.82 ± 0.16 (R² = 0.83). The slope is confirmed by Theil-Sen regression, bootstrap resampling, and multiple quality thresholds. A train/validation split demonstrates predictive power, with 88% of validation galaxies reproduced within 0.5 dex. Submitted to Physical Review D.