Percolation Saturation of Baryonic Anchoring in SPARC Galaxy Rotation Curves

We report a tight correlation between the exponential correction to Newtonian rotation curves and the HI disk properties of 156 SPARC galaxies. We find that the anchoring correction factor k, defined through v_model = v_bar * exp(kR), follows k = S_max * (1 - exp(-w_gas / w_c)) / R_HI, where w_gas is the gas mass fraction, R_HI is the HI disk radius, and S_max and w_c are free parameters. Fitting yields S_max = 0.83 ± 0.06 and w_c = 0.126 ± 0.03. The 5-fold cross-validated R² is 0.66. A 100-iteration random split test gives training R² = 0.70 ± 0.08 and independent test R² = 0.68 ± 0.08, confirming no overfitting. The saturation value S_max is consistent with 1 - φ_c, where φ_c ≈ 0.16 is the well-established critical volume fraction for 3D continuum percolation. The characteristic gas fraction w_c matches the excluded-volume scaling argument for overlapping spheres, w_c = 1/8. We further find a sharp transition in k at the onset of bulge formation: bulgeless galaxies (N=124) have median k = 0.057, while bulged galaxies (N=32) have median k = 0.008 (p = 2 × 10⁻¹⁴). These results suggest that the baryonic anchoring effect in galactic disks is controlled by the percolation connectivity of the HI gas network.