Two-Layer Anchoring: Stellar Disks Obey Newton, Gas Disks Deviate

We analyze the rotation curves of 159 SPARC galaxies using a single-parameter anchoring formula v(R) = v_bar(R) * exp(kR), where k is the anchoring-push net gain per kpc. We find that k correlates linearly with gas mass fraction w_gas (Spearman rho = 0.73, R^2 = 0.47, 5-fold CV R^2 = 0.41). The intercept gives the stellar-layer net gain k_star = 0.005 +/- 0.005 /kpc, consistent with zero: stellar disks obey pure Newtonian gravity. The gas layer deviates from Newtonian gravity with characteristic length ~4.1 kpc. Crucially, we find that the gas-layer net gain is driven by two independent physical quantities: the gas mass fraction w_gas and the HI disk radius R_HI. The double-variable model k = 0.127 * w_gas + 0.530 / R_HI achieves 5-fold CV R^2 = 0.62 (compared to 0.41 for w_gas alone and 0.54 for 1/R_HI alone). The two variables are correlated but not degenerate (Spearman rho = -0.56); residual analysis confirms both contribute independently (p < 10^-6). This indicates that anchoring strength is determined by both mass effect (how much gas) and scale effect (how compact the gas disk is). We cross-validate with 14 overlapping galaxies in the THINGS survey; massive galaxies show consistent k between SPARC and THINGS (< 0.03 difference). This provides a dark-matter-free explanation of flat rotation curves, distinguishable from MOND because MOND does not differentiate between mass types or distribution scales.