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 = 0.44). 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 slope gives the gas-layer net gain k_gas = 0.244 +/- 0.022 /kpc, significantly non-zero: gas disks deviate from Newtonian gravity, with characteristic length 1/k_gas ~ 4.1 kpc. The result is stable across fitting cutoffs R_cut in [1.0, 4.0] and independent of scale length R_d. We find k_gas ~ C/R_d with C ~ 0.15 a dimensionless constant. 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.