This Paper sets out to measure the dimensionless gravitational compactness: lambda = frac{G,M_{m bar}}{R_{m eff},c^2}for 175 disk galaxies in the SPARC sample, using infrared—derived baryonic masses and 3.6 μm effective radii. This explorations lead to a surprise, and discovered: These λ values cluster very tightly around a median of 2.45times10^{-8}, roughly log-normal in shape and more than two orders of magnitude below the scale at which many modified-gravity ideas predict observable effects.Next , we asked the question whether a simple global tweak like: V_{m model}^2 = V_{m bary}^2Bigl(1 + kappa,lambda^betaBigr) could reproduce galaxy rotation curves ? Fitting kappa and beta to 3,387 data points gives an RMSE of 40.8 km/s, only a small improvement over the purely Newtonian result (43.3 km/s) and well behind MOND (∼13 km/s) or NFW dark-matter fits (∼25 km/s). Worse still, the best fit requires kappaapprox1.8times10^4, a coupling strength that feels implausibly large; an indication that this global prescription simply misses essential physics.Although this is a null result for λ-only modifications, it still yields something valuable: a new empirical benchmark at lambdasim10^{-8}. We hope that future theories - whether they invoke local accelerations, environmental dependencies, or entirely different mechanisms; will honor this scale when tackling the stubborn puzzle of flat galaxy rotation curves.