We consider an effective gravitational potential whose extra term is a regularised two-dimensional logarithmic potential — the logarithmic Green''s function of the two-dimensional Poisson equation. We derive its source surface density, Σ(R) ∝ rc^2/[(R^2 + rc^2)^2] (a two-dimensional Plummer-like distribution), and show that its total mass satisfies M = Vflat^2/G2 exactly, so that the model has a well-defined physical normalisation. The circular-velocity contribution is V2D^2(R) = Vflat^2 R^2/(R^2 + rc^2), which differs from a pseudo-isothermal (PI) halo in the approach to the flat asymptote (1/R^2 vs. 1/R corrections). We fit this model, MOND (two interpolating functions), NFW, PI and Burkert halos to the SPARC sample of 175 disk galaxies (3391 velocity measurements), with the stellar mass-to-light ratio free per galaxy and a systematic error floor scanned over 0—15%. At the reference 10% floor, the cored models give lower total χ^2 than NFW and both MOND forms: χ^2/N = 0.57 (2D), 0.57 (Burkert), 0.60 (PI), versus 0.79 (NFW), 1.38 (MOND-simple) and 1.66 (MOND-standard). The three cored models (2D, Burkert, PI) have similar goodness of fit, but the information criteria moderately favour the 2D model over PI (∆AIC ≃ 93) and provide only a modest preference over Burkert (∆AIC ≃ 13); the present data do not establish a decisive physical distinction among them. The discriminating observable is the shape of the transition to the flat asymptote: 1/R^2 for the 2D potential, 1/R for PI, and a peak followed by a slow decline for Burkert. We show that SPARC covers the relevant radial range only partially (23% of data points in the discrimination zone). Against MOND the result depends on the model-selection criterion, because MOND has substantially fewer global parameters. Among the models evaluated at each error-floor value, the 2D model gives the lowest total χ^2; MOND-standard is evaluated only at the reference 10% floor. We conclude that the soft-logarithmic potential is a viable, normalised member of the cored-model family, with a specific falsifiable prediction for the transition region.