A Pressure-Geometry Interpretation of Cored Galaxy Profiles: SPARC Fits and a Bounded KiDS Consistency Test

We examine whether a phenomenological galaxy halo can be represented as a boundary-conditioned pressure configuration in an effectively incompressible gravitational medium. Under an adopted quasi-cylindrical exterior reduction, Laplace equilibrium gives a radial pressure gradient proportional to 1/r and hence a flat outer circular-speed plateau. For finite-radius testing we adopt the minimal cored completion v_P²(r) = V∞² r²/(r² + r_c²), equivalent to the pseudo-isothermal profile; this completion is an ansatz, not a unique consequence of the exterior equation. Fits are obtained for 171 of 175 SPARC galaxies under a Gaussian stellar mass-to-light prior (median χ²/dof = 0.64), and the cored profile is preferred to canonical NFW in 132 of 171 galaxies, including on the subset of NFW fits free of parameter-bound contact. We then perform a bounded population-level consistency test against KiDS late-type-galaxy weak lensing. The SPARC and KiDS objects are distinct samples connected through baryonic-mass bins, and the stack uses mass weighting in place of the unavailable survey weights. For SPARC galaxies with R_last/r_c > 3, whose fitted asymptotic amplitude is reached by the data, the four binned predictions give χ²/N between 0.92 and 1.39 without refitting to the lensing points (radial bins treated as uncorrelated); without this criterion the first bin shows a tension (χ²/N = 3.54). Bins 2–4 are insensitive to the stacking weights; the first bin is not. Because R ≫ r_c at lensing radii, the comparison chiefly tests transfer of the asymptotic amplitude, not the core or the boundary mechanism. The boundary admittance law and a relativistic pressure-lensing derivation remain open.