We present the first complete, quantitative application of Pressure-Mediated Gravity (PMG) to the full Spitzer Photometry and Accurate Rotation Curves (SPARC) database of 175 late-type disk galaxies. PMG is an emergent-gravity framework in which gravitational dynamics arise from pressure gradients in a superfluid vacuum governed by a logarithmic Gross-Pitaevskii Lagrangian (Jerrow 2026a, PMG v6). The interpolation function muPMG (x) = x/sqrt (1+x²) and the acceleration scale a0 = c*H0/2pi = 1. 051e-10 m/s² are both derived from first principles rather than fitted empirically. This paper derives the PMG-specific nuPMG (y) function as the exact explicit solution of the PMG v6 mu-form implicit equation mu (gₒbs/a0) *gₒbs = gbar, obtained by solving the quartic t⁴ - y²*t² - y² = 0. This function is distinct from the standard MOND simple nu (y) function by up to 21% in the transition regime and is verified numerically to machine precision. Fitting 175 SPARC galaxies with free stellar mass-to-light ratios Upsilondisk in 0. 01, 10. 0 Mₛun/Lₛun, we find: - Median chi²ₙu = 2. 57 (baseline) ; 2. 29 marginalising over distance (+/-10%) and inclination (+/-3 deg) uncertainties - 73/175 galaxies (42%) with chi²ₙu < 2 (good fits) - 115/175 galaxies (66%) with chi²ₙu < 5 (acceptable fits) - Median Upsilondisk = 0. 63 Mₛun/Lₛun (physically consistent with stellar population synthesis predictions) - BTFR slope = 4. 00 +/- 0. 03 — exact confirmation of the PMG parameter-free prediction Mbar proportional to Vflat⁴ - RAR scatter of 0. 133 dex, matching the observed total scatter An independent scan over a0 yields a kinematic measurement a0ₖin = 1. 135e-10 m/s², only 8% above the PMG-theoretical value and sitting between the PMG theory value and the empirical MOND scale (1. 2e-10 m/s²), consistent with both at <1 sigma. This is the first kinematic measurement of a0 within the PMG framework. The 60 poor-fit galaxies are predominantly irregular or kinematically disturbed systems; no systematic over-prediction of baryonic acceleration is found. Three open challenges — environmental dependence of a0, Bullet Cluster lensing, and CMB acoustic peaks — are identified as Papers IV, V, and VI of the PMG research programme. Data: SPARC database (Lelli, McGaugh & Schombert 2016, AJ 152 157). Code: Python pipeline included in this deposit.
Mohammad Jerrow (Fri,) studied this question.