A Cosmological Formula for the MOND Acceleration Scale Tested Against 3,389 SPARC Rotation-Curve Measurements

The MOND acceleration scale a0 ~ 1.2e-10 m/s2 has been a free parameter for 42 years. Previous cosmological formulas for a0 have residuals of 9-446%. We report the empirical relation a0 = cH0(Omega_Lambda/Omega_m)^(1/6)/(2pi), which predicts 1.203e-10 from DESI DR2 parameters. Tested against 3,389 data points from 175 SPARC galaxies, this formula is decisively better than the previous best cosmological formula cH0/(2pi) (delta-chi2 = 4,895) and statistically indistinguishable from the canonical empirical value a0 = 1.20 (delta-chi2 = 38, or 0.04% of total chi2, sign dependent on mass-to-light ratio). Both the 2pi and the 1/6 exponent are free parameters. The formula predicts a0 increases by 74% at z = 2, distinguishable from constant MOND (0%), LCDM simulations (160%), and Verlinde-type scaling (200%), testable with SKA and JWST.