The Zimmerman Formula: Derivation and Testable Predictions

We derive the MOND acceleration scale from cosmological first principles: a₀ = c√(Gρc)/2 = cH₀/5.79 where 5.79 = 2√(8π/3) emerges from the Friedmann equation structure. KEY RESULTS: • 0.5% agreement with observed a₀ • Predicts H₀ = 71.5 km/s/Mpc (between Planck and SH0ES) • Predicts redshift evolution: a₀(z) = a₀(0) × E(z) • 2× better fit to JWST z > 6 data than constant a₀ • BTFR slope = 4.000 exactly from 175 SPARC galaxies FALSIFIABLE PREDICTIONS: • BTFR offset at z=2: -0.47 dex • RAR scale evolution with redshift • Mass discrepancy ratios ~3× higher at z > 6 • Growth rate +5-10% enhancement at z > 1 Code: https://github.com/carlzimmerman/zimmerman-formula