Gravity Theory Divergence: Newton vs MOND

We present a complete formal proof suite establishing the mathematical foundations of Modified Newtonian Dynamics (MOND) and its divergence from Newtonian gravity. The 21 verified theorems cover five interconnected domains: (I) foundational predictions showing that Newton predicts Keplerian decline while MOND predicts flat rotation curves; (II) observational consequences including the Tully-Fisher relation, radial acceleration relation, and MOND's zero-parameter predictive power; (III) MOND's cluster-scale failures and theoretical completions via Verlinde emergence and superfluid dark matter; (IV) the full interpolation framework proving boundedness and limit behaviors; and (V) the external field effect, MOND's most distinctive falsifiable prediction. All theorems are kernel-verified at Level 3 with zero axiom debt. The proofs are algebraic derivations from first principles, providing a rigorous mathematical foundation for comparing gravitational theories at galactic scales.

Keywords: MOND, Modified Newtonian Dynamics, galaxy rotation curves, dark matter, Tully-Fisher relation, radial acceleration relation, external field effect, formal verification

MSC 2020: 70F15 (Celestial mechanics), 83D05 (Relativistic gravitational theories), 85A15 (Galactic and stellar dynamics)