Emergent MOND Dynamics from a Cosine Substrate in a Cosmological Gradient

We show that Modified Newtonian Dynamics (MOND) emerges from a scalar field with a cosine potential embedded in a cosmological background gradient. Using a controlled background-field expansion and coarse-graining over the periodic substrate, we derive an effective field equation with a gradient-dependent kinetic term. The MOND interpolating function µ(x) arises from wavefunction renormalization rather than being postulated. The characteristic acceleration scale is identified as a0 = cH0, and more generally a0(z) = cH(z), directly linking galactic dynamics to cosmology. The framework predicts anisotropic corrections and redshift evolution, providing observational tests that distinguish it from existing MOND theories.