Deriving MOND from Complexity Binding Theory: Field Equation Solutions and Falsifiable Predictions

This paper derives Modified Newtonian Dynamics (MOND) directly from the scalar binding field of Complexity Binding Theory (CBT), without assuming MOND a priori. Solving the static field equilibrium equation yields an interpolation function that differs from standard MOND in the deep regime (x < 0. 1): CBT predicts declining outer rotation curves where MOND predicts flat curves. Testing on 22 SPARC galaxies with observed declining rotation curves confirms this prediction, with CBT outperforming MOND on all 22 galaxies (mean χ² ratio 24: 1). The theory is further validated at cosmological scales using the CLASS Boltzmann code, with the CBT-predicted dark matter density ωcdm = ωb × 2e = 0. 1216 (fixed, not fitted) matching Planck 2018 TT+TE+EE power spectra at χ²/dof = 1. 09 — comparable to ΛCDM's 1. 10 with one fewer free parameter. This is Paper III of the CBT program; Paper I established empirical success on 175 SPARC galaxies, and Paper II provided the theoretical foundations.