Design Criteria for the Radial Acceleration Relation in Kinetic Completions of RCD

We derive the analytic conditions that any kinetic completion K(X) of RCD must satisfy to reproduce the observed radial acceleration relation (RAR) with the correct scale a_0, slope, and scatter. These design criteria connect the asymptotic behavior of K(X) at large X to the deep-MOND slope, the transition sharpness to the RAR scatter (~0.13 dex), and the normalization to the population-level knee. The criteria provide a constructive path for engineering K(X) functions beyond B' and B'' that satisfy galactic, solar-system, and cosmological constraints simultaneously.