TheMOND InterpolationFunction from Causal Processing Resource Allocation Derivation,observational tests,and covariantformulation

Milgrom’s Modified Newtonian Dynamics (MOND, 1983) successfully predicts galaxy rotation curves, the baryonic Tully–Fisher relation, and the Radial Acceleration Relation using a single acceleration scale 𝑎0 = 1.2 ×10−10 m s−2. However, the interpolation function 𝜇(𝑥)governing the transition between the Newtonianregime(𝑔≫𝑎0)andthedeep-MONDregime(𝑔≪𝑎0)hasremainedaphenomenologicalchoice. Two functional formsare commonly used: the simple 𝜇(𝑥)=𝑥/(1 +𝑥)and the standard 𝜇(𝑥)=𝑥/√1 +𝑥2 . Neither has been derived from a physical principle. This paper derives the interpolation function from a specific physical mechanism: causal processing resource allocation. The derivation does not assume MOND; it produces MOND as a consequence. The resulting functionistested againstthemostprecise available data, andacovariant action is constructed. DISCLAIMER Generative AI was used to assist with literature screening / coding support / draft language revision. All AI-assisted outputs were independently checked by the author, and the author takes full responsibility for the final analysis and text. This is encompassing all the work that has been done and will be done. All code is under MIT licensing. All research papers are under Creative Commons License. All code, outputs and notes are included in the reproducibility bundle zip file.