Prime-Fractal Interactions under the Universal Model Framework

The Universal Model Framework (UMF) posits that space, time, and fields emerge from discrete primebased fractal structures. We extend this perspective to relate the four fundamental forces—gravity, strong, electromagnetic, and weak interactions—plus the Higgs sector, to prime-modulated potential terms. Using explicit numerical evaluations, we find that entropic gravity and fractal strong-force potentials exhibit distance-dependent behaviors reminiscent of 1/r2 and Yukawa-like forms, respectively.Additionally, we compute a prime-based electromagnetic permittivity, a weak decay coupling, and a drastically suppressed Higgs vacuum expectation value. While further refinement is needed to reconcile these results with observational data, the overall picture supports a potential route for the UMF to unify force laws through prime-fractal adjacency and fractal scaling principles. This project was developed by Marco Gericke, with structured assistance from a large language model. All scientific concepts and conclusions were generated, verified, and interpreted by the author. Dedicated to Peter Plichta, who envisioned the code before it could be computed.