Paper IV — Local Interactions and Potentials from Operational Locality DescriptionThis paper shows how local interaction terms and effective potentials arise from operational locality constraints. By analyzing admissible deformations of free ordered dynamics, we derive interaction structure without invoking classical force laws or background geometry. The results clarify why local potentials dominate physical dynamics and how interaction terms reflect operationally constrained information exchange. Keywordslocal interactions; emergent potentials; operational physics; quantum dynamics; reconstruction theory; locality