Self-Consistent Two-Mode Solutions and Screening Effects in the Scalar Temporal Field Ontology

This work presents an explicit two-mode solution within the Scalar Temporal Field Ontology (STFO), extending the previously developed many-mode framework into a concrete computational regime. Using a controlled approximation in which bound modes are modeled by hydrogen-like profiles, we compute the effective temporal density, derive the induced screening potential, and determine the resulting shift in the effective coupling. We show that the presence of a second occupied mode reduces the effective attractive strength of the temporal field, leading to a decrease in binding energy and an increase in characteristic spatial scale. These results provide an explicit quantitative illustration of screening and occupation-dependent dynamics within the STFO framework. The analysis demonstrates that multi-mode interactions produce measurable modifications to bound-state structure, providing a foundation for further development of atomic and molecular predictions in scalar temporal field models.