Multi-Mode Temporal Field Configurations and Emergent Shell Formation in the Scalar Temporal Field Ontology

This work investigates multi-mode configurations within the Scalar Temporal Field Ontology (STFO) and examines how structured occupation patterns emerge as the number of bound modes increases. Building on previous results demonstrating screening and angular dependence in two-mode systems, we analyze configurations with three or more modes and study the resulting interaction and energy structure. Using controlled approximations, we show that identical-mode stacking leads to increased density concentration, enhanced screening, and reduced effective coupling, making such configurations progressively less favorable as occupation increases. In contrast, configurations involving distinct modes distribute density more broadly and reduce interaction energy. These effects produce structured mode occupation driven by the competition between binding and interaction energy, providing a dynamical pathway toward shell-like organization in multi-mode temporal field systems. The results indicate that multi-mode temporal field systems naturally develop structured configurations reminiscent of atomic shell structure.