Quantitative Mode Ordering and Effective Coupling Hierarchy in the Scalar Temporal Field Ontology

This work investigates mode ordering within the Scalar Temporal Field Ontology (STFO) by analyzing how spatial structure influences screening and effective coupling. Building on previous results demonstrating multi-mode screening, angular dependence, and emergent shell-like organization, we compare representative bound modes with differing radial and angular structure. Using controlled hydrogen-like approximations, we examine the behavior of ground and excited modes near the origin and determine their relative contributions to screening. We show that modes with greater central density produce stronger screening, leading to reduced effective coupling and weaker binding, while modes with reduced central density experience weaker screening and retain stronger effective coupling. These effects generate a hierarchy of effective binding strength that depends on spatial structure, providing a quantitative mechanism for mode ordering within the STFO framework. In particular, degeneracy between states of equal principal number is lifted through mode-dependent screening effects.