Full Spatial Integral Evaluation of Screening in the Scalar Temporal Field Ontology

This work extends previous analyses of screening in the Scalar Temporal Field Ontology (STFO) by replacing central-density approximations with full spatial integrals over mode profiles. A mode-dependent screening functional is introduced, incorporating a short-range weighting kernel that captures nonlinear field interactions. Using hydrogen-like approximations for representative bound modes, we evaluate the resulting integrals and extract scaling behavior for 1s, 2s, and 2p modes. We show that spatial structure continues to govern screening strength when full integrals are used, with angular and radial features reducing effective contributions relative to compact modes. The results support previous semi-quantitative estimates and demonstrate that mode ordering and screening hierarchies are robust under more complete treatment. This establishes a stronger quantitative foundation for multi-mode dynamics within the STFO framework.