Asymptotic Evaluation of Benchmark Screening Functionals in the Scalar Temporal Field Ontology

We analyze the asymptotic behavior of benchmark nonlocal screening functionals in the Scalar Temporal Field Ontology (STFO). Building on the previously derived semi-analytic formulation, we examine the limits of strong and weak screening corresponding to large and small values of the dimensionless parameter x = μa. In both regimes, the screening functional simplifies, allowing a qualitative determination of the ordering of screening strength across the 1s, 2s, and 2p bound states. We find that both asymptotic limits support the hierarchy 1s > 2s > 2p. The intermediate regime remains the key domain for full quantitative evaluation of the screening functional and provides the primary test of the STFO framework.