Semi-Analytic Comparison of Benchmark Screening Functionals in the Scalar Temporal Field Ontology

We develop a semi-analytic comparison of benchmark nonlocal screening functionals in the Scalar Temporal Field Ontology (STFO). Building on the previously defined Yukawa-type screening functional for bound-state configurations, we rewrite the screening strengths of the 1s, 2s, and 2p benchmark states in dimensionless form. This reduces the comparison problem to three explicit double integrals depending on a single dimensionless screening parameter x = μa. The resulting formulation provides the first direct framework for comparing mode-dependent screening strengths across benchmark bound states. The work establishes explicit benchmark quantities whose evaluation will determine whether the predicted hierarchy of screening strength persists quantitatively.