Parameter Regimes and Ordering Transitions in STFO Screening

We analyze parameter regimes and ordering behavior in the Scalar Temporal Field Ontology (STFO) screening model using a benchmark semi-analytic kernel. Building on prior work deriving the response operator and Yukawa screening kernel, we study the dependence of mode-dependent screening coefficients on the dimensionless parameter x = μₑff a_τ. We find that compact modes remain the most strongly screened across the benchmark regimes studied, while the relative ordering of radial and angular modes undergoes a transition at x = 1. Specifically, the ordering f₂s > f₂p holds in the short-range regime (x > 1), while the ordering reverses for (x < 1). This establishes a regime-dependent screening structure and identifies a crossover scale in the STFO benchmark model.