Finite evaluation is not an endpoint

For each fixed $t$, a finite proxy program may use the specified constant $\hat{U}(t)$. The acyclic program terminates by Theorem thm:adequacy. This says nothing by itself about $t\to \infty$, uniform regulator control, disappearance of a residual, or existence of an outgoing receiver.

An outgoing scattering representation may define the target of a later finite receiver approximation. It need not be a terminal configuration of the finite syntax.