What makes the present class bounded

The production envelope leaves the unpropagated parts of a rule unspecified. We make one precise choice: those parts are parameter-local, and the only new propagation is at most one application of ${G_{\mathrm{gr}}}^{\mathrm{R}}=-\mathcal{P}{E}_0^{\mathrm{R}}$.

This is an explicit restriction defining the tested class. It is made before the witness is used in a calculation. The theorem below does not exclude arbitrary nonlocal transformations of Cauchy data outside this realization.