Definition: Admissible first-order prescription

An admissible scalar response prescription is a real distribution ${\mathcal{R}}^{\mathsf{P}}=\hslash K^{\mathsf{P}}$ on $M$ satisfying:

1. $K^{\mathsf{P}}{|}_{M\setminus \{0\}}={\mathcal{R}}^{\circ }/\hslash$;

2. $\mathrm{supp}{K}^{\mathsf{P}}\subset J^{+}(0)$;

3. proper orthochronous Lorentz invariance; its associated joint kernel depends only on $x-y$;

4. ${\mathrm{sd}}_0(K^{\mathsf{P}})\le 4$.

The physical data and calibrations of Section sec:model are fixed. If a regulator is used, its limit must exist and satisfy these conditions. An unsuccessful regulator does not become a prescription merely by being named.