Assumption: Declared flat-space improvement data

Independently supply:

1. Hermitian field distributions $T_{\mu \nu }=T_{\nu \mu }$, $V_{\mu }$, and a Hermitian scalar $L$, with their specified actions on $\mathcal{E}$;

2. the distributional identities

   $${\partial }^{\mu }{T}_{\mu \nu }=0,T^{\mu }{}_{\mu }={\partial }^{\mu }{V}_{\mu }=\square L;$$

3. whenever physical-net conclusions are sought, the necessary mixed products, locality identities on $\mathcal{E}$, and compatible closed affiliated realizations of the smears involved.

When scaling grades are used, $T,V,L$ are declared to have grades $4,3,2$, respectively.