The Einstein comparator

For a declared smooth geometric metric $q$, a declared covariant source tensor ${\mathsf{T}}_{\mu \nu }$, constants $\Lambda$ and ${\kappa }_{\mathrm{grav}}\ne 0$, define the comparison equation

This equation is not a rule already contained in (eq:instrument). A finite conditional density matrix is not a covariant spacetime tensor until a field, observable, state, renormalization prescription, and map to tensor-valued distributions are supplied.