Assumption: Simultaneous source-sector prescription

For this section only, let $P$ be the declared formally self-adjoint field operator and let $H_F$ be a declared Feynman fundamental solution with

The source presentation is $j=Ph$, and differential compatibility requires the time-ordered contracted $jh$ kernel to be obtained by applying $P_x$ to the contracted $hh$ kernel. The domain includes tests detecting the diagonal contact.