Feedback compiled into a local hybrid network

Let a finite site set $X$ carry local algebras

The local classical variables include all controller records read at that site. The global algebra is ${⨂}_{x\in X}{\mathfrak{X}}_x$, equivalently a direct sum over classical configurations.

At instruction $t$, suppose a fixed envelope $R_t\subseteq X$ contains every quantum and classical register read or written by that instruction, and the complete instruction is a channel

Within $R_t$, the channel may select different operations from its classical controller blocks. The envelope must nevertheless include those controls.

For $Y\subseteq X$, define backwards