The complete device extension and boundary compatibility

The sector-swap map is a valid abstract UCP automorphism of $M_2\oplus M_2$. It is not thereby an admissible exterior-fixing physical device. This is an explicit failure of arbitrary independent regional operation closure.

Likewise, two separately assigned snapshots on $\mathfrak{A}(\{1,2\})$ and $\mathfrak{A}(\{3\})$ cannot be restrictions of one global state if they assign different probabilities to their common projection $e_{+}$.