Two necessary corrections to the proposed route

First, proving that an operation fixes exterior observables does not, without an additional argument, place a pulled-back observable in a chosen regional algebra. It may only place it in a commutant. Our implementation theorem proves membership by multiplication inside a declared larger regional algebra.

Second, specifying the restriction of a global device to its own regional algebra need not specify its action on observables extending across the boundary. We give an explicit gauge example in Section sec:deviceextension. Matched replacements therefore retain complete device actions or specified realizations, not merely their regional restrictions.

These corrections are needed to turn the plan into a valid tensor-free causal-network argument.