The encoded report is not a field observable

Thus the instrument licenses the phrase “observed encoded residual report” on its declared interface. It does not supply the stronger physical identification suggested by calling the unsmeared BV residual an observable of an interacting quantum theory.

The finite residual $A$ returned by the instrument and the mathematical master residual ${\mathcal{R}}_{\mathrm{ME}}$ are different objects despite the shared word “residual”.