A fixed-interface approximation theorem

This is a fixed binary-probability encoding. Small numerical changes of deterministic, mutually orthogonal output words do not in general have small diamond distance. No such false continuity claim is used.

The abstract instrument is implementable under the inherited finite unitary and destructive-readout permissions, using a calibrated basis change and, for the binary report, a finite probe rotation. An exact abstract gate permission is not a hardware synthesis or a field-to-qubit preparation certificate.