Proposition: Permitted changes have separate meanings

The following operations do not identify quantum factors with geometric coordinates:

1. a clock basis change replaces $P_k$ and generally changes the instrument, not the coordinate $T$;

2. a coupling before readout replaces ${\mathcal{M}}_C$ by ${\mathcal{M}}_C\circ {\mathrm{Ad}}_U$, not by a metric back-reaction law;

3. code-selected continuation chooses the declared response setting or finite matrix;

4. fresh clock allocation creates new names and a new reading event, not a continuum clock or a returned old clock.

Proof. The first two assertions follow by substituting the changed projectors or precomposition into the Kraus formula. The latter two change the instruction tree and its data. None changes the supplied spacetime or establishes a new field equation.