Example: One law does not determine a local instrument

The identity qubit channel and computational-basis dephasing give the same deterministic computational readout on input $|0⟩⟨0|$. They differ on $|+⟩⟨+|$, and on a Bell-entangled input. Consequently convergence of that one terminal law cannot identify a reference-preserving channel, its local slots, or its responses to replacement instruments.