Proposition: Calibration limits

If a fixed readout event $e$ has distinct labels $t_k$ satisfying

at most one label has positive probability. Nontrivial multi-outcome programme or history readout therefore does not assert that all labels equal the time of one event.

The clock channel has no universal left inverse on its full input space.

Proof. Distinct labels prove the first assertion. For the second, the two clock states $(|{\tau }_0⟩\pm |{\tau }_1⟩)/\sqrt{2}$, tensored with the same payload, give identical destructive outputs. A universal left inverse could not recover both.