Proposition: Exact agreement at a fixed event

For a readout at a fixed event $e$, suppose exact event-time calibration requires

Then at most one outcome has positive probability. A normalized exactly calibrated input exists only when one label equals $T(e)$; the corresponding outcome is deterministic.

For several fixed readout events, the same statement applies separately at each event.

Proof. Distinctness permits at most one matching label. Normalization then gives its probability one. If no label matches, normalization is impossible.