Proposition: Event-time and history-label calibration

At one actual readout event $e$, exact event-time matching

with distinct ${\theta }_a$ permits at most one outcome. If $T(e)$ equals no ${\theta }_a$, no normalized preparation satisfies that matching rule.

By contrast, a multi-outcome history experiment can be read at one later fixed event and interpreted through the separate history dictionary.

Proof. There is at most one label equal to $T(e)$, and probabilities sum to one. The history interpretation makes no equality claim between every ${\theta }_a$ and the one apparatus coordinate.