Proposition: Calibration and finite clock limitations

If distinct readings $t_j$ must equal a fixed event time $T_e$ on every positive-probability branch of a normalized input, there is one deterministic matching outcome. A prepared basis clock separately reads its installed word deterministically. Finite matrices cannot satisfy $[T,H]=\mathrm{i}\hslash I$ for $\hslash \ne 0$.

Proof. At most one distinct reading matches $T_e$, and probabilities sum to one. Basis readout follows from (eq:instrument). The trace of the proposed commutator would give $0=\mathrm{i}\hslash D$.