Proposition: Calibration agreement and nonuniqueness

The dictionaries agree on the admitted events by evaluation: $T(\kappa (k))=T_k$, carrier rods equal their assigned coordinates, and scheduled ancestry lies in the output metric past.

At one fixed readout event, exact event-time calibration with distinct $T_k$ permits at most one supported outcome. A nontrivial multi-outcome reading therefore uses the separate history map rather than identifying every code with the time of that fixed event.

The instrument does not uniquely determine any of these dictionaries.

Proof. The first assertions are the definitions and causal transitivity. For fixed-event calibration, every supported code must satisfy $T_k=T(e)$; distinct readings allow at most one.

For nonuniqueness, keep all matrices and preparations unchanged and permute the history assignments of two codes. The clock channel is unchanged while its interpreted history events differ. Likewise the same finite matrices can be installed at different causally permitted regular ports. A continuation depending on the dictionary must be separately specified for either choice.