Proposition: Agreement and nonuniqueness

On the declared finite events:

1. code $k$ has history time $t_k=T(\kappa (k))$;

2. named carriers have the prescribed rod coordinates;

3. scheduled ancestry is mapped into the output metric past.

None of these dictionaries is selected uniquely by ${\mathcal{M}}_C$.

Proof. The agreements are the evaluations of the three specified maps, with causal transitivity for (iii).

For nonuniqueness, keep the complete instrument and its input unchanged, but exchange the history assignments of codes $0$ and $1$. Every matrix and probability in (eq:clock) is unchanged, while the interpreted event changes. One can likewise install the same matrices at different allowed regular port positions and schedules. The instrument formula alone does not distinguish those geometric specifications.