Proposition: Fresh allocation and finite clocks

Fresh clock allocation creates a new named reading event. It does not produce a continuum limit of the contact catalogue. Moreover no finite clock admits a canonical commutator $[T_C,H_C]=i{I}_C$.

Proof. Fresh allocation extends the finite instruction tree and live-name ledger. It changes neither the field degree nor derivative bound defining $\mathcal{V}$, so it changes no catalogue entry.

For the second assertion, $\mathrm{Tr}[T_C,H_C]=0$, whereas $\mathrm{Tr}(i{I}_C)=4i\ne 0$.