Same-scalar coherent displacement

For a one-particle vector $z$, let

Coherent vectors are not in the algebraic core unless $z=0$, but belong to $\mathrm{Dom}(N^k)$ for every $k$. For Schwartz $z$, their number truncations lie in ${\mathcal{D}}_{\mathrm{mix}}$ and converge in number-graph norms.