Proposition: The host is not evolved

The two maps, a regulator-description replacement, and an installed-table update do not change $G,\mathcal{W},T$, or the supplied future relation. A different regulator may change the auxiliary analytical prescription and its values.

Proof. The host components were fixed in Assumption ass:host. The constructed maps return free-field classes or finite operational outputs. No map returning a new host metric has been defined.