Proposition: Host stability

The response map, a regulator-label replacement, a change of installed evaluation table, or a proposed subtraction-scale label does not evolve $G,\mathcal{W},T$, or the supplied future relation. A regulator replacement may change the auxiliary classical prescription and its values.

Proof. The inherited host data are fixed before the field construction. Every map constructed here returns a free-algebra class or a finite operational output. No map with a new host metric as its output has been defined.