Proposition: Fixed host

Replacing the ramp width, a regulator description, an evaluation-table entry, or a proposed subtraction-scale label does not evolve $G$, $\mathcal{W}$, or its geometric time axis. Such a replacement may change the auxiliary classical prescription and its values.

Proof. The host data (eq:host) are fixed before the analytical prescription. No rule constructed here returns a new host metric. The changed analytical coefficient is a different entry in the prescribed calculation or description register.