Regulator removal is a separate operation

The finite interface contains no declared regulated quantum family $O_{ϵ}$, state, topology, or removal theorem. Increasing a history horizon, refining a register, and removing a field regulator are not identical limits.

Even bounded numerical families need not converge: $a_n=(-1{)}^n$ is bounded and has no limit. Thus finite boundedness or acceptance, by itself, is not a regulator-removal argument. The relevant family and topology must first be defined.