A controlled finite-compression limit

The norm and channel language are standard Watrous; the needed estimate has been proved here. The limit concerns one fixed finite catalogue. It is not a finite-dimensional one-particle space, a finite-qubit field instrument, or a continuum-field limit.

No acquisition map from an unknown scalar–metric configuration to ${\mathcal{H}}_X$ has been supplied. The returned finite word does not determine an arbitrary real coefficient exactly in one shot. Its scored mean realizes a declared finite evaluation. Local field measurements require a separately specified coupling and dynamical comparison FV.