A common finite response carrier

Let

The external field acts as $I_g\otimes \hat{\varphi }(q)$; the mixed coefficient acts as in (eq:mixed); and the cubic form is extended by the identity oscillator form.

Choose an isometry

whose image is spanned by finitely many orthonormal vectors of ${\mathcal{D}}_{\mathrm{mix}}$. For each setting $k$, choose one of the symmetric response forms proved above and define its finite matrix

For operator settings this is the usual compression. For the cubic setting it is a form compression, requiring no unproved unregulated operator.

The finite matrix is not an invariant subspace realization of the full response operator. In particular,

is not identified with a compression of a continuum unitary. The compressed matrix is the operational observable declared here.

Choose a common $B>0$ with $B>{\max }_k\Vert A_k\Vert$, and define