Proposition: Record control and constant contact coefficients

Classical control that chooses the evaluation label $\delta (k)$ does not enlarge the frozen contact class, provided the setting and contact coefficient vector are fixed across labels. Allowing an independently selected $\theta (k)$ changes the response contract.

Proof. For fixed $\theta$, the evaluated correction is

These are evaluations of one allowed constant-coefficient combination. By contrast,

uses row-dependent coefficients and need not be the restriction of any single combination on $\mathcal{X}$. The original quantifier has been replaced.