Definition: Finite comparison package

A finite comparison package supplies:

1. finite-dimensional real normed spaces $X,Y$;

2. a fixed linear comparator $L:X\to Y$, explicitly identified with the relevant restriction or projection of ${\mathsf{E}}_{\eta }$;

3. predeclared maps $a(D)\in X$ and $s(D)\in Y$ obtained from the geometric and source rules;

4. a fixed nonzero coupling ${\kappa }_{\mathrm{cmp}}$;

5. the residual

   $$r(D)=La(D)-{\kappa }_{\mathrm{cmp}}s(D).$$

The selected matching is $r(D)=0$. The separate ansatz-feasibility question asks whether there exists some $a\in X$ with $La={\kappa }_{\mathrm{cmp}}s(D)$.