Null targets and a frozen-carrier obstruction

The theorem does not deny approximation on a revised operational carrier or with moving source labels whose correspondence is proved. It says that either change is substantive. It also does not obstruct a theorem restricted to a named subset of already represented null pairs.

-vacuous target declaration. A later approximation theorem must state its target set $\mathcal{T}$ and prove that it is nonempty. A claim uniform over ${{\mathcal{N}}_{\mathcal{D}}}^{\mathrm{pair}}$ could otherwise be vacuous.

For all-direction approximation, a typical coordinate target set has

Its endpoints require an operational realization or extension; (eq:generated) alone does not provide them.