Proposition: Copy-certified screening is a hitting-set condition

For a deleted set $C\subseteq Q$, the perfect-copy certificate screens every split pair exactly when

Thus minimum copy-certified screening sets are minimum hitting sets of the hypergraph. This equivalence concerns the copy certificate, not every possible reason for a reduced cross operator to vanish.

Proof. The intersection condition says precisely that each pair has a deleted perfect member of a differing class. Apply Proposition prop:screening. If the intersection condition fails, that particular copy certificate does not screen the unhit pair, although residual distinguishability may still do so.