H-exclusion is an audit obligation

The countermodel's process, interventions, event carrier, and extraction must be identified before comparing cones. One cannot transfer the geometry of a predecessor model to a different extraction by sharing its name.

If an unchanged relevant countermodel satisfies all the proposed premises, the selection claim is false. If every named countermodel has been excluded, the selection claim is merely not refuted by those countermodels. A positive theorem still requires its representation and cone-selection argument CheungEn08A,CheungXXIIA.