The three relations

“Complete” means that retained quantum systems and classical histories are included and that equality is stable under an untouched reference. Instrument outcomes are either retained or summed according to a declared deterministic interface. Normalized postselected branches are not substituted for complete channels. Shared entanglement and conditional steering do not by themselves constitute unconditional signalling Beckman,CheungVIIJ.

Direct operational influence is a directed relation, but it is not assumed here to be transitive. If a later extraction uses its transitive closure, an acyclic restriction, or a quotient, that operation must be named. The relation being represented must then be the resulting relation, not an unannounced replacement of $R_{\inf }$.