Representation and selecting properties

The rule in this specification is a parameter of the implication, not a construction supplied by the note. Properties (K2)–(K3) can make a legitimate conditional theorem; assuming them does not establish their operational origin.

A revised carrier is a separate predeclared branch. It must have a stated order, a map from $E_D$, and a proof of any claimed preservation

Definitions and certificates must then be restated on that carrier. There is no post hoc switch of carrier to obtain classification.