2.5 Claim discipline and the theorem ladder

The program separates six layers. A claim may be presentational, concerning what evidence is revealed; predictive, concerning answers to admissible probes; categorical, concerning typed composition; developmental, concerning preservation or revision of the core doctrine; decision-theoretic, concerning the selection of actions; or causal, when intervention semantics justify that stronger reading. No implication between adjacent layers is automatic.

The book develops seven theorem families: identification, realization, invariance, comparison, repair, stability, and transport. Identification is the ORACLE semantic problem; realization, effective probing, and online repair become UOCL questions. Each family also has a tangent form once variation structure is part of the hypothesis, and a decision form once an action mechanism and observer have been declared.