8.10 What PACC does and does not promise

PACC makes exact UOCL identification the zero-risk, complete-doctrine limit. It also gives approximate categorical learning a falsifiable semantics: name the probes, answer equivalences, loss, coverage, and confidence source. It does not license a raw graph-edit distance between arbitrary presentations, turn high predictive accuracy into equivalence of categories, or convert observational queries into causal ones. Nor does it guarantee that a behaviorally accurate world is suitable for a new decision declaration.

The central research questions are now sharper. Which structural coverage conditions turn small probe risk into approximate fullness, faithfulness, or preservation of universal properties? Which categorical dimensions control infinite hypothesis classes? When do active probes reduce sample complexity without changing the world being identified? And which tangent-sensitive probe doctrines make a PACC hypothesis DIAL-ready? These questions connect statistical learning theory to the compositional obligations unique to ORACLE.