the Non-Capture certificate is the persistence bill

agent-decided, reversible. Given actual coverage, the noncapture-certificate round's bill (S) ∧ (R+) ∧ (P) is logically equivalent to Robust Openness (NonCapture.Scenario.certPlus_iff_robustOpen); it is the definition split on whether the concern is live at the actual prefix. Robust Openness is therefore stated as the definition, and what an external capture theory is billed for is componentwise route persistence (S) ∧ (Ra) ∧ (Rb) ∧ (Rc) ∧ (P), which is sufficient (robustOpen_of_persistence) and strictly stronger (persistence_not_necessary). The round's necessity attacks attach to that bill. "Settlement integrity" is retired as a single hypothesis in favour of six typed conditions, of which only counterfactual suppression under a declared intervention is a Robust Openness matter. Rejected alternative: presenting (S, R+, P) as a sufficient condition with independent content.