Evidence‑grounded NLP systems often need to verify nested text spans sequentially, and confirming one span constrains the others. We formalize this process as Online Evidence‑Containment Prediction (OECP): each candidate span is predicted before exact verification and each query is issued at most once. Span containment forms a triangular 2‑D product order, making OECP equivalent to distinct‑query online isotonic regression. With multiple admissible targets, the worst‑case regret is near‑linear, $\widetilde{\Theta}(m_{\mathrm{eff}})$, where $m_{\mathrm{eff}}$ denotes the effective scale after endpoint‑rank compression; for a single fixed target (as in standard QA) we provide a polynomial‑time learner achieving optimal $\Theta(\log m_{\mathrm{eff}})$ regret, validated on real Natural Questions episodes. Experiments on Natural Questions show that leveraging containment yields a large deductive gain and a smaller learned gain on unresolved candidates, reproducible across two backbones and DPR hierarchies. We introduce Expected Search‑space Reduction (ESR) to turn probabilities into decisions, localizing evidence with fewer verifier calls on SciFact, ERASER, and DPR hierarchies. Under call‑budget constraints ESR outperforms four recent external selectors on DPR hierarchies and raises fixed‑reader F1 beyond learned and generator‑greedy scheduling. Review