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In this paper, we determine the exact values of $ex_{_\\mathcal{OP}}(n,S_{p,q})$ for all $q\\ge p\\ge 2$, with the sole exception of $p=2$ and $q=3$; for the latter, we establi"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We determine the exact values of ex_OP(n,S_{p,q}) for all q≥p≥2, with the sole exception of p=2 and q=3; for the latter, we establish a lower bound.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The determination rests on the premise that the extremal outerplanar graphs for these forbidden subgraphs admit a uniform structural description (e.g., a cycle plus pendant trees of bounded size) that can be verified by case analysis on p and q; this structural claim is not stated in the abstract but is required for the exact formulas to 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