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We prove that the Hausdorff approximation error satisfies $\\delta_H(P_k, A) = O(k^{2/(1-q)})$ for \\emph{every} $p \\in (1,\\infty)$, where $q$ is the n"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that the Hausdorff approximation error satisfies δ_H(P_k, A) = O(k^{2/(1-q)}) for every p ∈ (1,∞)","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The technique assumes the ambient space is R^q with its standard inner product structure, which enables the quadratic bound on hyperplane distance; this may not extend directly to non-Euclidean settings or infinite dimensions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The Hausdorff error for ℓ_p-norm based outer approximations in convex vector optimization converges at the optimal rate O(k^{2/(1-q)}) independently of p.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The Hausdorff approximation error converges at rate O(k^{2/(1-q)}) for every ℓ_p norm in convex vector optimization.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"9801f7ba844be2fded2bf6206c34636fd78689b724b006ae543948207c4e4e3a"},"source":{"id":"2605.14324","kind":"arxiv","version":1},"verdict":{"id":"29928b0c-8c2c-4561-87af-e2f5167777e6","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:34:52.741938Z","strongest_claim":"We prove that the Hausdorff approximation error satisfies δ_H(P_k, A) = O(k^{2/(1-q)}) for every p ∈ (1,∞)","one_line_summary":"The Hausdorff error for ℓ_p-norm based outer approximations in convex vector optimization converges at the optimal rate O(k^{2/(1-q)}) independently of p.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The technique assumes the ambient space is R^q with its standard inner product structure, which enables the quadratic bound on hyperplane distance; 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