{"paper":{"title":"Degree Bounds for Positivstellens\\\"atze of general semialgebraic sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Juan C. Vera, Luis F. Zuluaga, Olga Heijmans-Kuryatnikova","submitted_at":"2026-05-15T10:19:31Z","abstract_excerpt":"Let $p_{\\min}$ denote the minimum of a polynomial $p$ over a (general) compact semialgebraic set $S \\subseteq \\mathbb{R}^n$. A standard way to approximate $p_{\\min}$ is via hierarchies built from Positivstellens\\\"atze, which certify nonnegativity of polynomials on $S$ using sums of squares or other classes of globally nonnegative polynomials. As the degree of the certificate grows, the values generated by these hierarchies converge asymptotically to $p_{\\min}$. A natural question is, then, to determine explicit bounds on the certificate's degree needed to obtain a prescribed $\\varepsilon$-appr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.15821","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15821/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:48.724641Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:21:55.872501Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"84c82d9c5c3c2e822ecc3366ef7485601c39530fba0aa49908f4745a0a35407c"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}