{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:7IYFJTM73OFCA2KJ5TW2RBE35Z","short_pith_number":"pith:7IYFJTM7","schema_version":"1.0","canonical_sha256":"fa3054cd9fdb8a206949eceda8849bee6e0b14a740e4776cf5a355c56d2b7ada","source":{"kind":"arxiv","id":"1409.2707","version":3},"attestation_state":"computed","paper":{"title":"Deciding positivity of multisymmetric polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Cordian Riener, Paul G\\\"orlach, Tillmann Wei{\\ss}er","submitted_at":"2014-09-09T12:18:35Z","abstract_excerpt":"The question how to certify non-negativity of a polynomial function lies at the heart of Real Algebra and also has important applications to Optimization. In this article we investigate the question of non-negativity in the context of multisymmetric polynomials. In this setting we generalize the characterization of non-negative symmetric polynomials by adapting the method of proof developed by the second author. One particular case where our results can be applied is the question of certifying that a (multi-)symmetric polynomial defines a convex function. As a direct corollary of our main resu"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1409.2707","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-09-09T12:18:35Z","cross_cats_sorted":[],"title_canon_sha256":"b9b5dadd2106735e816fd696dbca01f23f19aaec078b74adcc6f65ac6622d18f","abstract_canon_sha256":"7f4276c611adab6b82e646288322d7cecd2935356942019c44d85a3673eba638"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:19.637079Z","signature_b64":"nfCXuaiOD9op8btgPUwFHmP3sMF2gYXzG85lMTL69U7QYmRL5FDxGDTFvyWhQT/JfEJVKNSIAtocZZUwivGdCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa3054cd9fdb8a206949eceda8849bee6e0b14a740e4776cf5a355c56d2b7ada","last_reissued_at":"2026-05-18T01:26:19.636656Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:19.636656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Deciding positivity of multisymmetric polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Cordian Riener, Paul G\\\"orlach, Tillmann Wei{\\ss}er","submitted_at":"2014-09-09T12:18:35Z","abstract_excerpt":"The question how to certify non-negativity of a polynomial function lies at the heart of Real Algebra and also has important applications to Optimization. In this article we investigate the question of non-negativity in the context of multisymmetric polynomials. In this setting we generalize the characterization of non-negative symmetric polynomials by adapting the method of proof developed by the second author. One particular case where our results can be applied is the question of certifying that a (multi-)symmetric polynomial defines a convex function. As a direct corollary of our main resu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2707","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1409.2707","created_at":"2026-05-18T01:26:19.636723+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.2707v3","created_at":"2026-05-18T01:26:19.636723+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2707","created_at":"2026-05-18T01:26:19.636723+00:00"},{"alias_kind":"pith_short_12","alias_value":"7IYFJTM73OFC","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"7IYFJTM73OFCA2KJ","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"7IYFJTM7","created_at":"2026-05-18T12:28:19.803747+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7IYFJTM73OFCA2KJ5TW2RBE35Z","json":"https://pith.science/pith/7IYFJTM73OFCA2KJ5TW2RBE35Z.json","graph_json":"https://pith.science/api/pith-number/7IYFJTM73OFCA2KJ5TW2RBE35Z/graph.json","events_json":"https://pith.science/api/pith-number/7IYFJTM73OFCA2KJ5TW2RBE35Z/events.json","paper":"https://pith.science/paper/7IYFJTM7"},"agent_actions":{"view_html":"https://pith.science/pith/7IYFJTM73OFCA2KJ5TW2RBE35Z","download_json":"https://pith.science/pith/7IYFJTM73OFCA2KJ5TW2RBE35Z.json","view_paper":"https://pith.science/paper/7IYFJTM7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.2707&json=true","fetch_graph":"https://pith.science/api/pith-number/7IYFJTM73OFCA2KJ5TW2RBE35Z/graph.json","fetch_events":"https://pith.science/api/pith-number/7IYFJTM73OFCA2KJ5TW2RBE35Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7IYFJTM73OFCA2KJ5TW2RBE35Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7IYFJTM73OFCA2KJ5TW2RBE35Z/action/storage_attestation","attest_author":"https://pith.science/pith/7IYFJTM73OFCA2KJ5TW2RBE35Z/action/author_attestation","sign_citation":"https://pith.science/pith/7IYFJTM73OFCA2KJ5TW2RBE35Z/action/citation_signature","submit_replication":"https://pith.science/pith/7IYFJTM73OFCA2KJ5TW2RBE35Z/action/replication_record"}},"created_at":"2026-05-18T01:26:19.636723+00:00","updated_at":"2026-05-18T01:26:19.636723+00:00"}