{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7IYFJTM73OFCA2KJ5TW2RBE35Z","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7f4276c611adab6b82e646288322d7cecd2935356942019c44d85a3673eba638","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-09-09T12:18:35Z","title_canon_sha256":"b9b5dadd2106735e816fd696dbca01f23f19aaec078b74adcc6f65ac6622d18f"},"schema_version":"1.0","source":{"id":"1409.2707","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.2707","created_at":"2026-05-18T01:26:19Z"},{"alias_kind":"arxiv_version","alias_value":"1409.2707v3","created_at":"2026-05-18T01:26:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2707","created_at":"2026-05-18T01:26:19Z"},{"alias_kind":"pith_short_12","alias_value":"7IYFJTM73OFC","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7IYFJTM73OFCA2KJ","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7IYFJTM7","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:b94537041a31f40d96112b00c9d6af68e74e273d5b6ca18c927a584463c6d156","target":"graph","created_at":"2026-05-18T01:26:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Cordian Riener, Paul G\\\"orlach, Tillmann Wei{\\ss}er","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-09-09T12:18:35Z","title":"Deciding positivity of multisymmetric polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2707","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:eee038a7ba80ffab018cc42c84018382a2a4ec658846e6a584ea0ac98199d03b","target":"record","created_at":"2026-05-18T01:26:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7f4276c611adab6b82e646288322d7cecd2935356942019c44d85a3673eba638","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-09-09T12:18:35Z","title_canon_sha256":"b9b5dadd2106735e816fd696dbca01f23f19aaec078b74adcc6f65ac6622d18f"},"schema_version":"1.0","source":{"id":"1409.2707","kind":"arxiv","version":3}},"canonical_sha256":"fa3054cd9fdb8a206949eceda8849bee6e0b14a740e4776cf5a355c56d2b7ada","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa3054cd9fdb8a206949eceda8849bee6e0b14a740e4776cf5a355c56d2b7ada","first_computed_at":"2026-05-18T01:26:19.636656Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:19.636656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nfCXuaiOD9op8btgPUwFHmP3sMF2gYXzG85lMTL69U7QYmRL5FDxGDTFvyWhQT/JfEJVKNSIAtocZZUwivGdCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:19.637079Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.2707","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eee038a7ba80ffab018cc42c84018382a2a4ec658846e6a584ea0ac98199d03b","sha256:b94537041a31f40d96112b00c9d6af68e74e273d5b6ca18c927a584463c6d156"],"state_sha256":"17ed1954b72f815d14e4139c7c58c2efa703926b32435ae5190b8b8f56aa9aac"}