{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BPKHHTEGQWIUBF6YMBSGGK4IZZ","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":"7a9b5748caa319825e3eb066fa6a3aec60ea5ecb3400da556734ad724799bd4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-20T10:17:45Z","title_canon_sha256":"c342979c15632e715e6b3064213ea3ceb6e6544da8c129ca580b4cf95bec0a00"},"schema_version":"1.0","source":{"id":"1503.06034","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06034","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06034v2","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06034","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"pith_short_12","alias_value":"BPKHHTEGQWIU","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BPKHHTEGQWIUBF6Y","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BPKHHTEG","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:6db2e8816248d029c6d724506fdb35491fc3c81c2ebf86ffd488c4492785996b","target":"graph","created_at":"2026-05-18T01:13:00Z","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 matrix Fej\\'er-Riesz theorem characterizes positive semidefinite matrix polynomials on the real line $\\mathbb{R}$. We extend a characterization to arbitrary closed semialgebraic sets $K\\subseteq \\mathbb{R}$ by the use of matrix preorderings from real algebraic geometry. In the compact case a denominator-free characterization exists, while in the non-compact case there are counterexamples. However, there is a weaker characterization with denominators in the non-compact case. At the end we extend the results to algebraic curves.","authors_text":"Alja\\v{z} Zalar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-20T10:17:45Z","title":"Matrix Fej\\'er-Riesz theorem with gaps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06034","kind":"arxiv","version":2},"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":"sha256:4bf5334d80ce8e689a9a3e7ba083a115c5119b6d93ded365b48d6aa0830380cb","target":"record","created_at":"2026-05-18T01:13:00Z","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":"7a9b5748caa319825e3eb066fa6a3aec60ea5ecb3400da556734ad724799bd4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-20T10:17:45Z","title_canon_sha256":"c342979c15632e715e6b3064213ea3ceb6e6544da8c129ca580b4cf95bec0a00"},"schema_version":"1.0","source":{"id":"1503.06034","kind":"arxiv","version":2}},"canonical_sha256":"0bd473cc8685914097d86064632b88ce51eaa05ef21cfafcedf0a67ce6b74ca8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0bd473cc8685914097d86064632b88ce51eaa05ef21cfafcedf0a67ce6b74ca8","first_computed_at":"2026-05-18T01:13:00.410476Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:00.410476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6k5jNGaXxE6Kk34vkeYuUHwVZNC4al1gRkyMQVgZOrr8P31lyD9j20JeCvnBsRQlervtJR3fBzkUdTam0gAcAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:00.410828Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.06034","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4bf5334d80ce8e689a9a3e7ba083a115c5119b6d93ded365b48d6aa0830380cb","sha256:6db2e8816248d029c6d724506fdb35491fc3c81c2ebf86ffd488c4492785996b"],"state_sha256":"25415a34e2076697b76aaabc111b1cac9468e6145c0dc6320baee5df9c57ebeb"}