{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:D2UUFGWSZ32BQJZP3RFJIYWYTA","short_pith_number":"pith:D2UUFGWS","schema_version":"1.0","canonical_sha256":"1ea9429ad2cef418272fdc4a9462d89819b9ab8a2cda406f332ee4fa6e35b8bc","source":{"kind":"arxiv","id":"1811.06005","version":4},"attestation_state":"computed","paper":{"title":"Factoring Non-negative Operator Valued Trigonometric Polynomials in Two Variables","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Michael A. Dritschel","submitted_at":"2018-11-14T19:05:20Z","abstract_excerpt":"It is shown using Schur complement techniques that on finite dimensional Hilbert spaces, a non-negative operator valued trigonometric polynomial in two variables with degree $(d_1,d_2)$ can be written as a finite sum of hermitian squares of at most $2d_2$ analytic polynomials."},"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":"1811.06005","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.FA","submitted_at":"2018-11-14T19:05:20Z","cross_cats_sorted":[],"title_canon_sha256":"4752726da46ced3b23c7bc36cc93416cbe6885f169174fbd977fbace787ec580","abstract_canon_sha256":"b90ab505ab0121da0d5369c5d23b2605eddb897cf225432675c8c2b2559a83a6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:53:35.971814Z","signature_b64":"EdzeZaggpjPHrAnXNs82pTcxut0lOi5g7QmRiOr1UbtQVfjwgiBHp38sYK6EoD4YbvmZXtvBIyye18IbJPZsBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ea9429ad2cef418272fdc4a9462d89819b9ab8a2cda406f332ee4fa6e35b8bc","last_reissued_at":"2026-07-05T08:53:35.971363Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:53:35.971363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Factoring Non-negative Operator Valued Trigonometric Polynomials in Two Variables","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Michael A. Dritschel","submitted_at":"2018-11-14T19:05:20Z","abstract_excerpt":"It is shown using Schur complement techniques that on finite dimensional Hilbert spaces, a non-negative operator valued trigonometric polynomial in two variables with degree $(d_1,d_2)$ can be written as a finite sum of hermitian squares of at most $2d_2$ analytic polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.06005","kind":"arxiv","version":4},"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/1811.06005/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1811.06005","created_at":"2026-07-05T08:53:35.971425+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.06005v4","created_at":"2026-07-05T08:53:35.971425+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.06005","created_at":"2026-07-05T08:53:35.971425+00:00"},{"alias_kind":"pith_short_12","alias_value":"D2UUFGWSZ32B","created_at":"2026-07-05T08:53:35.971425+00:00"},{"alias_kind":"pith_short_16","alias_value":"D2UUFGWSZ32BQJZP","created_at":"2026-07-05T08:53:35.971425+00:00"},{"alias_kind":"pith_short_8","alias_value":"D2UUFGWS","created_at":"2026-07-05T08:53:35.971425+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/D2UUFGWSZ32BQJZP3RFJIYWYTA","json":"https://pith.science/pith/D2UUFGWSZ32BQJZP3RFJIYWYTA.json","graph_json":"https://pith.science/api/pith-number/D2UUFGWSZ32BQJZP3RFJIYWYTA/graph.json","events_json":"https://pith.science/api/pith-number/D2UUFGWSZ32BQJZP3RFJIYWYTA/events.json","paper":"https://pith.science/paper/D2UUFGWS"},"agent_actions":{"view_html":"https://pith.science/pith/D2UUFGWSZ32BQJZP3RFJIYWYTA","download_json":"https://pith.science/pith/D2UUFGWSZ32BQJZP3RFJIYWYTA.json","view_paper":"https://pith.science/paper/D2UUFGWS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.06005&json=true","fetch_graph":"https://pith.science/api/pith-number/D2UUFGWSZ32BQJZP3RFJIYWYTA/graph.json","fetch_events":"https://pith.science/api/pith-number/D2UUFGWSZ32BQJZP3RFJIYWYTA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D2UUFGWSZ32BQJZP3RFJIYWYTA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D2UUFGWSZ32BQJZP3RFJIYWYTA/action/storage_attestation","attest_author":"https://pith.science/pith/D2UUFGWSZ32BQJZP3RFJIYWYTA/action/author_attestation","sign_citation":"https://pith.science/pith/D2UUFGWSZ32BQJZP3RFJIYWYTA/action/citation_signature","submit_replication":"https://pith.science/pith/D2UUFGWSZ32BQJZP3RFJIYWYTA/action/replication_record"}},"created_at":"2026-07-05T08:53:35.971425+00:00","updated_at":"2026-07-05T08:53:35.971425+00:00"}