{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:FHXKIF5B3U5NSREPIVXTP2UPGG","short_pith_number":"pith:FHXKIF5B","schema_version":"1.0","canonical_sha256":"29eea417a1dd3ad9448f456f37ea8f31a2b9d5cd0c1c14ab403a87e5ee5282ac","source":{"kind":"arxiv","id":"1409.0570","version":4},"attestation_state":"computed","paper":{"title":"Multivariate orthogonal polynomial and integrable systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RA","nlin.SI"],"primary_cat":"math.CA","authors_text":"Gerardo Ariznabarreta, Manuel Ma\\~nas","submitted_at":"2014-09-01T21:42:24Z","abstract_excerpt":"Multivariate orthogonal polynomials in $D$ real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials, associated second kind functions, Jacobi type matrices and associated three term relations and also Christoffel-Darboux formul{\\ae}. The multivariate orthogonal polynomials, its second kind functions and the corresponding Christoffel-Darboux kernels are shown to be quasi-determinants --as well as Schur complements-- of bordered truncations of the moment matr"},"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":"1409.0570","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-09-01T21:42:24Z","cross_cats_sorted":["math-ph","math.MP","math.RA","nlin.SI"],"title_canon_sha256":"4511a7c1d973c6daa54b5f629fe028930c68261b5f536bf9fb6953cba5287b4d","abstract_canon_sha256":"bb2082052133671c386ed27b781baa59bfab77b704f20b3ec2bbf5436f3ae80a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:45.336759Z","signature_b64":"jCSagcspuKgV5BCypi8O1AfI6qjiVIgSqiTmcsjS1QvWx4hqRV9yqWNPcQLHgmQDNk6j8bN5i3mUFnU4x/sSAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29eea417a1dd3ad9448f456f37ea8f31a2b9d5cd0c1c14ab403a87e5ee5282ac","last_reissued_at":"2026-05-18T01:08:45.336309Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:45.336309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multivariate orthogonal polynomial and integrable systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RA","nlin.SI"],"primary_cat":"math.CA","authors_text":"Gerardo Ariznabarreta, Manuel Ma\\~nas","submitted_at":"2014-09-01T21:42:24Z","abstract_excerpt":"Multivariate orthogonal polynomials in $D$ real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials, associated second kind functions, Jacobi type matrices and associated three term relations and also Christoffel-Darboux formul{\\ae}. The multivariate orthogonal polynomials, its second kind functions and the corresponding Christoffel-Darboux kernels are shown to be quasi-determinants --as well as Schur complements-- of bordered truncations of the moment matr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0570","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":""},"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":"1409.0570","created_at":"2026-05-18T01:08:45.336383+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.0570v4","created_at":"2026-05-18T01:08:45.336383+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0570","created_at":"2026-05-18T01:08:45.336383+00:00"},{"alias_kind":"pith_short_12","alias_value":"FHXKIF5B3U5N","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"FHXKIF5B3U5NSREP","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"FHXKIF5B","created_at":"2026-05-18T12:28:28.263976+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/FHXKIF5B3U5NSREPIVXTP2UPGG","json":"https://pith.science/pith/FHXKIF5B3U5NSREPIVXTP2UPGG.json","graph_json":"https://pith.science/api/pith-number/FHXKIF5B3U5NSREPIVXTP2UPGG/graph.json","events_json":"https://pith.science/api/pith-number/FHXKIF5B3U5NSREPIVXTP2UPGG/events.json","paper":"https://pith.science/paper/FHXKIF5B"},"agent_actions":{"view_html":"https://pith.science/pith/FHXKIF5B3U5NSREPIVXTP2UPGG","download_json":"https://pith.science/pith/FHXKIF5B3U5NSREPIVXTP2UPGG.json","view_paper":"https://pith.science/paper/FHXKIF5B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.0570&json=true","fetch_graph":"https://pith.science/api/pith-number/FHXKIF5B3U5NSREPIVXTP2UPGG/graph.json","fetch_events":"https://pith.science/api/pith-number/FHXKIF5B3U5NSREPIVXTP2UPGG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FHXKIF5B3U5NSREPIVXTP2UPGG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FHXKIF5B3U5NSREPIVXTP2UPGG/action/storage_attestation","attest_author":"https://pith.science/pith/FHXKIF5B3U5NSREPIVXTP2UPGG/action/author_attestation","sign_citation":"https://pith.science/pith/FHXKIF5B3U5NSREPIVXTP2UPGG/action/citation_signature","submit_replication":"https://pith.science/pith/FHXKIF5B3U5NSREPIVXTP2UPGG/action/replication_record"}},"created_at":"2026-05-18T01:08:45.336383+00:00","updated_at":"2026-05-18T01:08:45.336383+00:00"}