{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:FHXKIF5B3U5NSREPIVXTP2UPGG","short_pith_number":"pith:FHXKIF5B","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"},"canonical_sha256":"29eea417a1dd3ad9448f456f37ea8f31a2b9d5cd0c1c14ab403a87e5ee5282ac","source":{"kind":"arxiv","id":"1409.0570","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0570","created_at":"2026-05-18T01:08:45Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0570v4","created_at":"2026-05-18T01:08:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0570","created_at":"2026-05-18T01:08:45Z"},{"alias_kind":"pith_short_12","alias_value":"FHXKIF5B3U5N","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FHXKIF5B3U5NSREP","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FHXKIF5B","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:FHXKIF5B3U5NSREPIVXTP2UPGG","target":"record","payload":{"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"},"canonical_sha256":"29eea417a1dd3ad9448f456f37ea8f31a2b9d5cd0c1c14ab403a87e5ee5282ac","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"},"source_kind":"arxiv","source_id":"1409.0570","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:08:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KWoZ5l1NMkeLF1/8vBQqQOTebgdvjlfx5vLFe6/jeh15to1BcsRWzBP89q+MA72lRY+jNnJ2gJZykYZeHCyLBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T11:18:01.123877Z"},"content_sha256":"dfe47af6d5845a3e2cff4dc8f0fcb053d379e1ff23bd3b30c8320eb692689193","schema_version":"1.0","event_id":"sha256:dfe47af6d5845a3e2cff4dc8f0fcb053d379e1ff23bd3b30c8320eb692689193"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:FHXKIF5B3U5NSREPIVXTP2UPGG","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:08:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BJGU3em9awNargvMQlXxgr7xBrRZUdKCd4kILx4iTDdBPasPF0JjSeMscS8STmTnbu1zuCY8Jc9y+YOqIg6PBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T11:18:01.124610Z"},"content_sha256":"6afbf79b7087f36fb8c4fe9529e6cad1fe79f1ec0f28d011a11d16b290940f0b","schema_version":"1.0","event_id":"sha256:6afbf79b7087f36fb8c4fe9529e6cad1fe79f1ec0f28d011a11d16b290940f0b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FHXKIF5B3U5NSREPIVXTP2UPGG/bundle.json","state_url":"https://pith.science/pith/FHXKIF5B3U5NSREPIVXTP2UPGG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FHXKIF5B3U5NSREPIVXTP2UPGG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-11T11:18:01Z","links":{"resolver":"https://pith.science/pith/FHXKIF5B3U5NSREPIVXTP2UPGG","bundle":"https://pith.science/pith/FHXKIF5B3U5NSREPIVXTP2UPGG/bundle.json","state":"https://pith.science/pith/FHXKIF5B3U5NSREPIVXTP2UPGG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FHXKIF5B3U5NSREPIVXTP2UPGG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FHXKIF5B3U5NSREPIVXTP2UPGG","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":"bb2082052133671c386ed27b781baa59bfab77b704f20b3ec2bbf5436f3ae80a","cross_cats_sorted":["math-ph","math.MP","math.RA","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-09-01T21:42:24Z","title_canon_sha256":"4511a7c1d973c6daa54b5f629fe028930c68261b5f536bf9fb6953cba5287b4d"},"schema_version":"1.0","source":{"id":"1409.0570","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0570","created_at":"2026-05-18T01:08:45Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0570v4","created_at":"2026-05-18T01:08:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0570","created_at":"2026-05-18T01:08:45Z"},{"alias_kind":"pith_short_12","alias_value":"FHXKIF5B3U5N","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FHXKIF5B3U5NSREP","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FHXKIF5B","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:6afbf79b7087f36fb8c4fe9529e6cad1fe79f1ec0f28d011a11d16b290940f0b","target":"graph","created_at":"2026-05-18T01:08:45Z","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":"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","authors_text":"Gerardo Ariznabarreta, Manuel Ma\\~nas","cross_cats":["math-ph","math.MP","math.RA","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-09-01T21:42:24Z","title":"Multivariate orthogonal polynomial and integrable systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0570","kind":"arxiv","version":4},"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:dfe47af6d5845a3e2cff4dc8f0fcb053d379e1ff23bd3b30c8320eb692689193","target":"record","created_at":"2026-05-18T01:08:45Z","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":"bb2082052133671c386ed27b781baa59bfab77b704f20b3ec2bbf5436f3ae80a","cross_cats_sorted":["math-ph","math.MP","math.RA","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-09-01T21:42:24Z","title_canon_sha256":"4511a7c1d973c6daa54b5f629fe028930c68261b5f536bf9fb6953cba5287b4d"},"schema_version":"1.0","source":{"id":"1409.0570","kind":"arxiv","version":4}},"canonical_sha256":"29eea417a1dd3ad9448f456f37ea8f31a2b9d5cd0c1c14ab403a87e5ee5282ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29eea417a1dd3ad9448f456f37ea8f31a2b9d5cd0c1c14ab403a87e5ee5282ac","first_computed_at":"2026-05-18T01:08:45.336309Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:45.336309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jCSagcspuKgV5BCypi8O1AfI6qjiVIgSqiTmcsjS1QvWx4hqRV9yqWNPcQLHgmQDNk6j8bN5i3mUFnU4x/sSAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:45.336759Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.0570","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfe47af6d5845a3e2cff4dc8f0fcb053d379e1ff23bd3b30c8320eb692689193","sha256:6afbf79b7087f36fb8c4fe9529e6cad1fe79f1ec0f28d011a11d16b290940f0b"],"state_sha256":"c584b15f28bd911e254156705ba88502d5b3756473aa5a7fdc7fc79b305e153c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+BgwF93pQbLJY/N8iCfhN/kmkGtSC2iV4s92RkLLX+qyc5LEIoxKeGb9kLCEeHbzgWM20layrwlga7pe+iRWBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T11:18:01.128300Z","bundle_sha256":"354e769fdbdf3891c54e1ed361d6ea6bc8bb28f09f9a31326a5af9e6abff4e6f"}}