{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:4YQSEVTOPJGFCJLDCETFO4XNT6","short_pith_number":"pith:4YQSEVTO","canonical_record":{"source":{"id":"1411.2268","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-11-09T19:14:57Z","cross_cats_sorted":[],"title_canon_sha256":"3b7aad9352fbe455f21fca0aa00baeb17389540ffbd6ba5df32c51c7b3493e42","abstract_canon_sha256":"f39e4598359e6e2c304ecb3ac2b36ff40857e326d6e06904faa37ea3dd7957d3"},"schema_version":"1.0"},"canonical_sha256":"e62122566e7a4c51256311265772ed9fbc55b4ce50ce3f9e0108e8c12c32b70b","source":{"kind":"arxiv","id":"1411.2268","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2268","created_at":"2026-05-18T02:38:07Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2268v1","created_at":"2026-05-18T02:38:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2268","created_at":"2026-05-18T02:38:07Z"},{"alias_kind":"pith_short_12","alias_value":"4YQSEVTOPJGF","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4YQSEVTOPJGFCJLD","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4YQSEVTO","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:4YQSEVTOPJGFCJLDCETFO4XNT6","target":"record","payload":{"canonical_record":{"source":{"id":"1411.2268","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-11-09T19:14:57Z","cross_cats_sorted":[],"title_canon_sha256":"3b7aad9352fbe455f21fca0aa00baeb17389540ffbd6ba5df32c51c7b3493e42","abstract_canon_sha256":"f39e4598359e6e2c304ecb3ac2b36ff40857e326d6e06904faa37ea3dd7957d3"},"schema_version":"1.0"},"canonical_sha256":"e62122566e7a4c51256311265772ed9fbc55b4ce50ce3f9e0108e8c12c32b70b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:07.985888Z","signature_b64":"yyQc7+fwyJcZTbUlU2wB5769k10VB+WQ5B3zEpzrjrW37oIVOb3ZuofswEJn0Wr/ZMQJ7nP46cIIWqps2nvzDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e62122566e7a4c51256311265772ed9fbc55b4ce50ce3f9e0108e8c12c32b70b","last_reissued_at":"2026-05-18T02:38:07.985214Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:07.985214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.2268","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:38:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8cGUqEbkK5vlbZz3PIb1xvYy4NeIxu0WmtkbBUhTxOVfB11Brwkvk2MucdccLxygGygtZvPNvY/0AE6EUY27Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:29:14.016696Z"},"content_sha256":"a2552ebaf5d5f21502f2785ad9fad2ee89a256d32f3c7e25dfa1b481059ee58d","schema_version":"1.0","event_id":"sha256:a2552ebaf5d5f21502f2785ad9fad2ee89a256d32f3c7e25dfa1b481059ee58d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:4YQSEVTOPJGFCJLDCETFO4XNT6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Matrix Pearson equations satisfied by Koornwinder weights in two variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Francisco Marcell\\'an, Miguel A. Pi\\~nar, Misael E. Marriaga, Teresa E. P\\'erez","submitted_at":"2014-11-09T19:14:57Z","abstract_excerpt":"We consider Koornwinder's method for constructing orthogonal polynomials in two variables from orthogonal polynomials in one variable. If semiclassical orthogonal polynomials in one variable are used, then Koornwinder's construction generates semiclassical orthogonal polynomials in two variables. We consider two methods for deducing matrix Pearson equations for weight functions associated with these polynomials, and consequently, we deduce the second order linear partial differential operators for classical Koornwinder polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2268","kind":"arxiv","version":1},"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":"2026-05-18T02:38:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zUwNLLSgbBCo3gj0ji0SSO5JwmCdNSIG36Zx8ujWn/jX89Df0pu7gy+hhTLlMrLoiZUoWY3OY5jQTxuA92x7AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:29:14.017354Z"},"content_sha256":"dd8a20b00b3251e9c1be0ec97c4ff37ced874039bc50c73e7b9eed3424d4f434","schema_version":"1.0","event_id":"sha256:dd8a20b00b3251e9c1be0ec97c4ff37ced874039bc50c73e7b9eed3424d4f434"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4YQSEVTOPJGFCJLDCETFO4XNT6/bundle.json","state_url":"https://pith.science/pith/4YQSEVTOPJGFCJLDCETFO4XNT6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4YQSEVTOPJGFCJLDCETFO4XNT6/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":"2026-05-31T02:29:14Z","links":{"resolver":"https://pith.science/pith/4YQSEVTOPJGFCJLDCETFO4XNT6","bundle":"https://pith.science/pith/4YQSEVTOPJGFCJLDCETFO4XNT6/bundle.json","state":"https://pith.science/pith/4YQSEVTOPJGFCJLDCETFO4XNT6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4YQSEVTOPJGFCJLDCETFO4XNT6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4YQSEVTOPJGFCJLDCETFO4XNT6","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":"f39e4598359e6e2c304ecb3ac2b36ff40857e326d6e06904faa37ea3dd7957d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-11-09T19:14:57Z","title_canon_sha256":"3b7aad9352fbe455f21fca0aa00baeb17389540ffbd6ba5df32c51c7b3493e42"},"schema_version":"1.0","source":{"id":"1411.2268","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2268","created_at":"2026-05-18T02:38:07Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2268v1","created_at":"2026-05-18T02:38:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2268","created_at":"2026-05-18T02:38:07Z"},{"alias_kind":"pith_short_12","alias_value":"4YQSEVTOPJGF","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4YQSEVTOPJGFCJLD","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4YQSEVTO","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:dd8a20b00b3251e9c1be0ec97c4ff37ced874039bc50c73e7b9eed3424d4f434","target":"graph","created_at":"2026-05-18T02:38:07Z","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":"We consider Koornwinder's method for constructing orthogonal polynomials in two variables from orthogonal polynomials in one variable. If semiclassical orthogonal polynomials in one variable are used, then Koornwinder's construction generates semiclassical orthogonal polynomials in two variables. We consider two methods for deducing matrix Pearson equations for weight functions associated with these polynomials, and consequently, we deduce the second order linear partial differential operators for classical Koornwinder polynomials.","authors_text":"Francisco Marcell\\'an, Miguel A. Pi\\~nar, Misael E. Marriaga, Teresa E. P\\'erez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-11-09T19:14:57Z","title":"Matrix Pearson equations satisfied by Koornwinder weights in two variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2268","kind":"arxiv","version":1},"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:a2552ebaf5d5f21502f2785ad9fad2ee89a256d32f3c7e25dfa1b481059ee58d","target":"record","created_at":"2026-05-18T02:38:07Z","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":"f39e4598359e6e2c304ecb3ac2b36ff40857e326d6e06904faa37ea3dd7957d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-11-09T19:14:57Z","title_canon_sha256":"3b7aad9352fbe455f21fca0aa00baeb17389540ffbd6ba5df32c51c7b3493e42"},"schema_version":"1.0","source":{"id":"1411.2268","kind":"arxiv","version":1}},"canonical_sha256":"e62122566e7a4c51256311265772ed9fbc55b4ce50ce3f9e0108e8c12c32b70b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e62122566e7a4c51256311265772ed9fbc55b4ce50ce3f9e0108e8c12c32b70b","first_computed_at":"2026-05-18T02:38:07.985214Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:07.985214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yyQc7+fwyJcZTbUlU2wB5769k10VB+WQ5B3zEpzrjrW37oIVOb3ZuofswEJn0Wr/ZMQJ7nP46cIIWqps2nvzDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:07.985888Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.2268","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2552ebaf5d5f21502f2785ad9fad2ee89a256d32f3c7e25dfa1b481059ee58d","sha256:dd8a20b00b3251e9c1be0ec97c4ff37ced874039bc50c73e7b9eed3424d4f434"],"state_sha256":"096a37a657be18aa5e170f1b856dba369e0fbdbba668ca807b10d2ff79d3cc7a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8OZaQXoLMx231YYE6IojOb11eOPwp3VZ8SFpBS2/w62KGozLNlEZYMWNq/W6DDVV2JV2kpe6Jt8SgMdhvcNFCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T02:29:14.020698Z","bundle_sha256":"39d21d7527bf14c80b394ae4fccda612cc668e95ae89bb42b27e29ea08ecc6d7"}}