{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:EQIBWTKRCXXZAHI2FO5EC6D33F","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":"6a21d238759027830e718a63e18f76aaeee04facf8e9414eb30545448482a0dc","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CA","submitted_at":"2010-04-22T13:30:57Z","title_canon_sha256":"6ad7fa431d7c86ecbac1c8802145c8bb32a3685b9485c04604e549d0b6ba54b2"},"schema_version":"1.0","source":{"id":"1004.3916","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.3916","created_at":"2026-05-18T03:07:55Z"},{"alias_kind":"arxiv_version","alias_value":"1004.3916v4","created_at":"2026-05-18T03:07:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.3916","created_at":"2026-05-18T03:07:55Z"},{"alias_kind":"pith_short_12","alias_value":"EQIBWTKRCXXZ","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"EQIBWTKRCXXZAHI2","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"EQIBWTKR","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:accf8fb7864b2913151ab0f76ac3b89fb1966cdd5aca6a83def28446c5a4b127","target":"graph","created_at":"2026-05-18T03:07:55Z","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":"Multiple orthogonality is considered in the realm of a Gauss--Borel factorization problem for a semi-infinite moment matrix. Perfect combinations of weights and a finite Borel measure are constructed in terms of M-Nikishin systems. These perfect combinations ensure that the problem of mixed multiple orthogonality has a unique solution, that can be obtained from the solution of a Gauss--Borel factorization problem for a semi-infinite matrix, which plays the role of a moment matrix. This leads to sequences of multiple orthogonal polynomials, their duals and second kind functions. It also gives t","authors_text":"Carlos \\'Alvarez-Fern\\'andez, Manuel Ma\\~nas, Ulises Fidalgo Prieto","cross_cats":["math-ph","math.MP","nlin.SI"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CA","submitted_at":"2010-04-22T13:30:57Z","title":"Multiple orthogonal polynomials of mixed type: Gauss-Borel factorization and the multi-component 2D Toda hierarchy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3916","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:d7df06aeb49a9c5191f9b7b2d1949807964191d95e020d236189cb71faaa8cfb","target":"record","created_at":"2026-05-18T03:07:55Z","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":"6a21d238759027830e718a63e18f76aaeee04facf8e9414eb30545448482a0dc","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CA","submitted_at":"2010-04-22T13:30:57Z","title_canon_sha256":"6ad7fa431d7c86ecbac1c8802145c8bb32a3685b9485c04604e549d0b6ba54b2"},"schema_version":"1.0","source":{"id":"1004.3916","kind":"arxiv","version":4}},"canonical_sha256":"24101b4d5115ef901d1a2bba41787bd975d78ce991dbb07ac03644699d8fd90b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24101b4d5115ef901d1a2bba41787bd975d78ce991dbb07ac03644699d8fd90b","first_computed_at":"2026-05-18T03:07:55.215704Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:55.215704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d+YC5Ps+7T1xGc24MmytQB/N0sDaHaNlQKDxccAWCFZQHJQAyjxwO6kUihf04nEe7Gh6y76L7SeJpmFDLRG5CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:55.216269Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.3916","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7df06aeb49a9c5191f9b7b2d1949807964191d95e020d236189cb71faaa8cfb","sha256:accf8fb7864b2913151ab0f76ac3b89fb1966cdd5aca6a83def28446c5a4b127"],"state_sha256":"418113026d40158facfdf26ba3792f2ab6e54938465d01e101189cfe32ee5427"}