{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:UMCZVG2DGK354GIVBXROFVBN55","short_pith_number":"pith:UMCZVG2D","canonical_record":{"source":{"id":"1907.03156","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-07-06T17:06:44Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ff40be179f93607dff4c140e6505d1ac607e9c297b97d03c8a7eb320bbc1a152","abstract_canon_sha256":"f34eb9aef3bc4dd9025de39014979c81b6fe00d6db1e1c42c995b7680689d182"},"schema_version":"1.0"},"canonical_sha256":"a3059a9b4332b7de19150de2e2d42def420fea5eeb4937b395f45d265eb6f202","source":{"kind":"arxiv","id":"1907.03156","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.03156","created_at":"2026-05-17T23:41:18Z"},{"alias_kind":"arxiv_version","alias_value":"1907.03156v1","created_at":"2026-05-17T23:41:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.03156","created_at":"2026-05-17T23:41:18Z"},{"alias_kind":"pith_short_12","alias_value":"UMCZVG2DGK35","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"UMCZVG2DGK354GIV","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"UMCZVG2D","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:UMCZVG2DGK354GIVBXROFVBN55","target":"record","payload":{"canonical_record":{"source":{"id":"1907.03156","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-07-06T17:06:44Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ff40be179f93607dff4c140e6505d1ac607e9c297b97d03c8a7eb320bbc1a152","abstract_canon_sha256":"f34eb9aef3bc4dd9025de39014979c81b6fe00d6db1e1c42c995b7680689d182"},"schema_version":"1.0"},"canonical_sha256":"a3059a9b4332b7de19150de2e2d42def420fea5eeb4937b395f45d265eb6f202","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:18.785468Z","signature_b64":"wnWpPs9nAEx7Z2S4otp18oJpsrPa2SpNlO7AzxhCtSLwwQ9+/1F38yI0dOjQCVEnIZdeT8H085IcPepMvEnZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3059a9b4332b7de19150de2e2d42def420fea5eeb4937b395f45d265eb6f202","last_reissued_at":"2026-05-17T23:41:18.784930Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:18.784930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.03156","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":"2026-05-17T23:41:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O9khhE/tNIjvb52UkvrFAmZymjfmiQOVmmK+M0UA7eDWBook1v2Q6+LKw59uvZZp4Gla5jjoBVjBBM2cbvZ6Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:03:23.084825Z"},"content_sha256":"0d8e87170b90ce96833df6c6f443e6fec8cfa3ab5443df4bd76c4c2f56d79dae","schema_version":"1.0","event_id":"sha256:0d8e87170b90ce96833df6c6f443e6fec8cfa3ab5443df4bd76c4c2f56d79dae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:UMCZVG2DGK354GIVBXROFVBN55","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Riemann-Hilbert Problem for the Matrix Laguerre Biorthogonal Polynomials: Eigenvalue Problems and the Matrix Discrete Painlev\\'e IV","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"Amilcar Branquinho, Ana Foulqui\\'e Moreno, Manuel Ma\\~nas","submitted_at":"2019-07-06T17:06:44Z","abstract_excerpt":"In this paper the Riemann-Hilbert problem, with jump supported on a appropriate curve on the complex plane with a finite endpoint at the origin, is used for the study of corresponding matrix biorthogonal polynomials associated with Laguerre type matrices of weights ---which are constructed in terms of a given matrix Pearson equation. First and second order differential systems for the fundamental matrix, solution of the mentioned Riemann-Hilbert problem are derived. An explicit and general example is presented to illustrate the theoretical results of the work. Related matrix eigenvalue problem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.03156","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":"2026-05-17T23:41:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XmGoBuvs3P1lm4efEnHGqpOSp88MZUMwqCVTnCG4UzU7uDRtD9rAr/2OluADkXRDouqKzX0R4a0D0aMLxRkSBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:03:23.085225Z"},"content_sha256":"917df2ead4799cd32320d3474a353b696be79e427e3f8af3de79947f8f40e0bb","schema_version":"1.0","event_id":"sha256:917df2ead4799cd32320d3474a353b696be79e427e3f8af3de79947f8f40e0bb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UMCZVG2DGK354GIVBXROFVBN55/bundle.json","state_url":"https://pith.science/pith/UMCZVG2DGK354GIVBXROFVBN55/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UMCZVG2DGK354GIVBXROFVBN55/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":"2026-05-25T12:03:23Z","links":{"resolver":"https://pith.science/pith/UMCZVG2DGK354GIVBXROFVBN55","bundle":"https://pith.science/pith/UMCZVG2DGK354GIVBXROFVBN55/bundle.json","state":"https://pith.science/pith/UMCZVG2DGK354GIVBXROFVBN55/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UMCZVG2DGK354GIVBXROFVBN55/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:UMCZVG2DGK354GIVBXROFVBN55","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":"f34eb9aef3bc4dd9025de39014979c81b6fe00d6db1e1c42c995b7680689d182","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-07-06T17:06:44Z","title_canon_sha256":"ff40be179f93607dff4c140e6505d1ac607e9c297b97d03c8a7eb320bbc1a152"},"schema_version":"1.0","source":{"id":"1907.03156","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.03156","created_at":"2026-05-17T23:41:18Z"},{"alias_kind":"arxiv_version","alias_value":"1907.03156v1","created_at":"2026-05-17T23:41:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.03156","created_at":"2026-05-17T23:41:18Z"},{"alias_kind":"pith_short_12","alias_value":"UMCZVG2DGK35","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"UMCZVG2DGK354GIV","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"UMCZVG2D","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:917df2ead4799cd32320d3474a353b696be79e427e3f8af3de79947f8f40e0bb","target":"graph","created_at":"2026-05-17T23:41:18Z","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":"In this paper the Riemann-Hilbert problem, with jump supported on a appropriate curve on the complex plane with a finite endpoint at the origin, is used for the study of corresponding matrix biorthogonal polynomials associated with Laguerre type matrices of weights ---which are constructed in terms of a given matrix Pearson equation. First and second order differential systems for the fundamental matrix, solution of the mentioned Riemann-Hilbert problem are derived. An explicit and general example is presented to illustrate the theoretical results of the work. Related matrix eigenvalue problem","authors_text":"Amilcar Branquinho, Ana Foulqui\\'e Moreno, Manuel Ma\\~nas","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-07-06T17:06:44Z","title":"Riemann-Hilbert Problem for the Matrix Laguerre Biorthogonal Polynomials: Eigenvalue Problems and the Matrix Discrete Painlev\\'e IV"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.03156","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":"sha256:0d8e87170b90ce96833df6c6f443e6fec8cfa3ab5443df4bd76c4c2f56d79dae","target":"record","created_at":"2026-05-17T23:41:18Z","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":"f34eb9aef3bc4dd9025de39014979c81b6fe00d6db1e1c42c995b7680689d182","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-07-06T17:06:44Z","title_canon_sha256":"ff40be179f93607dff4c140e6505d1ac607e9c297b97d03c8a7eb320bbc1a152"},"schema_version":"1.0","source":{"id":"1907.03156","kind":"arxiv","version":1}},"canonical_sha256":"a3059a9b4332b7de19150de2e2d42def420fea5eeb4937b395f45d265eb6f202","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3059a9b4332b7de19150de2e2d42def420fea5eeb4937b395f45d265eb6f202","first_computed_at":"2026-05-17T23:41:18.784930Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:18.784930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wnWpPs9nAEx7Z2S4otp18oJpsrPa2SpNlO7AzxhCtSLwwQ9+/1F38yI0dOjQCVEnIZdeT8H085IcPepMvEnZDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:18.785468Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.03156","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d8e87170b90ce96833df6c6f443e6fec8cfa3ab5443df4bd76c4c2f56d79dae","sha256:917df2ead4799cd32320d3474a353b696be79e427e3f8af3de79947f8f40e0bb"],"state_sha256":"855e067edeaf47e68f8c548a31a871b3294e5defdbae8a25f23f52fbd10cc9ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D1bwjCR2FHMklzwTTV56TWzytCqHsW2cfN8JgwJ7URCEYPiGcH43ov309pQTUpWd/0nuX5UxWl1BS/yqu8z/Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T12:03:23.088144Z","bundle_sha256":"b8ea7e66c9e4a05c262fb8a2cd764de4e455e5df1bb35d8c577abf4173c1ebfb"}}