{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:GD6OZBHCUBMQHA44MAF6TE3JYK","short_pith_number":"pith:GD6OZBHC","canonical_record":{"source":{"id":"2411.18362","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-11-27T14:09:00Z","cross_cats_sorted":["math-ph","math.CO","math.MP","math.NT","math.RT"],"title_canon_sha256":"8861f5a2fc6270248d678a57172bc4a518a8664f4626fe200da6cb110ec9340e","abstract_canon_sha256":"5134cb5a73cede57d335d7228d742e6c6d694b99bddb175ee54223c247baa8e1"},"schema_version":"1.0"},"canonical_sha256":"30fcec84e2a05903839c600be99369c29a7a2263589aca27498e2830755983b7","source":{"kind":"arxiv","id":"2411.18362","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.18362","created_at":"2026-07-05T11:59:09Z"},{"alias_kind":"arxiv_version","alias_value":"2411.18362v2","created_at":"2026-07-05T11:59:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.18362","created_at":"2026-07-05T11:59:09Z"},{"alias_kind":"pith_short_12","alias_value":"GD6OZBHCUBMQ","created_at":"2026-07-05T11:59:09Z"},{"alias_kind":"pith_short_16","alias_value":"GD6OZBHCUBMQHA44","created_at":"2026-07-05T11:59:09Z"},{"alias_kind":"pith_short_8","alias_value":"GD6OZBHC","created_at":"2026-07-05T11:59:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:GD6OZBHCUBMQHA44MAF6TE3JYK","target":"record","payload":{"canonical_record":{"source":{"id":"2411.18362","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-11-27T14:09:00Z","cross_cats_sorted":["math-ph","math.CO","math.MP","math.NT","math.RT"],"title_canon_sha256":"8861f5a2fc6270248d678a57172bc4a518a8664f4626fe200da6cb110ec9340e","abstract_canon_sha256":"5134cb5a73cede57d335d7228d742e6c6d694b99bddb175ee54223c247baa8e1"},"schema_version":"1.0"},"canonical_sha256":"30fcec84e2a05903839c600be99369c29a7a2263589aca27498e2830755983b7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:59:09.232720Z","signature_b64":"cNhR1hxF7KIt41gUhcxXEWvP17ljmgh4e3aP2EShqZIMHBzvRRv/Pho5ClJQD91sXA+k/xILru1b3+7N1r+7Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30fcec84e2a05903839c600be99369c29a7a2263589aca27498e2830755983b7","last_reissued_at":"2026-07-05T11:59:09.232311Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:59:09.232311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.18362","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:59:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rJUDx5TtEP1jk9LKHL/fyu+jhmEnpRzK0CjBG37FoO7o0RI/ripn/XVYr7I+13ltXeAOmU6kTXvWNpl1gvdPBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:06:34.910147Z"},"content_sha256":"3034b128141c032e018b1c6809683bc3e7983aa6d7b75545f2e3c738c6059ba2","schema_version":"1.0","event_id":"sha256:3034b128141c032e018b1c6809683bc3e7983aa6d7b75545f2e3c738c6059ba2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:GD6OZBHCUBMQHA44MAF6TE3JYK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An evolution of matrix-valued orthogonal polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP","math.NT","math.RT"],"primary_cat":"math.CA","authors_text":"Erik Koelink, Pablo Rom\\'an, Wadim Zudilin","submitted_at":"2024-11-27T14:09:00Z","abstract_excerpt":"We establish new explicit connections between classical (scalar) and matrix Gegenbauer polynomials, which result in new symmetries of the latter and further give access to several properties that have been out of reach before: generating functions, distribution of zeros for individual entries of the matrices and new type of differential-difference structure. We further speculate about other potentials of the connection formulas found. Part of our proofs makes use of creative telescoping in a matrix setting$-$the strategy which is not yet developed algorithmically."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.18362","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.18362/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:59:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2jtkGHCbY+vDBQy1B8fMKmEjA0OYotlXvcJ8UyRXyuYgn6Rj83kK4gEk/PN30wm1iET/1wgzK1OCE0Ts8JBsAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:06:34.910920Z"},"content_sha256":"7216af43c11734ddd5810183187f312603fbfa903d0328fcfde73f727e804cda","schema_version":"1.0","event_id":"sha256:7216af43c11734ddd5810183187f312603fbfa903d0328fcfde73f727e804cda"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GD6OZBHCUBMQHA44MAF6TE3JYK/bundle.json","state_url":"https://pith.science/pith/GD6OZBHCUBMQHA44MAF6TE3JYK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GD6OZBHCUBMQHA44MAF6TE3JYK/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":"2026-08-12T22:06:34Z","links":{"resolver":"https://pith.science/pith/GD6OZBHCUBMQHA44MAF6TE3JYK","bundle":"https://pith.science/pith/GD6OZBHCUBMQHA44MAF6TE3JYK/bundle.json","state":"https://pith.science/pith/GD6OZBHCUBMQHA44MAF6TE3JYK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GD6OZBHCUBMQHA44MAF6TE3JYK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:GD6OZBHCUBMQHA44MAF6TE3JYK","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":"5134cb5a73cede57d335d7228d742e6c6d694b99bddb175ee54223c247baa8e1","cross_cats_sorted":["math-ph","math.CO","math.MP","math.NT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-11-27T14:09:00Z","title_canon_sha256":"8861f5a2fc6270248d678a57172bc4a518a8664f4626fe200da6cb110ec9340e"},"schema_version":"1.0","source":{"id":"2411.18362","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.18362","created_at":"2026-07-05T11:59:09Z"},{"alias_kind":"arxiv_version","alias_value":"2411.18362v2","created_at":"2026-07-05T11:59:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.18362","created_at":"2026-07-05T11:59:09Z"},{"alias_kind":"pith_short_12","alias_value":"GD6OZBHCUBMQ","created_at":"2026-07-05T11:59:09Z"},{"alias_kind":"pith_short_16","alias_value":"GD6OZBHCUBMQHA44","created_at":"2026-07-05T11:59:09Z"},{"alias_kind":"pith_short_8","alias_value":"GD6OZBHC","created_at":"2026-07-05T11:59:09Z"}],"graph_snapshots":[{"event_id":"sha256:7216af43c11734ddd5810183187f312603fbfa903d0328fcfde73f727e804cda","target":"graph","created_at":"2026-07-05T11:59:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.18362/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish new explicit connections between classical (scalar) and matrix Gegenbauer polynomials, which result in new symmetries of the latter and further give access to several properties that have been out of reach before: generating functions, distribution of zeros for individual entries of the matrices and new type of differential-difference structure. We further speculate about other potentials of the connection formulas found. Part of our proofs makes use of creative telescoping in a matrix setting$-$the strategy which is not yet developed algorithmically.","authors_text":"Erik Koelink, Pablo Rom\\'an, Wadim Zudilin","cross_cats":["math-ph","math.CO","math.MP","math.NT","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-11-27T14:09:00Z","title":"An evolution of matrix-valued orthogonal polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.18362","kind":"arxiv","version":2},"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":"sha256:3034b128141c032e018b1c6809683bc3e7983aa6d7b75545f2e3c738c6059ba2","target":"record","created_at":"2026-07-05T11:59:09Z","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":"5134cb5a73cede57d335d7228d742e6c6d694b99bddb175ee54223c247baa8e1","cross_cats_sorted":["math-ph","math.CO","math.MP","math.NT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-11-27T14:09:00Z","title_canon_sha256":"8861f5a2fc6270248d678a57172bc4a518a8664f4626fe200da6cb110ec9340e"},"schema_version":"1.0","source":{"id":"2411.18362","kind":"arxiv","version":2}},"canonical_sha256":"30fcec84e2a05903839c600be99369c29a7a2263589aca27498e2830755983b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30fcec84e2a05903839c600be99369c29a7a2263589aca27498e2830755983b7","first_computed_at":"2026-07-05T11:59:09.232311Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:59:09.232311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cNhR1hxF7KIt41gUhcxXEWvP17ljmgh4e3aP2EShqZIMHBzvRRv/Pho5ClJQD91sXA+k/xILru1b3+7N1r+7Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:59:09.232720Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.18362","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3034b128141c032e018b1c6809683bc3e7983aa6d7b75545f2e3c738c6059ba2","sha256:7216af43c11734ddd5810183187f312603fbfa903d0328fcfde73f727e804cda"],"state_sha256":"56f45ac915121a89dad6cd65831c5508b21faaab8652537d68b8a1fa8e8e4160"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gD63VLvfW2BA29efe0khH7ael/th3ioWhw69RNqovn/sSzuj8pNs6IkNWKLRQXoLN/okASNC7wNKs0yianxHBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T22:06:34.916063Z","bundle_sha256":"6957ba2646670a75acbaba165f185153ca08fcb354152e2b4e039839240373b9"}}