{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:S7HGPHKX6GFUXJCXEMLX5RKTOV","short_pith_number":"pith:S7HGPHKX","canonical_record":{"source":{"id":"2504.20802","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-04-29T14:14:50Z","cross_cats_sorted":[],"title_canon_sha256":"63ca5ad70a852d788ef1276d9ecbf15f319504a98939d3f35ff8c41bd3b84fa4","abstract_canon_sha256":"09e089ced55c86511d0472f2d3aaf00a388f9228d65f0be0100c0cd42b96b1a4"},"schema_version":"1.0"},"canonical_sha256":"97ce679d57f18b4ba45723177ec5537564203e74e637b02123635a517873dbc3","source":{"kind":"arxiv","id":"2504.20802","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.20802","created_at":"2026-07-05T10:55:49Z"},{"alias_kind":"arxiv_version","alias_value":"2504.20802v1","created_at":"2026-07-05T10:55:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.20802","created_at":"2026-07-05T10:55:49Z"},{"alias_kind":"pith_short_12","alias_value":"S7HGPHKX6GFU","created_at":"2026-07-05T10:55:49Z"},{"alias_kind":"pith_short_16","alias_value":"S7HGPHKX6GFUXJCX","created_at":"2026-07-05T10:55:49Z"},{"alias_kind":"pith_short_8","alias_value":"S7HGPHKX","created_at":"2026-07-05T10:55:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:S7HGPHKX6GFUXJCXEMLX5RKTOV","target":"record","payload":{"canonical_record":{"source":{"id":"2504.20802","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-04-29T14:14:50Z","cross_cats_sorted":[],"title_canon_sha256":"63ca5ad70a852d788ef1276d9ecbf15f319504a98939d3f35ff8c41bd3b84fa4","abstract_canon_sha256":"09e089ced55c86511d0472f2d3aaf00a388f9228d65f0be0100c0cd42b96b1a4"},"schema_version":"1.0"},"canonical_sha256":"97ce679d57f18b4ba45723177ec5537564203e74e637b02123635a517873dbc3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:55:49.079663Z","signature_b64":"egYddLNIp0SedVi4OZ/5pzoneCAZT/Lfym92VCkNKYA/29uIkKl+jc7TkYWJNZgAl2KNY3dc4cAYeUW08ZWVDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97ce679d57f18b4ba45723177ec5537564203e74e637b02123635a517873dbc3","last_reissued_at":"2026-07-05T10:55:49.079180Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:55:49.079180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.20802","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":"2026-07-05T10:55:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zn6zagfWFZzONb0k6aeda4P8zTIrEEB5eeJ79seIE7VIE529/jywEjZyLlu76pOhjvzzCJahOMaatFiddzzdAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T04:10:42.618446Z"},"content_sha256":"27da411aa4e48488295671f11eef5c69a2e12fb7162ca93e178a9503f746f83a","schema_version":"1.0","event_id":"sha256:27da411aa4e48488295671f11eef5c69a2e12fb7162ca93e178a9503f746f83a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:S7HGPHKX6GFUXJCXEMLX5RKTOV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Contiguity relations for finite families of orthogonal polynomials in the Askey scheme","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Lucia Morey, Luc Vinet, Meri Zaimi, Nicolas Cramp\\'e","submitted_at":"2025-04-29T14:14:50Z","abstract_excerpt":"This paper classifies the contiguity relations for finite families of polynomials within the ($q$-)Askey scheme. The necessary and sufficient conditions for the existence of these contiguity relations are presented first. These conditions are then solved, yielding a comprehensive list of contiguity relations for these various families of polynomials. Furthermore, we demonstrate that all contiguity relations correspond to spectral transforms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.20802","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.20802/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":"2026-07-05T10:55:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yI7nZu3xWmI2tAoPFa1cTJTn1t+ZlI2EPWNbPYIG0l3ji/xR1+R/dR8ez2e2VY0DXvQroJQRGqcypaqmGUcbBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T04:10:42.619440Z"},"content_sha256":"8387a9855094506ed43b71ae604173c5c882d69e816275604a3f41d50ebf6a25","schema_version":"1.0","event_id":"sha256:8387a9855094506ed43b71ae604173c5c882d69e816275604a3f41d50ebf6a25"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S7HGPHKX6GFUXJCXEMLX5RKTOV/bundle.json","state_url":"https://pith.science/pith/S7HGPHKX6GFUXJCXEMLX5RKTOV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S7HGPHKX6GFUXJCXEMLX5RKTOV/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":"2026-08-09T04:10:42Z","links":{"resolver":"https://pith.science/pith/S7HGPHKX6GFUXJCXEMLX5RKTOV","bundle":"https://pith.science/pith/S7HGPHKX6GFUXJCXEMLX5RKTOV/bundle.json","state":"https://pith.science/pith/S7HGPHKX6GFUXJCXEMLX5RKTOV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S7HGPHKX6GFUXJCXEMLX5RKTOV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:S7HGPHKX6GFUXJCXEMLX5RKTOV","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":"09e089ced55c86511d0472f2d3aaf00a388f9228d65f0be0100c0cd42b96b1a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-04-29T14:14:50Z","title_canon_sha256":"63ca5ad70a852d788ef1276d9ecbf15f319504a98939d3f35ff8c41bd3b84fa4"},"schema_version":"1.0","source":{"id":"2504.20802","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.20802","created_at":"2026-07-05T10:55:49Z"},{"alias_kind":"arxiv_version","alias_value":"2504.20802v1","created_at":"2026-07-05T10:55:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.20802","created_at":"2026-07-05T10:55:49Z"},{"alias_kind":"pith_short_12","alias_value":"S7HGPHKX6GFU","created_at":"2026-07-05T10:55:49Z"},{"alias_kind":"pith_short_16","alias_value":"S7HGPHKX6GFUXJCX","created_at":"2026-07-05T10:55:49Z"},{"alias_kind":"pith_short_8","alias_value":"S7HGPHKX","created_at":"2026-07-05T10:55:49Z"}],"graph_snapshots":[{"event_id":"sha256:8387a9855094506ed43b71ae604173c5c882d69e816275604a3f41d50ebf6a25","target":"graph","created_at":"2026-07-05T10:55:49Z","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/2504.20802/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper classifies the contiguity relations for finite families of polynomials within the ($q$-)Askey scheme. The necessary and sufficient conditions for the existence of these contiguity relations are presented first. These conditions are then solved, yielding a comprehensive list of contiguity relations for these various families of polynomials. Furthermore, we demonstrate that all contiguity relations correspond to spectral transforms.","authors_text":"Lucia Morey, Luc Vinet, Meri Zaimi, Nicolas Cramp\\'e","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-04-29T14:14:50Z","title":"Contiguity relations for finite families of orthogonal polynomials in the Askey scheme"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.20802","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":"sha256:27da411aa4e48488295671f11eef5c69a2e12fb7162ca93e178a9503f746f83a","target":"record","created_at":"2026-07-05T10:55:49Z","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":"09e089ced55c86511d0472f2d3aaf00a388f9228d65f0be0100c0cd42b96b1a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-04-29T14:14:50Z","title_canon_sha256":"63ca5ad70a852d788ef1276d9ecbf15f319504a98939d3f35ff8c41bd3b84fa4"},"schema_version":"1.0","source":{"id":"2504.20802","kind":"arxiv","version":1}},"canonical_sha256":"97ce679d57f18b4ba45723177ec5537564203e74e637b02123635a517873dbc3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97ce679d57f18b4ba45723177ec5537564203e74e637b02123635a517873dbc3","first_computed_at":"2026-07-05T10:55:49.079180Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:55:49.079180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"egYddLNIp0SedVi4OZ/5pzoneCAZT/Lfym92VCkNKYA/29uIkKl+jc7TkYWJNZgAl2KNY3dc4cAYeUW08ZWVDw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:55:49.079663Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.20802","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27da411aa4e48488295671f11eef5c69a2e12fb7162ca93e178a9503f746f83a","sha256:8387a9855094506ed43b71ae604173c5c882d69e816275604a3f41d50ebf6a25"],"state_sha256":"19d52cd95642c45ef8172ab05933e461ab29cb21d8c0ca585bb8b50f296742b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lC+f5FiCVBMrBQmTcgTMWZhprtVsESQpkV1QYR1k5MxIoDSJBa29DHf2WvhXLy7f8QLBmj5scLxU05ruCquwDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T04:10:42.638256Z","bundle_sha256":"797ec9f23423145fe108a88e2ed8d13e865f3371cfcf3b3307a5413809a91bf6"}}