{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:JP2XFJFOCN6DKKACJXDSLLE6V2","short_pith_number":"pith:JP2XFJFO","canonical_record":{"source":{"id":"math/0305356","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2003-05-26T00:30:08Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"92f77b3dab98545e6033d1bcdac348e17e0bd90a7bac2bdfb112f4af34199eb3","abstract_canon_sha256":"d622088eae0133931111f10e2d870144f1abaae874f25e9e2f059ea58cd1d0d9"},"schema_version":"1.0"},"canonical_sha256":"4bf572a4ae137c3528024dc725ac9eae8bb06aab47b54c724cf8dd4cb3e35b9c","source":{"kind":"arxiv","id":"math/0305356","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0305356","created_at":"2026-07-04T14:37:20Z"},{"alias_kind":"arxiv_version","alias_value":"math/0305356v1","created_at":"2026-07-04T14:37:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0305356","created_at":"2026-07-04T14:37:20Z"},{"alias_kind":"pith_short_12","alias_value":"JP2XFJFOCN6D","created_at":"2026-07-04T14:37:20Z"},{"alias_kind":"pith_short_16","alias_value":"JP2XFJFOCN6DKKAC","created_at":"2026-07-04T14:37:20Z"},{"alias_kind":"pith_short_8","alias_value":"JP2XFJFO","created_at":"2026-07-04T14:37:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:JP2XFJFOCN6DKKACJXDSLLE6V2","target":"record","payload":{"canonical_record":{"source":{"id":"math/0305356","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2003-05-26T00:30:08Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"92f77b3dab98545e6033d1bcdac348e17e0bd90a7bac2bdfb112f4af34199eb3","abstract_canon_sha256":"d622088eae0133931111f10e2d870144f1abaae874f25e9e2f059ea58cd1d0d9"},"schema_version":"1.0"},"canonical_sha256":"4bf572a4ae137c3528024dc725ac9eae8bb06aab47b54c724cf8dd4cb3e35b9c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:37:20.187150Z","signature_b64":"54H1D54q6efhAoj50JfQ3DQwVfRN70L0NsWyDr3Bscf2Pe6lBkq0KLCEbMuKlgiyYiOSwZcaVZ+DayAWUjJGBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bf572a4ae137c3528024dc725ac9eae8bb06aab47b54c724cf8dd4cb3e35b9c","last_reissued_at":"2026-07-04T14:37:20.186740Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:37:20.186740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0305356","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":"2026-07-04T14:37:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qs9XTEpVCjf6Fu4vMcSVx48rzD8OcxAowt3skmT5gclipUA3/8DZBtuB8zwwIpmbq7jnZ+V2rHkWMFhqVEd5Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T06:13:11.367684Z"},"content_sha256":"7d5a8b4788d7cd36ecdeafd96c336595757324f8717bed56cf8c7f6673c3e151","schema_version":"1.0","event_id":"sha256:7d5a8b4788d7cd36ecdeafd96c336595757324f8717bed56cf8c7f6673c3e151"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:JP2XFJFOCN6DKKACJXDSLLE6V2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Leonard pairs and the Askey-Wilson relations","license":"","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"Paul Terwilliger, Raimundas Vidunas","submitted_at":"2003-05-26T00:30:08Z","abstract_excerpt":"Let K denote a field and let $V$ denote a vector space over K with finite positive dimension. We consider an ordered pair of linear transformations $A:V\\to V$ and $A^*:V\\to V$ which satisfy the following two properties:\n  (i) There exists a basis for $V$ with respect to which the matrix representing $A$ is irreducible tridiagonal and the matrix representing $A^*$ is diagonal.\n  (ii) There exists a basis for $V$ with respect to which the matrix representing $A^*$ is irreducible tridiagonal and the matrix representing $A$ is diagonal.\n  We call such a pair a Leonard pair on $V$. Referring to the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0305356","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/math/0305356/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":"2026-07-04T14:37:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"knL1Tpy6l3XREqd1NBl1V19e6NwoEOHB7vQ5cdOIQWl89aiKfDfok70iDYZKFqM8UVBfXee4th/iNhqZ/l7JCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T06:13:11.368204Z"},"content_sha256":"4b01e12ab877f2af6a427641967fa55bd964b408a8741f52037ab01f744a6d5c","schema_version":"1.0","event_id":"sha256:4b01e12ab877f2af6a427641967fa55bd964b408a8741f52037ab01f744a6d5c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JP2XFJFOCN6DKKACJXDSLLE6V2/bundle.json","state_url":"https://pith.science/pith/JP2XFJFOCN6DKKACJXDSLLE6V2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JP2XFJFOCN6DKKACJXDSLLE6V2/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":"2026-08-10T06:13:11Z","links":{"resolver":"https://pith.science/pith/JP2XFJFOCN6DKKACJXDSLLE6V2","bundle":"https://pith.science/pith/JP2XFJFOCN6DKKACJXDSLLE6V2/bundle.json","state":"https://pith.science/pith/JP2XFJFOCN6DKKACJXDSLLE6V2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JP2XFJFOCN6DKKACJXDSLLE6V2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:JP2XFJFOCN6DKKACJXDSLLE6V2","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":"d622088eae0133931111f10e2d870144f1abaae874f25e9e2f059ea58cd1d0d9","cross_cats_sorted":["math.RA"],"license":"","primary_cat":"math.QA","submitted_at":"2003-05-26T00:30:08Z","title_canon_sha256":"92f77b3dab98545e6033d1bcdac348e17e0bd90a7bac2bdfb112f4af34199eb3"},"schema_version":"1.0","source":{"id":"math/0305356","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0305356","created_at":"2026-07-04T14:37:20Z"},{"alias_kind":"arxiv_version","alias_value":"math/0305356v1","created_at":"2026-07-04T14:37:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0305356","created_at":"2026-07-04T14:37:20Z"},{"alias_kind":"pith_short_12","alias_value":"JP2XFJFOCN6D","created_at":"2026-07-04T14:37:20Z"},{"alias_kind":"pith_short_16","alias_value":"JP2XFJFOCN6DKKAC","created_at":"2026-07-04T14:37:20Z"},{"alias_kind":"pith_short_8","alias_value":"JP2XFJFO","created_at":"2026-07-04T14:37:20Z"}],"graph_snapshots":[{"event_id":"sha256:4b01e12ab877f2af6a427641967fa55bd964b408a8741f52037ab01f744a6d5c","target":"graph","created_at":"2026-07-04T14:37:20Z","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/math/0305356/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let K denote a field and let $V$ denote a vector space over K with finite positive dimension. We consider an ordered pair of linear transformations $A:V\\to V$ and $A^*:V\\to V$ which satisfy the following two properties:\n  (i) There exists a basis for $V$ with respect to which the matrix representing $A$ is irreducible tridiagonal and the matrix representing $A^*$ is diagonal.\n  (ii) There exists a basis for $V$ with respect to which the matrix representing $A^*$ is irreducible tridiagonal and the matrix representing $A$ is diagonal.\n  We call such a pair a Leonard pair on $V$. Referring to the","authors_text":"Paul Terwilliger, Raimundas Vidunas","cross_cats":["math.RA"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2003-05-26T00:30:08Z","title":"Leonard pairs and the Askey-Wilson relations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0305356","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":"sha256:7d5a8b4788d7cd36ecdeafd96c336595757324f8717bed56cf8c7f6673c3e151","target":"record","created_at":"2026-07-04T14:37:20Z","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":"d622088eae0133931111f10e2d870144f1abaae874f25e9e2f059ea58cd1d0d9","cross_cats_sorted":["math.RA"],"license":"","primary_cat":"math.QA","submitted_at":"2003-05-26T00:30:08Z","title_canon_sha256":"92f77b3dab98545e6033d1bcdac348e17e0bd90a7bac2bdfb112f4af34199eb3"},"schema_version":"1.0","source":{"id":"math/0305356","kind":"arxiv","version":1}},"canonical_sha256":"4bf572a4ae137c3528024dc725ac9eae8bb06aab47b54c724cf8dd4cb3e35b9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4bf572a4ae137c3528024dc725ac9eae8bb06aab47b54c724cf8dd4cb3e35b9c","first_computed_at":"2026-07-04T14:37:20.186740Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:37:20.186740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"54H1D54q6efhAoj50JfQ3DQwVfRN70L0NsWyDr3Bscf2Pe6lBkq0KLCEbMuKlgiyYiOSwZcaVZ+DayAWUjJGBA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:37:20.187150Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0305356","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d5a8b4788d7cd36ecdeafd96c336595757324f8717bed56cf8c7f6673c3e151","sha256:4b01e12ab877f2af6a427641967fa55bd964b408a8741f52037ab01f744a6d5c"],"state_sha256":"64db48f65b6edfc9637a684d36a5f5af06ba88ff40dc93c5a54da5f8fd8583b7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IQiUt2v2OLS/WtjuzFHGneBrqXLCxU6gQobLQau3iZYX9A9jCAcCUJxTyq+IqEUPGu92a7hd4dOhwQC8QKOpBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T06:13:11.375480Z","bundle_sha256":"8af4b50fe9404172879bf8e84c9430a6f27b0529fa4e44e41963b831b009652d"}}