{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MFGJHKHFT3H5MQO6N5JJAW7SWA","short_pith_number":"pith:MFGJHKHF","canonical_record":{"source":{"id":"1507.01821","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math-ph","submitted_at":"2015-07-07T14:13:35Z","cross_cats_sorted":["math.CA","math.MP"],"title_canon_sha256":"5509dfe17c4a172552e8658f5218cefab81ae625fd9c5a085ede443be7b1b257","abstract_canon_sha256":"d7ca4fed274a4c332e851ba2cfa480347be4e08250e32af39413da5f6ef2d762"},"schema_version":"1.0"},"canonical_sha256":"614c93a8e59ecfd641de6f52905bf2b005755512d593715659fbc4ccb213e763","source":{"kind":"arxiv","id":"1507.01821","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01821","created_at":"2026-05-18T01:16:29Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01821v3","created_at":"2026-05-18T01:16:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01821","created_at":"2026-05-18T01:16:29Z"},{"alias_kind":"pith_short_12","alias_value":"MFGJHKHFT3H5","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MFGJHKHFT3H5MQO6","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MFGJHKHF","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MFGJHKHFT3H5MQO6N5JJAW7SWA","target":"record","payload":{"canonical_record":{"source":{"id":"1507.01821","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math-ph","submitted_at":"2015-07-07T14:13:35Z","cross_cats_sorted":["math.CA","math.MP"],"title_canon_sha256":"5509dfe17c4a172552e8658f5218cefab81ae625fd9c5a085ede443be7b1b257","abstract_canon_sha256":"d7ca4fed274a4c332e851ba2cfa480347be4e08250e32af39413da5f6ef2d762"},"schema_version":"1.0"},"canonical_sha256":"614c93a8e59ecfd641de6f52905bf2b005755512d593715659fbc4ccb213e763","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:29.691902Z","signature_b64":"xx1YCGV2X2Uf3LeqY/eG4whOMyGcS+XjiOe8YDNKVv8Q18d9i2Emcxt7CJAZSpdaRPkmCFqeOX1Wnd1ml5mSBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"614c93a8e59ecfd641de6f52905bf2b005755512d593715659fbc4ccb213e763","last_reissued_at":"2026-05-18T01:16:29.691277Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:29.691277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.01821","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:16:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KRTZROo/mcphDKnyp3OHpf5ZDx/ibIdeUFeiUZsfsnhmHdUDCssxXA763bnYM1OAJumXClN5P621bbvZ6/ncAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:01:39.593691Z"},"content_sha256":"014c534f493a6306cf1243e34f85d7bd41690b7871816f8f6eed04846f4c8620","schema_version":"1.0","event_id":"sha256:014c534f493a6306cf1243e34f85d7bd41690b7871816f8f6eed04846f4c8620"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MFGJHKHFT3H5MQO6N5JJAW7SWA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Doubling (Dual) Hahn Polynomials: Classification and Applications","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.CA","math.MP"],"primary_cat":"math-ph","authors_text":"Joris Van der Jeugt, Roy Oste","submitted_at":"2015-07-07T14:13:35Z","abstract_excerpt":"We classify all pairs of recurrence relations in which two Hahn or dual Hahn polynomials with different parameters appear. Such couples are referred to as (dual) Hahn doubles. The idea and interest comes from an example appearing in a finite oscillator model [Jafarov E.I., Stoilova N.I., Van der Jeugt J., J. Phys. A: Math. Theor. 44 (2011), 265203, 15 pages, arXiv:1101.5310]. Our classification shows there exist three dual Hahn doubles and four Hahn doubles. The same technique is then applied to Racah polynomials, yielding also four doubles. Each dual Hahn (Hahn, Racah) double gives rise to an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01821","kind":"arxiv","version":3},"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":"2026-05-18T01:16:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YbM0QG/wMY5RUvtyc3GPMSCAoBWbKdRcwRJjOw6MoWp5IdLz8lKYcJGrtHvdyl4gl+IbTdZ2Y7pA8mmNeXlKDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:01:39.594355Z"},"content_sha256":"4e72c23c973c5877c2c8174e5f34311b07c073dd5e398e1d85343477f33708a3","schema_version":"1.0","event_id":"sha256:4e72c23c973c5877c2c8174e5f34311b07c073dd5e398e1d85343477f33708a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MFGJHKHFT3H5MQO6N5JJAW7SWA/bundle.json","state_url":"https://pith.science/pith/MFGJHKHFT3H5MQO6N5JJAW7SWA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MFGJHKHFT3H5MQO6N5JJAW7SWA/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":"2026-06-09T09:01:39Z","links":{"resolver":"https://pith.science/pith/MFGJHKHFT3H5MQO6N5JJAW7SWA","bundle":"https://pith.science/pith/MFGJHKHFT3H5MQO6N5JJAW7SWA/bundle.json","state":"https://pith.science/pith/MFGJHKHFT3H5MQO6N5JJAW7SWA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MFGJHKHFT3H5MQO6N5JJAW7SWA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MFGJHKHFT3H5MQO6N5JJAW7SWA","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":"d7ca4fed274a4c332e851ba2cfa480347be4e08250e32af39413da5f6ef2d762","cross_cats_sorted":["math.CA","math.MP"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math-ph","submitted_at":"2015-07-07T14:13:35Z","title_canon_sha256":"5509dfe17c4a172552e8658f5218cefab81ae625fd9c5a085ede443be7b1b257"},"schema_version":"1.0","source":{"id":"1507.01821","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01821","created_at":"2026-05-18T01:16:29Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01821v3","created_at":"2026-05-18T01:16:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01821","created_at":"2026-05-18T01:16:29Z"},{"alias_kind":"pith_short_12","alias_value":"MFGJHKHFT3H5","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MFGJHKHFT3H5MQO6","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MFGJHKHF","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:4e72c23c973c5877c2c8174e5f34311b07c073dd5e398e1d85343477f33708a3","target":"graph","created_at":"2026-05-18T01:16:29Z","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":"We classify all pairs of recurrence relations in which two Hahn or dual Hahn polynomials with different parameters appear. Such couples are referred to as (dual) Hahn doubles. The idea and interest comes from an example appearing in a finite oscillator model [Jafarov E.I., Stoilova N.I., Van der Jeugt J., J. Phys. A: Math. Theor. 44 (2011), 265203, 15 pages, arXiv:1101.5310]. Our classification shows there exist three dual Hahn doubles and four Hahn doubles. The same technique is then applied to Racah polynomials, yielding also four doubles. Each dual Hahn (Hahn, Racah) double gives rise to an","authors_text":"Joris Van der Jeugt, Roy Oste","cross_cats":["math.CA","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math-ph","submitted_at":"2015-07-07T14:13:35Z","title":"Doubling (Dual) Hahn Polynomials: Classification and Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01821","kind":"arxiv","version":3},"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":"sha256:014c534f493a6306cf1243e34f85d7bd41690b7871816f8f6eed04846f4c8620","target":"record","created_at":"2026-05-18T01:16:29Z","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":"d7ca4fed274a4c332e851ba2cfa480347be4e08250e32af39413da5f6ef2d762","cross_cats_sorted":["math.CA","math.MP"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math-ph","submitted_at":"2015-07-07T14:13:35Z","title_canon_sha256":"5509dfe17c4a172552e8658f5218cefab81ae625fd9c5a085ede443be7b1b257"},"schema_version":"1.0","source":{"id":"1507.01821","kind":"arxiv","version":3}},"canonical_sha256":"614c93a8e59ecfd641de6f52905bf2b005755512d593715659fbc4ccb213e763","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"614c93a8e59ecfd641de6f52905bf2b005755512d593715659fbc4ccb213e763","first_computed_at":"2026-05-18T01:16:29.691277Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:29.691277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xx1YCGV2X2Uf3LeqY/eG4whOMyGcS+XjiOe8YDNKVv8Q18d9i2Emcxt7CJAZSpdaRPkmCFqeOX1Wnd1ml5mSBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:29.691902Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.01821","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:014c534f493a6306cf1243e34f85d7bd41690b7871816f8f6eed04846f4c8620","sha256:4e72c23c973c5877c2c8174e5f34311b07c073dd5e398e1d85343477f33708a3"],"state_sha256":"e5b6b3fa523fb5e0cf4b6d71ff3160e0bda3ec00a396d1e21bc9b977d5d1d06f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OPQ8lYtipttOUX6YhVlVec8ZvgARKvC5ESOiI9rgD0Bfo6f7fUnY8o9Nu/TKMS0Nj1yWwsF2LtYOQElIkXE+BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T09:01:39.598377Z","bundle_sha256":"3de2fd669bab5d93d88cc31f97a196ea05a87ce9440c33282304d6f895570fed"}}