{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:SIEEOB2CIA6GRBFT3QNCQQQSGA","short_pith_number":"pith:SIEEOB2C","schema_version":"1.0","canonical_sha256":"9208470742403c6884b3dc1a2842123005d7f62845086158b7d85050f3c45909","source":{"kind":"arxiv","id":"1808.10520","version":2},"attestation_state":"computed","paper":{"title":"A discrete realization of the higher rank Racah algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA"],"primary_cat":"math.CA","authors_text":"Hendrik De Bie, Wouter van de Vijver","submitted_at":"2018-08-21T13:52:13Z","abstract_excerpt":"In previous work a higher rank generalization $R(n)$ of the Racah algebra was defined abstractly. The special case of rank one encodes the bispectrality of the univariate Racah polynomials and is known to admit an explicit realization in terms of the operators associated to these polynomials. Starting from the Dunkl model for which we have an action by $R(n)$ on the Dunkl-harmonics, we show that connection coefficients between bases of Dunkl-harmonics diagonalizing certain Abelian subalgebra are multivariate Racah polynomials. By lifting the action of $R(n)$ to the connection coefficients, we "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1808.10520","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-08-21T13:52:13Z","cross_cats_sorted":["math-ph","math.MP","math.QA"],"title_canon_sha256":"ac9513bfe58a0a9c57b9ad11e34a55fda2df1756648848bb555380d98def7cc9","abstract_canon_sha256":"8652c7246715a265f4faaad8a5ebd2350127e7b28d01b8fc5b1cfad38eb35922"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:55.187708Z","signature_b64":"lnMDejG4uWwMtdH0p34wK5Pn7lzWlWM4uy6DA2p2IrApAyiaA6dSv40/lLJn84clIpIHksYrkD9fE9kv4Kx5AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9208470742403c6884b3dc1a2842123005d7f62845086158b7d85050f3c45909","last_reissued_at":"2026-05-17T23:46:55.187070Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:55.187070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A discrete realization of the higher rank Racah algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA"],"primary_cat":"math.CA","authors_text":"Hendrik De Bie, Wouter van de Vijver","submitted_at":"2018-08-21T13:52:13Z","abstract_excerpt":"In previous work a higher rank generalization $R(n)$ of the Racah algebra was defined abstractly. The special case of rank one encodes the bispectrality of the univariate Racah polynomials and is known to admit an explicit realization in terms of the operators associated to these polynomials. Starting from the Dunkl model for which we have an action by $R(n)$ on the Dunkl-harmonics, we show that connection coefficients between bases of Dunkl-harmonics diagonalizing certain Abelian subalgebra are multivariate Racah polynomials. By lifting the action of $R(n)$ to the connection coefficients, we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.10520","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1808.10520","created_at":"2026-05-17T23:46:55.187179+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.10520v2","created_at":"2026-05-17T23:46:55.187179+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.10520","created_at":"2026-05-17T23:46:55.187179+00:00"},{"alias_kind":"pith_short_12","alias_value":"SIEEOB2CIA6G","created_at":"2026-05-18T12:32:53.628368+00:00"},{"alias_kind":"pith_short_16","alias_value":"SIEEOB2CIA6GRBFT","created_at":"2026-05-18T12:32:53.628368+00:00"},{"alias_kind":"pith_short_8","alias_value":"SIEEOB2C","created_at":"2026-05-18T12:32:53.628368+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SIEEOB2CIA6GRBFT3QNCQQQSGA","json":"https://pith.science/pith/SIEEOB2CIA6GRBFT3QNCQQQSGA.json","graph_json":"https://pith.science/api/pith-number/SIEEOB2CIA6GRBFT3QNCQQQSGA/graph.json","events_json":"https://pith.science/api/pith-number/SIEEOB2CIA6GRBFT3QNCQQQSGA/events.json","paper":"https://pith.science/paper/SIEEOB2C"},"agent_actions":{"view_html":"https://pith.science/pith/SIEEOB2CIA6GRBFT3QNCQQQSGA","download_json":"https://pith.science/pith/SIEEOB2CIA6GRBFT3QNCQQQSGA.json","view_paper":"https://pith.science/paper/SIEEOB2C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.10520&json=true","fetch_graph":"https://pith.science/api/pith-number/SIEEOB2CIA6GRBFT3QNCQQQSGA/graph.json","fetch_events":"https://pith.science/api/pith-number/SIEEOB2CIA6GRBFT3QNCQQQSGA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SIEEOB2CIA6GRBFT3QNCQQQSGA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SIEEOB2CIA6GRBFT3QNCQQQSGA/action/storage_attestation","attest_author":"https://pith.science/pith/SIEEOB2CIA6GRBFT3QNCQQQSGA/action/author_attestation","sign_citation":"https://pith.science/pith/SIEEOB2CIA6GRBFT3QNCQQQSGA/action/citation_signature","submit_replication":"https://pith.science/pith/SIEEOB2CIA6GRBFT3QNCQQQSGA/action/replication_record"}},"created_at":"2026-05-17T23:46:55.187179+00:00","updated_at":"2026-05-17T23:46:55.187179+00:00"}