{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:4FHOYYYKUOPBMKGZMYRMXOOM6D","short_pith_number":"pith:4FHOYYYK","schema_version":"1.0","canonical_sha256":"e14eec630aa39e1628d96622cbb9ccf0c813a1d80783c81aeeb3b1f5599706dc","source":{"kind":"arxiv","id":"2003.09668","version":1},"attestation_state":"computed","paper":{"title":"Notes on the Leonard system classification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Paul Terwilliger","submitted_at":"2020-03-21T14:20:11Z","abstract_excerpt":"Around 2001 we classified the Leonard systems up to isomorphism. The proof was lengthy and involved considerable computation. In this paper we give a proof that is shorter and involves minimal computation. We also give a comprehensive descriptionof the intersection numbers of a Leonard system."},"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":"2003.09668","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-03-21T14:20:11Z","cross_cats_sorted":[],"title_canon_sha256":"3648f52e3e45e9c29d65ab56b2ffef84d1e2a5e8a920149fc40d30b389fe21fc","abstract_canon_sha256":"90d225c0f3acba764d634d9c958b4fa1f7ac89b07945ec1e90328d3c62aa4b89"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:49:45.933373Z","signature_b64":"VNnhbmBuMnuwoAEOE0tFlLDlJZ2w4enWf5l4XnzDLLd1lpIvuDYSu/uUW6dIzvLIse0bUvq+uJiIcgDz8xsXAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e14eec630aa39e1628d96622cbb9ccf0c813a1d80783c81aeeb3b1f5599706dc","last_reissued_at":"2026-07-05T00:49:45.933001Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:49:45.933001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Notes on the Leonard system classification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Paul Terwilliger","submitted_at":"2020-03-21T14:20:11Z","abstract_excerpt":"Around 2001 we classified the Leonard systems up to isomorphism. The proof was lengthy and involved considerable computation. In this paper we give a proof that is shorter and involves minimal computation. We also give a comprehensive descriptionof the intersection numbers of a Leonard system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.09668","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/2003.09668/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2003.09668","created_at":"2026-07-05T00:49:45.933064+00:00"},{"alias_kind":"arxiv_version","alias_value":"2003.09668v1","created_at":"2026-07-05T00:49:45.933064+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.09668","created_at":"2026-07-05T00:49:45.933064+00:00"},{"alias_kind":"pith_short_12","alias_value":"4FHOYYYKUOPB","created_at":"2026-07-05T00:49:45.933064+00:00"},{"alias_kind":"pith_short_16","alias_value":"4FHOYYYKUOPBMKGZ","created_at":"2026-07-05T00:49:45.933064+00:00"},{"alias_kind":"pith_short_8","alias_value":"4FHOYYYK","created_at":"2026-07-05T00:49:45.933064+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.05688","citing_title":"Circular Hessenberg pairs and the tridiagonal relations","ref_index":18,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4FHOYYYKUOPBMKGZMYRMXOOM6D","json":"https://pith.science/pith/4FHOYYYKUOPBMKGZMYRMXOOM6D.json","graph_json":"https://pith.science/api/pith-number/4FHOYYYKUOPBMKGZMYRMXOOM6D/graph.json","events_json":"https://pith.science/api/pith-number/4FHOYYYKUOPBMKGZMYRMXOOM6D/events.json","paper":"https://pith.science/paper/4FHOYYYK"},"agent_actions":{"view_html":"https://pith.science/pith/4FHOYYYKUOPBMKGZMYRMXOOM6D","download_json":"https://pith.science/pith/4FHOYYYKUOPBMKGZMYRMXOOM6D.json","view_paper":"https://pith.science/paper/4FHOYYYK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2003.09668&json=true","fetch_graph":"https://pith.science/api/pith-number/4FHOYYYKUOPBMKGZMYRMXOOM6D/graph.json","fetch_events":"https://pith.science/api/pith-number/4FHOYYYKUOPBMKGZMYRMXOOM6D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4FHOYYYKUOPBMKGZMYRMXOOM6D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4FHOYYYKUOPBMKGZMYRMXOOM6D/action/storage_attestation","attest_author":"https://pith.science/pith/4FHOYYYKUOPBMKGZMYRMXOOM6D/action/author_attestation","sign_citation":"https://pith.science/pith/4FHOYYYKUOPBMKGZMYRMXOOM6D/action/citation_signature","submit_replication":"https://pith.science/pith/4FHOYYYKUOPBMKGZMYRMXOOM6D/action/replication_record"}},"created_at":"2026-07-05T00:49:45.933064+00:00","updated_at":"2026-07-05T00:49:45.933064+00:00"}