{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:L5YQFX2DLTZAFFHRROXK6TTJ6U","short_pith_number":"pith:L5YQFX2D","schema_version":"1.0","canonical_sha256":"5f7102df435cf20294f18baeaf4e69f51497070dcfcd42adcf9d178e716e90ab","source":{"kind":"arxiv","id":"1408.2180","version":2},"attestation_state":"computed","paper":{"title":"The end-parameters of a Leonard pair","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Kazumasa Nomura","submitted_at":"2014-08-10T03:22:40Z","abstract_excerpt":"Fix an algebraically closed field $\\F$ and an integer $d \\geq 3$. Let $V$ be a vector space over $\\F$ with dimension $d+1$. A Leonard pair on $V$ is a pair of diagonalizable linear transformations $A: V \\to V$ and $A^* : V \\to V$, each acting in an irreducible tridiagonal fashion on an eigenbasis for the other one. There is an object related to a Leonard pair called a Leonard system. It is known that a Leonard system is determined up to isomorphism by a sequence of scalars $(\\{\\th_i\\}_{i=0}^d, \\{\\th^*_i\\}_{i=0}^d, \\{\\vphi_i\\}_{i=1}^d, \\{\\phi_i\\}_{i=1}^d)$, called its parameter array. The scala"},"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":"1408.2180","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-08-10T03:22:40Z","cross_cats_sorted":[],"title_canon_sha256":"c843c8aa680a6cbc03095bfe919924a0e10c67c07eeff709027dff5778b3d5a4","abstract_canon_sha256":"8169b00b8fb10d581bd5a2de5697b6430437fb9b8bdd6b9451caf881ca2b89ec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:25.352215Z","signature_b64":"tqetYpi7sH7s33Pq5/WM13M16ndEAv3Fi41MvmiXDiyb0wWoEPZTVfzs3M2doppLEy+oqjh5ZGOUXIGnZ2JACQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f7102df435cf20294f18baeaf4e69f51497070dcfcd42adcf9d178e716e90ab","last_reissued_at":"2026-05-18T02:44:25.351809Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:25.351809Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The end-parameters of a Leonard pair","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Kazumasa Nomura","submitted_at":"2014-08-10T03:22:40Z","abstract_excerpt":"Fix an algebraically closed field $\\F$ and an integer $d \\geq 3$. Let $V$ be a vector space over $\\F$ with dimension $d+1$. A Leonard pair on $V$ is a pair of diagonalizable linear transformations $A: V \\to V$ and $A^* : V \\to V$, each acting in an irreducible tridiagonal fashion on an eigenbasis for the other one. There is an object related to a Leonard pair called a Leonard system. It is known that a Leonard system is determined up to isomorphism by a sequence of scalars $(\\{\\th_i\\}_{i=0}^d, \\{\\th^*_i\\}_{i=0}^d, \\{\\vphi_i\\}_{i=1}^d, \\{\\phi_i\\}_{i=1}^d)$, called its parameter array. The scala"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2180","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":"1408.2180","created_at":"2026-05-18T02:44:25.351879+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.2180v2","created_at":"2026-05-18T02:44:25.351879+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2180","created_at":"2026-05-18T02:44:25.351879+00:00"},{"alias_kind":"pith_short_12","alias_value":"L5YQFX2DLTZA","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"L5YQFX2DLTZAFFHR","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"L5YQFX2D","created_at":"2026-05-18T12:28:35.611951+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/L5YQFX2DLTZAFFHRROXK6TTJ6U","json":"https://pith.science/pith/L5YQFX2DLTZAFFHRROXK6TTJ6U.json","graph_json":"https://pith.science/api/pith-number/L5YQFX2DLTZAFFHRROXK6TTJ6U/graph.json","events_json":"https://pith.science/api/pith-number/L5YQFX2DLTZAFFHRROXK6TTJ6U/events.json","paper":"https://pith.science/paper/L5YQFX2D"},"agent_actions":{"view_html":"https://pith.science/pith/L5YQFX2DLTZAFFHRROXK6TTJ6U","download_json":"https://pith.science/pith/L5YQFX2DLTZAFFHRROXK6TTJ6U.json","view_paper":"https://pith.science/paper/L5YQFX2D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.2180&json=true","fetch_graph":"https://pith.science/api/pith-number/L5YQFX2DLTZAFFHRROXK6TTJ6U/graph.json","fetch_events":"https://pith.science/api/pith-number/L5YQFX2DLTZAFFHRROXK6TTJ6U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L5YQFX2DLTZAFFHRROXK6TTJ6U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L5YQFX2DLTZAFFHRROXK6TTJ6U/action/storage_attestation","attest_author":"https://pith.science/pith/L5YQFX2DLTZAFFHRROXK6TTJ6U/action/author_attestation","sign_citation":"https://pith.science/pith/L5YQFX2DLTZAFFHRROXK6TTJ6U/action/citation_signature","submit_replication":"https://pith.science/pith/L5YQFX2DLTZAFFHRROXK6TTJ6U/action/replication_record"}},"created_at":"2026-05-18T02:44:25.351879+00:00","updated_at":"2026-05-18T02:44:25.351879+00:00"}