{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:LRBYDAEIW3HYDPZVUMXV7TKXTU","short_pith_number":"pith:LRBYDAEI","schema_version":"1.0","canonical_sha256":"5c43818088b6cf81bf35a32f5fcd579d350521fd6a24d83ed21b435b3fde6a02","source":{"kind":"arxiv","id":"1409.4333","version":1},"attestation_state":"computed","paper":{"title":"Leonard pairs having specified end-entries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Kazumasa Nomura","submitted_at":"2014-09-15T17:09:45Z","abstract_excerpt":"Fix an algebraically closed field $\\mathbb{F}$ and an integer $d \\geq 3$. Let $V$ be a vector space over $\\mathbb{F}$ with dimension $d+1$. A Leonard pair on $V$ is an ordered 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. Let $\\{v_i\\}_{i=0}^d$ (resp.\\ $\\{v^*_i\\}_{i=0}^d$) be such an eigenbasis for $A$ (resp.\\ $A^*$). For $0 \\leq i \\leq d$ define a linear transformation $E_i : V \\to V$ such that $E_i v_i=v_i$ and $E_i v_j =0$ if $j \\neq i$ $(0 \\leq j \\leq d)$. Define $E^*_i : "},"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":"1409.4333","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-09-15T17:09:45Z","cross_cats_sorted":[],"title_canon_sha256":"3bd001c597bc8b78db52d25d2f6b3d6997b692b62428960362d9c03bcc987324","abstract_canon_sha256":"b6b37d97d56cb7dd74303c50d610d719213ee8688fe0f8daed5610cf562f2baa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:47.060963Z","signature_b64":"8cfy8cdHCrKgfuE99a4vTdhu979+AzSg/ewIPp85pcyo6APoSXaHsoPZcjVm7WHoyyfIGLmGRY4xU/JWLmekAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c43818088b6cf81bf35a32f5fcd579d350521fd6a24d83ed21b435b3fde6a02","last_reissued_at":"2026-05-18T02:42:47.060477Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:47.060477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Leonard pairs having specified end-entries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Kazumasa Nomura","submitted_at":"2014-09-15T17:09:45Z","abstract_excerpt":"Fix an algebraically closed field $\\mathbb{F}$ and an integer $d \\geq 3$. Let $V$ be a vector space over $\\mathbb{F}$ with dimension $d+1$. A Leonard pair on $V$ is an ordered 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. Let $\\{v_i\\}_{i=0}^d$ (resp.\\ $\\{v^*_i\\}_{i=0}^d$) be such an eigenbasis for $A$ (resp.\\ $A^*$). For $0 \\leq i \\leq d$ define a linear transformation $E_i : V \\to V$ such that $E_i v_i=v_i$ and $E_i v_j =0$ if $j \\neq i$ $(0 \\leq j \\leq d)$. Define $E^*_i : "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4333","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":""},"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":"1409.4333","created_at":"2026-05-18T02:42:47.060556+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.4333v1","created_at":"2026-05-18T02:42:47.060556+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4333","created_at":"2026-05-18T02:42:47.060556+00:00"},{"alias_kind":"pith_short_12","alias_value":"LRBYDAEIW3HY","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_16","alias_value":"LRBYDAEIW3HYDPZV","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_8","alias_value":"LRBYDAEI","created_at":"2026-05-18T12:28:38.356838+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/LRBYDAEIW3HYDPZVUMXV7TKXTU","json":"https://pith.science/pith/LRBYDAEIW3HYDPZVUMXV7TKXTU.json","graph_json":"https://pith.science/api/pith-number/LRBYDAEIW3HYDPZVUMXV7TKXTU/graph.json","events_json":"https://pith.science/api/pith-number/LRBYDAEIW3HYDPZVUMXV7TKXTU/events.json","paper":"https://pith.science/paper/LRBYDAEI"},"agent_actions":{"view_html":"https://pith.science/pith/LRBYDAEIW3HYDPZVUMXV7TKXTU","download_json":"https://pith.science/pith/LRBYDAEIW3HYDPZVUMXV7TKXTU.json","view_paper":"https://pith.science/paper/LRBYDAEI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.4333&json=true","fetch_graph":"https://pith.science/api/pith-number/LRBYDAEIW3HYDPZVUMXV7TKXTU/graph.json","fetch_events":"https://pith.science/api/pith-number/LRBYDAEIW3HYDPZVUMXV7TKXTU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LRBYDAEIW3HYDPZVUMXV7TKXTU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LRBYDAEIW3HYDPZVUMXV7TKXTU/action/storage_attestation","attest_author":"https://pith.science/pith/LRBYDAEIW3HYDPZVUMXV7TKXTU/action/author_attestation","sign_citation":"https://pith.science/pith/LRBYDAEIW3HYDPZVUMXV7TKXTU/action/citation_signature","submit_replication":"https://pith.science/pith/LRBYDAEIW3HYDPZVUMXV7TKXTU/action/replication_record"}},"created_at":"2026-05-18T02:42:47.060556+00:00","updated_at":"2026-05-18T02:42:47.060556+00:00"}