{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:QX4DO35XFYQMOLG4JHAGLMTVE3","short_pith_number":"pith:QX4DO35X","schema_version":"1.0","canonical_sha256":"85f8376fb72e20c72cdc49c065b27526f3d635aa6f8f8f070ae8907f1cb39eab","source":{"kind":"arxiv","id":"1110.3434","version":1},"attestation_state":"computed","paper":{"title":"Two commuting operators associated with a tridiagonal pair","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Sarah Bockting-Conrad","submitted_at":"2011-10-15T19:25:51Z","abstract_excerpt":"Let \\K denote a field and let V denote a vector space over \\K with finite positive dimension. We consider an ordered pair of linear transformations A:V\\to V and A*:V \\to V that satisfy the following four conditions: (i) Each of A,A* is diagonalizable; (ii) there exists an ordering {V_i}_{i=0}^d of the eigenspaces of A such that A*V_i\\subseteq V_{i-1}+V_i+V_{i+1} for 0\\leq i\\leq d, where V_{-1}=0 and V_{d+1}=0; (iii) there exists an ordering {V*_i}_{i=0}^{\\delta} of the eigenspaces of A* such that AV*_i\\subseteq V*_{i-1}+V*_i+V*_{i+1} for 0\\leq i\\leq\\delta, where V*_{-1}=0 and V*_{\\delta+1}=0; "},"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":"1110.3434","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-10-15T19:25:51Z","cross_cats_sorted":[],"title_canon_sha256":"56af6b9192f00bb43ef87446493b4c04d7c271f763d191f2f6cacbe818082b2f","abstract_canon_sha256":"025454713ade47070739936fa2a7afa804e716294e04d378fccdf77594479cdd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:55.778525Z","signature_b64":"QJQX/UE8E44GLxnvBGA9hVnCZQadxSkSAtJUOc/BxVOMP5BWaqGyb+hYUeDRuoZYpTIwT+DrszBfV27QR9yUDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85f8376fb72e20c72cdc49c065b27526f3d635aa6f8f8f070ae8907f1cb39eab","last_reissued_at":"2026-05-18T04:10:55.777758Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:55.777758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Two commuting operators associated with a tridiagonal pair","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Sarah Bockting-Conrad","submitted_at":"2011-10-15T19:25:51Z","abstract_excerpt":"Let \\K denote a field and let V denote a vector space over \\K with finite positive dimension. We consider an ordered pair of linear transformations A:V\\to V and A*:V \\to V that satisfy the following four conditions: (i) Each of A,A* is diagonalizable; (ii) there exists an ordering {V_i}_{i=0}^d of the eigenspaces of A such that A*V_i\\subseteq V_{i-1}+V_i+V_{i+1} for 0\\leq i\\leq d, where V_{-1}=0 and V_{d+1}=0; (iii) there exists an ordering {V*_i}_{i=0}^{\\delta} of the eigenspaces of A* such that AV*_i\\subseteq V*_{i-1}+V*_i+V*_{i+1} for 0\\leq i\\leq\\delta, where V*_{-1}=0 and V*_{\\delta+1}=0; "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3434","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":"1110.3434","created_at":"2026-05-18T04:10:55.777866+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.3434v1","created_at":"2026-05-18T04:10:55.777866+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3434","created_at":"2026-05-18T04:10:55.777866+00:00"},{"alias_kind":"pith_short_12","alias_value":"QX4DO35XFYQM","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"QX4DO35XFYQMOLG4","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"QX4DO35X","created_at":"2026-05-18T12:26:39.201973+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/QX4DO35XFYQMOLG4JHAGLMTVE3","json":"https://pith.science/pith/QX4DO35XFYQMOLG4JHAGLMTVE3.json","graph_json":"https://pith.science/api/pith-number/QX4DO35XFYQMOLG4JHAGLMTVE3/graph.json","events_json":"https://pith.science/api/pith-number/QX4DO35XFYQMOLG4JHAGLMTVE3/events.json","paper":"https://pith.science/paper/QX4DO35X"},"agent_actions":{"view_html":"https://pith.science/pith/QX4DO35XFYQMOLG4JHAGLMTVE3","download_json":"https://pith.science/pith/QX4DO35XFYQMOLG4JHAGLMTVE3.json","view_paper":"https://pith.science/paper/QX4DO35X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.3434&json=true","fetch_graph":"https://pith.science/api/pith-number/QX4DO35XFYQMOLG4JHAGLMTVE3/graph.json","fetch_events":"https://pith.science/api/pith-number/QX4DO35XFYQMOLG4JHAGLMTVE3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QX4DO35XFYQMOLG4JHAGLMTVE3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QX4DO35XFYQMOLG4JHAGLMTVE3/action/storage_attestation","attest_author":"https://pith.science/pith/QX4DO35XFYQMOLG4JHAGLMTVE3/action/author_attestation","sign_citation":"https://pith.science/pith/QX4DO35XFYQMOLG4JHAGLMTVE3/action/citation_signature","submit_replication":"https://pith.science/pith/QX4DO35XFYQMOLG4JHAGLMTVE3/action/replication_record"}},"created_at":"2026-05-18T04:10:55.777866+00:00","updated_at":"2026-05-18T04:10:55.777866+00:00"}