{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:VMXFDWDT243ONCS35SJ7MPTSRE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d04cc0763fb15b4f09df6491465c1117ae9023b834799d776e275f959de038f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-10-31T18:00:33Z","title_canon_sha256":"77106ccaf159b92a265094e3ecae268f52afa93d46be95b4f7a04e5bb59b188a"},"schema_version":"1.0","source":{"id":"0911.0098","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.0098","created_at":"2026-07-04T16:21:35Z"},{"alias_kind":"arxiv_version","alias_value":"0911.0098v1","created_at":"2026-07-04T16:21:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.0098","created_at":"2026-07-04T16:21:35Z"},{"alias_kind":"pith_short_12","alias_value":"VMXFDWDT243O","created_at":"2026-07-04T16:21:35Z"},{"alias_kind":"pith_short_16","alias_value":"VMXFDWDT243ONCS3","created_at":"2026-07-04T16:21:35Z"},{"alias_kind":"pith_short_8","alias_value":"VMXFDWDT","created_at":"2026-07-04T16:21:35Z"}],"graph_snapshots":[{"event_id":"sha256:c81ca136f6fee3766eb96b484dcbf7aca7182a8d879426bca575829be209e04a","target":"graph","created_at":"2026-07-04T16:21:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0911.0098/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $V$ denote a vector space with finite positive dimension. We consider an ordered pair of linear transformations $A: V\\to V$ and $A^*: V\\to V$ that satisfy (i) and (ii) below:\n  (i) There exists a basis for $V$ with respect to which the matrix representing $A$ is irreducible tridiagonal and the matrix representing $A^*$ is diagonal.\n  (ii) There exists a basis for $V$ with respect to which the matrix representing $A^*$ is irreducible tridiagonal and the matrix representing $A$ is diagonal.\n  We call such a pair a Leonard pair on $V$. In this paper, we characterize the Leonard pairs using th","authors_text":"Edward Hanson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-10-31T18:00:33Z","title":"A characterization of Leonard pairs using the notion of a tail"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.0098","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d21dae9cd8aaa2c2790afe66b06e6f59013cb8c0431d616a4d53801b1724da0c","target":"record","created_at":"2026-07-04T16:21:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d04cc0763fb15b4f09df6491465c1117ae9023b834799d776e275f959de038f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-10-31T18:00:33Z","title_canon_sha256":"77106ccaf159b92a265094e3ecae268f52afa93d46be95b4f7a04e5bb59b188a"},"schema_version":"1.0","source":{"id":"0911.0098","kind":"arxiv","version":1}},"canonical_sha256":"ab2e51d873d736e68a5bec93f63e7289197fbc8c8b45aa659b94cb81b61bd136","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab2e51d873d736e68a5bec93f63e7289197fbc8c8b45aa659b94cb81b61bd136","first_computed_at":"2026-07-04T16:21:35.249874Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:21:35.249874Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qsq3pXuQfgfaoAz1A9/HB8a+DHrZoOC1XkEaOI9BZ7GIZPPALg9KqyYDSzEWyelB00HZ+MomQr3hRyVhXWQyDA==","signature_status":"signed_v1","signed_at":"2026-07-04T16:21:35.250266Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.0098","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d21dae9cd8aaa2c2790afe66b06e6f59013cb8c0431d616a4d53801b1724da0c","sha256:c81ca136f6fee3766eb96b484dcbf7aca7182a8d879426bca575829be209e04a"],"state_sha256":"93358f6a3d5287834302b85a85ef1499db9dc8ed4ffbbdf0594b5bbad800cdf4"}