{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QKKKX2H57NCMHHCHPDLJNRZZLE","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":"51916f8b7daef320940893a98bd613e0a77097c1cffcaf53b0a34948ae08620a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-03-18T01:34:46Z","title_canon_sha256":"bf001b4fc1d8838c13072d92f901929e44ce16b29b1fc92938dbb8c60c789b44"},"schema_version":"1.0","source":{"id":"1503.05262","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05262","created_at":"2026-05-18T02:21:50Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05262v1","created_at":"2026-05-18T02:21:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05262","created_at":"2026-05-18T02:21:50Z"},{"alias_kind":"pith_short_12","alias_value":"QKKKX2H57NCM","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QKKKX2H57NCMHHCH","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QKKKX2H5","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:282d382e2bd9a0747a1dacba047b5fc154498fe0f12c3ff8fd084631d07e57c5","target":"graph","created_at":"2026-05-18T02:21:50Z","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"},"paper":{"abstract_excerpt":"Fix an algebraically closed field $\\mathbb{F}$ and an integer $n \\geq 1$. Let $\\text{Mat}_n(\\mathbb{F})$ denote the $\\mathbb{F}$-algebra consisting of the $n \\times n$ matrices that have all entries in $\\mathbb{F}$. We consider a pair of diagonalizable matrices in $\\text{Mat}_{n}(\\mathbb{F})$, each acting in an irreducible tridiagonal fashion on an eigenbasis for the other one. Such a pair is called a Leonard pair in $\\text{Mat}_{n}(\\mathbb{F})$. In the present paper, we find all Leonard pairs $A,A^*$ in $\\text{Mat}_{n}(\\mathbb{F})$ such that each of $A$ and $A^*$ is irreducible tridiagonal wi","authors_text":"Kazumasa Nomura","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-03-18T01:34:46Z","title":"Leonard pairs having zero-diagonal TD-TD form"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05262","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":"sha256:09c51b65f723a3425d600db46ff21b8c923a6ffeb2258fdae2039d5d65e15cdb","target":"record","created_at":"2026-05-18T02:21:50Z","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":"51916f8b7daef320940893a98bd613e0a77097c1cffcaf53b0a34948ae08620a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-03-18T01:34:46Z","title_canon_sha256":"bf001b4fc1d8838c13072d92f901929e44ce16b29b1fc92938dbb8c60c789b44"},"schema_version":"1.0","source":{"id":"1503.05262","kind":"arxiv","version":1}},"canonical_sha256":"8294abe8fdfb44c39c4778d696c739591d9acdf919dfd8c47aea47bf879f9009","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8294abe8fdfb44c39c4778d696c739591d9acdf919dfd8c47aea47bf879f9009","first_computed_at":"2026-05-18T02:21:50.942492Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:50.942492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YlV7oPwdItsI1QZ1m9X4G6UxD8Yrnvbm6pHabZ185FMWaUW6CwD1rZe/dFoyYhpguMkEFu8mCw/SbrjuaeXIAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:50.943079Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.05262","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09c51b65f723a3425d600db46ff21b8c923a6ffeb2258fdae2039d5d65e15cdb","sha256:282d382e2bd9a0747a1dacba047b5fc154498fe0f12c3ff8fd084631d07e57c5"],"state_sha256":"1a6f180eb8e184cd21f1014cbab2df442f3ae7e73558ba1963dd30d11e574c38"}