{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:Q3QAC25BAUZPCLXI3QLHTMWAOQ","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":"92b091d8c2edb938f0a7bca494e981b32f78987e511b7b447d4afefe88ffcd06","cross_cats_sorted":[],"license":"","primary_cat":"math.RT","submitted_at":"1998-03-12T00:00:00Z","title_canon_sha256":"405e72be87b8f24d2a0bf20dc72f4a058d30d3318f4a17c9ca136a15502fb17f"},"schema_version":"1.0","source":{"id":"math/9803159","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9803159","created_at":"2026-05-18T01:05:34Z"},{"alias_kind":"arxiv_version","alias_value":"math/9803159v1","created_at":"2026-05-18T01:05:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9803159","created_at":"2026-05-18T01:05:34Z"},{"alias_kind":"pith_short_12","alias_value":"Q3QAC25BAUZP","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"Q3QAC25BAUZPCLXI","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"Q3QAC25B","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:868d7c0a6d055e262cc04dae0aadbe88bd9eeac109bee6076c27c6f1fa47f2f3","target":"graph","created_at":"2026-05-18T01:05:34Z","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":"The algebra generated by the down and up operators on a differential partially ordered set (poset) encodes essential enumerative and structural properties of the poset. Motivated by the algebras generated by the down and up operators on posets, we introduce here a family of infinite-dimensional associative algebras called down-up algebras. We show that down-up algebras exhibit many of the important features of the universal enveloping algebra $U(\\fsl)$ of the Lie algebra $\\fsl$ including a Poincar\\'e-Birkhoff-Witt type basis and a well-behaved representation theory. We investigate the structur","authors_text":"Georgia Benkart, Tom Roby","cross_cats":[],"headline":"","license":"","primary_cat":"math.RT","submitted_at":"1998-03-12T00:00:00Z","title":"Down-up Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9803159","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:ffece9fe213d8744739582a175383a4a6e8dfa9e75270b04742856236190e7c5","target":"record","created_at":"2026-05-18T01:05:34Z","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":"92b091d8c2edb938f0a7bca494e981b32f78987e511b7b447d4afefe88ffcd06","cross_cats_sorted":[],"license":"","primary_cat":"math.RT","submitted_at":"1998-03-12T00:00:00Z","title_canon_sha256":"405e72be87b8f24d2a0bf20dc72f4a058d30d3318f4a17c9ca136a15502fb17f"},"schema_version":"1.0","source":{"id":"math/9803159","kind":"arxiv","version":1}},"canonical_sha256":"86e0016ba10532f12ee8dc1679b2c07412337c25c3b2b9e12fe3d3e40d579d3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86e0016ba10532f12ee8dc1679b2c07412337c25c3b2b9e12fe3d3e40d579d3d","first_computed_at":"2026-05-18T01:05:34.215423Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:34.215423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"81eEhi/vUsvoxDl7T6zQux+8/DiN/OKaj5eiwlrd7O9QYxvf14va/1k5csJOnFiLv73WomDmjDAbLP7ftybqCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:34.216142Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9803159","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffece9fe213d8744739582a175383a4a6e8dfa9e75270b04742856236190e7c5","sha256:868d7c0a6d055e262cc04dae0aadbe88bd9eeac109bee6076c27c6f1fa47f2f3"],"state_sha256":"6f1b7281d46e70e2dfad7bbcfdd8ce022e5a439d0ff4ab47a36c5767313ac6da"}