{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:W5G6SGLTZ52M2DSPJ5BPMUXZWK","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":"31ccefc4e499acd9eccca24638a7068c0e7bce2c65a9c1630c573d8ebf5268f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-06-03T15:21:45Z","title_canon_sha256":"b3666d753af6a1ea6a1b41a5708fdfa63a6ac8bc25e33fc60af21538d80cdf1d"},"schema_version":"1.0","source":{"id":"1206.0455","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.0455","created_at":"2026-05-18T03:54:17Z"},{"alias_kind":"arxiv_version","alias_value":"1206.0455v1","created_at":"2026-05-18T03:54:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0455","created_at":"2026-05-18T03:54:17Z"},{"alias_kind":"pith_short_12","alias_value":"W5G6SGLTZ52M","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"W5G6SGLTZ52M2DSP","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"W5G6SGLT","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:74d724a187f93b8fd59e46ee5bf9c7502d51b6c1ecf4fd7f5fde96c48754f641","target":"graph","created_at":"2026-05-18T03:54:17Z","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":"Motivated by the structure of the uniform posets we introduce the notion of an augmented down-up (or ADU) algebra. We discuss how ADU algebras are related to the down-up algebras defined by Benkart and Roby. For each ADU algebra we give two presentations by generators and relations. We also display a $Z$-grading and a linear basis. In addition we show that the center is isomorphic to a polynomial algebra in two variables. We display seven families of uniform posets and show that each gives an ADU algebra module in a natural way. The main inspiration for the ADU algebra concept comes from the s","authors_text":"Chalermpong Worawannotai, Paul Terwilliger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-06-03T15:21:45Z","title":"Augmented down-up algebras and uniform posets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0455","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:d3c0dd964d20a3e2e0d055e8bae0d5b28d87670716c36e4459e5a521851ee163","target":"record","created_at":"2026-05-18T03:54:17Z","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":"31ccefc4e499acd9eccca24638a7068c0e7bce2c65a9c1630c573d8ebf5268f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-06-03T15:21:45Z","title_canon_sha256":"b3666d753af6a1ea6a1b41a5708fdfa63a6ac8bc25e33fc60af21538d80cdf1d"},"schema_version":"1.0","source":{"id":"1206.0455","kind":"arxiv","version":1}},"canonical_sha256":"b74de91973cf74cd0e4f4f42f652f9b287779248568f0a1a5e017d5d30dba137","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b74de91973cf74cd0e4f4f42f652f9b287779248568f0a1a5e017d5d30dba137","first_computed_at":"2026-05-18T03:54:17.630238Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:17.630238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s0FEoJVbFAFufkbMt4iOi5ZRDpGsJoHFMdO1Okmgc3+MAwFw/1NwZ5+tyW7f+mOAUfiM3YgS3394GQN5GlxYBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:17.630917Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.0455","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3c0dd964d20a3e2e0d055e8bae0d5b28d87670716c36e4459e5a521851ee163","sha256:74d724a187f93b8fd59e46ee5bf9c7502d51b6c1ecf4fd7f5fde96c48754f641"],"state_sha256":"6c95d3fa8f018219f62c2d6eda9e1773d4de9ce3e8e86f2dc796a301a89cd516"}