{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QQ4TM543ZLFZHP2RDK6E7CMOAP","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":"09d0f004b549ba5d211a261d4291c0f1397059c82d4d5cb0e89f34246e5be1e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-06-28T23:15:46Z","title_canon_sha256":"de4dc1ddaf608d86bf40969b90db1723758ec054d2360112877bfae3ee1172f3"},"schema_version":"1.0","source":{"id":"1806.11228","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.11228","created_at":"2026-05-18T00:12:03Z"},{"alias_kind":"arxiv_version","alias_value":"1806.11228v1","created_at":"2026-05-18T00:12:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.11228","created_at":"2026-05-18T00:12:03Z"},{"alias_kind":"pith_short_12","alias_value":"QQ4TM543ZLFZ","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QQ4TM543ZLFZHP2R","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QQ4TM543","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:f7a15f0eb3dcfdd70b8e6d0f2df9f9fda6f82de8dbe633ee9b0e66069893f1b5","target":"graph","created_at":"2026-05-18T00:12:03Z","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 positive part $U^+_q$ of $U_q({\\widehat {\\mathfrak{sl}}}_2)$ has a presentation with two generators $A,B$ that satisfy the cubic $q$-Serre relations. In 1993 I. Damiani obtained a PBW basis for\n  $U^+_q$, consisting of some elements $\\lbrace E_{n\\delta+\\alpha_0}\\rbrace_{n=0}^\\infty$, $\\lbrace E_{n\\delta+\\alpha_1}\\rbrace_{n=0}^\\infty$, $\\lbrace E_{n\\delta}\\rbrace_{n=1}^\\infty$ that are defined recursively. Our goal is to describe these elements in closed form. We achieve this goal using Catalan words and a $q$-shuffle algebra.","authors_text":"Paul Terwilliger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-06-28T23:15:46Z","title":"Using Catalan words and a $q$-shuffle algebra to describe a PBW basis for the positive part of $U_q({\\widehat {\\mathfrak{sl}}}_2)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.11228","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":"sha256:1b5914de1cdda1dd712e2f398d98f520c2c64573e6e907363996952ea6ed801c","target":"record","created_at":"2026-05-18T00:12:03Z","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":"09d0f004b549ba5d211a261d4291c0f1397059c82d4d5cb0e89f34246e5be1e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-06-28T23:15:46Z","title_canon_sha256":"de4dc1ddaf608d86bf40969b90db1723758ec054d2360112877bfae3ee1172f3"},"schema_version":"1.0","source":{"id":"1806.11228","kind":"arxiv","version":1}},"canonical_sha256":"843936779bcacb93bf511abc4f898e03fb303c4034cb7c1c410f7490f5772976","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"843936779bcacb93bf511abc4f898e03fb303c4034cb7c1c410f7490f5772976","first_computed_at":"2026-05-18T00:12:03.159937Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:03.159937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YhGSbP3EzOZfaAznL+Py2dBLX0BZLHtPIZWDRD4G9txp8yVBOhG9MpmFk979ltWMPUl4lQ/S2a8E/Fk8VSJQCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:03.160485Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.11228","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b5914de1cdda1dd712e2f398d98f520c2c64573e6e907363996952ea6ed801c","sha256:f7a15f0eb3dcfdd70b8e6d0f2df9f9fda6f82de8dbe633ee9b0e66069893f1b5"],"state_sha256":"9156d15ae2c6807d75380c70d824adb2a7f38d0c3d08c15f37557d4e6d8afd49"}