{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VUEBZHHIGG4HKAV5CQBKHXTSYB","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":"119cd8e0d3f19647e2e71b65a2a3aa710ce5e90556d00b4358f179d8444d7294","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-07-29T13:37:00Z","title_canon_sha256":"00945fce3d1ec8e99b9e5460a3676be2acad6fadaaebae6a8a0af63e2caaaba7"},"schema_version":"1.0","source":{"id":"1307.7572","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7572","created_at":"2026-05-18T03:17:22Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7572v1","created_at":"2026-05-18T03:17:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7572","created_at":"2026-05-18T03:17:22Z"},{"alias_kind":"pith_short_12","alias_value":"VUEBZHHIGG4H","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VUEBZHHIGG4HKAV5","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VUEBZHHI","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:1f0fe8ff88b1f56da9fa8d4d526e31b02648e48d0faf633ba66a3c6639727e02","target":"graph","created_at":"2026-05-18T03:17:22Z","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":"We discuss a connection between the algebra $U_q({\\mathfrak{sl}_2})$ and the tridiagonal pairs of $q$-Racah type. To describe the connection, let $x,y^{\\pm 1},z$ denote the equitable generators for $U_q({\\mathfrak{sl}_2})$. Let $U^\\vee_q$ denote the subalgebra of $U_q({\\mathfrak{sl}_2})$ generated by $x,y^{-1},z$. Using a tridiagonal pair of $q$-Racah type we construct two finite-dimensional $U^\\vee_q$-modules. The constructions yield two nonstandard presentations of $U^\\vee_q$ by generators and relations. These presentations are investigated in detail.","authors_text":"Paul Terwilliger, Sarah Bockting-Conrad","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-07-29T13:37:00Z","title":"The algebra $U_q({\\mathfrak{sl}_2})$ in disguise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7572","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:de28da2cfc8993f33a93c453386d2ecddaf35d448defd4de3ba45a625f89e40c","target":"record","created_at":"2026-05-18T03:17:22Z","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":"119cd8e0d3f19647e2e71b65a2a3aa710ce5e90556d00b4358f179d8444d7294","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-07-29T13:37:00Z","title_canon_sha256":"00945fce3d1ec8e99b9e5460a3676be2acad6fadaaebae6a8a0af63e2caaaba7"},"schema_version":"1.0","source":{"id":"1307.7572","kind":"arxiv","version":1}},"canonical_sha256":"ad081c9ce831b87502bd1402a3de72c07836bbe8370bbf980c6344156939887f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad081c9ce831b87502bd1402a3de72c07836bbe8370bbf980c6344156939887f","first_computed_at":"2026-05-18T03:17:22.941572Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:22.941572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rqtvckc/N13eEWz1DiWfM8OqQvMZyGr9dDEN5jbv9l9OHL4e4hRqY0lz3Z4JvhY+X1PGPRGwg8c66PKj1aeaDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:22.942190Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.7572","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de28da2cfc8993f33a93c453386d2ecddaf35d448defd4de3ba45a625f89e40c","sha256:1f0fe8ff88b1f56da9fa8d4d526e31b02648e48d0faf633ba66a3c6639727e02"],"state_sha256":"01c90682114a6512882345997ea77ccc6066c3983ae3dd9b8bbaae12771bea95"}