{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:A3CBF42QVX4JT3XAX4R62IFIAT","short_pith_number":"pith:A3CBF42Q","schema_version":"1.0","canonical_sha256":"06c412f350adf899eee0bf23ed20a804c5c3365fbb68cd35307920b83dd73a59","source":{"kind":"arxiv","id":"2106.11706","version":2},"attestation_state":"computed","paper":{"title":"On the second realization for the positive part of $U_q(\\widehat{sl_2})$ of equitable type","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Pascal Baseilhac","submitted_at":"2021-06-22T12:25:08Z","abstract_excerpt":"The equitable presentation of the quantum algebra $U_q(\\widehat{sl_2})$ is considered. This presentation was originally introduced by T. Ito and P. Terwilliger. In this paper, following Terwilliger's recent works the (nonstandard) positive part of $U_q(\\widehat{sl_2})$ of equitable type $U_q^{IT,+}$ and its second realization (current algebra) $U_q^{T,+}$ are introduced and studied. A presentation for $U_q^{T,+}$ is given in terms of a K-operator satisfying a Freidel-Maillet type equation and a condition on its quantum determinant. Realizations of the K-operator in terms of Ding-Frenkel L-oper"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2106.11706","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2021-06-22T12:25:08Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d5b6c543708787b212341f738c8ced6128e97c2c235135bb97dadc312b6295be","abstract_canon_sha256":"7abc4add9ff9ae3088fe612c103c2d846e9d24abf44c69b9971aa20fb3d6164c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:52:59.789987Z","signature_b64":"qOUp08jvFMtcyZeBZ4SaIHqp/c3NWFvlgI9HZoPhlSaLf6qdnMBpGnR4VbSDXHQp7Uz9spEgdshBYVIIlGBTCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06c412f350adf899eee0bf23ed20a804c5c3365fbb68cd35307920b83dd73a59","last_reissued_at":"2026-07-05T03:52:59.789497Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:52:59.789497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the second realization for the positive part of $U_q(\\widehat{sl_2})$ of equitable type","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Pascal Baseilhac","submitted_at":"2021-06-22T12:25:08Z","abstract_excerpt":"The equitable presentation of the quantum algebra $U_q(\\widehat{sl_2})$ is considered. This presentation was originally introduced by T. Ito and P. Terwilliger. In this paper, following Terwilliger's recent works the (nonstandard) positive part of $U_q(\\widehat{sl_2})$ of equitable type $U_q^{IT,+}$ and its second realization (current algebra) $U_q^{T,+}$ are introduced and studied. A presentation for $U_q^{T,+}$ is given in terms of a K-operator satisfying a Freidel-Maillet type equation and a condition on its quantum determinant. Realizations of the K-operator in terms of Ding-Frenkel L-oper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.11706","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.11706/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2106.11706","created_at":"2026-07-05T03:52:59.789554+00:00"},{"alias_kind":"arxiv_version","alias_value":"2106.11706v2","created_at":"2026-07-05T03:52:59.789554+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.11706","created_at":"2026-07-05T03:52:59.789554+00:00"},{"alias_kind":"pith_short_12","alias_value":"A3CBF42QVX4J","created_at":"2026-07-05T03:52:59.789554+00:00"},{"alias_kind":"pith_short_16","alias_value":"A3CBF42QVX4JT3XA","created_at":"2026-07-05T03:52:59.789554+00:00"},{"alias_kind":"pith_short_8","alias_value":"A3CBF42Q","created_at":"2026-07-05T03:52:59.789554+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/A3CBF42QVX4JT3XAX4R62IFIAT","json":"https://pith.science/pith/A3CBF42QVX4JT3XAX4R62IFIAT.json","graph_json":"https://pith.science/api/pith-number/A3CBF42QVX4JT3XAX4R62IFIAT/graph.json","events_json":"https://pith.science/api/pith-number/A3CBF42QVX4JT3XAX4R62IFIAT/events.json","paper":"https://pith.science/paper/A3CBF42Q"},"agent_actions":{"view_html":"https://pith.science/pith/A3CBF42QVX4JT3XAX4R62IFIAT","download_json":"https://pith.science/pith/A3CBF42QVX4JT3XAX4R62IFIAT.json","view_paper":"https://pith.science/paper/A3CBF42Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2106.11706&json=true","fetch_graph":"https://pith.science/api/pith-number/A3CBF42QVX4JT3XAX4R62IFIAT/graph.json","fetch_events":"https://pith.science/api/pith-number/A3CBF42QVX4JT3XAX4R62IFIAT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A3CBF42QVX4JT3XAX4R62IFIAT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A3CBF42QVX4JT3XAX4R62IFIAT/action/storage_attestation","attest_author":"https://pith.science/pith/A3CBF42QVX4JT3XAX4R62IFIAT/action/author_attestation","sign_citation":"https://pith.science/pith/A3CBF42QVX4JT3XAX4R62IFIAT/action/citation_signature","submit_replication":"https://pith.science/pith/A3CBF42QVX4JT3XAX4R62IFIAT/action/replication_record"}},"created_at":"2026-07-05T03:52:59.789554+00:00","updated_at":"2026-07-05T03:52:59.789554+00:00"}