{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:O5TGZK63EJRUIL76NBKVCYK25W","short_pith_number":"pith:O5TGZK63","schema_version":"1.0","canonical_sha256":"77666cabdb2263442ffe685551615aedb1f19b57d73527a1f679eb7f64402adf","source":{"kind":"arxiv","id":"1307.7816","version":2},"attestation_state":"computed","paper":{"title":"An odd categorification of quantum sl(2)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Aaron D. Lauda, Alexander P. Ellis","submitted_at":"2013-07-30T04:54:29Z","abstract_excerpt":"We define a 2-category that categorifies the covering Kac-Moody algebra for sl(2) introduced by Clark and Wang. This categorification forms the structure of a super-2-category as formulated by Kang, Kashiwara, and Oh. The super-2-category structure introduces a (Z x Z_2)-grading giving its Grothendieck group the structure of a free module over the group algebra of Z x Z_2. By specializing the Z_2-action to +1 or to -1, the construction specializes to an \"odd\" categorification of sl(2) and to a supercategorification of osp(1|2), respectively."},"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":"1307.7816","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-07-30T04:54:29Z","cross_cats_sorted":[],"title_canon_sha256":"a3e7b956b39105b04967a691c1b0a5faa2cd0d2366f731cd3d41b8d997f5a35d","abstract_canon_sha256":"973054b3e8b6e584faa954277aac0fa4a09311ed66f13520c9b77b581925043b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:18.717729Z","signature_b64":"EL0WOzV5KLI0vQ434xdsD2+i7M/btdKkbQ/favdaI7ep9XA+XxjfyqpdqTlsB62B5t+GKBNJluuH8ASiaJDoCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77666cabdb2263442ffe685551615aedb1f19b57d73527a1f679eb7f64402adf","last_reissued_at":"2026-05-18T01:11:18.717260Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:18.717260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An odd categorification of quantum sl(2)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Aaron D. Lauda, Alexander P. Ellis","submitted_at":"2013-07-30T04:54:29Z","abstract_excerpt":"We define a 2-category that categorifies the covering Kac-Moody algebra for sl(2) introduced by Clark and Wang. This categorification forms the structure of a super-2-category as formulated by Kang, Kashiwara, and Oh. The super-2-category structure introduces a (Z x Z_2)-grading giving its Grothendieck group the structure of a free module over the group algebra of Z x Z_2. By specializing the Z_2-action to +1 or to -1, the construction specializes to an \"odd\" categorification of sl(2) and to a supercategorification of osp(1|2), respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7816","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":""},"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":"1307.7816","created_at":"2026-05-18T01:11:18.717324+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.7816v2","created_at":"2026-05-18T01:11:18.717324+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7816","created_at":"2026-05-18T01:11:18.717324+00:00"},{"alias_kind":"pith_short_12","alias_value":"O5TGZK63EJRU","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"O5TGZK63EJRUIL76","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"O5TGZK63","created_at":"2026-05-18T12:27:54.935989+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/O5TGZK63EJRUIL76NBKVCYK25W","json":"https://pith.science/pith/O5TGZK63EJRUIL76NBKVCYK25W.json","graph_json":"https://pith.science/api/pith-number/O5TGZK63EJRUIL76NBKVCYK25W/graph.json","events_json":"https://pith.science/api/pith-number/O5TGZK63EJRUIL76NBKVCYK25W/events.json","paper":"https://pith.science/paper/O5TGZK63"},"agent_actions":{"view_html":"https://pith.science/pith/O5TGZK63EJRUIL76NBKVCYK25W","download_json":"https://pith.science/pith/O5TGZK63EJRUIL76NBKVCYK25W.json","view_paper":"https://pith.science/paper/O5TGZK63","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.7816&json=true","fetch_graph":"https://pith.science/api/pith-number/O5TGZK63EJRUIL76NBKVCYK25W/graph.json","fetch_events":"https://pith.science/api/pith-number/O5TGZK63EJRUIL76NBKVCYK25W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O5TGZK63EJRUIL76NBKVCYK25W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O5TGZK63EJRUIL76NBKVCYK25W/action/storage_attestation","attest_author":"https://pith.science/pith/O5TGZK63EJRUIL76NBKVCYK25W/action/author_attestation","sign_citation":"https://pith.science/pith/O5TGZK63EJRUIL76NBKVCYK25W/action/citation_signature","submit_replication":"https://pith.science/pith/O5TGZK63EJRUIL76NBKVCYK25W/action/replication_record"}},"created_at":"2026-05-18T01:11:18.717324+00:00","updated_at":"2026-05-18T01:11:18.717324+00:00"}