{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:U7ABFSDQOZTQ5ZACK76OLNOPXA","short_pith_number":"pith:U7ABFSDQ","schema_version":"1.0","canonical_sha256":"a7c012c87076670ee40257fce5b5cfb814ae4b4b1a37fc1ea3d9a8eb2aadcbde","source":{"kind":"arxiv","id":"1203.5545","version":4},"attestation_state":"computed","paper":{"title":"Highest weight sl_2-categorifications II: structure theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.CT"],"primary_cat":"math.RT","authors_text":"Ivan Losev","submitted_at":"2012-03-25T21:13:54Z","abstract_excerpt":"This paper continues the study of highest weight categorical sl_2-actions started in part I. We start by refining the definition given there and showing that all examples considered in part I are also highest weight categorifications in the refined sense. Then we prove that any highest weight sl_2-categorification can be filtered in such a way that the successive quotients are so called basic highest weight sl_2-categorifications. For a basic highest weight categorification we determine minimal projective resolutions of standard objects. We use this, in particular, to examine the structure of "},"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":"1203.5545","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-03-25T21:13:54Z","cross_cats_sorted":["math.CO","math.CT"],"title_canon_sha256":"31b4e758b9ce9f93e3c039b1f12d9e098aae8bdf9bb461d112622dea7f71689d","abstract_canon_sha256":"558bf56edc3db2ec48e149fe0603bf2ba4b06740da2a23eff83e0576bfd0ba61"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:03.564864Z","signature_b64":"KBbh76tmRcc7ZQyu2eRsEONF84O7u58QttlW3u9Sd7IRB3oL6HFkRmK8z3gN2TBhSoB8eEH531bC7lApDFiyDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7c012c87076670ee40257fce5b5cfb814ae4b4b1a37fc1ea3d9a8eb2aadcbde","last_reissued_at":"2026-05-18T02:40:03.564427Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:03.564427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Highest weight sl_2-categorifications II: structure theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.CT"],"primary_cat":"math.RT","authors_text":"Ivan Losev","submitted_at":"2012-03-25T21:13:54Z","abstract_excerpt":"This paper continues the study of highest weight categorical sl_2-actions started in part I. We start by refining the definition given there and showing that all examples considered in part I are also highest weight categorifications in the refined sense. Then we prove that any highest weight sl_2-categorification can be filtered in such a way that the successive quotients are so called basic highest weight sl_2-categorifications. For a basic highest weight categorification we determine minimal projective resolutions of standard objects. We use this, in particular, to examine the structure of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5545","kind":"arxiv","version":4},"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":"1203.5545","created_at":"2026-05-18T02:40:03.564498+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.5545v4","created_at":"2026-05-18T02:40:03.564498+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.5545","created_at":"2026-05-18T02:40:03.564498+00:00"},{"alias_kind":"pith_short_12","alias_value":"U7ABFSDQOZTQ","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"U7ABFSDQOZTQ5ZAC","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"U7ABFSDQ","created_at":"2026-05-18T12:27:23.164592+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/U7ABFSDQOZTQ5ZACK76OLNOPXA","json":"https://pith.science/pith/U7ABFSDQOZTQ5ZACK76OLNOPXA.json","graph_json":"https://pith.science/api/pith-number/U7ABFSDQOZTQ5ZACK76OLNOPXA/graph.json","events_json":"https://pith.science/api/pith-number/U7ABFSDQOZTQ5ZACK76OLNOPXA/events.json","paper":"https://pith.science/paper/U7ABFSDQ"},"agent_actions":{"view_html":"https://pith.science/pith/U7ABFSDQOZTQ5ZACK76OLNOPXA","download_json":"https://pith.science/pith/U7ABFSDQOZTQ5ZACK76OLNOPXA.json","view_paper":"https://pith.science/paper/U7ABFSDQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.5545&json=true","fetch_graph":"https://pith.science/api/pith-number/U7ABFSDQOZTQ5ZACK76OLNOPXA/graph.json","fetch_events":"https://pith.science/api/pith-number/U7ABFSDQOZTQ5ZACK76OLNOPXA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U7ABFSDQOZTQ5ZACK76OLNOPXA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U7ABFSDQOZTQ5ZACK76OLNOPXA/action/storage_attestation","attest_author":"https://pith.science/pith/U7ABFSDQOZTQ5ZACK76OLNOPXA/action/author_attestation","sign_citation":"https://pith.science/pith/U7ABFSDQOZTQ5ZACK76OLNOPXA/action/citation_signature","submit_replication":"https://pith.science/pith/U7ABFSDQOZTQ5ZACK76OLNOPXA/action/replication_record"}},"created_at":"2026-05-18T02:40:03.564498+00:00","updated_at":"2026-05-18T02:40:03.564498+00:00"}