{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:5OW5ZD3MQA2AN5HTF5LGRGBGXR","short_pith_number":"pith:5OW5ZD3M","schema_version":"1.0","canonical_sha256":"ebaddc8f6c803406f4f32f56689826bc7842115aabc472c85b77dff4306e55d7","source":{"kind":"arxiv","id":"1309.1533","version":4},"attestation_state":"computed","paper":{"title":"Integrable representations of affine A(m, n) and C(m) superalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"R. B. Zhang, Yuezhu Wu","submitted_at":"2013-09-06T03:52:50Z","abstract_excerpt":"Rao and Zhao classified the irreducible integrable modules with finite dimensional weight spaces for the untwisted affine superalgebras which are not $\\hat{A}(m,n)$ ($m\\ne n$) or $\\hat{C}(m)$. Here we treat the latter affine superalgebras to complete the classification. The problem boils down to classifying the irreducible zero-level integrable modules with finite dimensional weight spaces for these affine superalgebras, which is solved in this paper. We note in particular that such modules for $\\hat{A}(m,n)$ ($m\\ne n$) and $\\hat{C}(m)$ must be of highest weight type, but are not necessarily l"},"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":"1309.1533","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-09-06T03:52:50Z","cross_cats_sorted":[],"title_canon_sha256":"a9c195f6ae9edb5b58a419362ce184c52ab21242d42752a9bb21b6c0c975bcd1","abstract_canon_sha256":"b29842b7f336574675e7ea1452388f09cae032656f962c54360a1aac1922ba8c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:03.955747Z","signature_b64":"PFCDni/wADBqlnExHxXSscEtuCnilqBFRI1rXj6UD91eZol5uEB7qIK35b4wsV3/zwsqNvkqkZGN3Ivf+fbFCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ebaddc8f6c803406f4f32f56689826bc7842115aabc472c85b77dff4306e55d7","last_reissued_at":"2026-05-18T02:55:03.955083Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:03.955083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integrable representations of affine A(m, n) and C(m) superalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"R. B. Zhang, Yuezhu Wu","submitted_at":"2013-09-06T03:52:50Z","abstract_excerpt":"Rao and Zhao classified the irreducible integrable modules with finite dimensional weight spaces for the untwisted affine superalgebras which are not $\\hat{A}(m,n)$ ($m\\ne n$) or $\\hat{C}(m)$. Here we treat the latter affine superalgebras to complete the classification. The problem boils down to classifying the irreducible zero-level integrable modules with finite dimensional weight spaces for these affine superalgebras, which is solved in this paper. We note in particular that such modules for $\\hat{A}(m,n)$ ($m\\ne n$) and $\\hat{C}(m)$ must be of highest weight type, but are not necessarily l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1533","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":"1309.1533","created_at":"2026-05-18T02:55:03.955178+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.1533v4","created_at":"2026-05-18T02:55:03.955178+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1533","created_at":"2026-05-18T02:55:03.955178+00:00"},{"alias_kind":"pith_short_12","alias_value":"5OW5ZD3MQA2A","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_16","alias_value":"5OW5ZD3MQA2AN5HT","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_8","alias_value":"5OW5ZD3M","created_at":"2026-05-18T12:27:34.582898+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/5OW5ZD3MQA2AN5HTF5LGRGBGXR","json":"https://pith.science/pith/5OW5ZD3MQA2AN5HTF5LGRGBGXR.json","graph_json":"https://pith.science/api/pith-number/5OW5ZD3MQA2AN5HTF5LGRGBGXR/graph.json","events_json":"https://pith.science/api/pith-number/5OW5ZD3MQA2AN5HTF5LGRGBGXR/events.json","paper":"https://pith.science/paper/5OW5ZD3M"},"agent_actions":{"view_html":"https://pith.science/pith/5OW5ZD3MQA2AN5HTF5LGRGBGXR","download_json":"https://pith.science/pith/5OW5ZD3MQA2AN5HTF5LGRGBGXR.json","view_paper":"https://pith.science/paper/5OW5ZD3M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.1533&json=true","fetch_graph":"https://pith.science/api/pith-number/5OW5ZD3MQA2AN5HTF5LGRGBGXR/graph.json","fetch_events":"https://pith.science/api/pith-number/5OW5ZD3MQA2AN5HTF5LGRGBGXR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5OW5ZD3MQA2AN5HTF5LGRGBGXR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5OW5ZD3MQA2AN5HTF5LGRGBGXR/action/storage_attestation","attest_author":"https://pith.science/pith/5OW5ZD3MQA2AN5HTF5LGRGBGXR/action/author_attestation","sign_citation":"https://pith.science/pith/5OW5ZD3MQA2AN5HTF5LGRGBGXR/action/citation_signature","submit_replication":"https://pith.science/pith/5OW5ZD3MQA2AN5HTF5LGRGBGXR/action/replication_record"}},"created_at":"2026-05-18T02:55:03.955178+00:00","updated_at":"2026-05-18T02:55:03.955178+00:00"}