{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5OW5ZD3MQA2AN5HTF5LGRGBGXR","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":"b29842b7f336574675e7ea1452388f09cae032656f962c54360a1aac1922ba8c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-09-06T03:52:50Z","title_canon_sha256":"a9c195f6ae9edb5b58a419362ce184c52ab21242d42752a9bb21b6c0c975bcd1"},"schema_version":"1.0","source":{"id":"1309.1533","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1533","created_at":"2026-05-18T02:55:03Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1533v4","created_at":"2026-05-18T02:55:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1533","created_at":"2026-05-18T02:55:03Z"},{"alias_kind":"pith_short_12","alias_value":"5OW5ZD3MQA2A","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5OW5ZD3MQA2AN5HT","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5OW5ZD3M","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:51f80fe241725b9e3b16458042acb8a88fe939d9edded81c752753a216411916","target":"graph","created_at":"2026-05-18T02:55:03Z","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":"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","authors_text":"R. B. Zhang, Yuezhu Wu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-09-06T03:52:50Z","title":"Integrable representations of affine A(m, n) and C(m) superalgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1533","kind":"arxiv","version":4},"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":"sha256:122d1e5b41e5927dbb572476639b65a291b5ad2dbbbf3a9c6d3b611186c9380b","target":"record","created_at":"2026-05-18T02:55:03Z","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":"b29842b7f336574675e7ea1452388f09cae032656f962c54360a1aac1922ba8c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-09-06T03:52:50Z","title_canon_sha256":"a9c195f6ae9edb5b58a419362ce184c52ab21242d42752a9bb21b6c0c975bcd1"},"schema_version":"1.0","source":{"id":"1309.1533","kind":"arxiv","version":4}},"canonical_sha256":"ebaddc8f6c803406f4f32f56689826bc7842115aabc472c85b77dff4306e55d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ebaddc8f6c803406f4f32f56689826bc7842115aabc472c85b77dff4306e55d7","first_computed_at":"2026-05-18T02:55:03.955083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:03.955083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PFCDni/wADBqlnExHxXSscEtuCnilqBFRI1rXj6UD91eZol5uEB7qIK35b4wsV3/zwsqNvkqkZGN3Ivf+fbFCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:03.955747Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1533","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:122d1e5b41e5927dbb572476639b65a291b5ad2dbbbf3a9c6d3b611186c9380b","sha256:51f80fe241725b9e3b16458042acb8a88fe939d9edded81c752753a216411916"],"state_sha256":"326228beee1ffd6c2db7906524459adaeda74b846be56505a81873b184e9b5e3"}