{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:5OW5ZD3MQA2AN5HTF5LGRGBGXR","short_pith_number":"pith:5OW5ZD3M","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"},"canonical_sha256":"ebaddc8f6c803406f4f32f56689826bc7842115aabc472c85b77dff4306e55d7","source":{"kind":"arxiv","id":"1309.1533","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:5OW5ZD3MQA2AN5HTF5LGRGBGXR","target":"record","payload":{"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"},"canonical_sha256":"ebaddc8f6c803406f4f32f56689826bc7842115aabc472c85b77dff4306e55d7","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"},"source_kind":"arxiv","source_id":"1309.1533","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:55:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TqHTd9Zs8PIUO85bjf1OWSCmh5Ouvotu9t78YATUoq2FI1VHfHrfZU9i3Txsng0Aq87Div+Kfy3ZTjxFeKa9Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:11:31.207637Z"},"content_sha256":"122d1e5b41e5927dbb572476639b65a291b5ad2dbbbf3a9c6d3b611186c9380b","schema_version":"1.0","event_id":"sha256:122d1e5b41e5927dbb572476639b65a291b5ad2dbbbf3a9c6d3b611186c9380b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:5OW5ZD3MQA2AN5HTF5LGRGBGXR","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:55:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"617tQ4iLJ07o2LV1S7W1yuq8Uc+TMolgkDcNaGiQlKd4hkMTrK+xTi+fwpgwHQzl4esANec9W43T4SfbZBhiCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:11:31.207982Z"},"content_sha256":"51f80fe241725b9e3b16458042acb8a88fe939d9edded81c752753a216411916","schema_version":"1.0","event_id":"sha256:51f80fe241725b9e3b16458042acb8a88fe939d9edded81c752753a216411916"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5OW5ZD3MQA2AN5HTF5LGRGBGXR/bundle.json","state_url":"https://pith.science/pith/5OW5ZD3MQA2AN5HTF5LGRGBGXR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5OW5ZD3MQA2AN5HTF5LGRGBGXR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T21:11:31Z","links":{"resolver":"https://pith.science/pith/5OW5ZD3MQA2AN5HTF5LGRGBGXR","bundle":"https://pith.science/pith/5OW5ZD3MQA2AN5HTF5LGRGBGXR/bundle.json","state":"https://pith.science/pith/5OW5ZD3MQA2AN5HTF5LGRGBGXR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5OW5ZD3MQA2AN5HTF5LGRGBGXR/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KCRSfBEkrgE31Z+gqVhEcMHB1k2+95EVuAK/0ZEGT6dMstPprh2ToBdVT5fVdXTbw3GfzurRbEkkwPVfVgm1Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T21:11:31.210282Z","bundle_sha256":"cc44e7d08c82fac5f440fcf27461289f10a9f37ca560b316b312daec9bc27432"}}