{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3RZC4WRIE6JBONOEF26I6NRXNT","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":"eeb7923d8e136b63a8c6b112a8170d8f5ffe97f1bda3c7ad8d0d2256951f45e5","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-09-04T02:36:00Z","title_canon_sha256":"fb1776d8a0609f377c98aefec9c8dcd10ab49eb57ce060648f6e378cab2ebb9c"},"schema_version":"1.0","source":{"id":"1409.1305","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.1305","created_at":"2026-05-18T02:25:34Z"},{"alias_kind":"arxiv_version","alias_value":"1409.1305v2","created_at":"2026-05-18T02:25:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1305","created_at":"2026-05-18T02:25:34Z"},{"alias_kind":"pith_short_12","alias_value":"3RZC4WRIE6JB","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3RZC4WRIE6JBONOE","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3RZC4WRI","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:0a536ad3510b8b1ece3ade4c5993643e88fb0125344e8f1a835dfae4b58af388","target":"graph","created_at":"2026-05-18T02:25:34Z","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":"We give a formula for the superdimension of a finite-dimensional simple gl(m|n)-module using the Su-Zhang character formula. As a corollary, we obtain a simple algebraic proof of a conjecture of Kac-Wakimoto for gl(m|n), namely, a simple module has nonzero superdimension if and only if it has maximal degree of atypicality. This conjecture was proven originally by Serganova using the Duflo-Serganova associated variety.","authors_text":"Michael Chmutov, Rachel Karpman, Shifra Reif","cross_cats":["math-ph","math.CO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-09-04T02:36:00Z","title":"A superdimension formula for gl(m|n) modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1305","kind":"arxiv","version":2},"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":"sha256:7b43584c308af4d5532f14b8c7fa081de0f421fb39dbd30862347564af4378bf","target":"record","created_at":"2026-05-18T02:25:34Z","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":"eeb7923d8e136b63a8c6b112a8170d8f5ffe97f1bda3c7ad8d0d2256951f45e5","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-09-04T02:36:00Z","title_canon_sha256":"fb1776d8a0609f377c98aefec9c8dcd10ab49eb57ce060648f6e378cab2ebb9c"},"schema_version":"1.0","source":{"id":"1409.1305","kind":"arxiv","version":2}},"canonical_sha256":"dc722e5a2827921735c42ebc8f36376cee9260e3eed82ef567a08f9771a65f83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc722e5a2827921735c42ebc8f36376cee9260e3eed82ef567a08f9771a65f83","first_computed_at":"2026-05-18T02:25:34.008732Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:34.008732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SrSNAyqYNshvrRi4jPi9dGCBftuoFc0C2DPnWnKzKVo4v5v5A9+XDXRvBeOLY8iyyDNG6eBqCvfewXdSmMaoDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:34.009117Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.1305","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b43584c308af4d5532f14b8c7fa081de0f421fb39dbd30862347564af4378bf","sha256:0a536ad3510b8b1ece3ade4c5993643e88fb0125344e8f1a835dfae4b58af388"],"state_sha256":"a40515e1b9fe887b6abae4c63e6409e8d33cca64e13260f5a4a9a46408bf8c0e"}