{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:J3BSED7U7RH5GNWLO4RZWO2UL3","short_pith_number":"pith:J3BSED7U","schema_version":"1.0","canonical_sha256":"4ec3220ff4fc4fd336cb77239b3b545eca955d7fdc0d8985b5dab29e8de892ab","source":{"kind":"arxiv","id":"2606.11551","version":1},"attestation_state":"computed","paper":{"title":"Gelfand--Kirillov dimensions of highest weight modules for basic classical Lie superalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jing Jiang","submitted_at":"2026-06-10T01:21:50Z","abstract_excerpt":"In this paper we develop a combinatorial algorithm to compute the Gelfand--Kirillov (GK) dimension of simple highest weight modules for basic classical Lie superalgebras. Building upon the results for classical Lie algebras via Lusztig's {\\bf a}-function and the Robinson--Schensted (RS) insertion algorithm, we extend these techniques to the super setting, providing explicit formulas for types $\\mathfrak{sl}(m|n)$ and $\\mathfrak{osp}(2|2n)$. Our results show that the GK dimension of a simple highest weight module is determined entirely by the even part of the Lie superalgebras."},"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":"2606.11551","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-06-10T01:21:50Z","cross_cats_sorted":[],"title_canon_sha256":"53853f661690c900c936bbd8de86e43dbf0096acd59de6a466b24c85e0ff42a4","abstract_canon_sha256":"8a90142bc34532aaf6851b21b3056fe05ed0dd4473c52c5734ae6ae842b7ba40"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-11T01:09:55.603902Z","signature_b64":"crbdIwTJJnvleBNg5rPJ9a8PaGKHRa40DCN2sCCYRFsO5nuEayAbSf5mPwwQKAZz0lfYPLmJtF5aZvx929jdCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ec3220ff4fc4fd336cb77239b3b545eca955d7fdc0d8985b5dab29e8de892ab","last_reissued_at":"2026-06-11T01:09:55.603010Z","signature_status":"signed_v1","first_computed_at":"2026-06-11T01:09:55.603010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gelfand--Kirillov dimensions of highest weight modules for basic classical Lie superalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jing Jiang","submitted_at":"2026-06-10T01:21:50Z","abstract_excerpt":"In this paper we develop a combinatorial algorithm to compute the Gelfand--Kirillov (GK) dimension of simple highest weight modules for basic classical Lie superalgebras. Building upon the results for classical Lie algebras via Lusztig's {\\bf a}-function and the Robinson--Schensted (RS) insertion algorithm, we extend these techniques to the super setting, providing explicit formulas for types $\\mathfrak{sl}(m|n)$ and $\\mathfrak{osp}(2|2n)$. Our results show that the GK dimension of a simple highest weight module is determined entirely by the even part of the Lie superalgebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11551","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.11551/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.11551","created_at":"2026-06-11T01:09:55.603152+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.11551v1","created_at":"2026-06-11T01:09:55.603152+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.11551","created_at":"2026-06-11T01:09:55.603152+00:00"},{"alias_kind":"pith_short_12","alias_value":"J3BSED7U7RH5","created_at":"2026-06-11T01:09:55.603152+00:00"},{"alias_kind":"pith_short_16","alias_value":"J3BSED7U7RH5GNWL","created_at":"2026-06-11T01:09:55.603152+00:00"},{"alias_kind":"pith_short_8","alias_value":"J3BSED7U","created_at":"2026-06-11T01:09:55.603152+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/J3BSED7U7RH5GNWLO4RZWO2UL3","json":"https://pith.science/pith/J3BSED7U7RH5GNWLO4RZWO2UL3.json","graph_json":"https://pith.science/api/pith-number/J3BSED7U7RH5GNWLO4RZWO2UL3/graph.json","events_json":"https://pith.science/api/pith-number/J3BSED7U7RH5GNWLO4RZWO2UL3/events.json","paper":"https://pith.science/paper/J3BSED7U"},"agent_actions":{"view_html":"https://pith.science/pith/J3BSED7U7RH5GNWLO4RZWO2UL3","download_json":"https://pith.science/pith/J3BSED7U7RH5GNWLO4RZWO2UL3.json","view_paper":"https://pith.science/paper/J3BSED7U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.11551&json=true","fetch_graph":"https://pith.science/api/pith-number/J3BSED7U7RH5GNWLO4RZWO2UL3/graph.json","fetch_events":"https://pith.science/api/pith-number/J3BSED7U7RH5GNWLO4RZWO2UL3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J3BSED7U7RH5GNWLO4RZWO2UL3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J3BSED7U7RH5GNWLO4RZWO2UL3/action/storage_attestation","attest_author":"https://pith.science/pith/J3BSED7U7RH5GNWLO4RZWO2UL3/action/author_attestation","sign_citation":"https://pith.science/pith/J3BSED7U7RH5GNWLO4RZWO2UL3/action/citation_signature","submit_replication":"https://pith.science/pith/J3BSED7U7RH5GNWLO4RZWO2UL3/action/replication_record"}},"created_at":"2026-06-11T01:09:55.603152+00:00","updated_at":"2026-06-11T01:09:55.603152+00:00"}