{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:ZF32YZBFHQIYKO6WLUGS4VUOS6","short_pith_number":"pith:ZF32YZBF","schema_version":"1.0","canonical_sha256":"c977ac64253c11853bd65d0d2e568e97ae92c57a0d5ea55fcd3ad6f6e04f1428","source":{"kind":"arxiv","id":"2606.06913","version":1},"attestation_state":"computed","paper":{"title":"Whittaker Category and Finite W-superalgebras for Cartan Type Lie Superalgebras","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Bin Shu, Priyanshu Chakraborty, Yuhui Shen","submitted_at":"2026-06-05T05:23:21Z","abstract_excerpt":"Let $W(n)$ be the finite-dimensional simple Lie superalgebra of fundamental type in the Cartan type series of Kac's classification result \\cite{Kac77} over an algebraically closed field of characteristic $0$. Let $\\mathbf{g}$ be the graded-zero part of $W(n)$ which is isomorphic to $\\mathfrak{gl}(n)$. In the first part of this paper, following the basic idea of taking the ``minimal\" parabolic subalgebra $\\mathsf{P}$ as a working platform in \\cite{DSY} we introduce the Whittaker category $\\mscrw$ for representations of $W(n)$ associated with a nilpotent element $e$ in $\\mathbf{g}_0$ and with $W"},"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":"2606.06913","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.RT","submitted_at":"2026-06-05T05:23:21Z","cross_cats_sorted":[],"title_canon_sha256":"236a7fb6791c35639dcc3e0d9bd8e91088ea195d7087a12b284fd3dd0bb45c20","abstract_canon_sha256":"46280ef43dd047d6366975529e5469d3fe15000177b0b2295ff3928532dc63ec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-08T01:04:35.461614Z","signature_b64":"rtUB0/9l7+J+XWkH0ZFyd6NO5eAN2GQ3H8GYrDGzlak+IQ+xbxEHQ8r8l/o3uk7CQShP6ohzgAnMA6VsRE2DBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c977ac64253c11853bd65d0d2e568e97ae92c57a0d5ea55fcd3ad6f6e04f1428","last_reissued_at":"2026-06-08T01:04:35.460826Z","signature_status":"signed_v1","first_computed_at":"2026-06-08T01:04:35.460826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Whittaker Category and Finite W-superalgebras for Cartan Type Lie Superalgebras","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Bin Shu, Priyanshu Chakraborty, Yuhui Shen","submitted_at":"2026-06-05T05:23:21Z","abstract_excerpt":"Let $W(n)$ be the finite-dimensional simple Lie superalgebra of fundamental type in the Cartan type series of Kac's classification result \\cite{Kac77} over an algebraically closed field of characteristic $0$. Let $\\mathbf{g}$ be the graded-zero part of $W(n)$ which is isomorphic to $\\mathfrak{gl}(n)$. In the first part of this paper, following the basic idea of taking the ``minimal\" parabolic subalgebra $\\mathsf{P}$ as a working platform in \\cite{DSY} we introduce the Whittaker category $\\mscrw$ for representations of $W(n)$ associated with a nilpotent element $e$ in $\\mathbf{g}_0$ and with $W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06913","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/2606.06913/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":"2606.06913","created_at":"2026-06-08T01:04:35.460956+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.06913v1","created_at":"2026-06-08T01:04:35.460956+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06913","created_at":"2026-06-08T01:04:35.460956+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZF32YZBFHQIY","created_at":"2026-06-08T01:04:35.460956+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZF32YZBFHQIYKO6W","created_at":"2026-06-08T01:04:35.460956+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZF32YZBF","created_at":"2026-06-08T01:04:35.460956+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/ZF32YZBFHQIYKO6WLUGS4VUOS6","json":"https://pith.science/pith/ZF32YZBFHQIYKO6WLUGS4VUOS6.json","graph_json":"https://pith.science/api/pith-number/ZF32YZBFHQIYKO6WLUGS4VUOS6/graph.json","events_json":"https://pith.science/api/pith-number/ZF32YZBFHQIYKO6WLUGS4VUOS6/events.json","paper":"https://pith.science/paper/ZF32YZBF"},"agent_actions":{"view_html":"https://pith.science/pith/ZF32YZBFHQIYKO6WLUGS4VUOS6","download_json":"https://pith.science/pith/ZF32YZBFHQIYKO6WLUGS4VUOS6.json","view_paper":"https://pith.science/paper/ZF32YZBF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.06913&json=true","fetch_graph":"https://pith.science/api/pith-number/ZF32YZBFHQIYKO6WLUGS4VUOS6/graph.json","fetch_events":"https://pith.science/api/pith-number/ZF32YZBFHQIYKO6WLUGS4VUOS6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZF32YZBFHQIYKO6WLUGS4VUOS6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZF32YZBFHQIYKO6WLUGS4VUOS6/action/storage_attestation","attest_author":"https://pith.science/pith/ZF32YZBFHQIYKO6WLUGS4VUOS6/action/author_attestation","sign_citation":"https://pith.science/pith/ZF32YZBFHQIYKO6WLUGS4VUOS6/action/citation_signature","submit_replication":"https://pith.science/pith/ZF32YZBFHQIYKO6WLUGS4VUOS6/action/replication_record"}},"created_at":"2026-06-08T01:04:35.460956+00:00","updated_at":"2026-06-08T01:04:35.460956+00:00"}