{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZF32YZBFHQIYKO6WLUGS4VUOS6","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":"46280ef43dd047d6366975529e5469d3fe15000177b0b2295ff3928532dc63ec","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.RT","submitted_at":"2026-06-05T05:23:21Z","title_canon_sha256":"236a7fb6791c35639dcc3e0d9bd8e91088ea195d7087a12b284fd3dd0bb45c20"},"schema_version":"1.0","source":{"id":"2606.06913","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.06913","created_at":"2026-06-08T01:04:35Z"},{"alias_kind":"arxiv_version","alias_value":"2606.06913v1","created_at":"2026-06-08T01:04:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06913","created_at":"2026-06-08T01:04:35Z"},{"alias_kind":"pith_short_12","alias_value":"ZF32YZBFHQIY","created_at":"2026-06-08T01:04:35Z"},{"alias_kind":"pith_short_16","alias_value":"ZF32YZBFHQIYKO6W","created_at":"2026-06-08T01:04:35Z"},{"alias_kind":"pith_short_8","alias_value":"ZF32YZBF","created_at":"2026-06-08T01:04:35Z"}],"graph_snapshots":[{"event_id":"sha256:8f605a3cbee8a689f264d84a9c7427b177a3f2bf3d1468da29b2e6cb6d3ec1f5","target":"graph","created_at":"2026-06-08T01:04:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.06913/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Bin Shu, Priyanshu Chakraborty, Yuhui Shen","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.RT","submitted_at":"2026-06-05T05:23:21Z","title":"Whittaker Category and Finite W-superalgebras for Cartan Type Lie Superalgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06913","kind":"arxiv","version":1},"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:af362006ea658a9d1267868b6c35c133e0c8794f75397a6f22b408f757cc0ae2","target":"record","created_at":"2026-06-08T01:04:35Z","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":"46280ef43dd047d6366975529e5469d3fe15000177b0b2295ff3928532dc63ec","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.RT","submitted_at":"2026-06-05T05:23:21Z","title_canon_sha256":"236a7fb6791c35639dcc3e0d9bd8e91088ea195d7087a12b284fd3dd0bb45c20"},"schema_version":"1.0","source":{"id":"2606.06913","kind":"arxiv","version":1}},"canonical_sha256":"c977ac64253c11853bd65d0d2e568e97ae92c57a0d5ea55fcd3ad6f6e04f1428","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c977ac64253c11853bd65d0d2e568e97ae92c57a0d5ea55fcd3ad6f6e04f1428","first_computed_at":"2026-06-08T01:04:35.460826Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-08T01:04:35.460826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rtUB0/9l7+J+XWkH0ZFyd6NO5eAN2GQ3H8GYrDGzlak+IQ+xbxEHQ8r8l/o3uk7CQShP6ohzgAnMA6VsRE2DBQ==","signature_status":"signed_v1","signed_at":"2026-06-08T01:04:35.461614Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.06913","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af362006ea658a9d1267868b6c35c133e0c8794f75397a6f22b408f757cc0ae2","sha256:8f605a3cbee8a689f264d84a9c7427b177a3f2bf3d1468da29b2e6cb6d3ec1f5"],"state_sha256":"539837afa1a26bfb491d382a17243bbbb87ddafbb3d74e09bf9cf9a5d005bd62"}