{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HV4P5RN3IUTF7RGN3275KWLKY6","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":"1e88ac638854519c15e249f2d11e2551385e9beb80eb3b0d26c77b5f0a452450","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-08-28T16:25:39Z","title_canon_sha256":"ffa91383d570eb1588c9909f7858fdf958634654d08f3ab8b249696658a8d233"},"schema_version":"1.0","source":{"id":"1808.09388","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.09388","created_at":"2026-07-05T01:16:07Z"},{"alias_kind":"arxiv_version","alias_value":"1808.09388v4","created_at":"2026-07-05T01:16:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.09388","created_at":"2026-07-05T01:16:07Z"},{"alias_kind":"pith_short_12","alias_value":"HV4P5RN3IUTF","created_at":"2026-07-05T01:16:07Z"},{"alias_kind":"pith_short_16","alias_value":"HV4P5RN3IUTF7RGN","created_at":"2026-07-05T01:16:07Z"},{"alias_kind":"pith_short_8","alias_value":"HV4P5RN3","created_at":"2026-07-05T01:16:07Z"}],"graph_snapshots":[{"event_id":"sha256:4d7ad9934807c578a4894843a3904afeab5f2054c478705f0c60be98c55da0fa","target":"graph","created_at":"2026-07-05T01:16:07Z","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/1808.09388/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We generalize a construction in [BW18] (arXiv:1610.09271) by showing that the tensor product of a based $\\textbf{U}^{\\imath}$-module and a based $\\textbf{U}$-module is a based $\\textbf{U}^{\\imath}$-module. This is then used to formulate a Kazhdan-Lusztig theory for an arbitrary parabolic BGG category $\\mathcal{O}$ of the ortho-symplectic Lie superalgebras, extending a main result in [BW13] (arXiv:1310.0103).","authors_text":"Hideya Watanabe, Huanchen Bao, Weiqiang Wang","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-08-28T16:25:39Z","title":"Canonical bases for tensor products and super Kazhdan-Lusztig theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09388","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":"sha256:9917d644e9e3b56ee8da7a593407911fe6628afbd6ce88cbd110224ae7ac0c48","target":"record","created_at":"2026-07-05T01:16:07Z","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":"1e88ac638854519c15e249f2d11e2551385e9beb80eb3b0d26c77b5f0a452450","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-08-28T16:25:39Z","title_canon_sha256":"ffa91383d570eb1588c9909f7858fdf958634654d08f3ab8b249696658a8d233"},"schema_version":"1.0","source":{"id":"1808.09388","kind":"arxiv","version":4}},"canonical_sha256":"3d78fec5bb45265fc4cddebfd5596ac7b72f702dcc039ac8027c7c72249d231f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d78fec5bb45265fc4cddebfd5596ac7b72f702dcc039ac8027c7c72249d231f","first_computed_at":"2026-07-05T01:16:07.359337Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:16:07.359337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"63dS84AmPhHsPgQ61WFgADxAVYq5PsmPI62C+/UL1alU13D/YRlSYe3/kIiiG60dAMpcnRCc2+lqiRygX9jXDA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:16:07.359920Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.09388","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9917d644e9e3b56ee8da7a593407911fe6628afbd6ce88cbd110224ae7ac0c48","sha256:4d7ad9934807c578a4894843a3904afeab5f2054c478705f0c60be98c55da0fa"],"state_sha256":"ec4a67d5a184287458a0c7e4ce8c2686d5c36054aaefd3a978d1f5376b9378e8"}