{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QQX6HG7GUEFGITABYKDLI4JPRA","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":"8e756d3d7c9f5c979411e6f4ac89bc267769f8901adcc7f02ff09469ca2f6064","cross_cats_sorted":["math.QA","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-07-21T16:21:16Z","title_canon_sha256":"0b117194f65c59eb71f9640edd32897072af676c2d07b3e7816eee2c443fd129"},"schema_version":"1.0","source":{"id":"1507.05894","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05894","created_at":"2026-05-18T01:23:49Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05894v2","created_at":"2026-05-18T01:23:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05894","created_at":"2026-05-18T01:23:49Z"},{"alias_kind":"pith_short_12","alias_value":"QQX6HG7GUEFG","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QQX6HG7GUEFGITAB","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QQX6HG7G","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:60a6cec727f6f7c86c13a95fff4ca47c630d5404f751db8332ed4493eb0440a8","target":"graph","created_at":"2026-05-18T01:23:49Z","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 analyze the BGG Category $\\mathcal{O}$ over a large class of generalized Weyl algebras (henceforth termed GWAs). Given such a \"triangular\" GWA for which Category $\\mathcal{O}$ decomposes into a direct sum of subcategories, we study in detail the homological properties of blocks with finitely many simples. As consequences, we show that the endomorphism algebra of a projective generator of such a block is quasi-hereditary, finite-dimensional, and graded Koszul. We also classify all tilting modules in the block, as well as all submodules of all projective and tilting modules. Finally, we prese","authors_text":"Akaki Tikaradze, Apoorva Khare","cross_cats":["math.QA","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-07-21T16:21:16Z","title":"On Category $\\mathcal{O}$ over triangular Generalized Weyl Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05894","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:bb816ec658df1ac3029b463c069cfe700e6b0abfc3db94e84c4e7b29542f813a","target":"record","created_at":"2026-05-18T01:23:49Z","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":"8e756d3d7c9f5c979411e6f4ac89bc267769f8901adcc7f02ff09469ca2f6064","cross_cats_sorted":["math.QA","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-07-21T16:21:16Z","title_canon_sha256":"0b117194f65c59eb71f9640edd32897072af676c2d07b3e7816eee2c443fd129"},"schema_version":"1.0","source":{"id":"1507.05894","kind":"arxiv","version":2}},"canonical_sha256":"842fe39be6a10a644c01c286b4712f8811a3fd7f2e523941598263ce86496b4a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"842fe39be6a10a644c01c286b4712f8811a3fd7f2e523941598263ce86496b4a","first_computed_at":"2026-05-18T01:23:49.007698Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:49.007698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8wrTnnzMZRNx83SK+Vl8WKzZWgZC0jSljPThDNE1SLqZT/j2VURA0FIdYTnU/BdIKBqoMtXFVvVfhMf5CTViAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:49.008280Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.05894","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb816ec658df1ac3029b463c069cfe700e6b0abfc3db94e84c4e7b29542f813a","sha256:60a6cec727f6f7c86c13a95fff4ca47c630d5404f751db8332ed4493eb0440a8"],"state_sha256":"7a1bdc82b2867d6d5b577d331b81192ef74d9e61b17eb924b74023dc56d4289f"}