{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TH46WC6MNMIRKQBD5W5ILHX3CP","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":"264ed8e1d784f3e0a8270f8f775af83cae90e7492fa676d70fa95a457d8337a4","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-25T16:35:54Z","title_canon_sha256":"da25a484b3ef78d11509a57dee6a57c12c839ded0908bcaf230f73b02c412213"},"schema_version":"1.0","source":{"id":"1210.6900","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.6900","created_at":"2026-05-18T02:29:32Z"},{"alias_kind":"arxiv_version","alias_value":"1210.6900v4","created_at":"2026-05-18T02:29:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6900","created_at":"2026-05-18T02:29:32Z"},{"alias_kind":"pith_short_12","alias_value":"TH46WC6MNMIR","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TH46WC6MNMIRKQBD","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TH46WC6M","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:66dd9e40d77266bdc59c7d06ca68ab3b1d2f12d1f76edbdf679ee0fbad1cf16c","target":"graph","created_at":"2026-05-18T02:29:32Z","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 give an algebraic construction of standard modules (infinite dimensional modules categorifying the PBW basis of the underlying quantized enveloping algebra) for Khovanov-Lauda-Rouquier algebras in all finite types. This allows us to prove in an elementary way that these algebras satisfy the homological properties of an `affine quasi-hereditary algebra.' In simply-laced types these properties were established originally by Kato via a geometric approach. We also construct some Koszul-like projective resolutions of standard modules corresponding to multiplicity-free positive roots.","authors_text":"Alexander Kleshchev, Jonathan Brundan, Peter J. McNamara","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-25T16:35:54Z","title":"Homological properties of finite type Khovanov-Lauda-Rouquier algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6900","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":"sha256:813ef6c0fb886a9f8afa2f7db8ae8b61d5ee62ef9f99f640ef60351f693ce6c1","target":"record","created_at":"2026-05-18T02:29:32Z","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":"264ed8e1d784f3e0a8270f8f775af83cae90e7492fa676d70fa95a457d8337a4","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-25T16:35:54Z","title_canon_sha256":"da25a484b3ef78d11509a57dee6a57c12c839ded0908bcaf230f73b02c412213"},"schema_version":"1.0","source":{"id":"1210.6900","kind":"arxiv","version":4}},"canonical_sha256":"99f9eb0bcc6b11154023edba859efb13cbf0e33fc08a5ec0825c180e84d27917","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99f9eb0bcc6b11154023edba859efb13cbf0e33fc08a5ec0825c180e84d27917","first_computed_at":"2026-05-18T02:29:32.538064Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:32.538064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LpFjhz4x7ANFSVrFZuE3hb8gaTeLQoabKIwvVmLlbJrZLYQDzKzcvmG6U79Vf235Gcr0HDzXcybiuP4r2C9ZDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:32.538462Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.6900","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:813ef6c0fb886a9f8afa2f7db8ae8b61d5ee62ef9f99f640ef60351f693ce6c1","sha256:66dd9e40d77266bdc59c7d06ca68ab3b1d2f12d1f76edbdf679ee0fbad1cf16c"],"state_sha256":"bfd477556bfab75da14d871ccbaf36a1bf61e1c86f90b50151cd9d5a753e870a"}