{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:TH46WC6MNMIRKQBD5W5ILHX3CP","short_pith_number":"pith:TH46WC6M","schema_version":"1.0","canonical_sha256":"99f9eb0bcc6b11154023edba859efb13cbf0e33fc08a5ec0825c180e84d27917","source":{"kind":"arxiv","id":"1210.6900","version":4},"attestation_state":"computed","paper":{"title":"Homological properties of finite type Khovanov-Lauda-Rouquier algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Alexander Kleshchev, Jonathan Brundan, Peter J. McNamara","submitted_at":"2012-10-25T16:35:54Z","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."},"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":"1210.6900","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-25T16:35:54Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"da25a484b3ef78d11509a57dee6a57c12c839ded0908bcaf230f73b02c412213","abstract_canon_sha256":"264ed8e1d784f3e0a8270f8f775af83cae90e7492fa676d70fa95a457d8337a4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:32.538462Z","signature_b64":"LpFjhz4x7ANFSVrFZuE3hb8gaTeLQoabKIwvVmLlbJrZLYQDzKzcvmG6U79Vf235Gcr0HDzXcybiuP4r2C9ZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99f9eb0bcc6b11154023edba859efb13cbf0e33fc08a5ec0825c180e84d27917","last_reissued_at":"2026-05-18T02:29:32.538064Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:32.538064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homological properties of finite type Khovanov-Lauda-Rouquier algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Alexander Kleshchev, Jonathan Brundan, Peter J. McNamara","submitted_at":"2012-10-25T16:35:54Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6900","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1210.6900","created_at":"2026-05-18T02:29:32.538131+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.6900v4","created_at":"2026-05-18T02:29:32.538131+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6900","created_at":"2026-05-18T02:29:32.538131+00:00"},{"alias_kind":"pith_short_12","alias_value":"TH46WC6MNMIR","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"TH46WC6MNMIRKQBD","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"TH46WC6M","created_at":"2026-05-18T12:27:23.164592+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/TH46WC6MNMIRKQBD5W5ILHX3CP","json":"https://pith.science/pith/TH46WC6MNMIRKQBD5W5ILHX3CP.json","graph_json":"https://pith.science/api/pith-number/TH46WC6MNMIRKQBD5W5ILHX3CP/graph.json","events_json":"https://pith.science/api/pith-number/TH46WC6MNMIRKQBD5W5ILHX3CP/events.json","paper":"https://pith.science/paper/TH46WC6M"},"agent_actions":{"view_html":"https://pith.science/pith/TH46WC6MNMIRKQBD5W5ILHX3CP","download_json":"https://pith.science/pith/TH46WC6MNMIRKQBD5W5ILHX3CP.json","view_paper":"https://pith.science/paper/TH46WC6M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.6900&json=true","fetch_graph":"https://pith.science/api/pith-number/TH46WC6MNMIRKQBD5W5ILHX3CP/graph.json","fetch_events":"https://pith.science/api/pith-number/TH46WC6MNMIRKQBD5W5ILHX3CP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TH46WC6MNMIRKQBD5W5ILHX3CP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TH46WC6MNMIRKQBD5W5ILHX3CP/action/storage_attestation","attest_author":"https://pith.science/pith/TH46WC6MNMIRKQBD5W5ILHX3CP/action/author_attestation","sign_citation":"https://pith.science/pith/TH46WC6MNMIRKQBD5W5ILHX3CP/action/citation_signature","submit_replication":"https://pith.science/pith/TH46WC6MNMIRKQBD5W5ILHX3CP/action/replication_record"}},"created_at":"2026-05-18T02:29:32.538131+00:00","updated_at":"2026-05-18T02:29:32.538131+00:00"}