{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:JTPXRQJ2VZL3L5BNCXUCZS2DHL","short_pith_number":"pith:JTPXRQJ2","schema_version":"1.0","canonical_sha256":"4cdf78c13aae57b5f42d15e82ccb433af1d4995ea4ec75472d84a5804cd27d7f","source":{"kind":"arxiv","id":"1105.2181","version":4},"attestation_state":"computed","paper":{"title":"Koszul duality and mixed Hodge modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Pramod N. Achar, S. Kitchen","submitted_at":"2011-05-11T13:21:52Z","abstract_excerpt":"We prove that on a certain class of smooth complex varieties (those with \"affine even stratifications\"), the category of mixed Hodge modules is \"almost\" Koszul: it becomes Koszul after a few unwanted extensions are eliminated. We also give an equivalence between perverse sheaves on such a variety and modules for a certain graded ring, obtaining a formality result as a corollary. For flag varieties, these results were proved earlier by Beilinson-Ginzburg-Soergel using a rather different construction."},"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":"1105.2181","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-05-11T13:21:52Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"0534e37f5b816ff8b5bd3fe74bf9e71b2c3f40e56b0a97956bf5106caf98c1c9","abstract_canon_sha256":"5bfd8a4c7dffa6df685ae76f15fb09096e24e7259e3e2c84aa0e85e165f23731"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:28.318184Z","signature_b64":"7vzBpVbV2ua0MU1Me1t8l4PKJwPTKuXsI1xoKMwqDiEq0DkCBnTlJfHseVuYGdMl53n2DdWgHA2AwJpnKCICBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4cdf78c13aae57b5f42d15e82ccb433af1d4995ea4ec75472d84a5804cd27d7f","last_reissued_at":"2026-05-18T03:30:28.317454Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:28.317454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Koszul duality and mixed Hodge modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Pramod N. Achar, S. Kitchen","submitted_at":"2011-05-11T13:21:52Z","abstract_excerpt":"We prove that on a certain class of smooth complex varieties (those with \"affine even stratifications\"), the category of mixed Hodge modules is \"almost\" Koszul: it becomes Koszul after a few unwanted extensions are eliminated. We also give an equivalence between perverse sheaves on such a variety and modules for a certain graded ring, obtaining a formality result as a corollary. For flag varieties, these results were proved earlier by Beilinson-Ginzburg-Soergel using a rather different construction."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2181","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":"1105.2181","created_at":"2026-05-18T03:30:28.317556+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.2181v4","created_at":"2026-05-18T03:30:28.317556+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2181","created_at":"2026-05-18T03:30:28.317556+00:00"},{"alias_kind":"pith_short_12","alias_value":"JTPXRQJ2VZL3","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"JTPXRQJ2VZL3L5BN","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"JTPXRQJ2","created_at":"2026-05-18T12:26:32.869790+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/JTPXRQJ2VZL3L5BNCXUCZS2DHL","json":"https://pith.science/pith/JTPXRQJ2VZL3L5BNCXUCZS2DHL.json","graph_json":"https://pith.science/api/pith-number/JTPXRQJ2VZL3L5BNCXUCZS2DHL/graph.json","events_json":"https://pith.science/api/pith-number/JTPXRQJ2VZL3L5BNCXUCZS2DHL/events.json","paper":"https://pith.science/paper/JTPXRQJ2"},"agent_actions":{"view_html":"https://pith.science/pith/JTPXRQJ2VZL3L5BNCXUCZS2DHL","download_json":"https://pith.science/pith/JTPXRQJ2VZL3L5BNCXUCZS2DHL.json","view_paper":"https://pith.science/paper/JTPXRQJ2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.2181&json=true","fetch_graph":"https://pith.science/api/pith-number/JTPXRQJ2VZL3L5BNCXUCZS2DHL/graph.json","fetch_events":"https://pith.science/api/pith-number/JTPXRQJ2VZL3L5BNCXUCZS2DHL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JTPXRQJ2VZL3L5BNCXUCZS2DHL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JTPXRQJ2VZL3L5BNCXUCZS2DHL/action/storage_attestation","attest_author":"https://pith.science/pith/JTPXRQJ2VZL3L5BNCXUCZS2DHL/action/author_attestation","sign_citation":"https://pith.science/pith/JTPXRQJ2VZL3L5BNCXUCZS2DHL/action/citation_signature","submit_replication":"https://pith.science/pith/JTPXRQJ2VZL3L5BNCXUCZS2DHL/action/replication_record"}},"created_at":"2026-05-18T03:30:28.317556+00:00","updated_at":"2026-05-18T03:30:28.317556+00:00"}