{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:2UENUQVOXS4CQPREL5XOVQDQNR","short_pith_number":"pith:2UENUQVO","schema_version":"1.0","canonical_sha256":"d508da42aebcb8283e245f6eeac0706c4f627efbae4301b04c4f3ca3e7944ca3","source":{"kind":"arxiv","id":"0804.0923","version":2},"attestation_state":"computed","paper":{"title":"Linear Koszul Duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ivan Mirkovi\\'c, Simon Riche","submitted_at":"2008-04-06T17:52:43Z","abstract_excerpt":"In this paper we construct, for F_1 and F_2 subbundles of a vector bundle E, a \"Koszul duality\" equivalence between derived categories of G_m-equivariant coherent (dg-)sheaves on the derived intersection of F_1 and F_2 inside E, and the corresponding derived intersection of the orthogonals of F_1 and F_2 inside the dual vector bundle E^*. We also propose applications to Hecke algebras."},"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":"0804.0923","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2008-04-06T17:52:43Z","cross_cats_sorted":[],"title_canon_sha256":"ad5c5b119352c61d3cf04c84b06e8359cfbaf5ef31759d087a82b81a052b52ca","abstract_canon_sha256":"b8d6ccc83ff765f6a3d75f45392915b892fb02495877483cbfafee147ba2486e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:39.546410Z","signature_b64":"+8O8Kuywd3HMwkbS2UW6T3joQ1vu24lFb8+Gm7mpeKKPln2HI1fNCkY6MPRkA/HkwAqUVjap+nQx6igCNZ5xCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d508da42aebcb8283e245f6eeac0706c4f627efbae4301b04c4f3ca3e7944ca3","last_reissued_at":"2026-05-17T23:53:39.545694Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:39.545694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linear Koszul Duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ivan Mirkovi\\'c, Simon Riche","submitted_at":"2008-04-06T17:52:43Z","abstract_excerpt":"In this paper we construct, for F_1 and F_2 subbundles of a vector bundle E, a \"Koszul duality\" equivalence between derived categories of G_m-equivariant coherent (dg-)sheaves on the derived intersection of F_1 and F_2 inside E, and the corresponding derived intersection of the orthogonals of F_1 and F_2 inside the dual vector bundle E^*. We also propose applications to Hecke algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.0923","kind":"arxiv","version":2},"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":"0804.0923","created_at":"2026-05-17T23:53:39.545809+00:00"},{"alias_kind":"arxiv_version","alias_value":"0804.0923v2","created_at":"2026-05-17T23:53:39.545809+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0804.0923","created_at":"2026-05-17T23:53:39.545809+00:00"},{"alias_kind":"pith_short_12","alias_value":"2UENUQVOXS4C","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"2UENUQVOXS4CQPRE","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"2UENUQVO","created_at":"2026-05-18T12:25:56.245647+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/2UENUQVOXS4CQPREL5XOVQDQNR","json":"https://pith.science/pith/2UENUQVOXS4CQPREL5XOVQDQNR.json","graph_json":"https://pith.science/api/pith-number/2UENUQVOXS4CQPREL5XOVQDQNR/graph.json","events_json":"https://pith.science/api/pith-number/2UENUQVOXS4CQPREL5XOVQDQNR/events.json","paper":"https://pith.science/paper/2UENUQVO"},"agent_actions":{"view_html":"https://pith.science/pith/2UENUQVOXS4CQPREL5XOVQDQNR","download_json":"https://pith.science/pith/2UENUQVOXS4CQPREL5XOVQDQNR.json","view_paper":"https://pith.science/paper/2UENUQVO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0804.0923&json=true","fetch_graph":"https://pith.science/api/pith-number/2UENUQVOXS4CQPREL5XOVQDQNR/graph.json","fetch_events":"https://pith.science/api/pith-number/2UENUQVOXS4CQPREL5XOVQDQNR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2UENUQVOXS4CQPREL5XOVQDQNR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2UENUQVOXS4CQPREL5XOVQDQNR/action/storage_attestation","attest_author":"https://pith.science/pith/2UENUQVOXS4CQPREL5XOVQDQNR/action/author_attestation","sign_citation":"https://pith.science/pith/2UENUQVOXS4CQPREL5XOVQDQNR/action/citation_signature","submit_replication":"https://pith.science/pith/2UENUQVOXS4CQPREL5XOVQDQNR/action/replication_record"}},"created_at":"2026-05-17T23:53:39.545809+00:00","updated_at":"2026-05-17T23:53:39.545809+00:00"}