{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:A6SCR4YN67BJFBKQ4ZH45XX2TV","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":"280f230e0e8b95a9ecb283adac13c2493909cb2f82e982ea6012c5df3f1506b1","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.RA","submitted_at":"2000-12-29T13:21:37Z","title_canon_sha256":"349c6410c7688ab3c23c53cf52c5ed00e8f5da932f8ed93c6ec4c995a89f9875"},"schema_version":"1.0","source":{"id":"math/0012264","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0012264","created_at":"2026-05-18T04:06:31Z"},{"alias_kind":"arxiv_version","alias_value":"math/0012264v2","created_at":"2026-05-18T04:06:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0012264","created_at":"2026-05-18T04:06:31Z"},{"alias_kind":"pith_short_12","alias_value":"A6SCR4YN67BJ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"A6SCR4YN67BJFBKQ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"A6SCR4YN","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:b0aa48ba898d45abd64b87fc2b334f82233e5417c27dad0cb69554605f132d99","target":"graph","created_at":"2026-05-18T04:06:31Z","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":"Let A and A! be dual Koszul algebras. By Positselski a filtered algebra U with gr U = A is Koszul dual to differential graded algebra (A!,d). We relate the module categories of this dual pair by a tensor-Hom adjunction. This descends to give an equivalence of suitable quotient categories and generalizes work of Beilinson, Ginzburg and Soergel.","authors_text":"Gunnar Floystad","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"math.RA","submitted_at":"2000-12-29T13:21:37Z","title":"Koszul duality and equivalences of categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0012264","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:a6a3ebbed64117e9abd37bba04fdb7e178675556102593975ecc906ab7108df8","target":"record","created_at":"2026-05-18T04:06:31Z","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":"280f230e0e8b95a9ecb283adac13c2493909cb2f82e982ea6012c5df3f1506b1","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.RA","submitted_at":"2000-12-29T13:21:37Z","title_canon_sha256":"349c6410c7688ab3c23c53cf52c5ed00e8f5da932f8ed93c6ec4c995a89f9875"},"schema_version":"1.0","source":{"id":"math/0012264","kind":"arxiv","version":2}},"canonical_sha256":"07a428f30df7c2928550e64fcedefa9d4c54a6bdbb62c64e611031229143ea35","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07a428f30df7c2928550e64fcedefa9d4c54a6bdbb62c64e611031229143ea35","first_computed_at":"2026-05-18T04:06:31.650418Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:31.650418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ClPyL+FznTo+MNpMu9dVQnZxjkI9FcrD0tvIzp6HKsWPQONqkN+TC6oPE8AqYUM9k1vBJ/ALNUY+d56VLRZ7Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:31.651132Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0012264","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6a3ebbed64117e9abd37bba04fdb7e178675556102593975ecc906ab7108df8","sha256:b0aa48ba898d45abd64b87fc2b334f82233e5417c27dad0cb69554605f132d99"],"state_sha256":"d4b6d78d86f391ce2cd74712a02d2f6b8deae760aea80bb7e5ef7d5496a79b13"}