{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:YBGHFIGO2C4U5LKWCZM4QJH6RH","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":"ba9325b77992b4744133dedafd712c0024910d8bdc41722ac7f87c444575acbf","cross_cats_sorted":[],"license":"","primary_cat":"math.QA","submitted_at":"2003-03-13T19:22:06Z","title_canon_sha256":"44622fd9f4e1558621d3aedd451faff0f1460a8628e1da95cc939441aeef5ffc"},"schema_version":"1.0","source":{"id":"math/0303172","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0303172","created_at":"2026-05-17T23:41:40Z"},{"alias_kind":"arxiv_version","alias_value":"math/0303172v3","created_at":"2026-05-17T23:41:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0303172","created_at":"2026-05-17T23:41:40Z"},{"alias_kind":"pith_short_12","alias_value":"YBGHFIGO2C4U","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"YBGHFIGO2C4U5LKW","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"YBGHFIGO","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:6e5f77cb7dd1404a9c9efbf05e73bdfbc907c08f18a67055be140949af5be2d5","target":"graph","created_at":"2026-05-17T23:41:40Z","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 prove a vanishing theorem of the cohomology arising from the two Quantized Drinfeld-Sokolov reductions (``+'' and ``-'' reduction) introduced by Feigin-Frenkel and Frenkel-Kac-Wakimoto. As a consequence, the vanishing conjecture of Frenkel-Kac-Wakimoto is proved for the ``-'' reduction and partially for the ``+'' reduction.","authors_text":"Tomoyuki Arakawa","cross_cats":[],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2003-03-13T19:22:06Z","title":"Vanishing of cohomology associated to quantized Drinfeld-Sokolov reduction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0303172","kind":"arxiv","version":3},"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":"sha256:3d2a0355abc2ccbc0b35bd280179da8c816d2dd97f2c12ee88f3ca9fb343196e","target":"record","created_at":"2026-05-17T23:41:40Z","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":"ba9325b77992b4744133dedafd712c0024910d8bdc41722ac7f87c444575acbf","cross_cats_sorted":[],"license":"","primary_cat":"math.QA","submitted_at":"2003-03-13T19:22:06Z","title_canon_sha256":"44622fd9f4e1558621d3aedd451faff0f1460a8628e1da95cc939441aeef5ffc"},"schema_version":"1.0","source":{"id":"math/0303172","kind":"arxiv","version":3}},"canonical_sha256":"c04c72a0ced0b94ead561659c824fe89e69d3771c25adbe87d7359c6289f84d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c04c72a0ced0b94ead561659c824fe89e69d3771c25adbe87d7359c6289f84d7","first_computed_at":"2026-05-17T23:41:40.061762Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:40.061762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GVp8tAzs+gBZQEJ6P1yznMAqYPCRBAmbzCVlgVVn+m0s5HEt3LFSE9DhUcy2KB4i2DAyeRKwKkMrx9f2foC4AA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:40.062419Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0303172","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d2a0355abc2ccbc0b35bd280179da8c816d2dd97f2c12ee88f3ca9fb343196e","sha256:6e5f77cb7dd1404a9c9efbf05e73bdfbc907c08f18a67055be140949af5be2d5"],"state_sha256":"80246562ffa8f8c9d905b22eee15555a427c81b20f64ac017e1bd1facd1bcc32"}