{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:OXIAFRLR5NM7YF2F3T2UNVROS7","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":"48cb7feb4699c1322c57de2a8ffd995d8b645b46909d8d4d613f2892497c0ea5","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2009-06-25T08:02:43Z","title_canon_sha256":"f57e0e4659cf33c835e5076b2ef2a484e453be10a727bcb5ba65b3e402e85501"},"schema_version":"1.0","source":{"id":"0906.4623","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.4623","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"0906.4623v2","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.4623","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"OXIAFRLR5NM7","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"OXIAFRLR5NM7YF2F","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"OXIAFRLR","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:946fd29c14d71cb655503a8fbb5608f406c33e34ee9261985f7bb0673f9e22bc","target":"graph","created_at":"2026-05-18T02:18:41Z","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 that rational and 1-rational singularities of complex spaces are stable under taking quotients by holomorphic actions of reductive and compact Lie groups. This extends a result of Boutot to the analytic category and yields a refinement of his result in the algebraic category. As one of the main technical tools vanishing theorems for cohomology groups with support on fibres of resolutions are proven.","authors_text":"Daniel Greb","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2009-06-25T08:02:43Z","title":"Rational singularities and quotients by holomorphic group actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.4623","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:b9bc7f17e98cf3d9d177bee7f4a3f6f091140b4014669c274b825b0c84146036","target":"record","created_at":"2026-05-18T02:18:41Z","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":"48cb7feb4699c1322c57de2a8ffd995d8b645b46909d8d4d613f2892497c0ea5","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2009-06-25T08:02:43Z","title_canon_sha256":"f57e0e4659cf33c835e5076b2ef2a484e453be10a727bcb5ba65b3e402e85501"},"schema_version":"1.0","source":{"id":"0906.4623","kind":"arxiv","version":2}},"canonical_sha256":"75d002c571eb59fc1745dcf546d62e97ee7c1ce2b580fce133996ceebb123943","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75d002c571eb59fc1745dcf546d62e97ee7c1ce2b580fce133996ceebb123943","first_computed_at":"2026-05-18T02:18:41.375644Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:41.375644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mTOE3s4Tpfs4nlug8GSbpKsZnn+dYqI1I3RMft9Nf3GOXoEmgg3JpuWJVhnCJ05mlnCAE8L4C0kzoP1xMackCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:41.376449Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.4623","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9bc7f17e98cf3d9d177bee7f4a3f6f091140b4014669c274b825b0c84146036","sha256:946fd29c14d71cb655503a8fbb5608f406c33e34ee9261985f7bb0673f9e22bc"],"state_sha256":"55149299e1e95963923ddb51b737fef2f51fd8935fc266039ee0147fbc9b5fe8"}