{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:COH7UITCATQE3BOLTPTBPT45KY","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":"69d3105a3d02c6874b87a2482dba0d2463b0ab405f73a7157409e3cc18ecbbd5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-02-18T19:43:59Z","title_canon_sha256":"be3a47bd3d0a262733335a25c36b2c8a38ce4dce521b99f741cff7f9cdfb1a99"},"schema_version":"1.0","source":{"id":"1102.3893","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3893","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3893v4","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3893","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"pith_short_12","alias_value":"COH7UITCATQE","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"COH7UITCATQE3BOL","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"COH7UITC","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:232ad1202577a6925580c2a28aab2c2e0135b3b36d9edd107fd3ef89fbded65f","target":"graph","created_at":"2026-05-18T02:40:47Z","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":"In this short note we prove that any complete four dimensional anti-self-dual (or self-dual) quasi-Einstein manifolds is either Einstein or locally conformally flat. This generalizes a recent result of X. Chen and Y. Wang.","authors_text":"Giovanni Catino","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-02-18T19:43:59Z","title":"A note on four dimensional (anti-)self-dual quasi-Einstein manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3893","kind":"arxiv","version":4},"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":"sha256:5ce22e13dcc81d935c10b155026b9d4c62a81a35cc910a795a7b9ae36d73e838","target":"record","created_at":"2026-05-18T02:40:47Z","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":"69d3105a3d02c6874b87a2482dba0d2463b0ab405f73a7157409e3cc18ecbbd5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-02-18T19:43:59Z","title_canon_sha256":"be3a47bd3d0a262733335a25c36b2c8a38ce4dce521b99f741cff7f9cdfb1a99"},"schema_version":"1.0","source":{"id":"1102.3893","kind":"arxiv","version":4}},"canonical_sha256":"138ffa226204e04d85cb9be617cf9d5600a5d5c8f6c56f2f59ceb1c7beb78ac4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"138ffa226204e04d85cb9be617cf9d5600a5d5c8f6c56f2f59ceb1c7beb78ac4","first_computed_at":"2026-05-18T02:40:47.774845Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:47.774845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gKu8lh96TCmRUFyUw7NI53nnPmjf1eIkBBgaMN5fM7DDHpMcY926uasQNcfVw//0EghL3gKDZT909chYSiwrDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:47.775439Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.3893","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ce22e13dcc81d935c10b155026b9d4c62a81a35cc910a795a7b9ae36d73e838","sha256:232ad1202577a6925580c2a28aab2c2e0135b3b36d9edd107fd3ef89fbded65f"],"state_sha256":"814f01d74da825b1fb08d2f34df552a34b8359ff9346781242964c3df72c0932"}