{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:OROQN2V5LCJIR6SZYMGDBJW2WC","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":"e2c331803156ac952e7ad269da7fdef30ebe7c79f1650894c952a84c5fe28b78","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-10-19T08:20:35Z","title_canon_sha256":"16577599d25dd813d626314c371a389b261048d110316edb6291cbd94972931c"},"schema_version":"1.0","source":{"id":"1010.3822","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.3822","created_at":"2026-05-18T04:39:07Z"},{"alias_kind":"arxiv_version","alias_value":"1010.3822v1","created_at":"2026-05-18T04:39:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.3822","created_at":"2026-05-18T04:39:07Z"},{"alias_kind":"pith_short_12","alias_value":"OROQN2V5LCJI","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OROQN2V5LCJIR6SZ","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OROQN2V5","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:8992f49b0f047de0200ff5e32315ca4a634c33b627be404348ef3a0f7dbe449e","target":"graph","created_at":"2026-05-18T04:39:07Z","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":"A weakly Einstein manifold is a generalization of a 4-dimensional Einstein manifold, which is defined as an application of a curvature identity derived from the generalized Gauss-Bonnet formula for a 4-dimensional compact oriented Riemannian manifold. In this paper, we shall give a characterization of a weakly Einstein manifold.","authors_text":"J. H. Park, K. Sekigawa, Y. Euh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-10-19T08:20:35Z","title":"A generalization of a 4-dimensional Einstein manifold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3822","kind":"arxiv","version":1},"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":"sha256:601d7d779ad0df93369ae628d3712bc8da303dfa25f7dd3b94acb4860033318d","target":"record","created_at":"2026-05-18T04:39:07Z","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":"e2c331803156ac952e7ad269da7fdef30ebe7c79f1650894c952a84c5fe28b78","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-10-19T08:20:35Z","title_canon_sha256":"16577599d25dd813d626314c371a389b261048d110316edb6291cbd94972931c"},"schema_version":"1.0","source":{"id":"1010.3822","kind":"arxiv","version":1}},"canonical_sha256":"745d06eabd589288fa59c30c30a6dab0a10eceb8adc88fae2b988554743725f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"745d06eabd589288fa59c30c30a6dab0a10eceb8adc88fae2b988554743725f7","first_computed_at":"2026-05-18T04:39:07.493843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:07.493843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d7doQ/ft9TmcyGy2K9E/8Vi/RKE5RrVdpjkpGQfLiB2nbgWDucso9LhBxPo1Qhyz5TmvOX5CY1bS6Mki8gqqAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:07.494306Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.3822","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:601d7d779ad0df93369ae628d3712bc8da303dfa25f7dd3b94acb4860033318d","sha256:8992f49b0f047de0200ff5e32315ca4a634c33b627be404348ef3a0f7dbe449e"],"state_sha256":"515c49b7df9ba60ce1dcdea3a734f2a74227c085949bc1a0bb51ec279bdd55fb"}