{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:63SNHDJXN4X7ZC24RVSQXZQ5OP","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":"48528113a716e063ea2d917ef75bac48b078c92cafde4fcf16d216385c78925e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-04-14T09:26:10Z","title_canon_sha256":"f31836a6e50e1b5839a3c7b7031d9b086e3eb49bada1194d149320c6ff0d1af3"},"schema_version":"1.0","source":{"id":"1604.04087","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.04087","created_at":"2026-05-18T00:42:32Z"},{"alias_kind":"arxiv_version","alias_value":"1604.04087v2","created_at":"2026-05-18T00:42:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.04087","created_at":"2026-05-18T00:42:32Z"},{"alias_kind":"pith_short_12","alias_value":"63SNHDJXN4X7","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"63SNHDJXN4X7ZC24","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"63SNHDJX","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:29966277ad913e8cb35bf7d37049027124d737f3c023ef118ea828495f25b1c8","target":"graph","created_at":"2026-05-18T00:42:32Z","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":"On an $n$-dimensional complete manifold $M$, consider an $h$-almost gradient Ricci soliton, which is a generalization of a gradient Ricci soliton. We prove that if the manifold is Bach-flat and $dh/du>0$, then the manifold $M$ is either Einstein or rigid. In particular, such a manifold has harmonic Weyl curvature. Moreover, if the dimension of $M$ is four, the metric $g$ is conformally flat.","authors_text":"Gabjin Yun, Jinseok Co, Seungsu Hwang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-04-14T09:26:10Z","title":"Bach-flat h-almost gradient Ricci solitons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04087","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":"sha256:3e039a9ebde6fd1882db92b118d5d2429c53e7914457ec86982189b3bb60e8dc","target":"record","created_at":"2026-05-18T00:42:32Z","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":"48528113a716e063ea2d917ef75bac48b078c92cafde4fcf16d216385c78925e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-04-14T09:26:10Z","title_canon_sha256":"f31836a6e50e1b5839a3c7b7031d9b086e3eb49bada1194d149320c6ff0d1af3"},"schema_version":"1.0","source":{"id":"1604.04087","kind":"arxiv","version":2}},"canonical_sha256":"f6e4d38d376f2ffc8b5c8d650be61d73ce7231617fa86434d7381a9c2574cc78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6e4d38d376f2ffc8b5c8d650be61d73ce7231617fa86434d7381a9c2574cc78","first_computed_at":"2026-05-18T00:42:32.971056Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:32.971056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YDGEQMpMvvahGhm/S7wE9hRE8gOaPUmgmplUE4Upo/LxwcPgoGGIMhqiqvRQ0eY+iC3L+1juhj0tCMJIuwf6Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:32.971709Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.04087","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e039a9ebde6fd1882db92b118d5d2429c53e7914457ec86982189b3bb60e8dc","sha256:29966277ad913e8cb35bf7d37049027124d737f3c023ef118ea828495f25b1c8"],"state_sha256":"6e6812f4171de7ba6c819a1b44d5f0f1d23311a9eaf95624bad24bd152c56d24"}