{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:T4HJRMRJXIPOT4J7IOZAKZZD3Z","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":"d3dae83abf213774f687db88019dc1001028f309f98eeca0e078be0708e43b04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-09-12T20:22:55Z","title_canon_sha256":"a52c6d97ffbdbb3f910f20bb0214fd9e11d812b367e57c06441f049bdf1ea64c"},"schema_version":"1.0","source":{"id":"1209.2720","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.2720","created_at":"2026-05-18T03:12:12Z"},{"alias_kind":"arxiv_version","alias_value":"1209.2720v3","created_at":"2026-05-18T03:12:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2720","created_at":"2026-05-18T03:12:12Z"},{"alias_kind":"pith_short_12","alias_value":"T4HJRMRJXIPO","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"T4HJRMRJXIPOT4J7","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"T4HJRMRJ","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:0b9f0b1bf219d81abf9bb5732dbed58e2525da2335fc53b1d91713c098967f59","target":"graph","created_at":"2026-05-18T03:12:12Z","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":"The aim of this note is to prove that any compact non-trivial almost Ricci soliton $\\big(M^n,\\,g,\\,X,\\,\\lambda\\big)$ with constant scalar curvature is isometric to a Euclidean sphere $\\Bbb{S}^{n}$. As a consequence we obtain that every compact non-trivial almost Ricci soliton with constant scalar curvature is gradient. Moreover, the vector field $X$ decomposes as the sum of a Killing vector field $Y$ and the gradient of a suitable function.","authors_text":"Abd\\^enago Barros, Ernani Ribeiro Jr, Rondinelle Batista","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-09-12T20:22:55Z","title":"Compact almost Ricci solitons with constant scalar curvature are gradient"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2720","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":"sha256:1726e7e57cb60bb2410da5c6a20db5f4ab3e82c68c4a8c0aeeacf5cbe38b5d97","target":"record","created_at":"2026-05-18T03:12:12Z","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":"d3dae83abf213774f687db88019dc1001028f309f98eeca0e078be0708e43b04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-09-12T20:22:55Z","title_canon_sha256":"a52c6d97ffbdbb3f910f20bb0214fd9e11d812b367e57c06441f049bdf1ea64c"},"schema_version":"1.0","source":{"id":"1209.2720","kind":"arxiv","version":3}},"canonical_sha256":"9f0e98b229ba1ee9f13f43b2056723de5ac371de6645005db3c9a01661b87190","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f0e98b229ba1ee9f13f43b2056723de5ac371de6645005db3c9a01661b87190","first_computed_at":"2026-05-18T03:12:12.014654Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:12.014654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2kLna2Q0i8m5MyY8kftKyjO/dGqmxrA/tx6xSC6lGK0q0gaw5DKFPz781wCdxkSCaGvTN9bmsJskMrgeM2PcBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:12.015219Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.2720","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1726e7e57cb60bb2410da5c6a20db5f4ab3e82c68c4a8c0aeeacf5cbe38b5d97","sha256:0b9f0b1bf219d81abf9bb5732dbed58e2525da2335fc53b1d91713c098967f59"],"state_sha256":"a6fb90c0f641759306dbde7c02add7fe323f93f76d00c9ec8d8c3a31ccb88627"}