{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PZPQC2HONFCPLBVQLG2EOCU3VY","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":"67d0f9062e667383c781a736366199beb5da9627ad867eb29a5f35dba0d57156","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-15T22:43:51Z","title_canon_sha256":"9eeb558cf49eedf8a58920f596aa89000f369cf25028e23c03a99a1e385410d8"},"schema_version":"1.0","source":{"id":"1211.3770","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.3770","created_at":"2026-05-18T03:40:15Z"},{"alias_kind":"arxiv_version","alias_value":"1211.3770v3","created_at":"2026-05-18T03:40:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.3770","created_at":"2026-05-18T03:40:15Z"},{"alias_kind":"pith_short_12","alias_value":"PZPQC2HONFCP","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PZPQC2HONFCPLBVQ","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PZPQC2HO","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:d24e34988fd449d8210b9346630d580b42a3706dc7999123e71abbeafbb4fd24","target":"graph","created_at":"2026-05-18T03:40:15Z","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 paper, we study stable weighted minimal hypersurfaces in manifolds with nonnegative Bakry-Emery Ricci curvature. We will give some geometric and topological applications. In particular, we give some partial classification of complete 3-manifolds with nonnegative Bakry-Emery Ricci curvature assuming that $f$ is bounded.","authors_text":"Gang Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-15T22:43:51Z","title":"Stable weighted minimal surfaces in manifolds with nonnegative Bakry-Emery Ricci tensor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3770","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":"sha256:0ba57030616279a0a7e91a1e3f1d9d6853480f46b803ad04f946ae96226c56d7","target":"record","created_at":"2026-05-18T03:40:15Z","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":"67d0f9062e667383c781a736366199beb5da9627ad867eb29a5f35dba0d57156","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-15T22:43:51Z","title_canon_sha256":"9eeb558cf49eedf8a58920f596aa89000f369cf25028e23c03a99a1e385410d8"},"schema_version":"1.0","source":{"id":"1211.3770","kind":"arxiv","version":3}},"canonical_sha256":"7e5f0168ee6944f586b059b4470a9bae3ac391b32aa7b4d4f2cb0b98ec6ed325","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e5f0168ee6944f586b059b4470a9bae3ac391b32aa7b4d4f2cb0b98ec6ed325","first_computed_at":"2026-05-18T03:40:15.659465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:15.659465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5hEEaLHoDIrqdl5WdhHzbHcvjTsiSJtIDta085RsdG8Zg3up5+qKlemBF9ngo9px9XQJf3B1LjtGdhjU6JS0Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:15.660036Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.3770","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ba57030616279a0a7e91a1e3f1d9d6853480f46b803ad04f946ae96226c56d7","sha256:d24e34988fd449d8210b9346630d580b42a3706dc7999123e71abbeafbb4fd24"],"state_sha256":"69699986269a42ad6296932cee26ff47c157198b3ff649a89d431f584c2e549f"}