{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QKQKUCPS5GGRMS5JBHYR6CH5WR","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":"872743b9d47beeacffe2cea8aa3c03f5fcc009534a97d241c3988cc6376aa545","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-04-07T10:29:35Z","title_canon_sha256":"8a2a24e1cbb5a0bbb1cd819daa0e1eea6e874ccbfc791c87141af1f46e768ed6"},"schema_version":"1.0","source":{"id":"1404.1725","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1725","created_at":"2026-05-18T02:19:16Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1725v4","created_at":"2026-05-18T02:19:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1725","created_at":"2026-05-18T02:19:16Z"},{"alias_kind":"pith_short_12","alias_value":"QKQKUCPS5GGR","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QKQKUCPS5GGRMS5J","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QKQKUCPS","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:bca6fcb20a1ef17a5ed249e042814a43260aa9d10b99e1a58d7c479598d6291a","target":"graph","created_at":"2026-05-18T02:19:16Z","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":"We prove that every closed, smooth $n$-manifold $X$ admits a Riemannian metric together with a smooth, transversely oriented CMC foliation if and only if its Euler characteristic is zero, where by CMC foliation we mean a codimension-one, transversely oriented foliation with leaves of constant mean curvature and where the value of the constant mean curvature can vary from leaf to leaf. Furthermore, we prove that this CMC foliation of $X$ can be chosen so that the constant values of the mean curvatures of its leaves change sign. We also prove a general structure theorem for any such non-minimal ","authors_text":"Joaquin Perez, William H. Meeks III","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-04-07T10:29:35Z","title":"CMC foliations of closed manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1725","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":"sha256:6efe76b4f0dc95eec7f47f460e73510846483aa08fbe0afaa9abe50f645b8748","target":"record","created_at":"2026-05-18T02:19:16Z","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":"872743b9d47beeacffe2cea8aa3c03f5fcc009534a97d241c3988cc6376aa545","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-04-07T10:29:35Z","title_canon_sha256":"8a2a24e1cbb5a0bbb1cd819daa0e1eea6e874ccbfc791c87141af1f46e768ed6"},"schema_version":"1.0","source":{"id":"1404.1725","kind":"arxiv","version":4}},"canonical_sha256":"82a0aa09f2e98d164ba909f11f08fdb4468e8a27dc0e40604cb5df0dacadb117","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82a0aa09f2e98d164ba909f11f08fdb4468e8a27dc0e40604cb5df0dacadb117","first_computed_at":"2026-05-18T02:19:16.846484Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:16.846484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3C2kEkc5ScnctPHNZ4wZQ/z3kYWjfgokDWnPko5+QUQjtK4rfBlB9P3emFjT4CI4Jf6tAn5+GnqL6u0ZeIKcAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:16.847182Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.1725","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6efe76b4f0dc95eec7f47f460e73510846483aa08fbe0afaa9abe50f645b8748","sha256:bca6fcb20a1ef17a5ed249e042814a43260aa9d10b99e1a58d7c479598d6291a"],"state_sha256":"19132622a06ad560ce9b816f352799e3ef086394cbbff2f3e1a458b473cf0027"}