{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HPUYYWQEBHTTWCT54ZS33A7FHF","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":"1a8a161da8fd48e73668d139a32dc7e341f2d79eb2625f8dbb09926819e45366","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-17T18:07:21Z","title_canon_sha256":"a7c15b8fcd5ed3f0f6b6c0bfe465ecb40a5ba7c9014986a4d52e45c81522b6d8"},"schema_version":"1.0","source":{"id":"1101.3282","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3282","created_at":"2026-05-18T02:03:39Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3282v1","created_at":"2026-05-18T02:03:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3282","created_at":"2026-05-18T02:03:39Z"},{"alias_kind":"pith_short_12","alias_value":"HPUYYWQEBHTT","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HPUYYWQEBHTTWCT5","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HPUYYWQE","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:42b259d6985dd950201510906c3045142b0b0b35d1bcc2993851886c6a41e4a5","target":"graph","created_at":"2026-05-18T02:03:39Z","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 a totally umbilical biharmonic surface in any $3$-dimensional Riemannian manifold has constant mean curvature. We use this to show that a totally umbilical surface in Thurston's 3-dimensional geometries is proper biharmonic if and only if it is a part of $S^2(1/\\sqrt{2})$ in $S^3$. We also give complete classifications of constant mean curvature proper biharmonic surfaces in 3-dimensional geometries and in 3-dimensional Bianchi-Cartan-Vranceanu spaces, and a complete classifications of proper biharmonic Hopf cylinders in 3-dimensional Bianchi-Cartan-Vranceanu spaces.","authors_text":"Ye-Lin Ou, Ze-Ping Wang","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-17T18:07:21Z","title":"Constant mean curvature and totally umbilical biharmonic surfaces in 3-dimensional geometries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3282","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":"sha256:35198e9ed56a63e727f463a6daaba90e41884d60b7b3244171e513fb105e89a6","target":"record","created_at":"2026-05-18T02:03:39Z","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":"1a8a161da8fd48e73668d139a32dc7e341f2d79eb2625f8dbb09926819e45366","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-17T18:07:21Z","title_canon_sha256":"a7c15b8fcd5ed3f0f6b6c0bfe465ecb40a5ba7c9014986a4d52e45c81522b6d8"},"schema_version":"1.0","source":{"id":"1101.3282","kind":"arxiv","version":1}},"canonical_sha256":"3be98c5a0409e73b0a7de665bd83e5394ee3fc75d34994e7d0f207e9269b29e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3be98c5a0409e73b0a7de665bd83e5394ee3fc75d34994e7d0f207e9269b29e3","first_computed_at":"2026-05-18T02:03:39.073281Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:39.073281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L5pldqC0xZBHgUSCjhg/ZwCtlLTmGEZ4LOtMmSOYfytNknVQpazchA2TQtXl2GQU6uKiv4dOERAs5GCBXkFoDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:39.074071Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.3282","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35198e9ed56a63e727f463a6daaba90e41884d60b7b3244171e513fb105e89a6","sha256:42b259d6985dd950201510906c3045142b0b0b35d1bcc2993851886c6a41e4a5"],"state_sha256":"79363ff591ee3ee752262a1340706c06fbbbcd9fdd4d2e039b11d59927c42423"}