{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ND6ESGRHFYVQ47CD22634F2OLA","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":"bcb92f14be0066436e93d8464325fff91333045fec4666c76907ac509f8f914e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-07T01:18:57Z","title_canon_sha256":"6834518e74a62ba766af9fd1135b647f811b38f5cf1093662da7ec8c1bf42a5e"},"schema_version":"1.0","source":{"id":"1307.1825","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1825","created_at":"2026-05-18T03:19:03Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1825v1","created_at":"2026-05-18T03:19:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1825","created_at":"2026-05-18T03:19:03Z"},{"alias_kind":"pith_short_12","alias_value":"ND6ESGRHFYVQ","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"ND6ESGRHFYVQ47CD","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"ND6ESGRH","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:5b8aa67da2a5d18a85f28d22244d9f608387d75bdb7a69aa0d139d222b53dbf7","target":"graph","created_at":"2026-05-18T03:19:03Z","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":"Wintgen proved in [P. Wintgen, Sur l'in\\'egalit\\'e de Chen-Willmore, C. R. Acad. Sci. Paris, 288 (1979), 993--995] that the Gauss curvature $K$ and the normal curvature $K^D$ of a surface in the Euclidean 4-space $E^4$ satisfy $$K+|K^D|\\leq H^2,$$ where $H^2$ is the squared mean curvature. A surface $M$ in $\\E4$ is called a {Wintgen ideal} surface if it satisfies the equality case of the inequality identically. Wintgen ideal surfaces in $E^4$ form an important family of surfaces; namely, surfaces with circular ellipse of curvature. In this paper, we provide a brief survey on some old and recen","authors_text":"Bang-Yen Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-07T01:18:57Z","title":"On Wintgen ideal surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1825","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":"sha256:604b3b5f8f5c853afb636d74d5fd30d6bd260f00beb085ac91c2dcbdbf66fbfa","target":"record","created_at":"2026-05-18T03:19:03Z","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":"bcb92f14be0066436e93d8464325fff91333045fec4666c76907ac509f8f914e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-07T01:18:57Z","title_canon_sha256":"6834518e74a62ba766af9fd1135b647f811b38f5cf1093662da7ec8c1bf42a5e"},"schema_version":"1.0","source":{"id":"1307.1825","kind":"arxiv","version":1}},"canonical_sha256":"68fc491a272e2b0e7c43d6bdbe174e581619f0523fa55ae9eaffc9f02db704c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68fc491a272e2b0e7c43d6bdbe174e581619f0523fa55ae9eaffc9f02db704c6","first_computed_at":"2026-05-18T03:19:03.424447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:03.424447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OdTn1k52GoAOqwI4FFZe5sxDhi8LMBp+qG1UnGdsF4QNaBYCHbxPjOUVXr3bjIXmNzL0CF7+0HOrNcHsHPWJBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:03.425192Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.1825","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:604b3b5f8f5c853afb636d74d5fd30d6bd260f00beb085ac91c2dcbdbf66fbfa","sha256:5b8aa67da2a5d18a85f28d22244d9f608387d75bdb7a69aa0d139d222b53dbf7"],"state_sha256":"64ec26e92c0ea80fe4991159c127f685b4cbe6310e2639ecc6b4e8bf58db0f0d"}