{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:AJMQGNZMHDMHYNA344VSJBBOPM","short_pith_number":"pith:AJMQGNZM","schema_version":"1.0","canonical_sha256":"025903372c38d87c341be72b24842e7b399afae395e19bf91b99a80753697de1","source":{"kind":"arxiv","id":"1606.00806","version":1},"attestation_state":"computed","paper":{"title":"On complete hypersurfaces with constant mean and scalar curvatures in Euclidean spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Roberto Alonso N\\'u\\~nez","submitted_at":"2016-06-02T19:05:57Z","abstract_excerpt":"Generalizing a theorem of Huang, Cheng and Wan classified the complete hypersurfaces of $\\mathbb R^4$ with non-zero constant mean curvature and constant scalar curvature. In our work, we obtain results of this nature in higher dimensions. In particular, we prove that if a complete hypersurface of $\\mathbb R^5$ has constant mean curvature $H\\neq 0$ and constant scalar curvature $R\\geq\\frac{2}{3}H^2$, then $R=H^2$, $R=\\frac{8}{9}H^2$ or $R=\\frac{2}{3}H^2$. Moreover, we characterize the hypersurface in the cases $R=H^2$ and $R=\\frac{8}{9}H^2$, and provide an example in the case $R=\\frac{2}{3}H^2$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1606.00806","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-02T19:05:57Z","cross_cats_sorted":[],"title_canon_sha256":"f179cf31269c0f41ae92939e61c040aa578a952be9347c65b92bbc6218994512","abstract_canon_sha256":"e52c7cadf38d8aca40f212e889db1caceaebc4cd9c88b8074104ef1959202e66"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:00.564308Z","signature_b64":"A/3xPNEb7cyFlcbIpybQg5om+R1SIDDcZSg8OtIyi71z7tLylY9ek6LSM3tgmBUrf3Y6o468A/Jy2M+Xd4rjAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"025903372c38d87c341be72b24842e7b399afae395e19bf91b99a80753697de1","last_reissued_at":"2026-05-18T01:13:00.563709Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:00.563709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On complete hypersurfaces with constant mean and scalar curvatures in Euclidean spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Roberto Alonso N\\'u\\~nez","submitted_at":"2016-06-02T19:05:57Z","abstract_excerpt":"Generalizing a theorem of Huang, Cheng and Wan classified the complete hypersurfaces of $\\mathbb R^4$ with non-zero constant mean curvature and constant scalar curvature. In our work, we obtain results of this nature in higher dimensions. In particular, we prove that if a complete hypersurface of $\\mathbb R^5$ has constant mean curvature $H\\neq 0$ and constant scalar curvature $R\\geq\\frac{2}{3}H^2$, then $R=H^2$, $R=\\frac{8}{9}H^2$ or $R=\\frac{2}{3}H^2$. Moreover, we characterize the hypersurface in the cases $R=H^2$ and $R=\\frac{8}{9}H^2$, and provide an example in the case $R=\\frac{2}{3}H^2$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00806","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1606.00806","created_at":"2026-05-18T01:13:00.563800+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.00806v1","created_at":"2026-05-18T01:13:00.563800+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00806","created_at":"2026-05-18T01:13:00.563800+00:00"},{"alias_kind":"pith_short_12","alias_value":"AJMQGNZMHDMH","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"AJMQGNZMHDMHYNA3","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"AJMQGNZM","created_at":"2026-05-18T12:30:07.202191+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AJMQGNZMHDMHYNA344VSJBBOPM","json":"https://pith.science/pith/AJMQGNZMHDMHYNA344VSJBBOPM.json","graph_json":"https://pith.science/api/pith-number/AJMQGNZMHDMHYNA344VSJBBOPM/graph.json","events_json":"https://pith.science/api/pith-number/AJMQGNZMHDMHYNA344VSJBBOPM/events.json","paper":"https://pith.science/paper/AJMQGNZM"},"agent_actions":{"view_html":"https://pith.science/pith/AJMQGNZMHDMHYNA344VSJBBOPM","download_json":"https://pith.science/pith/AJMQGNZMHDMHYNA344VSJBBOPM.json","view_paper":"https://pith.science/paper/AJMQGNZM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.00806&json=true","fetch_graph":"https://pith.science/api/pith-number/AJMQGNZMHDMHYNA344VSJBBOPM/graph.json","fetch_events":"https://pith.science/api/pith-number/AJMQGNZMHDMHYNA344VSJBBOPM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AJMQGNZMHDMHYNA344VSJBBOPM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AJMQGNZMHDMHYNA344VSJBBOPM/action/storage_attestation","attest_author":"https://pith.science/pith/AJMQGNZMHDMHYNA344VSJBBOPM/action/author_attestation","sign_citation":"https://pith.science/pith/AJMQGNZMHDMHYNA344VSJBBOPM/action/citation_signature","submit_replication":"https://pith.science/pith/AJMQGNZMHDMHYNA344VSJBBOPM/action/replication_record"}},"created_at":"2026-05-18T01:13:00.563800+00:00","updated_at":"2026-05-18T01:13:00.563800+00:00"}