{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:AJMQGNZMHDMHYNA344VSJBBOPM","short_pith_number":"pith:AJMQGNZM","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"},"canonical_sha256":"025903372c38d87c341be72b24842e7b399afae395e19bf91b99a80753697de1","source":{"kind":"arxiv","id":"1606.00806","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.00806","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"arxiv_version","alias_value":"1606.00806v1","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00806","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"pith_short_12","alias_value":"AJMQGNZMHDMH","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AJMQGNZMHDMHYNA3","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AJMQGNZM","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:AJMQGNZMHDMHYNA344VSJBBOPM","target":"record","payload":{"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"},"canonical_sha256":"025903372c38d87c341be72b24842e7b399afae395e19bf91b99a80753697de1","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"},"source_kind":"arxiv","source_id":"1606.00806","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:13:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"issZfdOb1nHFymgBQE+p1HJf4R2pd14YkwGZlDA6n4zT5UP2wiom2cpQdoJNNGFnYVv+XgsU/Wu5wfrFYQ0hCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T14:28:46.760404Z"},"content_sha256":"1d67bbb2e73138761bdf0ee638aa3b86a1eb78800902b8d7c6facec291be55b6","schema_version":"1.0","event_id":"sha256:1d67bbb2e73138761bdf0ee638aa3b86a1eb78800902b8d7c6facec291be55b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:AJMQGNZMHDMHYNA344VSJBBOPM","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:13:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yLv2d8ET2jqxl/oJwI2b/jdf8F/k7qHJeKtlVs8D6I5+GMqCib6RFTf8MwW9/VnvdyWX5YrXTrTIdWYZvx7tDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T14:28:46.760763Z"},"content_sha256":"c4d9a0e38d13ff33e381bf8fe1a87e6fb82d04b41f6caab1b9c47451b81a13f7","schema_version":"1.0","event_id":"sha256:c4d9a0e38d13ff33e381bf8fe1a87e6fb82d04b41f6caab1b9c47451b81a13f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AJMQGNZMHDMHYNA344VSJBBOPM/bundle.json","state_url":"https://pith.science/pith/AJMQGNZMHDMHYNA344VSJBBOPM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AJMQGNZMHDMHYNA344VSJBBOPM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-11T14:28:46Z","links":{"resolver":"https://pith.science/pith/AJMQGNZMHDMHYNA344VSJBBOPM","bundle":"https://pith.science/pith/AJMQGNZMHDMHYNA344VSJBBOPM/bundle.json","state":"https://pith.science/pith/AJMQGNZMHDMHYNA344VSJBBOPM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AJMQGNZMHDMHYNA344VSJBBOPM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AJMQGNZMHDMHYNA344VSJBBOPM","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":"e52c7cadf38d8aca40f212e889db1caceaebc4cd9c88b8074104ef1959202e66","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-02T19:05:57Z","title_canon_sha256":"f179cf31269c0f41ae92939e61c040aa578a952be9347c65b92bbc6218994512"},"schema_version":"1.0","source":{"id":"1606.00806","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.00806","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"arxiv_version","alias_value":"1606.00806v1","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00806","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"pith_short_12","alias_value":"AJMQGNZMHDMH","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AJMQGNZMHDMHYNA3","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AJMQGNZM","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:c4d9a0e38d13ff33e381bf8fe1a87e6fb82d04b41f6caab1b9c47451b81a13f7","target":"graph","created_at":"2026-05-18T01:13:00Z","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":"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 $R=\\frac{2}{3}H^2$","authors_text":"Roberto Alonso N\\'u\\~nez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-02T19:05:57Z","title":"On complete hypersurfaces with constant mean and scalar curvatures in Euclidean spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00806","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":"sha256:1d67bbb2e73138761bdf0ee638aa3b86a1eb78800902b8d7c6facec291be55b6","target":"record","created_at":"2026-05-18T01:13:00Z","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":"e52c7cadf38d8aca40f212e889db1caceaebc4cd9c88b8074104ef1959202e66","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-02T19:05:57Z","title_canon_sha256":"f179cf31269c0f41ae92939e61c040aa578a952be9347c65b92bbc6218994512"},"schema_version":"1.0","source":{"id":"1606.00806","kind":"arxiv","version":1}},"canonical_sha256":"025903372c38d87c341be72b24842e7b399afae395e19bf91b99a80753697de1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"025903372c38d87c341be72b24842e7b399afae395e19bf91b99a80753697de1","first_computed_at":"2026-05-18T01:13:00.563709Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:00.563709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A/3xPNEb7cyFlcbIpybQg5om+R1SIDDcZSg8OtIyi71z7tLylY9ek6LSM3tgmBUrf3Y6o468A/Jy2M+Xd4rjAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:00.564308Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.00806","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d67bbb2e73138761bdf0ee638aa3b86a1eb78800902b8d7c6facec291be55b6","sha256:c4d9a0e38d13ff33e381bf8fe1a87e6fb82d04b41f6caab1b9c47451b81a13f7"],"state_sha256":"a30308d2748e7fe038a8887fe8675ee159e543859a7eff2b45e923d614d02b8e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ppSVgz0QV/olmdJIFEiXOO04oUWEqU7y3mwApKSbuYQtMM5f3Kfya58hwbpUl7/sJ9oQtaFxSzCJ9vXYaWBkDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T14:28:46.763004Z","bundle_sha256":"908b4397eee1875ad7f8547daf6b981c19f8f2c4ea844da6972508b82f6fd07c"}}