{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FOQAMX5IWP3NKSPZU36SKLV3YK","short_pith_number":"pith:FOQAMX5I","canonical_record":{"source":{"id":"1604.06150","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-04-21T00:56:15Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"67b4b21adad2534916722606654ad483de82e3acafab651a1cda5428304b23a7","abstract_canon_sha256":"75e16ba51bdc9ed3b6abd818f438afaed50bfd4eac669582a195026d4ece4b37"},"schema_version":"1.0"},"canonical_sha256":"2ba0065fa8b3f6d549f9a6fd252ebbc2ab48bb3a1ecb9c3cfefd7dc43e8a6f7f","source":{"kind":"arxiv","id":"1604.06150","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06150","created_at":"2026-05-18T00:47:14Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06150v2","created_at":"2026-05-18T00:47:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06150","created_at":"2026-05-18T00:47:14Z"},{"alias_kind":"pith_short_12","alias_value":"FOQAMX5IWP3N","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FOQAMX5IWP3NKSPZ","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FOQAMX5I","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FOQAMX5IWP3NKSPZU36SKLV3YK","target":"record","payload":{"canonical_record":{"source":{"id":"1604.06150","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-04-21T00:56:15Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"67b4b21adad2534916722606654ad483de82e3acafab651a1cda5428304b23a7","abstract_canon_sha256":"75e16ba51bdc9ed3b6abd818f438afaed50bfd4eac669582a195026d4ece4b37"},"schema_version":"1.0"},"canonical_sha256":"2ba0065fa8b3f6d549f9a6fd252ebbc2ab48bb3a1ecb9c3cfefd7dc43e8a6f7f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:14.957069Z","signature_b64":"SJkLsTMnwZf53qb6FGnccI4yvC2Pv4LxbpVuxXQPiMrHXF9z+HIafCQmpgQOGp3U7wpUz2N2CEVL5C+jlvN0Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ba0065fa8b3f6d549f9a6fd252ebbc2ab48bb3a1ecb9c3cfefd7dc43e8a6f7f","last_reissued_at":"2026-05-18T00:47:14.956431Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:14.956431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.06150","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:47:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gEZw5PuvdQEB3jN3bDuqkHceQz9wxpCbKC1Fpqej32MZp3irqA7ksvzRl6uOyue6S4MeO00cSk1gY/ZD7bnLDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T22:56:46.097200Z"},"content_sha256":"566938c719be34c3fc65ea7378e5e8fbf035829e96fa22fbbc11ac1defb9dd2c","schema_version":"1.0","event_id":"sha256:566938c719be34c3fc65ea7378e5e8fbf035829e96fa22fbbc11ac1defb9dd2c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FOQAMX5IWP3NKSPZU36SKLV3YK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Curvature estimates for immersed hypersurfaces in Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Pengfei Guan, Siyuan Lu","submitted_at":"2016-04-21T00:56:15Z","abstract_excerpt":"We establish mean curvature estimate for immersed hypersurface with nonnegative extrinsic scalar curvature in Riemannian manifold $(N^{n+1}, \\bar g)$ through regularity study of a degenerate fully nonlinear curvature equation in general Riemannian manifold. The estimate has a direct consequence for the Weyl isometric embedding problem of $(\\mathbb S^2, g)$ in $3$-dimensional warped product space $(N^3, \\bar g)$. We also discuss isometric embedding problem in spaces with horizon in general relativity, like the Anti-de Sitter-Schwarzschild manifolds and the Reissner-Nordstr\\\"om manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06150","kind":"arxiv","version":2},"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":"2026-05-18T00:47:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JKuWAqaOTPLHRlivWhEey0CDMGEP+sVxV0cV3O6BGRuxU71WWP+055shO8xa16klIOxoD0v8XRc5/GyFqV1ADA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T22:56:46.097943Z"},"content_sha256":"030e7b63f25d99de1f8f54512de45ef4f740108dbc44c74c0e9215941efc1f27","schema_version":"1.0","event_id":"sha256:030e7b63f25d99de1f8f54512de45ef4f740108dbc44c74c0e9215941efc1f27"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FOQAMX5IWP3NKSPZU36SKLV3YK/bundle.json","state_url":"https://pith.science/pith/FOQAMX5IWP3NKSPZU36SKLV3YK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FOQAMX5IWP3NKSPZU36SKLV3YK/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":"2026-05-31T22:56:46Z","links":{"resolver":"https://pith.science/pith/FOQAMX5IWP3NKSPZU36SKLV3YK","bundle":"https://pith.science/pith/FOQAMX5IWP3NKSPZU36SKLV3YK/bundle.json","state":"https://pith.science/pith/FOQAMX5IWP3NKSPZU36SKLV3YK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FOQAMX5IWP3NKSPZU36SKLV3YK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FOQAMX5IWP3NKSPZU36SKLV3YK","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":"75e16ba51bdc9ed3b6abd818f438afaed50bfd4eac669582a195026d4ece4b37","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-04-21T00:56:15Z","title_canon_sha256":"67b4b21adad2534916722606654ad483de82e3acafab651a1cda5428304b23a7"},"schema_version":"1.0","source":{"id":"1604.06150","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06150","created_at":"2026-05-18T00:47:14Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06150v2","created_at":"2026-05-18T00:47:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06150","created_at":"2026-05-18T00:47:14Z"},{"alias_kind":"pith_short_12","alias_value":"FOQAMX5IWP3N","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FOQAMX5IWP3NKSPZ","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FOQAMX5I","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:030e7b63f25d99de1f8f54512de45ef4f740108dbc44c74c0e9215941efc1f27","target":"graph","created_at":"2026-05-18T00:47:14Z","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 establish mean curvature estimate for immersed hypersurface with nonnegative extrinsic scalar curvature in Riemannian manifold $(N^{n+1}, \\bar g)$ through regularity study of a degenerate fully nonlinear curvature equation in general Riemannian manifold. The estimate has a direct consequence for the Weyl isometric embedding problem of $(\\mathbb S^2, g)$ in $3$-dimensional warped product space $(N^3, \\bar g)$. We also discuss isometric embedding problem in spaces with horizon in general relativity, like the Anti-de Sitter-Schwarzschild manifolds and the Reissner-Nordstr\\\"om manifolds.","authors_text":"Pengfei Guan, Siyuan Lu","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-04-21T00:56:15Z","title":"Curvature estimates for immersed hypersurfaces in Riemannian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06150","kind":"arxiv","version":2},"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":"sha256:566938c719be34c3fc65ea7378e5e8fbf035829e96fa22fbbc11ac1defb9dd2c","target":"record","created_at":"2026-05-18T00:47:14Z","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":"75e16ba51bdc9ed3b6abd818f438afaed50bfd4eac669582a195026d4ece4b37","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-04-21T00:56:15Z","title_canon_sha256":"67b4b21adad2534916722606654ad483de82e3acafab651a1cda5428304b23a7"},"schema_version":"1.0","source":{"id":"1604.06150","kind":"arxiv","version":2}},"canonical_sha256":"2ba0065fa8b3f6d549f9a6fd252ebbc2ab48bb3a1ecb9c3cfefd7dc43e8a6f7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ba0065fa8b3f6d549f9a6fd252ebbc2ab48bb3a1ecb9c3cfefd7dc43e8a6f7f","first_computed_at":"2026-05-18T00:47:14.956431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:14.956431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SJkLsTMnwZf53qb6FGnccI4yvC2Pv4LxbpVuxXQPiMrHXF9z+HIafCQmpgQOGp3U7wpUz2N2CEVL5C+jlvN0Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:14.957069Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.06150","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:566938c719be34c3fc65ea7378e5e8fbf035829e96fa22fbbc11ac1defb9dd2c","sha256:030e7b63f25d99de1f8f54512de45ef4f740108dbc44c74c0e9215941efc1f27"],"state_sha256":"3aceea5ea0ee09b9c8ebca1b2d137026dbc3495f729bee8628ae3a19ecca04b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VfgoFuMo5+P6n11rqNgUuP/3Xw7f5C/pRWFAo0KT4RNfGUwVKkHGWSGgMbWk8hOSN53NdnlU2cq4J+RiS5sxDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T22:56:46.101808Z","bundle_sha256":"a984b79dad89f37823ad99bc3982ca42a4c0e5dfc4d55f6e9ab70e35d2e29f05"}}