{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:CN7B4TAK6URXZM6JM6ZS7MEQED","short_pith_number":"pith:CN7B4TAK","canonical_record":{"source":{"id":"1208.1786","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-08-08T21:30:59Z","cross_cats_sorted":[],"title_canon_sha256":"794cdee74f4a2be7b848e76895b40db464474c070725f03f2e063d3b673c1397","abstract_canon_sha256":"bb9b86c614427adc8cc31362eb89d50090c3837fac0614dcf9bf9e59aad0bbca"},"schema_version":"1.0"},"canonical_sha256":"137e1e4c0af5237cb3c967b32fb09020d9b6c9ce1a0ae8f88035394348284e51","source":{"kind":"arxiv","id":"1208.1786","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1786","created_at":"2026-05-18T03:49:09Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1786v1","created_at":"2026-05-18T03:49:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1786","created_at":"2026-05-18T03:49:09Z"},{"alias_kind":"pith_short_12","alias_value":"CN7B4TAK6URX","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CN7B4TAK6URXZM6J","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CN7B4TAK","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:CN7B4TAK6URXZM6JM6ZS7MEQED","target":"record","payload":{"canonical_record":{"source":{"id":"1208.1786","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-08-08T21:30:59Z","cross_cats_sorted":[],"title_canon_sha256":"794cdee74f4a2be7b848e76895b40db464474c070725f03f2e063d3b673c1397","abstract_canon_sha256":"bb9b86c614427adc8cc31362eb89d50090c3837fac0614dcf9bf9e59aad0bbca"},"schema_version":"1.0"},"canonical_sha256":"137e1e4c0af5237cb3c967b32fb09020d9b6c9ce1a0ae8f88035394348284e51","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:09.953149Z","signature_b64":"YtQFncH7wrf4LVJxZtC7V+V9nFv8L4rRwrcRSuzDCgJNQDjFMZEUiPsGXNYSAjTln37rwX+Oh1ZRPiU/wxSlCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"137e1e4c0af5237cb3c967b32fb09020d9b6c9ce1a0ae8f88035394348284e51","last_reissued_at":"2026-05-18T03:49:09.952561Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:09.952561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.1786","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":"2026-05-18T03:49:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QONXHUWDZx1v+Qn+bMO1ZXzvIN+15TfZY4I3JV71D6aKSO/9PW6BB/DjcDHx/KEiEqNUo/AzlJyhmAfvNdicDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:03:59.499896Z"},"content_sha256":"929ce61326f63cd3daf50fd3645267f06de3b29539fbd2111fb4a07f469ce11f","schema_version":"1.0","event_id":"sha256:929ce61326f63cd3daf50fd3645267f06de3b29539fbd2111fb4a07f469ce11f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:CN7B4TAK6URXZM6JM6ZS7MEQED","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rigidity for nearly umbilical hypersurfaces in space forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Detang Zhou, Xu Cheng","submitted_at":"2012-08-08T21:30:59Z","abstract_excerpt":"Perez proved some $L^2$ inequalities for closed convex hypersurfaces immersed in the Euclidean space $\\mathbb{R}^{n+1}$, more generally, for closed hypersurfaces with non-negative Ricci curvature, immersed in an Einstein manifold. In this paper, we discuss the rigidity of these inequalities when the ambient manifold is $\\mathbb{R}^{n+1}$, the hyperbolic space $\\mathbb{H}^{n+1}$, or the closed hemisphere $\\mathbb{S}_+^{n+1}$. We also obtain a generalization of the Perez's theorem to the hypersurfaces without the hypothesis of non-negative Ricci curvature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1786","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":"2026-05-18T03:49:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DDfe84HVy5OaDC0O5DSE+KRLWONJOnqPfD/Jm7h8a431boCZASGIHLP37zmdQQ8ztSa/VFknkXFh4lqAnqdwDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:03:59.500456Z"},"content_sha256":"36b91076d005bcd02dd85f6ddba62173d43e0aa50678c64e521a2776cd45af44","schema_version":"1.0","event_id":"sha256:36b91076d005bcd02dd85f6ddba62173d43e0aa50678c64e521a2776cd45af44"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CN7B4TAK6URXZM6JM6ZS7MEQED/bundle.json","state_url":"https://pith.science/pith/CN7B4TAK6URXZM6JM6ZS7MEQED/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CN7B4TAK6URXZM6JM6ZS7MEQED/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":"2026-06-11T02:03:59Z","links":{"resolver":"https://pith.science/pith/CN7B4TAK6URXZM6JM6ZS7MEQED","bundle":"https://pith.science/pith/CN7B4TAK6URXZM6JM6ZS7MEQED/bundle.json","state":"https://pith.science/pith/CN7B4TAK6URXZM6JM6ZS7MEQED/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CN7B4TAK6URXZM6JM6ZS7MEQED/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CN7B4TAK6URXZM6JM6ZS7MEQED","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":"bb9b86c614427adc8cc31362eb89d50090c3837fac0614dcf9bf9e59aad0bbca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-08-08T21:30:59Z","title_canon_sha256":"794cdee74f4a2be7b848e76895b40db464474c070725f03f2e063d3b673c1397"},"schema_version":"1.0","source":{"id":"1208.1786","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1786","created_at":"2026-05-18T03:49:09Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1786v1","created_at":"2026-05-18T03:49:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1786","created_at":"2026-05-18T03:49:09Z"},{"alias_kind":"pith_short_12","alias_value":"CN7B4TAK6URX","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CN7B4TAK6URXZM6J","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CN7B4TAK","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:36b91076d005bcd02dd85f6ddba62173d43e0aa50678c64e521a2776cd45af44","target":"graph","created_at":"2026-05-18T03:49:09Z","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":"Perez proved some $L^2$ inequalities for closed convex hypersurfaces immersed in the Euclidean space $\\mathbb{R}^{n+1}$, more generally, for closed hypersurfaces with non-negative Ricci curvature, immersed in an Einstein manifold. In this paper, we discuss the rigidity of these inequalities when the ambient manifold is $\\mathbb{R}^{n+1}$, the hyperbolic space $\\mathbb{H}^{n+1}$, or the closed hemisphere $\\mathbb{S}_+^{n+1}$. We also obtain a generalization of the Perez's theorem to the hypersurfaces without the hypothesis of non-negative Ricci curvature.","authors_text":"Detang Zhou, Xu Cheng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-08-08T21:30:59Z","title":"Rigidity for nearly umbilical hypersurfaces in space forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1786","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":"sha256:929ce61326f63cd3daf50fd3645267f06de3b29539fbd2111fb4a07f469ce11f","target":"record","created_at":"2026-05-18T03:49:09Z","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":"bb9b86c614427adc8cc31362eb89d50090c3837fac0614dcf9bf9e59aad0bbca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-08-08T21:30:59Z","title_canon_sha256":"794cdee74f4a2be7b848e76895b40db464474c070725f03f2e063d3b673c1397"},"schema_version":"1.0","source":{"id":"1208.1786","kind":"arxiv","version":1}},"canonical_sha256":"137e1e4c0af5237cb3c967b32fb09020d9b6c9ce1a0ae8f88035394348284e51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"137e1e4c0af5237cb3c967b32fb09020d9b6c9ce1a0ae8f88035394348284e51","first_computed_at":"2026-05-18T03:49:09.952561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:09.952561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YtQFncH7wrf4LVJxZtC7V+V9nFv8L4rRwrcRSuzDCgJNQDjFMZEUiPsGXNYSAjTln37rwX+Oh1ZRPiU/wxSlCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:09.953149Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.1786","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:929ce61326f63cd3daf50fd3645267f06de3b29539fbd2111fb4a07f469ce11f","sha256:36b91076d005bcd02dd85f6ddba62173d43e0aa50678c64e521a2776cd45af44"],"state_sha256":"207172811d257b69926b653cc628784c9cca980b7621bcae8a9ef065b4e06303"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dcsSKXCqZUKBKmuFlLUmfE7wW/fMJaDvBEnUvPc9MFzBY1vXLNP1Gh+Qv8dJZCX/NcBLNbeuP0FE6HdjtJCjAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T02:03:59.504031Z","bundle_sha256":"54485dc4f1232d682c87b2993cb8b7130301a878e78a8e9110d8e919ae88a12b"}}