{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:23MLCQHRILLDYLTAQS2UCOHXIQ","short_pith_number":"pith:23MLCQHR","canonical_record":{"source":{"id":"1804.10748","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-04-28T06:26:05Z","cross_cats_sorted":[],"title_canon_sha256":"ea8e9fd60f2f9b5e0c5a735a35b1d1575f99f79701ee883021b838e4ce6995ad","abstract_canon_sha256":"873c2caeab67e85ebaae111ba98bc7c27d7b17bd49af9c949b8f9f66c4de9f16"},"schema_version":"1.0"},"canonical_sha256":"d6d8b140f142d63c2e6084b54138f7440ba5bc8e4e6f1b81c6664de8b2d5ab80","source":{"kind":"arxiv","id":"1804.10748","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.10748","created_at":"2026-05-18T00:17:15Z"},{"alias_kind":"arxiv_version","alias_value":"1804.10748v1","created_at":"2026-05-18T00:17:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10748","created_at":"2026-05-18T00:17:15Z"},{"alias_kind":"pith_short_12","alias_value":"23MLCQHRILLD","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"23MLCQHRILLDYLTA","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"23MLCQHR","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:23MLCQHRILLDYLTAQS2UCOHXIQ","target":"record","payload":{"canonical_record":{"source":{"id":"1804.10748","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-04-28T06:26:05Z","cross_cats_sorted":[],"title_canon_sha256":"ea8e9fd60f2f9b5e0c5a735a35b1d1575f99f79701ee883021b838e4ce6995ad","abstract_canon_sha256":"873c2caeab67e85ebaae111ba98bc7c27d7b17bd49af9c949b8f9f66c4de9f16"},"schema_version":"1.0"},"canonical_sha256":"d6d8b140f142d63c2e6084b54138f7440ba5bc8e4e6f1b81c6664de8b2d5ab80","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:15.671493Z","signature_b64":"qkEa4r7a+xXIEIs4QOAn57GcDNbszGTy51syYrlPIadpNBtz/Z7DKja9Zpz+JPLRiPFS/75lvYOVmL/6AANuAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6d8b140f142d63c2e6084b54138f7440ba5bc8e4e6f1b81c6664de8b2d5ab80","last_reissued_at":"2026-05-18T00:17:15.670958Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:15.670958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.10748","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":"2026-05-18T00:17:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x2cy2unBTVamJYtS+MqK1eOwD9rTS/CA5bcb12R44OSA5of7799uCWwrv66ak/KOyVK7m4kFp4TSDeJdkAgJBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T07:12:38.565184Z"},"content_sha256":"bfa2b25a997336b155c7fe14b5c8e003e4edf4c535e9c9d45ddf707769aae2ef","schema_version":"1.0","event_id":"sha256:bfa2b25a997336b155c7fe14b5c8e003e4edf4c535e9c9d45ddf707769aae2ef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:23MLCQHRILLDYLTAQS2UCOHXIQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rigidity of Einstein metrics as critical points of some quadratic curvature functionals on complete manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Guangyue Huang, Xingxiao Li, Yu Chen","submitted_at":"2018-04-28T06:26:05Z","abstract_excerpt":"In this paper, we consider some rigidity results for the Einstein metrics as the critical points of some known quadratic curvature functionals on complete manifolds, characterized by some point-wise inequalities. Moreover, we also provide rigidity results by the integral inequalities involving the Weyl curvature, the trace-less Ricci curvature and the Sobolev constant, accordingly."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10748","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":"2026-05-18T00:17:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q4rgm5euh4FPCsiqsHu/KmPmTTshQHAnNl0j3I9la9ap04hWkls7+touIftTgulAC2fCuZTje5KUDQHGM/AVBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T07:12:38.565793Z"},"content_sha256":"65ef6fc3cf9da0fdbacd0aee6c544a95f912c3ff46988e52000f059e67a069db","schema_version":"1.0","event_id":"sha256:65ef6fc3cf9da0fdbacd0aee6c544a95f912c3ff46988e52000f059e67a069db"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/23MLCQHRILLDYLTAQS2UCOHXIQ/bundle.json","state_url":"https://pith.science/pith/23MLCQHRILLDYLTAQS2UCOHXIQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/23MLCQHRILLDYLTAQS2UCOHXIQ/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":"2026-06-07T07:12:38Z","links":{"resolver":"https://pith.science/pith/23MLCQHRILLDYLTAQS2UCOHXIQ","bundle":"https://pith.science/pith/23MLCQHRILLDYLTAQS2UCOHXIQ/bundle.json","state":"https://pith.science/pith/23MLCQHRILLDYLTAQS2UCOHXIQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/23MLCQHRILLDYLTAQS2UCOHXIQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:23MLCQHRILLDYLTAQS2UCOHXIQ","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":"873c2caeab67e85ebaae111ba98bc7c27d7b17bd49af9c949b8f9f66c4de9f16","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-04-28T06:26:05Z","title_canon_sha256":"ea8e9fd60f2f9b5e0c5a735a35b1d1575f99f79701ee883021b838e4ce6995ad"},"schema_version":"1.0","source":{"id":"1804.10748","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.10748","created_at":"2026-05-18T00:17:15Z"},{"alias_kind":"arxiv_version","alias_value":"1804.10748v1","created_at":"2026-05-18T00:17:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10748","created_at":"2026-05-18T00:17:15Z"},{"alias_kind":"pith_short_12","alias_value":"23MLCQHRILLD","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"23MLCQHRILLDYLTA","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"23MLCQHR","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:65ef6fc3cf9da0fdbacd0aee6c544a95f912c3ff46988e52000f059e67a069db","target":"graph","created_at":"2026-05-18T00:17:15Z","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":"In this paper, we consider some rigidity results for the Einstein metrics as the critical points of some known quadratic curvature functionals on complete manifolds, characterized by some point-wise inequalities. Moreover, we also provide rigidity results by the integral inequalities involving the Weyl curvature, the trace-less Ricci curvature and the Sobolev constant, accordingly.","authors_text":"Guangyue Huang, Xingxiao Li, Yu Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-04-28T06:26:05Z","title":"Rigidity of Einstein metrics as critical points of some quadratic curvature functionals on complete manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10748","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:bfa2b25a997336b155c7fe14b5c8e003e4edf4c535e9c9d45ddf707769aae2ef","target":"record","created_at":"2026-05-18T00:17:15Z","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":"873c2caeab67e85ebaae111ba98bc7c27d7b17bd49af9c949b8f9f66c4de9f16","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-04-28T06:26:05Z","title_canon_sha256":"ea8e9fd60f2f9b5e0c5a735a35b1d1575f99f79701ee883021b838e4ce6995ad"},"schema_version":"1.0","source":{"id":"1804.10748","kind":"arxiv","version":1}},"canonical_sha256":"d6d8b140f142d63c2e6084b54138f7440ba5bc8e4e6f1b81c6664de8b2d5ab80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6d8b140f142d63c2e6084b54138f7440ba5bc8e4e6f1b81c6664de8b2d5ab80","first_computed_at":"2026-05-18T00:17:15.670958Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:15.670958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qkEa4r7a+xXIEIs4QOAn57GcDNbszGTy51syYrlPIadpNBtz/Z7DKja9Zpz+JPLRiPFS/75lvYOVmL/6AANuAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:15.671493Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.10748","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bfa2b25a997336b155c7fe14b5c8e003e4edf4c535e9c9d45ddf707769aae2ef","sha256:65ef6fc3cf9da0fdbacd0aee6c544a95f912c3ff46988e52000f059e67a069db"],"state_sha256":"2eea168c3fd77ba2949d10c80bd3802d2dd26f751bd9dda155c04f72423c7685"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r2vFPc57rmXrxjGaHhu0RjD0vWM4r6Jun/OyVgx6N3/XcBQX8tRMvLCpiduS1G7cHZIexCCSwyFx/d3O+37UDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T07:12:38.569085Z","bundle_sha256":"7e8dc53d2e4b02bf92d3e1d01aac01f87a703c5f50cf03ad8f673cfd690d9b82"}}