{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:VYFKYCBLNSAWWD3456MZSIKMLD","short_pith_number":"pith:VYFKYCBL","canonical_record":{"source":{"id":"1202.2912","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-02-14T02:37:11Z","cross_cats_sorted":[],"title_canon_sha256":"d7e5a135d12c937dbc6070ff332938e608eb42793b0114f3ce3da45864ff2fcb","abstract_canon_sha256":"6adc36c339912e1e03e519cf67032ca3cf1e8375bec13b1fd3695011bd1f4980"},"schema_version":"1.0"},"canonical_sha256":"ae0aac082b6c816b0f7cef9999214c58d779b409ecf208e0b7bbc8f80e90b547","source":{"kind":"arxiv","id":"1202.2912","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2912","created_at":"2026-05-18T04:02:24Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2912v1","created_at":"2026-05-18T04:02:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2912","created_at":"2026-05-18T04:02:24Z"},{"alias_kind":"pith_short_12","alias_value":"VYFKYCBLNSAW","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VYFKYCBLNSAWWD34","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VYFKYCBL","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:VYFKYCBLNSAWWD3456MZSIKMLD","target":"record","payload":{"canonical_record":{"source":{"id":"1202.2912","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-02-14T02:37:11Z","cross_cats_sorted":[],"title_canon_sha256":"d7e5a135d12c937dbc6070ff332938e608eb42793b0114f3ce3da45864ff2fcb","abstract_canon_sha256":"6adc36c339912e1e03e519cf67032ca3cf1e8375bec13b1fd3695011bd1f4980"},"schema_version":"1.0"},"canonical_sha256":"ae0aac082b6c816b0f7cef9999214c58d779b409ecf208e0b7bbc8f80e90b547","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:24.683832Z","signature_b64":"QjI3PpEhRCgna4Kufn+HReBuqwe0ol1sAZEsHY6YlxDaGeq9cMht/3tNj5Wn3YVmvcoPbWPPk9RiGAa6WWhyDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae0aac082b6c816b0f7cef9999214c58d779b409ecf208e0b7bbc8f80e90b547","last_reissued_at":"2026-05-18T04:02:24.683306Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:24.683306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.2912","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":"2026-05-18T04:02:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O8x4F56nPZT2uoZ+8BJpdOQ7uXJLMAuJiSXJLxK2VXcZ/rAoOlRTX4pV0wkXkJdOaPzDjjt+yeeZuTk3/O4TCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:05:15.878747Z"},"content_sha256":"c0cccb3448d400bfce0c15f97fee3f6a34d8162c3bc739d85e5a52a7a56ad1c4","schema_version":"1.0","event_id":"sha256:c0cccb3448d400bfce0c15f97fee3f6a34d8162c3bc739d85e5a52a7a56ad1c4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:VYFKYCBLNSAWWD3456MZSIKMLD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the structure of almost Einstein manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Bing Wang, Gang Tian","submitted_at":"2012-02-14T02:37:11Z","abstract_excerpt":"In this paper, we study the structure of the limit space of a sequence of almost Einstein manifolds, which are generalizations of Einstein manifolds. Roughly speaking, such manifolds are the initial manifolds of some normalized Ricci flows whose scalar curvatures are almost constants over space-time in the $L^1$-sense, Ricci curvatures are bounded from below at the initial time. Under the non-collapsed condition, we show that the limit space of a sequence of almost Einstein manifolds has most properties which is known for the limit space of Einstein manifolds. As applications, we can apply our"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2912","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":"2026-05-18T04:02:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6I+dIx4lMwV1dprDdecWlfYPilCUxYePnINCP9EpOfKFfEkbXYe3wt+TlNjdkbg2VDxxWYM8fTCKXH2opjBLDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:05:15.879091Z"},"content_sha256":"ddc4e38180deb55e3e6102270061d629f384acc54d1a0551fbc6ad8b23c08775","schema_version":"1.0","event_id":"sha256:ddc4e38180deb55e3e6102270061d629f384acc54d1a0551fbc6ad8b23c08775"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VYFKYCBLNSAWWD3456MZSIKMLD/bundle.json","state_url":"https://pith.science/pith/VYFKYCBLNSAWWD3456MZSIKMLD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VYFKYCBLNSAWWD3456MZSIKMLD/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":"2026-05-28T20:05:15Z","links":{"resolver":"https://pith.science/pith/VYFKYCBLNSAWWD3456MZSIKMLD","bundle":"https://pith.science/pith/VYFKYCBLNSAWWD3456MZSIKMLD/bundle.json","state":"https://pith.science/pith/VYFKYCBLNSAWWD3456MZSIKMLD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VYFKYCBLNSAWWD3456MZSIKMLD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VYFKYCBLNSAWWD3456MZSIKMLD","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":"6adc36c339912e1e03e519cf67032ca3cf1e8375bec13b1fd3695011bd1f4980","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-02-14T02:37:11Z","title_canon_sha256":"d7e5a135d12c937dbc6070ff332938e608eb42793b0114f3ce3da45864ff2fcb"},"schema_version":"1.0","source":{"id":"1202.2912","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2912","created_at":"2026-05-18T04:02:24Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2912v1","created_at":"2026-05-18T04:02:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2912","created_at":"2026-05-18T04:02:24Z"},{"alias_kind":"pith_short_12","alias_value":"VYFKYCBLNSAW","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VYFKYCBLNSAWWD34","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VYFKYCBL","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:ddc4e38180deb55e3e6102270061d629f384acc54d1a0551fbc6ad8b23c08775","target":"graph","created_at":"2026-05-18T04:02:24Z","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 study the structure of the limit space of a sequence of almost Einstein manifolds, which are generalizations of Einstein manifolds. Roughly speaking, such manifolds are the initial manifolds of some normalized Ricci flows whose scalar curvatures are almost constants over space-time in the $L^1$-sense, Ricci curvatures are bounded from below at the initial time. Under the non-collapsed condition, we show that the limit space of a sequence of almost Einstein manifolds has most properties which is known for the limit space of Einstein manifolds. As applications, we can apply our","authors_text":"Bing Wang, Gang Tian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-02-14T02:37:11Z","title":"On the structure of almost Einstein manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2912","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:c0cccb3448d400bfce0c15f97fee3f6a34d8162c3bc739d85e5a52a7a56ad1c4","target":"record","created_at":"2026-05-18T04:02:24Z","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":"6adc36c339912e1e03e519cf67032ca3cf1e8375bec13b1fd3695011bd1f4980","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-02-14T02:37:11Z","title_canon_sha256":"d7e5a135d12c937dbc6070ff332938e608eb42793b0114f3ce3da45864ff2fcb"},"schema_version":"1.0","source":{"id":"1202.2912","kind":"arxiv","version":1}},"canonical_sha256":"ae0aac082b6c816b0f7cef9999214c58d779b409ecf208e0b7bbc8f80e90b547","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae0aac082b6c816b0f7cef9999214c58d779b409ecf208e0b7bbc8f80e90b547","first_computed_at":"2026-05-18T04:02:24.683306Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:24.683306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QjI3PpEhRCgna4Kufn+HReBuqwe0ol1sAZEsHY6YlxDaGeq9cMht/3tNj5Wn3YVmvcoPbWPPk9RiGAa6WWhyDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:24.683832Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2912","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0cccb3448d400bfce0c15f97fee3f6a34d8162c3bc739d85e5a52a7a56ad1c4","sha256:ddc4e38180deb55e3e6102270061d629f384acc54d1a0551fbc6ad8b23c08775"],"state_sha256":"f2644fe6051e779be64d670ed05c6c4a71c63921200ecacefed3633a535e1ff1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4CxbnRqxpaMheLO9Fd4MGe1zWrJ2m7K7eqN7xd4ZDJhsJpzOZ2o++jOgNRWfUiAm4uXxhD/mHE8FwKmM5kIoCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:05:15.881240Z","bundle_sha256":"c03cb3fa1fe3a8c0162ca1b13d05fc47a705202c2c3f0a44e5532f1aaafcfbc5"}}