{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:TAY3LK6HFJOJMVQWYWJN2Y7VNK","short_pith_number":"pith:TAY3LK6H","canonical_record":{"source":{"id":"1804.08073","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-04-22T06:29:52Z","cross_cats_sorted":[],"title_canon_sha256":"14b9866b9a14b156f55cd982c990cbf7936a57885a7a6b50dd11914ff3ec2cb6","abstract_canon_sha256":"1ca1746b25752971d025378812e96672154b3bc0007ebe8b8c6dcf2009cac553"},"schema_version":"1.0"},"canonical_sha256":"9831b5abc72a5c965616c592dd63f56aaa9c90c6301c91ae6aa2459ee76f64b6","source":{"kind":"arxiv","id":"1804.08073","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.08073","created_at":"2026-05-18T00:13:36Z"},{"alias_kind":"arxiv_version","alias_value":"1804.08073v3","created_at":"2026-05-18T00:13:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.08073","created_at":"2026-05-18T00:13:36Z"},{"alias_kind":"pith_short_12","alias_value":"TAY3LK6HFJOJ","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TAY3LK6HFJOJMVQW","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TAY3LK6H","created_at":"2026-05-18T12:32:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:TAY3LK6HFJOJMVQWYWJN2Y7VNK","target":"record","payload":{"canonical_record":{"source":{"id":"1804.08073","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-04-22T06:29:52Z","cross_cats_sorted":[],"title_canon_sha256":"14b9866b9a14b156f55cd982c990cbf7936a57885a7a6b50dd11914ff3ec2cb6","abstract_canon_sha256":"1ca1746b25752971d025378812e96672154b3bc0007ebe8b8c6dcf2009cac553"},"schema_version":"1.0"},"canonical_sha256":"9831b5abc72a5c965616c592dd63f56aaa9c90c6301c91ae6aa2459ee76f64b6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:36.861162Z","signature_b64":"gq+P0zg+sB7RUVFldqkpSTMOJFcAsgAtH5NaBwcJuAfYiaxI7ZFK63aiXMnzpNOLUAuMFEL65G1eGOGn/S8lDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9831b5abc72a5c965616c592dd63f56aaa9c90c6301c91ae6aa2459ee76f64b6","last_reissued_at":"2026-05-18T00:13:36.860535Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:36.860535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.08073","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:13:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B6mpsuOo1DwsQr44/l096z+pPJuP3Xd+r5PDB1+9foZNJkS7D1rDcSJmOW4Et4HQk1ajk5tdSlFin58erv7LAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T14:08:09.059544Z"},"content_sha256":"18ef37772053c9d1213d8a1d3896d71ef70e54c779655990739444c44bf7250e","schema_version":"1.0","event_id":"sha256:18ef37772053c9d1213d8a1d3896d71ef70e54c779655990739444c44bf7250e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:TAY3LK6HFJOJMVQWYWJN2Y7VNK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ricci flow under local almost non-negative curvature conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Yi Lai","submitted_at":"2018-04-22T06:29:52Z","abstract_excerpt":"We find a local solution to the Ricci flow equation under a negative lower bound for many known curvature conditions. The flow exists for a uniform amount of time, during which the curvature stays bounded below by a controllable negative number. The curvature conditions we consider include 2-non-negative and weakly $\\textnormal{PIC}_1$ cases, of which the results are new. We complete the discussion of the almost preservation problem by Bamler-Cabezas-Rivas-Wilking, and the 2-non-negative case generalizes a result in 3D by Simon-Topping to higher dimensions. As an application, we use the local "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08073","kind":"arxiv","version":3},"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":"2026-05-18T00:13:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hgmiYigMrOEZiKKu9Ljo95/dfUWZnmJLKv1sQ8qwoGmwr+L1DfpxQjL0JhOAyGownlZexOA7Ps28kWXnw/ljBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T14:08:09.059889Z"},"content_sha256":"5e0c6a6867f67eef0181737a9f0b6c5a4e72fab94addb03a88cdb0285558d324","schema_version":"1.0","event_id":"sha256:5e0c6a6867f67eef0181737a9f0b6c5a4e72fab94addb03a88cdb0285558d324"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TAY3LK6HFJOJMVQWYWJN2Y7VNK/bundle.json","state_url":"https://pith.science/pith/TAY3LK6HFJOJMVQWYWJN2Y7VNK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TAY3LK6HFJOJMVQWYWJN2Y7VNK/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":"2026-06-24T14:08:09Z","links":{"resolver":"https://pith.science/pith/TAY3LK6HFJOJMVQWYWJN2Y7VNK","bundle":"https://pith.science/pith/TAY3LK6HFJOJMVQWYWJN2Y7VNK/bundle.json","state":"https://pith.science/pith/TAY3LK6HFJOJMVQWYWJN2Y7VNK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TAY3LK6HFJOJMVQWYWJN2Y7VNK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TAY3LK6HFJOJMVQWYWJN2Y7VNK","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":"1ca1746b25752971d025378812e96672154b3bc0007ebe8b8c6dcf2009cac553","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-04-22T06:29:52Z","title_canon_sha256":"14b9866b9a14b156f55cd982c990cbf7936a57885a7a6b50dd11914ff3ec2cb6"},"schema_version":"1.0","source":{"id":"1804.08073","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.08073","created_at":"2026-05-18T00:13:36Z"},{"alias_kind":"arxiv_version","alias_value":"1804.08073v3","created_at":"2026-05-18T00:13:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.08073","created_at":"2026-05-18T00:13:36Z"},{"alias_kind":"pith_short_12","alias_value":"TAY3LK6HFJOJ","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TAY3LK6HFJOJMVQW","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TAY3LK6H","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:5e0c6a6867f67eef0181737a9f0b6c5a4e72fab94addb03a88cdb0285558d324","target":"graph","created_at":"2026-05-18T00:13:36Z","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 find a local solution to the Ricci flow equation under a negative lower bound for many known curvature conditions. The flow exists for a uniform amount of time, during which the curvature stays bounded below by a controllable negative number. The curvature conditions we consider include 2-non-negative and weakly $\\textnormal{PIC}_1$ cases, of which the results are new. We complete the discussion of the almost preservation problem by Bamler-Cabezas-Rivas-Wilking, and the 2-non-negative case generalizes a result in 3D by Simon-Topping to higher dimensions. As an application, we use the local ","authors_text":"Yi Lai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-04-22T06:29:52Z","title":"Ricci flow under local almost non-negative curvature conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08073","kind":"arxiv","version":3},"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":"sha256:18ef37772053c9d1213d8a1d3896d71ef70e54c779655990739444c44bf7250e","target":"record","created_at":"2026-05-18T00:13:36Z","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":"1ca1746b25752971d025378812e96672154b3bc0007ebe8b8c6dcf2009cac553","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-04-22T06:29:52Z","title_canon_sha256":"14b9866b9a14b156f55cd982c990cbf7936a57885a7a6b50dd11914ff3ec2cb6"},"schema_version":"1.0","source":{"id":"1804.08073","kind":"arxiv","version":3}},"canonical_sha256":"9831b5abc72a5c965616c592dd63f56aaa9c90c6301c91ae6aa2459ee76f64b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9831b5abc72a5c965616c592dd63f56aaa9c90c6301c91ae6aa2459ee76f64b6","first_computed_at":"2026-05-18T00:13:36.860535Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:36.860535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gq+P0zg+sB7RUVFldqkpSTMOJFcAsgAtH5NaBwcJuAfYiaxI7ZFK63aiXMnzpNOLUAuMFEL65G1eGOGn/S8lDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:36.861162Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.08073","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18ef37772053c9d1213d8a1d3896d71ef70e54c779655990739444c44bf7250e","sha256:5e0c6a6867f67eef0181737a9f0b6c5a4e72fab94addb03a88cdb0285558d324"],"state_sha256":"9cd315e9bc238fd70543b4f064be2dfab52401bd44ef234863e6b27f3fcd39eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GM3Wwc+wYqpTx6eWTjG8iZk6FEpqUa2xJ9SSRpuk55bYAtIk4YS0XRjtL+DEkvCHVQzd/qQyPOVcTsqRXakZBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T14:08:09.061816Z","bundle_sha256":"24c5254dd1159b71e6a45bf101626d7cb55a8a7cba8e797059b3edda3b1e5c55"}}