{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:FMOYD6ODFSDPE3S7U5XP3SGQAW","short_pith_number":"pith:FMOYD6OD","canonical_record":{"source":{"id":"1408.6866","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-28T21:37:12Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"d57f08d9b9c4f80cc3629317be2907ff4da2da28114edd2c6d23f71ec072f5c3","abstract_canon_sha256":"86ac6808edcb9215f54fd31e12f653835c04857e006a2230cc6bc3d424870646"},"schema_version":"1.0"},"canonical_sha256":"2b1d81f9c32c86f26e5fa76efdc8d005a553b3edd3ee327ed0fe986eee79f2d1","source":{"kind":"arxiv","id":"1408.6866","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6866","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6866v1","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6866","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"pith_short_12","alias_value":"FMOYD6ODFSDP","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FMOYD6ODFSDPE3S7","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FMOYD6OD","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:FMOYD6ODFSDPE3S7U5XP3SGQAW","target":"record","payload":{"canonical_record":{"source":{"id":"1408.6866","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-28T21:37:12Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"d57f08d9b9c4f80cc3629317be2907ff4da2da28114edd2c6d23f71ec072f5c3","abstract_canon_sha256":"86ac6808edcb9215f54fd31e12f653835c04857e006a2230cc6bc3d424870646"},"schema_version":"1.0"},"canonical_sha256":"2b1d81f9c32c86f26e5fa76efdc8d005a553b3edd3ee327ed0fe986eee79f2d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:00.114952Z","signature_b64":"MdBpvwBCNyr2Mr5WSxYWVBow6aUi2LsHIOn8IKyKLA0OkBQxK16tqa2qikJbx0XPpB2sZzup0LyNoJXBixXsCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b1d81f9c32c86f26e5fa76efdc8d005a553b3edd3ee327ed0fe986eee79f2d1","last_reissued_at":"2026-05-18T02:44:00.114407Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:00.114407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.6866","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":"2026-05-18T02:44:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rTZ/xEqIE7X02X4TsL2LWdnSOTdwrSC7pW3L+N2LIpoDJGxqwpAYlW480UyY9yXQVszmOBW8t1QV8emKCuPADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:49:40.429894Z"},"content_sha256":"a8271b5d5e1b7eb676f88e2a1f335bf8d400e6d038a27e7c7ce73dcf52c45c0d","schema_version":"1.0","event_id":"sha256:a8271b5d5e1b7eb676f88e2a1f335bf8d400e6d038a27e7c7ce73dcf52c45c0d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:FMOYD6ODFSDPE3S7U5XP3SGQAW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ricci flows with unbounded curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Peter M. Topping","submitted_at":"2014-08-28T21:37:12Z","abstract_excerpt":"Until recently, Ricci flow was viewed almost exclusively as a way of deforming Riemannian metrics of bounded curvature. Unfortunately, the bounded curvature hypothesis is unnatural for many applications, but is hard to drop because so many new phenomena can occur in the general case. This article surveys some of the theory from the past few years that has sought to rectify the situation in different ways."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6866","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":"2026-05-18T02:44:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zkVab2IgiD3nhi2DlYYOPpXgtgqsLFNWQRtRfKpcJjLf2f5BalD6GFPnv58BUFcKwesMrWz3HuS0uoaJ4SroDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:49:40.430234Z"},"content_sha256":"e25d7ab9cbb59f7d098ab21372f085c4df5ff262a6aea8e6ce96382665ece7a7","schema_version":"1.0","event_id":"sha256:e25d7ab9cbb59f7d098ab21372f085c4df5ff262a6aea8e6ce96382665ece7a7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FMOYD6ODFSDPE3S7U5XP3SGQAW/bundle.json","state_url":"https://pith.science/pith/FMOYD6ODFSDPE3S7U5XP3SGQAW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FMOYD6ODFSDPE3S7U5XP3SGQAW/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":"2026-06-26T14:49:40Z","links":{"resolver":"https://pith.science/pith/FMOYD6ODFSDPE3S7U5XP3SGQAW","bundle":"https://pith.science/pith/FMOYD6ODFSDPE3S7U5XP3SGQAW/bundle.json","state":"https://pith.science/pith/FMOYD6ODFSDPE3S7U5XP3SGQAW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FMOYD6ODFSDPE3S7U5XP3SGQAW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FMOYD6ODFSDPE3S7U5XP3SGQAW","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":"86ac6808edcb9215f54fd31e12f653835c04857e006a2230cc6bc3d424870646","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-28T21:37:12Z","title_canon_sha256":"d57f08d9b9c4f80cc3629317be2907ff4da2da28114edd2c6d23f71ec072f5c3"},"schema_version":"1.0","source":{"id":"1408.6866","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6866","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6866v1","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6866","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"pith_short_12","alias_value":"FMOYD6ODFSDP","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FMOYD6ODFSDPE3S7","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FMOYD6OD","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:e25d7ab9cbb59f7d098ab21372f085c4df5ff262a6aea8e6ce96382665ece7a7","target":"graph","created_at":"2026-05-18T02:44:00Z","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":"Until recently, Ricci flow was viewed almost exclusively as a way of deforming Riemannian metrics of bounded curvature. Unfortunately, the bounded curvature hypothesis is unnatural for many applications, but is hard to drop because so many new phenomena can occur in the general case. This article surveys some of the theory from the past few years that has sought to rectify the situation in different ways.","authors_text":"Peter M. Topping","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-28T21:37:12Z","title":"Ricci flows with unbounded curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6866","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:a8271b5d5e1b7eb676f88e2a1f335bf8d400e6d038a27e7c7ce73dcf52c45c0d","target":"record","created_at":"2026-05-18T02:44:00Z","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":"86ac6808edcb9215f54fd31e12f653835c04857e006a2230cc6bc3d424870646","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-28T21:37:12Z","title_canon_sha256":"d57f08d9b9c4f80cc3629317be2907ff4da2da28114edd2c6d23f71ec072f5c3"},"schema_version":"1.0","source":{"id":"1408.6866","kind":"arxiv","version":1}},"canonical_sha256":"2b1d81f9c32c86f26e5fa76efdc8d005a553b3edd3ee327ed0fe986eee79f2d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b1d81f9c32c86f26e5fa76efdc8d005a553b3edd3ee327ed0fe986eee79f2d1","first_computed_at":"2026-05-18T02:44:00.114407Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:00.114407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MdBpvwBCNyr2Mr5WSxYWVBow6aUi2LsHIOn8IKyKLA0OkBQxK16tqa2qikJbx0XPpB2sZzup0LyNoJXBixXsCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:00.114952Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.6866","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8271b5d5e1b7eb676f88e2a1f335bf8d400e6d038a27e7c7ce73dcf52c45c0d","sha256:e25d7ab9cbb59f7d098ab21372f085c4df5ff262a6aea8e6ce96382665ece7a7"],"state_sha256":"46791c351564391d0a5f7a79a32af4fd53a0ae116e524884981caad27dae19f8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mzHHzig5kBuX+wbPz1Qcg820rIbnmWteciujRQWVAntzw0ACHXiz4a7X3NMkCH3xewVNVJSy5kNlW3S1Zh0XBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T14:49:40.432129Z","bundle_sha256":"597dd9e71ad707c88b52e202c33ce49f159a32960cb3702a48d3305cbc1731de"}}