{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UAQJNHL6PTWFR4EH62FSGJLJBH","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":"dcf434987d464590cf45c6c958c1ea71c07f44fb578a5c582b9ff0017d5286ba","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-17T16:06:27Z","title_canon_sha256":"a24fba1f8b15bc1ca66017f17151eaf856ed5249887a90a037128f12561c8209"},"schema_version":"1.0","source":{"id":"1110.3714","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3714","created_at":"2026-05-18T04:10:48Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3714v1","created_at":"2026-05-18T04:10:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3714","created_at":"2026-05-18T04:10:48Z"},{"alias_kind":"pith_short_12","alias_value":"UAQJNHL6PTWF","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UAQJNHL6PTWFR4EH","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UAQJNHL6","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:ef7542874016fc2524e4bbf539099302c0e5f2bc48fc5c960d926b6ae23db3a1","target":"graph","created_at":"2026-05-18T04:10:48Z","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":"A fundamental tool in the analysis of Ricci flow is a compactness result of Hamilton in the spirit of the work of Cheeger, Gromov and others. Roughly speaking it allows one to take a sequence of Ricci flows with uniformly bounded curvature and uniformly controlled injectivity radius, and extract a subsequence that converges to a complete limiting Ricci flow. A widely quoted extension of this result allows the curvature to be bounded uniformly only in a local sense. However, in this note we give a counterexample.","authors_text":"Peter Topping","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-17T16:06:27Z","title":"Remarks on Hamilton's Compactness Theorem for Ricci flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3714","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":"sha256:06c53d7da5fa987e7957c6392b3c67cebda9ca678dc6b7f25bd8a3589988ad4d","target":"record","created_at":"2026-05-18T04:10:48Z","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":"dcf434987d464590cf45c6c958c1ea71c07f44fb578a5c582b9ff0017d5286ba","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-17T16:06:27Z","title_canon_sha256":"a24fba1f8b15bc1ca66017f17151eaf856ed5249887a90a037128f12561c8209"},"schema_version":"1.0","source":{"id":"1110.3714","kind":"arxiv","version":1}},"canonical_sha256":"a020969d7e7cec58f087f68b23256909f1363ef2f1889450ae8d083fe8603497","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a020969d7e7cec58f087f68b23256909f1363ef2f1889450ae8d083fe8603497","first_computed_at":"2026-05-18T04:10:48.644556Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:48.644556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x8gpAKtU12phdOkwyUmXh33yH7Mf7PaqHxStN+UA+TjI4FEbuL51SnqcVkmwoRJ5Dv1bWiHnDGXygXaXA4vuDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:48.644964Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.3714","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06c53d7da5fa987e7957c6392b3c67cebda9ca678dc6b7f25bd8a3589988ad4d","sha256:ef7542874016fc2524e4bbf539099302c0e5f2bc48fc5c960d926b6ae23db3a1"],"state_sha256":"2c080dda37ab601136bdc9cbafef25f63ec479f0ba0a2b1d2f28cfb8f1769911"}