{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:ECPNTYPX7C3YIQBYQOGOSECG4E","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":"75a4bc718ef4e28faa3eb02d816d916f55126d8079d9a74b4de6e433923158f8","cross_cats_sorted":["math.MG"],"license":"","primary_cat":"math.DG","submitted_at":"2002-11-12T17:54:48Z","title_canon_sha256":"6fa8f4f8a1509d6a8f1fd8ee194f3faa03ed05f9050340ca121eae3636b1479e"},"schema_version":"1.0","source":{"id":"math/0211191","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0211191","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"arxiv_version","alias_value":"math/0211191v3","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0211191","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"pith_short_12","alias_value":"ECPNTYPX7C3Y","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"ECPNTYPX7C3YIQBY","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"ECPNTYPX","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:e9983ac78061101be69a3558193fde9125248acfc65398603b3a6dc32560b714","target":"graph","created_at":"2026-05-18T02:38:00Z","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":"Consider a sequence of pointed n-dimensional complete Riemannian manifolds {(M_i,g_i(t), O_i)} such that t in [0,T] are solutions to the Ricci flow and g_i(t) have uniformly bounded curvatures and derivatives of curvatures. Richard Hamilton showed that if the initial injectivity radii are uniformly bounded below then there is a subsequence which converges to an n-dimensional solution to the Ricci flow. We prove a generalization of this theorem where the initial metrics may collapse. Without injectivity radius bounds we must allow for convergence in the Gromov-Hausdorff sense to a space which i","authors_text":"David Glickenstein","cross_cats":["math.MG"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2002-11-12T17:54:48Z","title":"Precompactness of solutions to the Ricci flow in the absence of injectivity radius estimates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0211191","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:dd442a8e2f7c39c515fa92f11875b841fdcf6c67d9ac3b97b41e16f8ddbd9d54","target":"record","created_at":"2026-05-18T02:38:00Z","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":"75a4bc718ef4e28faa3eb02d816d916f55126d8079d9a74b4de6e433923158f8","cross_cats_sorted":["math.MG"],"license":"","primary_cat":"math.DG","submitted_at":"2002-11-12T17:54:48Z","title_canon_sha256":"6fa8f4f8a1509d6a8f1fd8ee194f3faa03ed05f9050340ca121eae3636b1479e"},"schema_version":"1.0","source":{"id":"math/0211191","kind":"arxiv","version":3}},"canonical_sha256":"209ed9e1f7f8b7844038838ce91046e13bbc2675396ec2681c8732e594ea389a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"209ed9e1f7f8b7844038838ce91046e13bbc2675396ec2681c8732e594ea389a","first_computed_at":"2026-05-18T02:38:00.529523Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:00.529523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q0zjiIjW/HkACZluYAwCP5Ns4Qy2GvwuthWo6RyAvTs9mm5VAGB7Xbr7i/nMdR0EkzurP09g7izuB7gMS7BsBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:00.530128Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0211191","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd442a8e2f7c39c515fa92f11875b841fdcf6c67d9ac3b97b41e16f8ddbd9d54","sha256:e9983ac78061101be69a3558193fde9125248acfc65398603b3a6dc32560b714"],"state_sha256":"07d30b6b91e021372a2cebab7e2b6a707c5c6fe354b6be445a6b7cce291e4214"}