{"as_of":"2026-08-04T14:20:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:8a5792c4d3c61c420973740a4b1e927d04e4985986c4fa72459a1209492b0ef6","coverage":[{"denominator":59,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":59,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-24T09:23:10.886561Z","state":"measured"},{"denominator":59,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":59,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-04T06:34:03.388597+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2302.04964/citation-record","integrity":"/paper/2302.04964/integrity","json":"/paper/2302.04964/citation-record.json","paper":"/paper/2302.04964"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Ancient solutions of Ric ci flow with type-I curvature growth","venue":null,"work_id":"0fa65387-74b8-4bbb-ae03-cd0d9f310eba","year":2024},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:ac54f7341f271bc526618922f8358bf1d5bb0434fbed5f920c5488910188ea5b","observation_id":"2aea40d0-2aa0-4b29-aad9-1bff093adaa6","resolution":{"observed_at":"2026-05-24T09:24:17.712970Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"The homotopy groups of the integ ral cycle groups","venue":null,"work_id":"389fa068-dfa2-4504-b8f4-20cc28479c3d","year":1962},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:717d84ba11e0e672078a41728677ab579b675018283a0500816b42eb7bee4cf2","observation_id":"707d331c-4534-431a-936c-3bb2073cc729","resolution":{"observed_at":"2026-05-24T09:24:17.724343Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"The Ricci flow in Riemannian geometry , volume 2011 of Lecture Notes in Mathematics","venue":null,"work_id":"ed09cc6b-6adf-4a9d-baf2-12f433fda1b3","year":2011},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:199e4c9d1f028a4b1559fdd2832806a6bc2fb965d22696898b30bca82fe60d25","observation_id":"b5a8cdf6-0fb6-46fd-a056-c3cc0a61ec40","resolution":{"observed_at":"2026-05-24T09:24:17.875742Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Unique asymp- totics of compact ancient solutions to three-dimensional Ricci flow","venue":null,"work_id":"fc194370-7828-420c-85e4-a65dcc77f244","year":2022},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:42b044c964425adb4bc69ff452df1f3e4fd00baf36ed645dcc240afbe2b40757","observation_id":"759259f6-340c-4a43-8819-954e9230748f","resolution":{"observed_at":"2026-05-24T09:24:17.716381Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Ancient solutions of Ricc i flow on spheres and general- ized Hopf fibrations","venue":null,"work_id":"954535b8-cb07-4684-adaf-a6aeb6cf8dc1","year":2012},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:d7dc99a7bd3e1eb35073fd3f0e9585fe973bae01cd6b52d8cbd82b02f4740a1d","observation_id":"9ab6208b-b9f6-4a0f-a790-46abc053009d","resolution":{"observed_at":"2026-05-24T09:24:17.840028Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"6bf5a7b9-d8f2-450c-88d8-88000cdb6805","year":1917},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:33ef767cee274ab0402824ab3bb0ee4ca7977394daef0b5009796833e4e89767","observation_id":"07773b1d-5f62-4dde-b038-bc590bbc0876","resolution":{"observed_at":"2026-05-24T09:24:17.882417Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Optimal curv ature estimates for homoge- neous Ricci flows","venue":null,"work_id":"d58faaa9-035f-4318-ab5a-572b1090ce28","year":2019},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:86676c478dcff4020b0b606cb61f6d05c206bb8be6d06bc43ed537709e15a216","observation_id":"22b4d99f-4a60-4620-b889-2a42e336ea16","resolution":{"observed_at":"2026-05-24T09:24:17.828665Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Manifolds with positive curv ature operators are space forms","venue":null,"work_id":"87ac952c-0213-4d1d-8d2c-2ef84e184c8d","year":2008},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:e28ee53167a44d44e86b01b670de70125b9384a40c5c1dd607660e3306914d43","observation_id":"50607d31-f115-423e-ac73-8bb5486ef1ca","resolution":{"observed_at":"2026-05-24T09:24:17.709480Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"On the ex istence of translating solutions of mean curvature flow in slab regions","venue":null,"work_id":"ebcf55c0-75ea-4fe2-8eb7-9c8347b9aafb","year":2020},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:a865f2f089ecbb4c47bfa58a8c7f468cf372833372350290d040a482d26ff189","observation_id":"a47fe00d-026b-4416-94b5-bc3cbab44b5e","resolution":{"observed_at":"2026-05-24T09:24:17.705913Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Collapsin g ancient solutions of mean curvature flow","venue":null,"work_id":"5a674df8-dc5d-4497-816b-e69aee846241","year":2021},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:291dc6003d5785bb558cdf935fcd104b91b7104fbff99e56a8266a8b1fffa95a","observation_id":"f8b06499-f757-479a-82ec-7add15064a21","resolution":{"observed_at":"2026-05-24T09:24:17.737365Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Ricci flow with surgery on manifolds with positive iso tropic curvature","venue":null,"work_id":"4320fbd8-ddd5-4f55-ac49-72d9a5993101","year":2019},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:7e098f589c3be91055b9ae95fbf16bcee347dcdae1d4a088013fc62ff57e806f","observation_id":"8569fad9-e27a-4444-bd83-f64c90cf4170","resolution":{"observed_at":"2026-05-24T09:24:17.818360Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Ancient solutions to the Ricci flow in dimension 3","venue":null,"work_id":"4b652af4-4148-4a84-ad0e-599e795b2d5e","year":2020},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:3cf1da908a49a1b543bc4bb0643ba5fb9a4fc5a7b4791bea2b884faab37517bc","observation_id":"35d7bf98-cfad-4c40-a30c-171056a4a557","resolution":{"observed_at":"2026-05-24T09:24:17.832157Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Uniqueness of com- pact ancient solutions to the higher-dimensional Ricci flow","venue":null,"work_id":"c27fd1c5-5dc2-4d32-b1ec-232c2d141ccb","year":2022},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:7fa04bd0d9ba70654d6a8aa647d9c6b2862d0d2b9f41c6d55938673f4d1a6442","observation_id":"77adc0c7-11c8-49c4-b6d1-7fb1fb946bf9","resolution":{"observed_at":"2026-05-24T09:24:17.698690Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Un iqueness of compact ancient solutions to three-dimensional Ricci flow","venue":null,"work_id":"69862368-2ae7-49b5-a4b4-c43f6909e4af","year":2021},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:40a37aebb72c7ece04e75f8696335cae7b25bcd087d7e9a890d69b79222891fc","observation_id":"1c5fef3c-a77f-428b-913d-1800dbe4f1f4","resolution":{"observed_at":"2026-05-24T09:24:17.886735Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Ancient s olutions to the Ricci flow with pinched curvature","venue":null,"work_id":"6fa516b6-3af4-425b-8246-c1967d415605","year":2011},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:09d9695c55c8f1a82b07711e5fe523abe0e5067d0cff2658adb23a4263f0ae83","observation_id":"433b9204-1830-4abb-bd63-04230bb40f78","resolution":{"observed_at":"2026-05-24T09:24:17.814966Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"SO(2) × SO(3)-invariant Ricci solitons and ancient flows on S4","venue":null,"work_id":"6a8e76c6-a1c0-409a-a356-459d3653daac","year":2022},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:2ea32b219070d825af14acaf25d90b7faedacd2ab0acb000ec1f39ce6ca34e2f","observation_id":"9c78e750-536e-43b1-8f16-65faffc0db60","resolution":{"observed_at":"2026-05-24T09:24:17.755112Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Ricci flow on homogeneous spaces with two isotro py summands","venue":null,"work_id":"140717f0-ae53-4920-814c-098556e6b901","year":2014},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:30d54fe65465bd785bd7a13d07bba2b4d9d57867319e805dfbd27e25fe6bda40","observation_id":"efda223c-88dc-4542-b56f-c9179bdd5e25","resolution":{"observed_at":"2026-05-24T09:24:17.744611Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Backward ricci flow on locally homogeneous 3-manifolds","venue":null,"work_id":"6b9fd079-c503-4bd7-a0d4-17b5e96235a4","year":2009},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:2cc9a2e8bfeee7300b1896008b650cbe2f99d32f6e7d861d08f948745de27cb4","observation_id":"68e7be14-8a06-4648-afe4-bbd60fddccc4","resolution":{"observed_at":"2026-05-24T09:24:17.674066Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Strong uniqueness of the Ricci flow","venue":null,"work_id":"50d43c12-d600-4b25-8452-b97f417f4fb7","year":2009},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:4fe7e053d0ea23cbc729312d2311fdb91fd1b36758352c81ccaccb8cdea6aec9","observation_id":"6e5ed6a3-ad07-48c1-b626-542a71068db0","resolution":{"observed_at":"2026-05-24T09:24:17.747977Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Local pinching estimates in 3-dim Ricci flow","venue":null,"work_id":"64122b44-33ab-43ef-8ad1-8ba042da8dd3","year":2013},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:4a7c93ec489eff7b8abde8efea9901fc1cb79c90c799d632b9eacbe8151eded5","observation_id":"95300be2-8f1e-492d-9c53-5933a4da445b","resolution":{"observed_at":"2026-05-24T09:24:17.677507Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"The Ricci flow: techniques and applications","venue":null,"work_id":"098f82b9-95f4-41a6-bf8a-3d70cdc62511","year":2008},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:987ae860380dde3412657b9ff49e55c30acc0fe6e446e370eae1e6322e082b8c","observation_id":"1a70ffeb-0dc8-4431-8e3d-9eafde3dd462","resolution":{"observed_at":"2026-05-24T09:24:17.687282Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"The Ricci flow: techniques and applica- tions","venue":null,"work_id":"8634282e-f0ad-4dbc-833c-bbe96096f010","year":2010},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:3201aa7547275e9710bf78c5bdf300e08c69db6efa17096c25b42eec0c11ead6","observation_id":"4659474f-f3b9-4576-b026-8ab11080c6cf","resolution":{"observed_at":"2026-05-24T09:24:17.770562Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Hamilton’s Ricci flow , volume 77 of Graduate Studies in Mathematics","venue":null,"work_id":"cfef02f2-7edc-431e-adcb-10ad17b9ff15","year":2006},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:71aaae9bb5f31e6b2362a344c2b4df3c9d6fc5ba9f6978eda6d46c734bb97ad0","observation_id":"ea1b3d00-f3d1-405b-a5f1-209653deac71","resolution":{"observed_at":"2026-05-24T09:24:17.702324Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Type II ancient solutions to the Ricci flow on surf aces","venue":null,"work_id":"725a5c2d-de3f-423e-895d-30bc4abf716a","year":2007},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:0ca966782a4e1c09cfb3be67f8b34be11fcc1ad7a1efc25b59a2ba09788110a1","observation_id":"fbe54f11-3ceb-43c8-816e-058292e7ba15","resolution":{"observed_at":"2026-05-24T09:24:17.758937Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Colding and William P","venue":null,"work_id":"b17902b9-8a23-4d20-868b-8bfec69b1bcf","year":2008},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:47ff1cc1672fa8d5ab6ea41c542f9ec486531765a984a1638d3fbece1e92d2a7","observation_id":"9f0dfb84-bd9a-4451-9360-f749bb4122a2","resolution":{"observed_at":"2026-05-24T09:24:17.793652Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Daskalopoulos and R","venue":null,"work_id":"054ece0c-6948-4bab-b424-ca5298544fbf","year":2004},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:bc6bf960b47d86f4f9ded5c8eeb90fc3fe2c40d0f264c811bacf65b3cb977f6f","observation_id":"968223dc-6f32-4d7b-9c8e-bf200efda9f6","resolution":{"observed_at":"2026-05-24T09:24:17.783169Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Daskalopoulos and N","venue":null,"work_id":"9ea27e10-94c9-4ca6-9d31-5ec1c99892cb","year":2006},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:3f02e2dabc912f494507729e4be6e11b2420d4f7bdb0c3d0caafdbc5250ebe2e","observation_id":"0c533cba-1692-4d02-9cf5-77776dc92929","resolution":{"observed_at":"2026-05-24T09:24:17.684160Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Ancient solutions to geometric flows","venue":null,"work_id":"d1d9eca6-7afe-4066-a02f-a2ff222a0253","year":2020},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:76f11b881e1e64ffc2324006b7f525a56ecc4e66e7bfa1af83d3110a8337dee7","observation_id":"98f6c62b-f397-4945-924f-6b279215e346","resolution":{"observed_at":"2026-05-24T09:24:17.777206Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Classification of ancient com- pact solutions to the Ricci flow on surfaces","venue":null,"work_id":"d2fa87e6-45f3-4a02-b34f-1e5ce6e0a4e8","year":2012},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:0688d03e8dd333a9f871bde7f34fc63ac9a13d7d8708e585ee9d584324b59f6f","observation_id":"ecb13432-bbe8-42e7-b59a-85c8e24a82c7","resolution":{"observed_at":"2026-05-24T09:24:17.774004Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"66ef5f5f-5139-4cd2-88ed-2f47820962a3","year":1995},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:34968c49e34d11d1d931bde72465703c07637b905ac0d63b68b00a5ce937e8f0","observation_id":"bda82f9e-d526-47b9-af5a-6e17dc887c3b","resolution":{"observed_at":"2026-05-24T09:24:17.790177Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"2c01472c-9d0b-4ebe-a2d4-aecaa0941e73","year":1996},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:4d30ae25f9f625cc6196d96cdfef27d01da33d68a6271079fe58f6848848787e","observation_id":"f1cddcdb-66af-42d1-9f6e-aa4f8e3373c5","resolution":{"observed_at":"2026-05-24T09:24:17.719854Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"7afd6ef5-ac90-4d98-9505-5bcdbbc71f2a","year":1993},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:7ecb2bd28c45a3daa7532eb894cd5042c93b72af4579e8f66fec61d8f991a688","observation_id":"becf39c8-46d9-4955-ad21-c840f76d437a","resolution":{"observed_at":"2026-05-24T09:24:17.835856Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Filling Riemannian manifolds","venue":null,"work_id":"4f810384-b1f9-43c6-a9c0-744f231292ea","year":1983},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:405d137955bfed3679cd79d2e1301abecf0cfe38ff8fbf00a7a43668574efbcf","observation_id":"8891fe0c-50b1-4c8b-9fbe-95079c282841","resolution":{"observed_at":"2026-05-24T09:24:17.843711Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Hamilton","venue":null,"work_id":"17ba625d-880f-45e4-8725-a698b4de559d","year":1986},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:4cbb09b10e1789ad8e368d6be6aeb673258ed5afd8c7224355d4c7d73f8be94b","observation_id":"7f89b29e-e3d0-46d7-89b0-47c850e29b30","resolution":{"observed_at":"2026-05-24T09:24:17.810574Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Hamilton","venue":null,"work_id":"4dff642d-e33c-4069-b482-68667a679a08","year":1986},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:46a34b693df78d2e6c2f5cbff0b78291d93df2f57c488f7fd17d87759748833e","observation_id":"7091c41d-beb1-4ad8-a3b3-bf84789d55b0","resolution":{"observed_at":"2026-05-24T09:24:17.766892Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Hamilton","venue":null,"work_id":"b394dac0-c719-4963-b2d2-b37fa0862547","year":1993},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:0f3f66003f2c7f467f357d999bcb3c252fc7d7221de1501c2f3b1b69b531aaf1","observation_id":"1b580d4f-62a3-40ad-9c93-5a262ae76881","resolution":{"observed_at":"2026-05-24T09:24:17.800198Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Hamilton","venue":null,"work_id":"2b748df0-7a11-45da-801f-9df8d2bce6f8","year":1999},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:95231f2d65c99416cc2535db37aaec063a5e4d85b0583f2bcfa8ebcdb365d739","observation_id":"aa5aae22-958e-476f-8f6d-e6ecefb25f2d","resolution":{"observed_at":"2026-05-24T09:24:17.751506Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"On κ-solutions and canonical neighborhoods in 4d Ricci flow","venue":null,"work_id":"759b457b-2a25-4c79-a4a7-0c3924007b38","year":null},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:3f5719f054690ed77f2c90d48af60d12a7167d83c1ecb769da162de5e07d0cfd","observation_id":"dd626e3b-d390-4c16-9d5d-c1cb4b778307","resolution":{"observed_at":"2026-05-24T09:24:17.897827Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"f2145a14-77cd-48ee-a111-004ddf5f78f9","year":1952},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:df55cca4a044633ab1720d14e77ecfbdba58b5d6add1b8da9ac636b7c64d0e09","observation_id":"e4020bbd-5483-4dae-8be2-ce3041a3ee9b","resolution":{"observed_at":"2026-05-24T09:24:17.740842Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Ricci flow of locally homoge neous geometries on closed manifolds","venue":null,"work_id":"b5a282df-1f15-43a2-b99f-718c3c90917c","year":1992},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:5f505e5cf0ed5d2c415b267eed09fdb3f7af0d2a40c41ffd57b05ba94d1babe7","observation_id":"8235bea4-2d6f-4fbd-b599-9155a9654b4d","resolution":{"observed_at":"2026-05-24T09:24:17.854307Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Ricci solitons on compact three-manifolds","venue":null,"work_id":"efc59e07-d904-4a02-88bc-12f7d4d417c2","year":1993},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:92d4a42f4feb0e4d222688e94a3f640cc2f76198780b6fa8514fb6f1b5018a32","observation_id":"8d72f532-9e48-460b-8690-2bb176e6accc","resolution":{"observed_at":"2026-05-24T09:24:17.690791Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"af201b9c-8c1b-40a8-8fac-f3ff9187148c","year":1993},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:de38d2b0a3236c0b0fc7f634f8577cb0ef325a3ce528eb64a48c45ad448ecdeb","observation_id":"937892d5-6839-4d3f-910b-a4030a5cb989","resolution":{"observed_at":"2026-05-24T09:24:17.803794Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Lectures on closed geodesics","venue":null,"work_id":"329af07a-4859-44e5-941c-aadde170a100","year":1978},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:70599bbca1b7a9ed480f8c6045cfc41f41604ecd0f9785e27de5b863e2e6b9f8","observation_id":"51909d89-2f8b-47c1-a408-8b951596301d","resolution":{"observed_at":"2026-05-24T09:24:17.733367Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2312.0146","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Toral s ymmetries of collapsed ancient solutions to the homogeneous Ricci flow","venue":null,"work_id":"580e0a9b-a295-4f47-9b2e-d3efb3786882","year":null},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:8a2fc94ab5805a72e14999076495de5f43d8b7cc485640c0ccf672de63744741","observation_id":"19800e57-f175-444f-b5fe-9eb7aeddd65b","resolution":{"observed_at":"2026-05-24T09:24:17.249693Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2207.02714","last_updated":"2022-07-06T14:37:55Z","snapshot_observed_at":"2026-07-06T13:28:27.905370Z","submitted_at":"2022-07-06T14:37:55Z","title":"3D flying wings for any asymptotic cones","version":1},"cited_work":{"arxiv_id":"2207.02714","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2207.02714","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"3d flying wings for any asymptotic cones","venue":null,"work_id":"626dc3ca-6ac4-4273-a868-1332e8a12e20","year":null},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"cited_paper":"/paper/2207.02714","citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:b5d84681c89cea3d4152f3a32c1e5714858ba56524f645f68366a4f47358bfdd","observation_id":"186fd57a-37ec-4ec7-8c79-5b48f00a3518","resolution":{"observed_at":"2026-05-24T09:24:17.237698Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"A family of 3D steady gradient solitons that are flying wings","venue":null,"work_id":"7e0c3efe-242d-4455-a842-7857af1a58e6","year":2024},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:49114e0d2b04a73681ad7d30869acb1a426f60beb7b690f5832dfb43ce416788","observation_id":"38c18b34-20e8-43ae-b50b-43eefea53629","resolution":{"observed_at":"2026-05-24T09:24:17.787063Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Ricci flow of homogeneous manifolds","venue":null,"work_id":"183033fc-d042-4f37-b98e-425e0862b276","year":2013},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:4b9c0d1afd2ea9d38d40a93b58c3dcb701012c300c8137ea1434770a8d583608","observation_id":"7d5f9795-2042-444a-bff3-f9d56b787c2d","resolution":{"observed_at":"2026-05-24T09:24:17.825137Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Compact blow-up limits of finite time singularities of ricci flow are shrinking ricci solitons","venue":null,"work_id":"2c0d3b28-0d24-47b5-ba5c-75170bb2d66a","year":2007},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:d1ffa9591e0a55e83267e3747fc9108b90d0c206f883490296f6e4a40de2e0c5","observation_id":"bee47c08-f41b-4f77-ad5f-b8680bbf18b4","resolution":{"observed_at":"2026-05-24T09:24:17.858522Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"165797eb-d779-4622-a325-8c250b057e6b","year":2017},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:546394f0b6a00f3c4197a4445a205d83a43a410a61cbd8e837ecb52ed9db25ed","observation_id":"6a47156f-cad9-4d06-af85-c3b2b35d1514","resolution":{"observed_at":"2026-05-24T09:24:17.729681Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Marques and Andr´ e Neves","venue":null,"work_id":"9b7c89d6-d78c-41d2-9b05-d0ed2eed172a","year":2016},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:ab76d258c340fa88b0463c4cb261a38e0998f0fa39f41af00e4eced24e65600b","observation_id":"fb1d1ad6-e19f-4941-a46b-151f82999460","resolution":{"observed_at":"2026-05-24T09:24:17.847864Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Collapsed ancient solutions of the Ricci flow on compact homogeneous spaces","venue":null,"work_id":"30562d53-5f93-4815-a74a-dbab2c5da833","year":2022},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:d4df26f10280340ddcf6cc5b866d76f86e5a4c47c656b6500cb73452887a318c","observation_id":"7c5d879e-ea67-434a-8d05-4cf1a0ec6711","resolution":{"observed_at":"2026-05-24T09:24:17.821856Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"The entropy formula for the Ricci flow and its g eometric applications","venue":null,"work_id":"ca5af132-67b4-4717-922e-3235470bab12","year":null},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:776cbc09297bc366c0e4ba7200a3045eec7afcdedce05a886d89b19da21321f4","observation_id":"b7a49b31-fa70-4263-985d-b509560111d7","resolution":{"observed_at":"2026-05-24T09:24:17.671029Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"math/0307245","last_updated":"2003-07-17T15:26:38Z","snapshot_observed_at":"2026-07-07T05:35:59.786340Z","submitted_at":"2003-07-17T15:26:38Z","title":"Finite extinction time for the solutions to the Ricci flow on certain three-manifolds","version":1},"cited_work":{"arxiv_id":"math/0307245","doi":null,"metadata_source":"pith","pith_arxiv_id":"math/0307245","snapshot_observed_at":"2026-07-03T16:28:39.441135Z","title":"Finite extinction time for the solutions to the Ricci flow on certain three-manifolds","venue":"math.DG","work_id":"3f51048e-ac27-40e7-8a59-ac4755852437","year":2003},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"cited_paper":"/paper/math/0307245","citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:1e52e81a1cbbae1871731fc826625390fbfdd7964625ba77cc9779832dbc8f3f","observation_id":"756055a3-016d-46e0-88bc-f2f6fd9f9685","resolution":{"observed_at":"2026-05-24T09:24:17.243252Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Ricci flow with surgery on three-manifolds","venue":null,"work_id":"6827ce61-0e03-47ac-a27f-e1d9b80cec34","year":null},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:385626c051ab5915a4ca55b60a3ece9e7887f6177d064fa0ede10595724ab10a","observation_id":"c345340e-392e-4a6b-a07a-02bb3a18e32f","resolution":{"observed_at":"2026-05-24T09:24:17.681039Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Riemannian geometry, volume 171 of Graduate Texts in Mathematics","venue":null,"work_id":"3a98afe1-fd66-4405-8690-c045bfcaf800","year":2016},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:c7b2f96fa4a247482a49504144c4755000750d347ec53ac1167562f62d906fa9","observation_id":"f2bbb073-dbb5-4a4e-9b2d-caf6a20ad138","resolution":{"observed_at":"2026-05-24T09:24:17.865213Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"365d25b4-ec66-456b-8ff2-c755882ef8b9","year":1981},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:c2fad9125938a0234f4e6db4aa2c63ca4631cf3be750e11dd73ba626131000e2","observation_id":"2ebf7549-030e-40bb-821c-da586e0dadbc","resolution":{"observed_at":"2026-05-24T09:24:17.667011Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"e9b438b1-5a50-407c-ade6-839a7a860faf","year":1995},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:e6596d3ac9407b705ce3ee2e5984bfdc6412d5f2d73cf3182f2f1bb090333370","observation_id":"a5ae17e0-da7d-4ee4-a2ae-119c0cbd5cc5","resolution":{"observed_at":"2026-05-24T09:24:17.695279Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"On the Ricci flow of homogeneous metrics on sphere s","venue":null,"work_id":"9b94d100-1798-4ec4-9176-151d28538f49","year":2022},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:d586893ccbbfedacc037365f80b5fd1b926842c69250b777ad0967601d0bc2d4","observation_id":"781007a0-072e-4b2c-9ce1-4cc460dc3a8b","resolution":{"observed_at":"2026-05-24T09:24:17.871946Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Deforming the metric on complete Riemannian manif olds","venue":null,"work_id":"e26e2643-5783-48d4-8a24-7971318df77f","year":1989},"citing_paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth","version":2},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-05-24T09:23:10.886561Z"},"links":{"citing_paper":"/paper/2302.04964"},"observation_digest":"sha256:172628eae4115ea836454db95536649048f12b15fd355908ede5fd101d383097","observation_id":"91ca2dc9-bbb3-4159-a2b2-044c8459b4d3","resolution":{"observed_at":"2026-05-24T09:24:17.892131Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2302.04964","last_updated":"2024-11-04T20:35:17Z","latest_version":2,"primary_category":"math.DG","snapshot_observed_at":"2026-07-06T14:50:14.766783Z","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth"},"reference_resolution":{"displayed":59,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":9,"verified_exact":3,"verified_fuzzy":47},"total_outbound_references":59},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"thesis":"As of 4 August 2026, this Paper Citation Record lists 59 of 59 outbound references and 0 inbound Pith citation observations for arXiv:2302.04964."}