{"as_of":"2026-08-12T22:23:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c63525f5ecf3a4590d822e661fad2471b081cf0b4ed7a0d30fa9721a910a9833","coverage":[{"denominator":161,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":100,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T20:22:44.669913Z","state":"measured"},{"denominator":101,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":101,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T21:57:27.918491Z","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":[{"citation":{"cited_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.05935","snapshot_observed_at":"2026-08-03T21:57:27.918491Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2511.13320","last_updated":"2026-07-28T06:52:07Z","snapshot_observed_at":"2026-08-10T06:04:58.449889Z","submitted_at":"2025-11-17T12:58:00Z","title":"Mosco-convergence of Cheeger energies on varying spaces satisfying curvature dimension conditions","version":3},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-03T21:57:27.918491Z"},"links":{"cited_paper":"/paper/2412.05935","citing_paper":"/paper/2511.13320"},"observation_digest":"sha256:79402c5961463b7d341b184d164f31691b94f47237afc666c54bf91f00f0b12a","observation_id":"712365ad-50df-464e-a5cf-cb81fcce8dc4","resolution":{"observed_at":"2026-08-03T21:57:27.918491Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2412.05935/citation-record","integrity":"/paper/2412.05935/integrity","json":"/paper/2412.05935/citation-record.json","paper":"/paper/2412.05935"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.233149Z","title":"Agostiniani, M","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.233149Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:84871092547c82f0aa42f3fbc18685146251f3958c4a57e08873a0dea1c4e3c4","observation_id":"9a926fbd-aee3-47e3-b13e-fc97ea2ef0fb","resolution":{"observed_at":"2026-08-11T20:22:44.233149Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.240911Z","title":"Ambrosio, Calculus, heat flow and curvature-dimension bounds in metric measure spaces , in Proceedings of the International Congress of Mathematicians—Rio de Janeiro 2018","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.240911Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:95e2301129ee82efd5ee8e70cf5acb44b9916e64f58336b06c51bfcc6eabc0da","observation_id":"1eb027da-d4ce-4091-924f-870d1b0d24a6","resolution":{"observed_at":"2026-08-11T20:22:44.240911Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.245497Z","title":"Ambrosio and S","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.245497Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:d9a9c302d22224504f5e8553c0002606ea74084bb2debfeeb714b8d0b2a7f115","observation_id":"47b93eda-ac23-4f57-bbe9-1209971b3cc4","resolution":{"observed_at":"2026-08-11T20:22:44.245497Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.251046Z","title":"Ambrosio, N","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.251046Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:d7bd72f566b74c6dbd339955062ebdbe91c0d7d3181289a3e4f83bcb31f895ad","observation_id":"f922691c-0aef-4a29-b656-4f5f43408a8f","resolution":{"observed_at":"2026-08-11T20:22:44.251046Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.256344Z","title":"Ambrosio, N","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.256344Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:ef094e57a3a7dfb48a850acb7c97ab27506f135af0009d080573f97ccf82c6a8","observation_id":"cc83366e-8309-41b8-9d8f-65361a5ffcde","resolution":{"observed_at":"2026-08-11T20:22:44.256344Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.261013Z","title":"J., 163 (2014), pp","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.261013Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:0eb7a24057a55b0a961b28a93dea132f38dbd4838e4506327a190c4b4a707de4","observation_id":"6bdab84d-3dbb-4b20-9f67-56f095d7fe06","resolution":{"observed_at":"2026-08-11T20:22:44.261013Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.266185Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.266185Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:c8df34035575b69b07bc94efaaf624eece39c0f245b13b143bc48563f43f0399","observation_id":"16c2c06a-5141-473a-ae6a-260160436d6d","resolution":{"observed_at":"2026-08-11T20:22:44.266185Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.270547Z","title":"Ambrosio and S","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.270547Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:3c5b7466feb70f8965fec849b7d9b1e7bac4deaa15b98960e0193b1bae80237e","observation_id":"41759727-c1d0-4b89-a430-6c452941e128","resolution":{"observed_at":"2026-08-11T20:22:44.270547Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.274314Z","title":"Ambrosio, A","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.274314Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:96b4cc46c86f7bb6e007ba22e77f3a5fef13865f0ace793b8fcc295a2b6049bf","observation_id":"b1c5d2e5-4084-4ee5-acd6-935b7770e56d","resolution":{"observed_at":"2026-08-11T20:22:44.274314Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.06934","last_updated":"2024-07-09T15:10:20Z","snapshot_observed_at":"2026-07-06T18:43:43.463452Z","submitted_at":"2024-07-09T15:10:20Z","title":"Quantitative stability of the total $Q$-curvature near minimizing metrics","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.06934","snapshot_observed_at":"2026-08-11T20:22:44.280167Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.280167Z"},"links":{"cited_paper":"/paper/2407.06934","citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:95f1d6305f990459ddc4377016f182a461cc96d835652e87371393263413154e","observation_id":"03948812-93bf-45c0-b113-770e69c4c922","resolution":{"observed_at":"2026-08-11T20:22:44.280167Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.284494Z","title":"Antonelli, E","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.284494Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:495ceb08e528be89462e8ccc38561b7522aa77011c243dca084480a559180e03","observation_id":"eec88f5a-eb45-4b66-86db-45e6dd55686b","resolution":{"observed_at":"2026-08-11T20:22:44.284494Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.289764Z","title":"Antonelli, M","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.289764Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:6593fe5f94f8c5bdb3c85faca4ea0c731ee906f991878b5dc833b96a65a8a1d1","observation_id":"74073d2d-e8de-4756-b720-3dc249be55ff","resolution":{"observed_at":"2026-08-11T20:22:44.289764Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.293922Z","title":"Antonelli, S","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.293922Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:488fdbd12cd2786b6fa88dfd721ae21e5ba6bad341226ee8cec183959f78448e","observation_id":"befae541-83b7-4746-8ed4-e24f0969b478","resolution":{"observed_at":"2026-08-11T20:22:44.293922Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.298658Z","title":"Antonelli, E","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.298658Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:2df99b904d4fb933b79b13aa3a9e241b7c7c422eb8c41cd1079154dd467e6e2b","observation_id":"db4cde41-982e-4ed6-b49a-c48bad27f010","resolution":{"observed_at":"2026-08-11T20:22:44.298658Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2201.04916","last_updated":"2023-10-07T08:57:06Z","snapshot_observed_at":"2026-08-12T09:14:38.612798Z","submitted_at":"2022-01-13T12:15:05Z","title":"Sharp isoperimetric comparison on non-collapsed spaces with lower Ricci bounds","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2201.04916","snapshot_observed_at":"2026-08-11T20:22:44.302572Z","title":"Antonelli, E","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.302572Z"},"links":{"cited_paper":"/paper/2201.04916","citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:1b4a7b576255176f957797f79c111a88acad220adcf740e7c73c04fd8512595c","observation_id":"334861dd-c17a-4e89-a944-93bb728f6ca4","resolution":{"observed_at":"2026-08-11T20:22:44.302572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.306525Z","title":"Antonelli, E","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.306525Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:e7b7a5350ca373179c0574f29f2dbed2dc4319b9e40dc849b669612cbb2726d9","observation_id":"5cf2b667-4da7-4bf4-ac31-c32a37853ba6","resolution":{"observed_at":"2026-08-11T20:22:44.306525Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.309927Z","title":"Antonelli, E","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.309927Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:a7919e8d0c32874a35f05e477eb22b9a7f5c91795fa156b5fdf114bfae6220c5","observation_id":"f94b2e86-b482-4f21-a960-206bdac2b7a2","resolution":{"observed_at":"2026-08-11T20:22:44.309927Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2302.10091","last_updated":"2025-03-15T12:24:35Z","snapshot_observed_at":"2026-07-06T14:53:45.768994Z","submitted_at":"2023-02-20T16:55:47Z","title":"Isoperimetric problem and structure at infinity on Alexandrov spaces with nonnegative curvature","version":3},"cited_work":{"arxiv_id":"2302.10091","doi":null,"metadata_source":"pith","pith_arxiv_id":"2302.10091","snapshot_observed_at":"2026-08-11T20:22:45.383416Z","title":"Isoperimetric problem and structure at infinity on Alexandrov spaces with nonnegative curvature","venue":"math.DG","work_id":"ec3c6b5b-4c50-4944-8176-0c265caaed6a","year":2023},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.313517Z"},"links":{"cited_paper":"/paper/2302.10091","citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:3b4a0746393148afb3b6cf0e70987a42285eeec4e36b329fed169f63c2e5b7a2","observation_id":"0f4870a3-4a3a-421d-9091-ccb9eb18467c","resolution":{"observed_at":"2026-08-11T20:22:45.387772Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.317232Z","title":"Aubin , ´Equations diff´ erentielles non lin´ eaires et probl` eme de Yamabe concernant la courbure scalaire, J","venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.317232Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:287dafa8992c5b7fe728fbcccf822e4ba702c806e2e7ea20b18a62c6e097087f","observation_id":"8e7ea066-535a-4513-b272-ae0a0fbead04","resolution":{"observed_at":"2026-08-11T20:22:44.317232Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.320886Z","title":"Differential Geometry, 11 (1976), pp","venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.320886Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:06704e25d552b542eee766cadec1de033816b9f2dace9c419560b94a6cc65121","observation_id":"5e091e30-e5e8-4ad9-82b2-56922c3516e7","resolution":{"observed_at":"2026-08-11T20:22:44.320886Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.324861Z","title":null,"venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.324861Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:c6642ac5e7db6586e9c3e5f1dcdb5f60eccbae7f6c047fef4a04bb99b07a0e80","observation_id":"bdaebec1-d6de-497d-b847-bcd4c76e03da","resolution":{"observed_at":"2026-08-11T20:22:44.324861Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.329048Z","title":"Baernstein, II, Symmetrization in analysis , vol","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.329048Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:692656553aa3a0828042eead7f4ccb6ca3562673812e11245e19e4612c8f7cf8","observation_id":"42d10fff-2e67-4c7a-b79f-5e241f90f300","resolution":{"observed_at":"2026-08-11T20:22:44.329048Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.333296Z","title":"Bakry, L’hypercontractivit´ e et son utilisation en th´ eorie des semigroupes, in Lectures on probability theory (Saint-Flour, 1992), vol","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.333296Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:e17c16c7981d9ac46b0b7fe13f86e9bc9eba814d7db435946f96574b8d951bc9","observation_id":"f6f2bffe-d7f9-4cb7-b7c1-51a3fd98b678","resolution":{"observed_at":"2026-08-11T20:22:44.333296Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.338305Z","title":"Bakry, I","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.338305Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:ba275cfb5fa06b3c941647b0de47c7ff8f9902b4a7089659e339bd7c8c4112a1","observation_id":"80c2584f-81dd-4619-bf1c-3f4775b27287","resolution":{"observed_at":"2026-08-11T20:22:44.338305Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.343098Z","title":"Bakry and M","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.343098Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:6373fcae529c44299e4c083eead941b9a61cbbafa8e9e69a547ccc18bf682a80","observation_id":"22286477-15b5-47f5-b96b-51cd4a0c4cb3","resolution":{"observed_at":"2026-08-11T20:22:44.343098Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.347604Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.347604Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:692d6cc6db2d81f0f494fa9c6fcbb7bbfa2aeb4aac40b7d40865f13443f87c4a","observation_id":"590386ef-5cb6-48dc-9773-9bd000eed995","resolution":{"observed_at":"2026-08-11T20:22:44.347604Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.351909Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.351909Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:7e4f83876b096a2df34d32a3b957446607297dd25e57dab3b624bd159aa65379","observation_id":"6e619749-608b-49bb-b2bd-a3c2d19bf741","resolution":{"observed_at":"2026-08-11T20:22:44.351909Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.355552Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.355552Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:c25dff6e71a9a81e758a66e3230dc737bce74ded154a1f45f74b26f038d077b0","observation_id":"b619e48a-5a7e-4537-97cf-7e5f34e7200f","resolution":{"observed_at":"2026-08-11T20:22:44.355552Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.359762Z","title":"Pure Appl","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.359762Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:42edf168cd30281c23ab19bbb71d619fc0113b52ec55f7215b0659d6c1e5d1ee","observation_id":"2eb886bf-4f1b-4829-a27e-a7a027bad62f","resolution":{"observed_at":"2026-08-11T20:22:44.359762Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.363897Z","title":"Part I: Duality and compactness , J","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.363897Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:bf999f96de7adbf13bf00e51897363cea2de8be15753e623f1e4c5cc93fc1984","observation_id":"8ccfd180-61d7-4bb3-86ea-a459800acc23","resolution":{"observed_at":"2026-08-11T20:22:44.363897Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.367769Z","title":"Beckner, Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality , Ann","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.367769Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:04963b97731a5f3a0822aeac9a0277900756c4f6561197b432466248142c6209","observation_id":"74958cf0-7c9d-4803-b958-2decb4853c0f","resolution":{"observed_at":"2026-08-11T20:22:44.367769Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.371670Z","title":"B´erard, G","venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.371670Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:b4fc962eae0c21da9d3c1372c59a205d0245196f339b366f5d38faf5573c5f89","observation_id":"8ef694ec-12b4-4755-acb8-ecfb333bae50","resolution":{"observed_at":"2026-08-11T20:22:44.371670Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.375518Z","title":"B ´erard and D","venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.375518Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:e852b1da8f377e745881763788999746a8173c5901936a95a31a923df1205a54","observation_id":"672a3706-e4a2-4943-a0c5-be8cdc003b96","resolution":{"observed_at":"2026-08-11T20:22:44.375518Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2207.11024","last_updated":"2022-07-22T11:57:08Z","snapshot_observed_at":"2026-07-06T13:34:09.609498Z","submitted_at":"2022-07-22T11:57:08Z","title":"Sharp quantitative stability of Poincare-Sobolev inequality in the hyperbolic space and applications to fast diffusion flows","version":1},"cited_work":{"arxiv_id":"2207.11024","doi":null,"metadata_source":"pith","pith_arxiv_id":"2207.11024","snapshot_observed_at":"2026-08-11T20:22:45.365814Z","title":"Sharp quantitative stability of Poincare-Sobolev inequality in the hyperbolic space and applications to fast diffusion flows","venue":"math.AP","work_id":"684b0d84-be3c-45e6-8241-1abe572ac1a4","year":2022},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.382123Z"},"links":{"cited_paper":"/paper/2207.11024","citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:ce3775278d69dc5571322ad706b79fdacedc896e050e5505ee7b2a569b245755","observation_id":"480fef11-2098-4297-beed-4ce5af04122f","resolution":{"observed_at":"2026-08-11T20:22:45.370755Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2211.14618","last_updated":"2023-04-21T14:29:54Z","snapshot_observed_at":"2026-08-10T01:03:01.852581Z","submitted_at":"2022-11-26T17:13:11Z","title":"Sharp quantitative stability of Struwe's decomposition of the Poincar\\'e-Sobolev inequalities on the hyperbolic space: Part I","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2211.14618","snapshot_observed_at":"2026-08-11T20:22:44.387450Z","title":"arXiv:2211.14618, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.387450Z"},"links":{"cited_paper":"/paper/2211.14618","citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:f37c5dd5ff16a312be05f2dda61073529534894615c24bb0edaa41e775487368","observation_id":"76c61abc-589e-43bb-8a56-5db3db660db9","resolution":{"observed_at":"2026-08-11T20:22:44.387450Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.392298Z","title":"Bianchi and H","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.392298Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:8bb59589bc3111e1cc24e7889896a4c2797ce6921bce8b065b87dd418e275ca6","observation_id":"009754fe-dc6a-4502-9380-65ba0fa18c38","resolution":{"observed_at":"2026-08-11T20:22:44.392298Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.396646Z","title":null,"venue":null,"work_id":null,"year":1930},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.396646Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:b4fc7f5e9882010a6a300d2a99c3d9a3c6d317d0b5050326cab39247d09d4f3f","observation_id":"c41d7eb2-359b-4e4e-a347-60f02b751dcb","resolution":{"observed_at":"2026-08-11T20:22:44.396646Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2306.00768","last_updated":"2025-08-04T12:00:57Z","snapshot_observed_at":"2026-08-11T15:39:21.221742Z","submitted_at":"2023-06-01T15:03:35Z","title":"Maps of bounded variation from PI spaces to metric spaces","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2306.00768","snapshot_observed_at":"2026-08-11T20:22:44.400966Z","title":"Brena, F","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.400966Z"},"links":{"cited_paper":"/paper/2306.00768","citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:bcb47eb0d8faa1fdb1e2022ddef53ec0f5deb5a080cc7c22a282e14ffd5a564b","observation_id":"7fa4041d-ce81-4e00-af10-bbcee911cbab","resolution":{"observed_at":"2026-08-11T20:22:44.400966Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.405396Z","title":"Brendle, Sobolev inequalities in manifolds with nonnegative curvature , Comm","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.405396Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:351dead46d6fa2ae06f54fc32f937b73144ec310b8a749486a23172f540c47cb","observation_id":"b16686f4-16ed-4869-8e27-cbca7159701a","resolution":{"observed_at":"2026-08-11T20:22:44.405396Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.410105Z","title":"Brendle and F","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.410105Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:e1e177df6af5f758db6a26dc95340846e94378b0b5f8bfb8b53ce42a34dc10ba","observation_id":"8f24b154-37a3-4f96-9cbc-8b5f20a8d2ed","resolution":{"observed_at":"2026-08-11T20:22:44.410105Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.415452Z","title":"Br´ezis and E","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.415452Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:27c7452ade79052ce75bbe33075608a78ef4088fd274d8476f7da518bdd3a1e3","observation_id":"ac6c6a3a-b3a0-4e51-86a8-b9994035f3d6","resolution":{"observed_at":"2026-08-11T20:22:44.415452Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.420061Z","title":"Brigati, J","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.420061Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:22ce6f8d4457487091e36e49e53b46120842a6f57115d1d19facd736dcaa54e3","observation_id":"8e2fb314-92a8-4e8a-9258-4bc4b6bdf5fa","resolution":{"observed_at":"2026-08-11T20:22:44.420061Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.424144Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.424144Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:cbd5b0466592cd71250621141d1c3949bb68cc33fa0773a7913bea28989bd813","observation_id":"7b0e20aa-c492-45ca-85fa-ca33bb5ed855","resolution":{"observed_at":"2026-08-11T20:22:44.424144Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.429812Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.429812Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:7750a8f28b6e94aae141d8dfd26a0407f74083f4d2c9e104a9c7cc876da28480","observation_id":"ca19d056-cd00-47c8-b379-563c8db9801f","resolution":{"observed_at":"2026-08-11T20:22:44.429812Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.433659Z","title":null,"venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.433659Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:766be6603b6c655593d6353174c493d0ae0e244b4334ef6bf022e4c7493e3c33","observation_id":"8a316253-50f7-465f-b16f-d2cca2ecc9f6","resolution":{"observed_at":"2026-08-11T20:22:44.433659Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.438174Z","title":"Cabr´e, X","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.438174Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:5b80d0de37075e82568de1d6839526ae9d47b9765e4d41faf51954125e54355b","observation_id":"7f2df3fe-579c-42d9-baef-a17e354c023b","resolution":{"observed_at":"2026-08-11T20:22:44.438174Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2203.03345","last_updated":"2022-03-18T07:35:15Z","snapshot_observed_at":"2026-08-12T08:12:00.670746Z","submitted_at":"2022-03-07T12:43:53Z","title":"Semilinear elliptic equations on manifolds with nonnegative Ricci curvature","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2203.03345","snapshot_observed_at":"2026-08-11T20:22:44.442381Z","title":"Catino and D","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.442381Z"},"links":{"cited_paper":"/paper/2203.03345","citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:7254ef3975d1042624ccd7270e15768c21db8de4865f9026ce0830c178959334","observation_id":"6cb559b1-862e-433b-852a-937d91ae4303","resolution":{"observed_at":"2026-08-11T20:22:44.442381Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.446837Z","title":"Cavalletti, F","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.446837Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:72c9b13b50bebfe8e80bd47fefcb0f798f4157afc6bc54a2950ebb5dc58549c6","observation_id":"2d5bb549-0477-41a5-b021-9deba2840a93","resolution":{"observed_at":"2026-08-11T20:22:44.446837Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2207.03423","last_updated":"2024-08-07T15:56:17Z","snapshot_observed_at":"2026-07-06T13:28:54.165063Z","submitted_at":"2022-07-07T16:48:55Z","title":"Rigidities of Isoperimetric inequality under nonnegative Ricci curvature","version":2},"cited_work":{"arxiv_id":"2207.03423","doi":null,"metadata_source":"pith","pith_arxiv_id":"2207.03423","snapshot_observed_at":"2026-08-11T20:22:45.306132Z","title":"Rigidities of Isoperimetric inequality under nonnegative Ricci curvature","venue":"math.MG","work_id":"9fe756ac-81b0-44d6-bd0c-5a702e460402","year":2022},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.454194Z"},"links":{"cited_paper":"/paper/2207.03423","citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:af1707f1cebf52117dd292fec32b2f47de03db9093d995ade8f28ad151ed2c8d","observation_id":"01a442fe-5461-4e60-86af-731f8b7d9955","resolution":{"observed_at":"2026-08-11T20:22:45.311196Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.459166Z","title":"Cavalletti and E","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.459166Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:52e1e97a1957096286c9b917818b64f9d769a1597f5495b43b35f4c071722417","observation_id":"e2c4123a-78e0-4a4c-be2e-282d705a34c7","resolution":{"observed_at":"2026-08-11T20:22:44.459166Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.463332Z","title":"Cavalletti and A","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.463332Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:fd9374d960ca0941afcd85050f4a2f27145141957073f4c58424e05cfd9d3b65","observation_id":"eaf3bcf3-4598-4da4-a47c-cea76e5d0e8b","resolution":{"observed_at":"2026-08-11T20:22:44.463332Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.467229Z","title":"Topol., 21 (2017), pp","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.467229Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:c191719edef5e9e4d4d61172bfbcdb945cc852738a877e64410f9c449c1004bc","observation_id":"f3963226-9084-414c-9051-e35857b548c4","resolution":{"observed_at":"2026-08-11T20:22:44.467229Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.471283Z","title":"Cavalletti, A","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.471283Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:875facef54c166c27534d827a1a16e5a76a47d00e7703423ecbb5fdcfd3f8b44","observation_id":"44e2f635-b7c1-4705-a71d-9491cee647d5","resolution":{"observed_at":"2026-08-11T20:22:44.471283Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2310.01054","last_updated":"2023-10-02T10:04:56Z","snapshot_observed_at":"2026-07-30T23:02:03.577447Z","submitted_at":"2023-10-02T10:04:56Z","title":"Lattice tilings minimizing nonlocal perimeters","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2310.01054","snapshot_observed_at":"2026-08-11T20:22:44.474558Z","title":"Cesaroni, I","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.474558Z"},"links":{"cited_paper":"/paper/2310.01054","citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:949da58e4cf486c0caf13897ffceb2e2567785e541c2ece072683fec4fac9bb5","observation_id":"e4396990-c784-4128-9b40-84d6c2561358","resolution":{"observed_at":"2026-08-11T20:22:44.474558Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2302.07112","last_updated":"2023-07-12T09:19:09Z","snapshot_observed_at":"2026-08-02T22:05:55.293198Z","submitted_at":"2023-02-14T15:15:26Z","title":"Minimal periodic foams with equal cells","version":2},"cited_work":{"arxiv_id":"2302.07112","doi":null,"metadata_source":"pith","pith_arxiv_id":"2302.07112","snapshot_observed_at":"2026-08-11T20:22:45.270985Z","title":"Minimal periodic foams with equal cells","venue":"math.AP","work_id":"b8bee5b4-c465-4acd-a713-5a07844133c8","year":2023},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.479153Z"},"links":{"cited_paper":"/paper/2302.07112","citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:0a419a8d1c2766ab39311f73ba43ce03fbc4392acedcf9e114a09f9954899a38","observation_id":"a46fe816-f879-40d5-909d-e8a013b42db2","resolution":{"observed_at":"2026-08-11T20:22:45.276643Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.483130Z","title":"Cesaroni and M","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.483130Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:e30adfbc122145944b35cf44d67c7d3372c441110a9b92928b55d910ce7f6521","observation_id":"a045e8fb-5ac4-4fd6-a7d1-96469efcd29f","resolution":{"observed_at":"2026-08-11T20:22:44.483130Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.486788Z","title":"Cheeger , Differentiability of Lipschitz functions on metric measure spaces , Geom","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.486788Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:d9c45f87d4937fda2ae14268033dd6b1cbb9862eb44052c67b34c031c6902991","observation_id":"8b6f8f89-6465-476a-9e10-860e5a4c06a8","resolution":{"observed_at":"2026-08-11T20:22:44.486788Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.491362Z","title":"Cheeger and T","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.491362Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:39610136796eca60d771b0a9990b93450ff8b137277348890c8f256c1e8e22ff","observation_id":"b0335b93-704e-4a9d-a4a4-13f81b6f669a","resolution":{"observed_at":"2026-08-11T20:22:44.491362Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.495668Z","title":null,"venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.495668Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:007d7b21fb19c48f79faeb75be4e329aa6239fef8d987a8d0408ac16a1bcddd0","observation_id":"c79c32c8-14ac-4f06-8e6b-50df2f7655a1","resolution":{"observed_at":"2026-08-11T20:22:44.495668Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.500216Z","title":null,"venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.500216Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:931e44f45fe3ad100eaf9c1120049c5aea07a4f6912b00eb6e18e0f39c76fff3","observation_id":"ebdeb8ef-282b-4993-a743-26b277f5b8e5","resolution":{"observed_at":"2026-08-11T20:22:44.500216Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.505224Z","title":null,"venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.505224Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:59986842568f2a94521694a8b76dd6feb74ff6068340bc6a89df8c12e962d907","observation_id":"bab5a32f-4620-40db-a64f-0da3c861ef2e","resolution":{"observed_at":"2026-08-11T20:22:44.505224Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2404.13961","last_updated":"2024-05-13T10:05:34Z","snapshot_observed_at":"2026-07-06T18:03:33.406287Z","submitted_at":"2024-04-22T08:08:07Z","title":"Sharp quantitative stability of the Yamabe problem","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.13961","snapshot_observed_at":"2026-08-11T20:22:44.508946Z","title":"Chen and S","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.508946Z"},"links":{"cited_paper":"/paper/2404.13961","citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:191e01452763ed9b88ff31cc81cd06432d8f742e04b73893004dd44d84d2cb0f","observation_id":"61159e58-3ee7-44d5-b90f-ec42e274a865","resolution":{"observed_at":"2026-08-11T20:22:44.508946Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.513239Z","title":"Chodosh, M","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.513239Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:07c941d714a4cfd8ece09b76ee786d588f0c43ff09bdbef220effd0c5b288f49","observation_id":"8fd80b13-cd9d-45b0-8448-606c0e20f5a2","resolution":{"observed_at":"2026-08-11T20:22:44.513239Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.517237Z","title":"Cianchi and N","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.517237Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:1d2e27e76bb20c631b46d5ec04473c25ed1f8fb5e623fe4d9cf546269a5d988d","observation_id":"dec8f3d2-80e5-46ee-85a8-9190b3bb9e19","resolution":{"observed_at":"2026-08-11T20:22:44.517237Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.521476Z","title":"Cianchi, N","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.521476Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:459e07543c7c808e1aec1bb1eb71b048152dea56cf02630ff204ae4b76958d8f","observation_id":"e248709a-e57e-41e1-ae0e-fcefd7b0930b","resolution":{"observed_at":"2026-08-11T20:22:44.521476Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.525385Z","title":"Ciraolo, A","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.525385Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:30564e672f60d60e79f55c09f304d64e0035479908daca5a287b2a315ebdb59e","observation_id":"83f13f39-e73e-47ca-b4c3-c0b41cba8ad2","resolution":{"observed_at":"2026-08-11T20:22:44.525385Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.529459Z","title":null,"venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.529459Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:747d83a6557586030b678810894268d3747551e7dd8a46bbed8618dd42cc5f77","observation_id":"f56fd912-22da-4945-8c9e-ab77548391a8","resolution":{"observed_at":"2026-08-11T20:22:44.529459Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.533231Z","title":"Cordero-Erausquin, B","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.533231Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:b9f8194f533780229a38a10153148b1a5e638f70431b9904591d92c28bee4636","observation_id":"6c8b99e6-3020-49d9-9639-bde4052421d1","resolution":{"observed_at":"2026-08-11T20:22:44.533231Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.536992Z","title":"De Philippis and N","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.536992Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:978ec8d9f25b1afd470a3b95202ce7a73a9841fcce580b051d32d4c397a64317","observation_id":"898e947d-3a73-4f50-a469-e50bbd47041e","resolution":{"observed_at":"2026-08-11T20:22:44.536992Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.541428Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.541428Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:92eefe115552b9dc6b57fb7028d9d7f18f21b1a0829f9fc3e55363f309ec888a","observation_id":"1264434e-0c78-4762-8c7e-72873b26a0c4","resolution":{"observed_at":"2026-08-11T20:22:44.541428Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2103.15360","last_updated":"2021-04-24T19:57:37Z","snapshot_observed_at":"2026-08-11T18:33:06.166151Z","submitted_at":"2021-03-29T06:24:52Z","title":"Sharp quantitative estimates of Struwe's Decomposition","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2103.15360","snapshot_observed_at":"2026-08-11T20:22:44.545435Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.545435Z"},"links":{"cited_paper":"/paper/2103.15360","citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:2307e2e3f49dfd6e4fda0c9007e7019f198e9524a49c3cbf3249606bda7f1b83","observation_id":"5812b341-ec4d-4ed3-b8ff-0e2c38de452d","resolution":{"observed_at":"2026-08-11T20:22:44.545435Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.550488Z","title":"Djadli and O","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.550488Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:a3cb4a660aa88986b96d9038d8cf882e5fe778c1e159e9bf29f44ba50d78c776","observation_id":"bbc69e2a-54ce-4ee0-8a82-0fe68d3ce24f","resolution":{"observed_at":"2026-08-11T20:22:44.550488Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.08527","last_updated":"2024-04-22T11:07:14Z","snapshot_observed_at":"2026-07-06T17:29:34.813390Z","submitted_at":"2024-02-13T15:29:50Z","title":"A short review on Improvements and stability for some interpolation inequalities","version":2},"cited_work":{"arxiv_id":"2402.08527","doi":null,"metadata_source":"pith","pith_arxiv_id":"2402.08527","snapshot_observed_at":"2026-08-11T20:22:45.224630Z","title":"A short review on Improvements and stability for some interpolation inequalities","venue":"math.AP","work_id":"559bb9b4-9089-4599-9366-81598cebbfae","year":2024},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.554272Z"},"links":{"cited_paper":"/paper/2402.08527","citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:3ab8e3980fba4cf1c8f40424e2fa6ceda480ee9f3ac12196ab0f96977cfbb531","observation_id":"81d03fba-88f6-469e-92bf-3d03a0e03eac","resolution":{"observed_at":"2026-08-11T20:22:45.229368Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2209.08651","last_updated":"2025-02-27T09:46:35Z","snapshot_observed_at":"2026-07-06T13:53:33.112275Z","submitted_at":"2022-09-18T20:39:09Z","title":"Sharp stability for Sobolev and log-Sobolev inequalities, with optimal dimensional dependence","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2209.08651","snapshot_observed_at":"2026-08-11T20:22:44.559218Z","title":"Dolbeault, M","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.559218Z"},"links":{"cited_paper":"/paper/2209.08651","citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:5fb73d1e64158a047ecf6e66d99298bf78163ff595eb14f96407d90ea89c39fa","observation_id":"bc6e1021-8d29-4980-8fdf-b39b22e9482f","resolution":{"observed_at":"2026-08-11T20:22:44.559218Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.563317Z","title":"Druet and E","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.563317Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:b2073596a0218ce5f3fe718af99e0f98676b92d4db8497fa73b667617a9defaf","observation_id":"6292c1d2-894b-4d07-ab8d-daaca90de31e","resolution":{"observed_at":"2026-08-11T20:22:44.563317Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.567038Z","title":"Druet, E","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":76,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.567038Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:64a27572b982469270b9b5249c4fe1646336aba1e2ecf3b5a8850d28e7856a18","observation_id":"f51ea7c2-b3be-4110-b2bd-bde9582f987d","resolution":{"observed_at":"2026-08-11T20:22:44.567038Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.571009Z","title":"45 of Mathematical Notes, Princeton University Press, Princeton, NJ, 2004","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":77,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.571009Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:430e49f57d29fe0326c0c6df4d258b8b86c69ea70f167e9cc634f762db484ba8","observation_id":"188e5ff6-48dc-417e-ba88-de5317b436d9","resolution":{"observed_at":"2026-08-11T20:22:44.571009Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.578409Z","title":"Dupaigne, I","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":78,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.578409Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:65c6a6ef013ace728f1836bd76a097aaa12b49f1867fa2738cef61f2078d65ab","observation_id":"4112cfc9-6afa-4bf8-859a-d4592ba9fc5a","resolution":{"observed_at":"2026-08-11T20:22:44.578409Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.582544Z","title":"Durand-Cartagena, S","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":79,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.582544Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:f82cd33c673e44b8d388906e41dcfccd3e97637a652891d9e3247010c8af58d9","observation_id":"462a75df-57ff-422d-b335-5c876d2c2c32","resolution":{"observed_at":"2026-08-11T20:22:44.582544Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.586284Z","title":"Eguchi and A","venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":80,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.586284Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:41e4f940fd0960f6da36b2fd13d3b1607349ddbb8873f95920472b7879b52efe","observation_id":"c8927935-75df-4323-b248-b9f1d627821a","resolution":{"observed_at":"2026-08-11T20:22:44.586284Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.589861Z","title":"Engelstein, R","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":81,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.589861Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:8bd40ef5caf1d37d136ef3265dd64209cc1766e147f975c916d112ea7128b004","observation_id":"1a57503c-c1b2-49dd-9a4e-146723901e8b","resolution":{"observed_at":"2026-08-11T20:22:44.589861Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.593407Z","title":"Erbar, K","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":82,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.593407Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:a93a7b79b1e2b396886924f315639a8da79dba087305d32546ca85806aa40bd0","observation_id":"cbaad5ea-f31c-4f79-b677-b42bac729d5e","resolution":{"observed_at":"2026-08-11T20:22:44.593407Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.596651Z","title":"F aber, Beweiss dass unter allen homogenen Membranen von gleicher Fl´ ache und gleicher Spannung die kreisf¨ ormgige den leifsten Grundton gibt","venue":null,"work_id":null,"year":1923},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":83,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.596651Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:1800ca44bd50ed3d33ddb0a1d622b4b8b0aca8505918d71e8e1f625a56929a0b","observation_id":"b7411d6f-a857-447b-9a50-332ba146bcd1","resolution":{"observed_at":"2026-08-11T20:22:44.596651Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.600549Z","title":"F athi, I","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":84,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.600549Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:660a21907a697e8996ae924ac6362139c43064b123098b51dc9bf98fbed416c8","observation_id":"dbb4fae5-48c7-4af6-b432-43068ba7a2c4","resolution":{"observed_at":"2026-08-11T20:22:44.600549Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.604154Z","title":"Ferone and R","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":85,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.604154Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:c84407da87a54c8d3141c34e32f37b74843e2c8741d163d5fa03d7e370c33665","observation_id":"49afbf54-9b03-43fa-ae8e-595d90743304","resolution":{"observed_at":"2026-08-11T20:22:44.604154Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.607924Z","title":"Figalli and F","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":86,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.607924Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:7ca3f6e734840c9308566f4881e7caba87dfb56708e92b5db01e3880569b30d4","observation_id":"31dbecb1-60fd-44b5-93cd-9155d5420bef","resolution":{"observed_at":"2026-08-11T20:22:44.607924Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.611728Z","title":"Figalli and R","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":87,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.611728Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:7dd49dbf29010445052d0365bfb19076ba2d8a8dc4d3a5144467504cdf4350e4","observation_id":"ef4c6ca4-be37-4285-a489-32abedd9833d","resolution":{"observed_at":"2026-08-11T20:22:44.611728Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.615441Z","title":"Figalli and Y","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":88,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.615441Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:377e2be50d70c0bb4760e6131b855238ef9ffc720f63524a28cab4e5a36665cc","observation_id":"435b270c-ec7b-40d3-ac9f-0083c30b78e6","resolution":{"observed_at":"2026-08-11T20:22:44.615441Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.619121Z","title":"Fogagnolo and L","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":89,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.619121Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:ec7d53a4e1ce1853d39f71b49b31edcb4207f1e7b0f3ab5c733924fe7af3e3bd","observation_id":"39129f06-5746-4747-92fd-ab5593cc8cf3","resolution":{"observed_at":"2026-08-11T20:22:44.619121Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.622776Z","title":"Fontenas, Sur les constantes de Sobolev des vari´ et´ es riemanniennes compactes et les fonctions extr´ emales des sph` eres, Bull","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":90,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.622776Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:6a7140f84220d90f3e2d0ad6230215e13284446e89489d5f59a59e2513ce19fb","observation_id":"579b0711-3d4a-4b78-bee9-627d5bba6288","resolution":{"observed_at":"2026-08-11T20:22:44.622776Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.628088Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":91,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.628088Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:e62d92055fa2f743b0738da4aa5dafb5f86516a094a950a7b643d261089d7238","observation_id":"351460ab-e743-4bbc-94c3-e045abe842f3","resolution":{"observed_at":"2026-08-11T20:22:44.628088Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.632696Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":92,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.632696Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:fc76a6d2a4a4317c50355eef5c887cf69c0d28d70753a28ae7b41c2e68f0322f","observation_id":"335ad7a6-468b-441e-9651-70f324ba272f","resolution":{"observed_at":"2026-08-11T20:22:44.632696Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.637473Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":93,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.637473Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:f3a8f1df28aabb869dde1ba4b668456197151449c426238057006a6a187db010","observation_id":"ca0f8f6b-198b-408a-870e-5dadb7d54c22","resolution":{"observed_at":"2026-08-11T20:22:44.637473Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.642854Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":94,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.642854Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:92322a1049dd07502111e915900512236bfda6af0ca8de2fad0d4fd705328791","observation_id":"d2574cbd-25d1-423b-aa55-13e3f1be766d","resolution":{"observed_at":"2026-08-11T20:22:44.642854Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.646979Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":95,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.646979Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:f043be88e72aec4e5192863bca46ff95da82310cbb24c6ae79275c8aef4b8380","observation_id":"5366b833-e8f7-43d9-9b88-1b6fc3fd6bbc","resolution":{"observed_at":"2026-08-11T20:22:44.646979Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:44.652262Z","title":"Gidas, W.-M","venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":96,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.652262Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:cac50c2a2e3d40fde278bc1a162a99a58809d1dae80e4c1498abd96b1af5f49a","observation_id":"c6d24984-8a48-4bd2-a19a-0ef536465991","resolution":{"observed_at":"2026-08-11T20:22:44.652262Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:46.276787Z","title":"Gigli, On the heat flow on metric measure spaces: existence, uniqueness and stability , Calc","venue":null,"work_id":"cdaf94d7-a85b-47cb-a8cd-e26e7a4d0f6a","year":2010},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":97,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.656560Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:c9aebbbbde90aea47c785c24ac5454f138a72a4d8d69fcb22fd31c74c643df77","observation_id":"45c31791-bc0a-4d9a-b135-09ceff22db15","resolution":{"observed_at":"2026-08-11T20:22:46.281024Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T20:22:46.265044Z","title":null,"venue":null,"work_id":"0879d3b9-98e1-46e6-a4c6-ebb684a4d888","year":2015},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":98,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.660924Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:e6a7d2112b16696ae01e14cdcca1be53767434be6a3f0d16337cb9b043578b77","observation_id":"2f1fb32e-2af3-4e46-9227-a386e96100a6","resolution":{"observed_at":"2026-08-11T20:22:46.269143Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2306.14604","last_updated":"2023-06-26T11:27:55Z","snapshot_observed_at":"2026-08-08T05:45:22.080002Z","submitted_at":"2023-06-26T11:27:55Z","title":"De Giorgi and Gromov working together","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2306.14604","snapshot_observed_at":"2026-08-11T20:22:44.665458Z","title":"Gigli, De Giorgi and Gromov working together","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":99,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.665458Z"},"links":{"cited_paper":"/paper/2306.14604","citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:d2f5a5758ea98e712e31a349bc844e4bdf01e78e1de3c08a327759acc73a264d","observation_id":"52e6198a-3527-4df2-8ac7-980f23ef6f98","resolution":{"observed_at":"2026-08-11T20:22:44.665458Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:22:46.252016Z","title":"Gigli and B","venue":null,"work_id":"330239cd-7279-4096-826f-989016c8b76d","year":2014},"citing_paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds","version":2},"reference_index":100,"source":"pdf_text","source_observed_at":"2026-08-11T20:22:44.669913Z"},"links":{"citing_paper":"/paper/2412.05935"},"observation_digest":"sha256:693a3af8b5a8b20cc650533cec57e2e2294efafa56073ea8bb8723e7354c066a","observation_id":"dfd15b2d-c3d0-4704-8644-b1e64c749a04","resolution":{"observed_at":"2026-08-11T20:22:46.256219Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.05935","last_updated":"2025-07-09T13:06:13Z","latest_version":2,"primary_category":"math.AP","snapshot_observed_at":"2026-08-12T12:22:25.963988Z","submitted_at":"2024-12-08T13:21:37Z","title":"An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds"},"reference_resolution":{"displayed":100,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":93,"verified_exact":5,"verified_fuzzy":2},"total_outbound_references":161},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 100 of 161 outbound references and 1 inbound Pith citation observation for arXiv:2412.05935."}