{"as_of":"2026-08-13T00:28:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:abe8516decdfaf5945ed5530ecb5bb9774e4bcb389b93bd2072255d5f2a7c8a8","coverage":[{"denominator":61,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":61,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-08T05:06:49.517590Z","state":"measured"},{"denominator":67,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":67,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":6,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":6,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T00:27:46.187279Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-14T18:12:33.233033Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.08495","snapshot_observed_at":"2026-08-05T18:34:56.897408Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2508.14497","last_updated":"2025-08-20T07:35:12Z","snapshot_observed_at":"2026-08-05T18:34:53.700762Z","submitted_at":"2025-08-20T07:35:12Z","title":"Liouville theorem of the subcritical biharmonic equation on complete manifolds","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-05T18:34:56.897408Z"},"links":{"cited_paper":"/paper/2502.08495","citing_paper":"/paper/2508.14497"},"observation_digest":"sha256:ae76f70720fe50f516ec99b61566b9aa4945170d31c5a594bec59002464f27ab","observation_id":"46217872-3dae-4e1a-abf8-1053f820c963","resolution":{"observed_at":"2026-08-05T18:34:56.897408Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.08495","snapshot_observed_at":"2026-08-04T08:05:57.632757Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2510.23243","last_updated":"2026-01-24T09:40:40Z","snapshot_observed_at":"2026-08-04T08:05:55.229519Z","submitted_at":"2025-10-27T11:56:04Z","title":"Classification results for bounded positive solutions to the critical $p$-Laplace equation","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-04T08:05:57.632757Z"},"links":{"cited_paper":"/paper/2502.08495","citing_paper":"/paper/2510.23243"},"observation_digest":"sha256:eb990461d97106e41d9ebfbd23bc11e663404a68960a59d66e7671de51b44dc5","observation_id":"f1366f48-584e-49f0-bd0a-e9c06a352cc4","resolution":{"observed_at":"2026-08-04T08:05:57.632757Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"cited_work":{"arxiv_id":"2502.08495","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2502.08495","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"3d569b9e-04a4-4d5c-9d83-7ea1a253bec1","year":2025},"citing_paper":{"arxiv_id":"2604.13758","last_updated":"2026-04-15T11:43:19Z","snapshot_observed_at":"2026-07-06T23:01:41.643335Z","submitted_at":"2026-04-15T11:43:19Z","title":"On the anisotropic critical $p$-Laplace equation: classification, decomposition, and stability results","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-05-10T12:48:28.444705Z"},"links":{"cited_paper":"/paper/2502.08495","citing_paper":"/paper/2604.13758"},"observation_digest":"sha256:c5cf0c63e4ac2aaec4f8f00ea8363f97aa53455ae2c1ae7b8b383ee11b79e131","observation_id":"c98d5768-ec9e-4d81-bcea-41d4ab99fd02","resolution":{"observed_at":"2026-05-10T12:50:25.001857Z","resolver_source":"arxiv_id","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":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"cited_work":{"arxiv_id":"2502.08495","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2502.08495","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"3d569b9e-04a4-4d5c-9d83-7ea1a253bec1","year":2025},"citing_paper":{"arxiv_id":"2604.27973","last_updated":"2026-04-30T15:03:53Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-30T15:03:53Z","title":"Classification results of Liouville equations and rigidity of Riemannian surfaces","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-07T07:35:40.906458Z"},"links":{"cited_paper":"/paper/2502.08495","citing_paper":"/paper/2604.27973"},"observation_digest":"sha256:0a8602ba673eb90a7e38889ab7ca36ef56d42ef170e07b92eb838bfd49845e38","observation_id":"28ffc4ac-9b5d-4402-9452-dddbd0fc28e3","resolution":{"observed_at":"2026-05-12T10:11:27.119673Z","resolver_source":"arxiv_id","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":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"cited_work":{"arxiv_id":"2502.08495","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2502.08495","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"3d569b9e-04a4-4d5c-9d83-7ea1a253bec1","year":2025},"citing_paper":{"arxiv_id":"2605.13447","last_updated":"2026-05-13T12:42:41Z","snapshot_observed_at":"2026-07-06T23:25:01.951546Z","submitted_at":"2026-05-13T12:42:41Z","title":"Classification of solutions to the singular Liouville's equation associated with the $N$ Finsler Laplacian","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-05-14T18:10:40.007762Z"},"links":{"cited_paper":"/paper/2502.08495","citing_paper":"/paper/2605.13447"},"observation_digest":"sha256:6f19cf0fb115e4eab6bedd750a388d9f6991db70d155fc780ab795e56c719e40","observation_id":"0cb41060-86b7-4ca7-9f15-7e70493a67ce","resolution":{"observed_at":"2026-05-14T18:12:33.236967Z","resolver_source":"arxiv_id","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":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.08495","snapshot_observed_at":"2026-08-07T00:27:46.187279Z","title":"Sun and Y","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.04422","last_updated":"2026-08-05T04:04:58Z","snapshot_observed_at":"2026-08-09T15:28:05.068782Z","submitted_at":"2026-08-05T04:04:58Z","title":"Optimal Rigidity and Classification Results for the $k$-Hessian Equation of Lane--Emden Type","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-07T00:27:46.187279Z"},"links":{"cited_paper":"/paper/2502.08495","citing_paper":"/paper/2608.04422"},"observation_digest":"sha256:6293ed98f8d90aee91ac6b2e1b7b6b524262066e287eab8efa1c358fffcd27fc","observation_id":"d91e8a8d-8f4d-4370-bd95-68bc5cfe1b96","resolution":{"observed_at":"2026-08-07T00:27:46.187279Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2502.08495/citation-record","integrity":"/paper/2502.08495/integrity","json":"/paper/2502.08495/citation-record.json","paper":"/paper/2502.08495"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T05:06:50.248957Z","title":"Interior regularity results for inhomogeneous anisotropic quasili near equations","venue":null,"work_id":"752b8675-a74d-425c-ba95-72b6621633bb","year":2023},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.300256Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:69d326dd03d5b73b35cc466005572223f56c95af76317374ce480f2a4ec19381","observation_id":"8a0d19b1-ec1b-44a6-9e20-b4393a095605","resolution":{"observed_at":"2026-08-08T05:06:50.252492Z","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":"2026-08-08T05:06:50.238599Z","title":"Probl` emes isop´ erim´ etriques et espaces de Sobolev","venue":null,"work_id":"86fb9811-69c4-42ad-9d14-1e1b74c25d15","year":1976},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.305009Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:1a0905655a9f865c8364277df916d1bbaad986686e844bea9639a57f8652b4f0","observation_id":"26168dcf-db4b-4a7b-adb7-52bd0bf9e098","resolution":{"observed_at":"2026-08-08T05:06:50.242366Z","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":"2026-08-08T05:06:50.226783Z","title":"Sharp isoperimetric and Sobolev inequalities in spaces with nonnegative Ricci c urvature","venue":null,"work_id":"27024370-745a-4562-aec4-1f20a36f7d72","year":2023},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.309052Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:db60f1a1de15e03d49f17dc5dd8db64a29a42c0a8e1ba6b8b054ad6c72df28ea","observation_id":"a731be56-0497-40a1-98e4-b12f961a9e22","resolution":{"observed_at":"2026-08-08T05:06:50.230201Z","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":"2026-08-08T05:06:50.216138Z","title":null,"venue":null,"work_id":"c45a2ba0-5bf2-4825-ae64-b8cce62bdd26","year":2023},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.312907Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:8bfdd73ca62fd9a81ee2ef06f29c157eabe50ab7fbe16355716e612db54ccb16","observation_id":"ff533b77-c3bb-4423-a09e-d804ad69794d","resolution":{"observed_at":"2026-08-08T05:06:50.219898Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T05:06:50.205474Z","title":"Stability an d qualitative properties of radial solutions of the Lane-Em den-Fowler equation on Riemannian models","venue":null,"work_id":"9667646b-1f5e-4a99-96e3-8e2d38252356","year":2014},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.316677Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:07995f01bc547295a494b0d0ac8e3737c6603271c2d7949f450dfb070a82ac80","observation_id":"a7d178e6-3bc1-44ed-abb1-bd9828438b6f","resolution":{"observed_at":"2026-08-08T05:06:50.209545Z","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":"2026-08-08T05:06:50.195303Z","title":"Classiﬁcation of radial solutions to the Emden-Fowler equation on the hyperbolic space","venue":null,"work_id":"3d546e11-48ad-4561-b5ff-f9b6d03a9b71","year":null},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.320550Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:f233bc1d150214093be30bafd67ff2b0f385c8251c2b9353e6814a9fa5946233","observation_id":"02deed48-19e2-483a-8f19-4f8a035aa1c7","resolution":{"observed_at":"2026-08-08T05:06:50.199030Z","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":"2026-08-08T05:06:50.185645Z","title":"Sobolev inequalities in manifolds wi th nonnegative curvature","venue":null,"work_id":"57be00ee-e3bd-4169-a321-f397da0f739d","year":2023},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.324432Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:128705b20ad22d47a362ab6a73cbd769724bbae3085cca176fe0c80c6243593d","observation_id":"0312cc7b-739e-40b1-9f7e-dd11625dad01","resolution":{"observed_at":"2026-08-08T05:06:50.189036Z","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":"2026-08-08T05:06:50.175782Z","title":"Polar factorization and monotone rea rrangement of vector-valued functions","venue":null,"work_id":"976974f3-110f-4c7c-bc4b-f1cc6988be07","year":1991},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.328248Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:d35f0898d7a8d769f2ac01695ea05df43bafbf32966586edee34e727bb5c9c51","observation_id":"a5921f50-682c-4e2d-af92-7ffc503a2e86","resolution":{"observed_at":"2026-08-08T05:06:50.179325Z","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":"2026-08-08T05:06:50.165802Z","title":"Uniform estimates and blow- up behavior for solutions of −∆u = V(x)eu in two dimensions","venue":null,"work_id":"8fa37654-3c9f-4edc-9612-79222c43662b","year":1991},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.331715Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:0d874e271408c4b6e3386e1c71da95d80fd022e3bb7528a3c36d3d3a4b76adfa","observation_id":"c7dbae2a-f4a4-4a17-9c97-9123e808944b","resolution":{"observed_at":"2026-08-08T05:06:50.169418Z","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":"2026-08-08T05:06:50.155290Z","title":"Asymptotic symme try and local behavior of semilinear elliptic equations wit h critical Sobolev growth","venue":null,"work_id":"c0b827bf-6715-470e-8c59-6382a722bc02","year":1989},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.335172Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:c37b8ae96f5a0d98112987a6ef4d86e5417cf6acb1cba453dca9a74556db3874","observation_id":"d8b2334b-59a9-48a6-bfab-55073ba67a0f","resolution":{"observed_at":"2026-08-08T05:06:50.159088Z","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":"2026-08-08T05:06:50.144662Z","title":"Liouville equations on complete surfaces with nonnegative Gauss curvature","venue":null,"work_id":"6007fa70-8ed7-42e0-b35c-e190dea22838","year":2024},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.338989Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:70a9ee4828ebfdde7473abc623bcbe1b8ff7a0acf70f7fd8809d00e025b07bc8","observation_id":"70b97596-2f41-4ce2-9c2f-594d1486e357","resolution":{"observed_at":"2026-08-08T05:06:50.148259Z","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":"2026-08-08T05:06:50.133536Z","title":"A liouville theorem in the Heisenberg group","venue":null,"work_id":"01b7a685-ec52-4bf0-a330-36ede6606530","year":2024},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.342584Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:ae73017dd6e8f7f47d6f15658c6cd2ee2d37dd728493691a35899b4f378692e1","observation_id":"f645ca1f-b082-4043-aecb-fbea33014c4f","resolution":{"observed_at":"2026-08-08T05:06:50.137432Z","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":"2026-08-08T05:06:50.122430Z","title":"Semilinear ellipt ic equations on manifolds with nonnegative Ricci curvature","venue":null,"work_id":"dfb13d11-570c-4ce7-bb5f-a3303efb2448","year":2024},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.346037Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:4fd964266168579f49a721619906877e232760ac0513abd1847018ed174b17a1","observation_id":"66261b9e-ab3d-4e21-8b89-50618b96bdca","resolution":{"observed_at":"2026-08-08T05:06:50.126597Z","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":"2026-08-08T05:06:50.112093Z","title":"On t he critical p-Laplace equation","venue":null,"work_id":"81640ef1-cb23-4137-9523-69d7ba0aaae7","year":2023},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.349443Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:6f879f19804839f6b335182b3ff0d30d943019f40f34864353e20bfc8570d14c","observation_id":"53b679a1-282c-455c-b38d-9d83e5b5cef3","resolution":{"observed_at":"2026-08-08T05:06:50.115658Z","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":"2026-08-08T05:06:50.102055Z","title":"Liouville theorems on pseudo-Hermitian manifolds w ith nonnegative Tanaka- Webster curvature","venue":null,"work_id":"6885ab92-5e25-42b1-93c1-6b057084b780","year":null},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.352698Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:f86a69dacec94ee908aa8d8511b490cddb6b2692827767d58f374be2db4e6bac","observation_id":"f4b4bc6f-297d-4846-b811-d8b46e18ab68","resolution":{"observed_at":"2026-08-08T05:06:50.105753Z","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":"2026-08-08T05:06:50.092225Z","title":"Classiﬁcation of solutions of some nonlinear elliptic equations","venue":null,"work_id":"229d0f35-30d5-4ebc-825f-a324367dd256","year":1991},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.356319Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:618b001573e6b26488600f5acc2be5057919dc2182e5970f79b9b55fd8f43c28","observation_id":"e54631eb-2632-40dd-adb7-9ac638201c74","resolution":{"observed_at":"2026-08-08T05:06:50.095622Z","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":"2026-08-08T05:06:50.082312Z","title":"On the structure of the conf ormal Gaussian curvature equation on R2","venue":null,"work_id":"aa75dded-3102-4902-919d-7681f09613dc","year":1991},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.359621Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:edbf98198abf846beff2724e145c02dec325343598d444aaa7acdb2642eb398d","observation_id":"489cb389-3b2e-491b-ae89-00c142879b84","resolution":{"observed_at":"2026-08-08T05:06:50.085806Z","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":"2026-08-08T05:06:50.072537Z","title":"Classiﬁc ation results, rigidity theorems and semilinear PDEs on Rie mannian manifolds: a P-function approach","venue":null,"work_id":"d842ae44-4848-4b5f-b25a-a974bddbbae9","year":2024},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.363118Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:10835291c4b701dc7fae303f19a703ee2f6fe917ce21ee2dab2b7dc8f34ef72c","observation_id":"9a3a306b-9e12-4340-b07b-bac58d54f5ac","resolution":{"observed_at":"2026-08-08T05:06:50.076163Z","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":"2026-08-08T05:06:50.061931Z","title":"Symmetr y results for critical anisotropic p-Laplacian equations in convex cones","venue":null,"work_id":"de410b28-723b-4297-b82f-a365b6084c81","year":2020},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.366434Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:89a372a44993156e88f0e81310bd65c2bdf50f4e5ef8aaac2faa1c98cad0ee2e","observation_id":"ab5f2328-846c-40c8-931f-e6ba8391a291","resolution":{"observed_at":"2026-08-08T05:06:50.065486Z","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":"2026-08-08T05:06:50.050539Z","title":"A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities","venue":null,"work_id":"536c24b4-627c-40b5-8d43-bb04f685146e","year":2004},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.369980Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:7db3afcabf93ff95f05429e47efa6bd07bfd33c098e82261f1eeeb053efaa032","observation_id":"3f53fee1-3d2b-4dfe-9f17-8aae30fd91a6","resolution":{"observed_at":"2026-08-08T05:06:50.054498Z","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":"2026-08-08T05:06:50.038807Z","title":null,"venue":null,"work_id":"be6c2d06-583d-4217-8ba6-c762a1ab5413","year":2014},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.373643Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:6f87896c39c68fecc2697615c28f11c04e31d53bce6fd723d4ed934c177b1c0d","observation_id":"92d3b0b0-f15b-4ae1-b43e-c392e50ee1e4","resolution":{"observed_at":"2026-08-08T05:06:50.042931Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T05:06:50.027213Z","title":"C1+α local regularity of weak solutions of degenerate elliptic e quations","venue":null,"work_id":"4d1695b4-e095-44af-b8ef-eb3f6f0eacbd","year":1983},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.376892Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:8821a93d0eb875cbbd51afda6190cc7312627fa40c89f87dfcca08fbea138427","observation_id":"cff45731-2b1e-4129-888b-2425fcaddd78","resolution":{"observed_at":"2026-08-08T05:06:50.031133Z","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":"2026-08-08T05:06:50.015826Z","title":"On a conformally invariant elliptic e quation on Rn","venue":null,"work_id":"05b690d0-0b76-42fe-8c39-4b9310527236","year":1986},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.380164Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:0878dd4bd985087ed3494ab48c04db30a31d80b4f5cfbd6f1d8c9ef9b43588e7","observation_id":"024e4206-f48b-4fd7-8cce-a781484fee45","resolution":{"observed_at":"2026-08-08T05:06:50.019604Z","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":"2026-08-08T05:06:50.002508Z","title":"On the elliptic equation ∆u + Ku(n+2)/(n−2) = 0 and related topics","venue":null,"work_id":"5e751cb3-d324-46e9-ba4f-ef42b3930e9e","year":1985},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.383646Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:02d074915ab029eab4c3f4983eccdc4e7cdfe3da4070338c310b2b5aba79b877","observation_id":"0d93376e-8e60-487d-bce8-e76111c6d2be","resolution":{"observed_at":"2026-08-08T05:06:50.007600Z","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":"2026-08-08T05:06:49.990324Z","title":"The AB program in geometric analysis: sharp Sobolev inequalities and related problems","venue":null,"work_id":"ce44e168-5a1a-44cf-9754-5d979ba11752","year":2002},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.386996Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:a26f2f556d4786eea3ccce9debad73b58d8099647fe6784e33a32852c0006de7","observation_id":"ef562d2b-2520-4a4a-a605-73c9d71ba611","resolution":{"observed_at":"2026-08-08T05:06:49.994353Z","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":"2026-08-08T05:06:49.978993Z","title":"A classiﬁcation result for the quas i-linear Liouville equation","venue":null,"work_id":"afb7d149-7876-4e06-9f31-eee750fa11d6","year":2018},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.390332Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:473b62a4bdcb429cf57919e06d4d508512af9e8df94ca5f2c11fa7c4781bd7d3","observation_id":"1e508e2c-4309-43a8-b7c6-d5289e0db564","resolution":{"observed_at":"2026-08-08T05:06:49.982849Z","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":"2026-08-08T05:06:49.967366Z","title":"A not e on the critical Laplace equation and Ricci curvature","venue":null,"work_id":"c8d55659-a186-4211-afe8-659cf16b04da","year":2023},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.393705Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:b28194fce1873cc8099ad3a45394f137b8848779b84cb374a773222f61107992","observation_id":"51e3cb89-16b3-42e7-a71f-06dc364701c3","resolution":{"observed_at":"2026-08-08T05:06:49.971112Z","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":"2026-08-08T05:06:49.956201Z","title":"Corr ection: A note on the critical Laplace equation and Ricci cur vature","venue":null,"work_id":"dfa7aba5-fdd1-4851-b21d-74ad96c8764e","year":2024},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.396931Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:14c0907db61686b7805b7c34a5f9f6848c2d36f14c5d568f4fc6c71fd71fce67","observation_id":"d63fd1ca-c49b-484d-8612-76369551b4f2","resolution":{"observed_at":"2026-08-08T05:06:49.959894Z","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":"2026-08-08T05:06:49.944398Z","title":"Some problems in the theory of qua silinear equations","venue":null,"work_id":"493324b1-e40f-4137-a035-7b4e467d1cb7","year":1963},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.400625Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:7c93063e85c4e3998916208e89fcfc801b2cb9269858d35bab170f0cc0599753","observation_id":"06186160-bb79-44d6-b3a2-a4a73cf0e7e9","resolution":{"observed_at":"2026-08-08T05:06:49.948512Z","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":"2026-08-08T05:06:49.932901Z","title":"Global and local behavior o f positive solutions of nonlinear elliptic equations","venue":null,"work_id":"8e22cc7f-396c-43fa-8a74-63bacb0ded4a","year":1981},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.404258Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:3ceb88b5358ffe672186476eb74bf953aba457c34422260f7fdcfde9e49812d7","observation_id":"d04482f9-7772-42bf-a156-22937fa449a2","resolution":{"observed_at":"2026-08-08T05:06:49.936691Z","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":"2026-08-08T05:06:49.920922Z","title":"Optimal Liouville theo rems for the Lane-Emden equation on Riemannian manifolds","venue":null,"work_id":"8c1bdb56-3fe0-4160-b863-2c656ae123d0","year":null},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.407978Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:bf41d68b065aa286d4fd15de8fce3418345c8f4fa3074f7f3ca8081c1f2cb489","observation_id":"904207a2-ed50-40c4-8f5b-92700ab3899c","resolution":{"observed_at":"2026-08-08T05:06:49.925006Z","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":"2026-08-08T05:06:49.904319Z","title":"Gradient estimate for s olutions of the equation ∆pv + avq = 0 on a complete Riemannian manifold","venue":null,"work_id":"ad9c0f68-c1c0-43fe-aba7-812c746e7fec","year":null},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.411704Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:100e9b633a76116d28bb1ddd36c25aedddf3f7a1ff5ca37f5427f226238ec5fd","observation_id":"b3a306b5-5e57-4977-9490-182e022ac72e","resolution":{"observed_at":"2026-08-08T05:06:49.910948Z","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":"2026-08-08T05:06:49.892997Z","title":"Subharmonic functions on real and compl ex manifolds","venue":null,"work_id":"b2d9c19a-a688-47fb-bd69-4eb255ee6795","year":1982},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.415811Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:1e16728efe93090a67041c94dd6e9349e86923a66230bd6eb30d2af1cd45e199","observation_id":"2ef46d23-ccff-47f4-ad7a-a9b256c7c547","resolution":{"observed_at":"2026-08-08T05:06:49.896738Z","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":"2026-08-08T05:06:49.881905Z","title":"Sharp Sobolev inequalities on non compact Riemannian manifolds with Ric ≥ 0 via optimal transport theory","venue":null,"work_id":"c3748629-0f24-479f-8bbe-4affb67c9a9a","year":2024},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.419779Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:0bc8aca0607232377d67da333440aefa3c109a1ab7c0698de10b12fe91db7fe1","observation_id":"8d89ab0c-d535-4799-8a00-cbff32112d39","resolution":{"observed_at":"2026-08-08T05:06:49.885656Z","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":"2026-08-08T05:06:49.870033Z","title":"On manifolds with non-negative Ricci curvature and Sobolev inequalities","venue":null,"work_id":"016c2c03-36f6-49fa-828b-3490b3183db7","year":1999},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.423429Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:3c4e86d3d20c03e4818f2e1bca36da1e55a375852f39d1af5e9bfbcab40305c0","observation_id":"7045743f-a898-4bce-b14d-d6078ecc774d","resolution":{"observed_at":"2026-08-08T05:06:49.874021Z","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":"2026-08-08T05:06:49.858128Z","title":"The Yamabe problem","venue":null,"work_id":"9fbd76ec-710f-4271-a5ed-13e4740b90ff","year":1987},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.427488Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:426a42fdb7b023106e210fa6ee93eb4640895e67741a07abc933c14dc947ff01","observation_id":"420479ec-c629-4278-88ec-b8204c414a19","resolution":{"observed_at":"2026-08-08T05:06:49.861852Z","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":"2026-08-08T05:06:49.845955Z","title":"On some conformally invariant fu lly nonlinear equations","venue":null,"work_id":"b404a7d1-d6d5-4f31-befb-80d67b5ab48d","year":2005},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.431324Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:7097a39fa870573a51b84e58199a51225ccbc3d6e8b2776545bdd1c84ddb42aa","observation_id":"03e98782-b5f0-4b1c-9523-8269f44899aa","resolution":{"observed_at":"2026-08-08T05:06:49.850103Z","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":"2026-08-08T05:06:49.833936Z","title":"Extremal functions for the Moser-Truding er inequalities on compact Riemannian manifolds","venue":null,"work_id":"dc588831-d3bc-4921-9d59-9a2591bf46d2","year":2005},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.435024Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:f8c8eb4ae672ab7837a0419b69f33581c86f133ddf7290ba24852b7dc5ef8669","observation_id":"7dfc5c88-2a94-41ca-bd62-7085e3434a05","resolution":{"observed_at":"2026-08-08T05:06:49.837751Z","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":"2026-08-08T05:06:49.821927Z","title":"Liouville type theorem for a cla ss quasilinear p-Laplace type equation on the sphere","venue":null,"work_id":"91f0b335-056b-43ef-a31c-dfe0d755ba83","year":2024},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.438626Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:70b3270fc8353781b3ad9bbdfe187cc16261826028f9ef8e7284da20eab617cc","observation_id":"97866e16-291e-4706-b68d-74c1edf730ba","resolution":{"observed_at":"2026-08-08T05:06:49.825907Z","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":"2026-08-08T05:06:49.809731Z","title":"On n-superharmonic functions and some geometric applications","venue":null,"work_id":"d65c968b-f83d-4ccd-9f75-39dfba10e5b6","year":2021},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.442780Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:f73f32db5c99e68a2a96f7dd194231993760ee82c2f3eceba153eb5cf1b9943d","observation_id":"94baa73b-a371-4e9f-ba80-95c187803c7a","resolution":{"observed_at":"2026-08-08T05:06:49.813700Z","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":"2026-08-08T05:06:49.798221Z","title":"A Liouville theorem for a class se milinear elliptic equations on the Heisenberg group","venue":null,"work_id":"5cd0a539-92dd-4c04-8f77-c8bb8bd5a6b8","year":2023},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.446835Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:1e43193b22a46cd740450b172d6cd622bf19c1c81b99c9a5cd5e1952ad11afac","observation_id":"e620faf1-818b-46ef-924e-98502d4b63ab","resolution":{"observed_at":"2026-08-08T05:06:49.801877Z","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":"2026-08-08T05:06:49.786290Z","title":"Some rigidity results fo r Sobolev inequalities and related PDEs on Cartan-Hadamard manifolds","venue":null,"work_id":"294d0012-b027-4345-9c78-8fb6194cf29c","year":2023},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.450463Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:6cb1370b172506f25ecc9727c88fe64873877b2e0f28b3c08734dfeded7bd42e","observation_id":"c7564a44-2d45-49ff-8bef-0afcafea1b2b","resolution":{"observed_at":"2026-08-08T05:06:49.790318Z","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":"2026-08-08T05:06:49.773883Z","title":"Fine P´ olya-Szeg˝ o rearrangement inequalities in metric spaces and applications","venue":null,"work_id":"2809f340-6cd7-4894-a82c-f1a9c6faf3a2","year":2024},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.454273Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:181e473daf08bfb63fcede48149fd79e1eb4280380f2cccb12f571a932df76ba","observation_id":"e98775f1-0f4e-4b10-a25f-8516099f95a6","resolution":{"observed_at":"2026-08-08T05:06:49.777801Z","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":"2026-08-08T05:06:49.760917Z","title":"On the classiﬁcation of entire solutions t o the critical p-Laplace equation","venue":null,"work_id":"6cf05e56-2ed1-4657-856c-7ff525996ff2","year":2022},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.457879Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:93a8d1c25b6672110efb0897e7c0d11bb846c34d1dadc0130b2109d1614a0083","observation_id":"b24a7265-ab6d-48a4-85a8-9df0491ff668","resolution":{"observed_at":"2026-08-08T05:06:49.765786Z","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":"2026-08-08T05:06:49.748847Z","title":"Optimal Liouville theorems for sup erlinear parabolic problems","venue":null,"work_id":"edac8015-3fea-4f4a-8ae1-58a98163c8fe","year":2021},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.461695Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:4de0f9d43c857be90df1fd9fc348e7580a797da290bdde73e12284784aa30a40","observation_id":"cc937968-1b07-4155-8666-f6a060c9d613","resolution":{"observed_at":"2026-08-08T05:06:49.753045Z","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":"2026-08-08T05:06:49.736387Z","title":"Uniformly elliptic operators on Riemanni an manifolds","venue":null,"work_id":"ad01a327-9dbb-4b88-8ee2-32ed187b9ba6","year":1992},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.465178Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:c203e408136b367be00ca41291680fbfd6f2d46cb8bd2a90e51e87da85c06743","observation_id":"2cdc42fb-3288-44f2-a8f5-590f66553254","resolution":{"observed_at":"2026-08-08T05:06:49.741160Z","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":"2026-08-08T05:06:49.724582Z","title":"Classiﬁcation of positive D1,p(RN )-solutions to the critical p-Laplace equation in RN","venue":null,"work_id":"145687f8-bd15-4fa3-b2a7-845f42c0d7c0","year":2016},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.468725Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:96fd7511b54b2f20aa5f4338765f8ea58ab3e371a30953bb5694610a3d287ad3","observation_id":"1bdad416-befe-4c7e-ab70-99c0d71268dc","resolution":{"observed_at":"2026-08-08T05:06:49.728621Z","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":"2026-08-08T05:06:49.711673Z","title":"Cauchy-Liouville and univer sal boundedness theorems for quasilinear elliptic equatio ns and inequalities","venue":null,"work_id":"f7f3e4fe-2695-4830-96f0-2d8f45a85dcb","year":2002},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.472256Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:7b9dc8169dc228762ccba75f18c72684a791d5034504dc5df7e0f5eacf507948","observation_id":"73e703a3-e25d-4ece-9659-8dd5394752a7","resolution":{"observed_at":"2026-08-08T05:06:49.716265Z","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":"2026-08-08T05:06:49.699512Z","title":"Best constant in Sobolev inequality","venue":null,"work_id":"20faa92f-eca9-4c6a-bfdc-32d90fcc71e6","year":1976},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.475806Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:5117700bb4e807afec4a80cf96590b00ffbb99b2b48247578b36ab4e76eba339","observation_id":"b9be4fca-36a3-4e8f-bc2b-1103eeb58c45","resolution":{"observed_at":"2026-08-08T05:06:49.703659Z","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":"2026-08-08T05:06:49.686492Z","title":"Complete Riemannian manifolds and s ome vector ﬁelds","venue":null,"work_id":"fd478515-22a6-43fa-bc2a-13b76dafb86b","year":1965},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.479023Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:f04248b2eb19642669c9cc66a7f1b1dd0240f834ab0862fd44aaef23c2cb1674","observation_id":"f5dc9566-2d65-486f-bf8f-4d9eac92dd32","resolution":{"observed_at":"2026-08-08T05:06:49.691271Z","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":"2026-08-08T05:06:49.672976Z","title":"Regularity for a more general clas s of quasilinear elliptic equations","venue":null,"work_id":"91f8f26c-f49f-4ea1-86aa-865be80fa304","year":1984},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.482479Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:a58dc489b0ec5f2fe743707274825c93a10cc0b7fdf7cb975b84385de41656b2","observation_id":"adfdbc72-d06f-4803-9a45-89db85cdbe5f","resolution":{"observed_at":"2026-08-08T05:06:49.677874Z","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":"2026-08-08T05:06:49.661516Z","title":"Regularity for a class of non-line ar elliptic systems","venue":null,"work_id":"cd6ea92a-e146-45c8-9baa-b82421bd05b6","year":1977},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.485899Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:83e93d586884042f881d656417a7f801c6c370ea0b7c8a11920999424354e906","observation_id":"3cf17b90-6586-492e-878e-db4c6ab5ef42","resolution":{"observed_at":"2026-08-08T05:06:49.665356Z","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":"2026-08-08T05:06:49.649094Z","title":"A priori estimates and application t o the symmetry of solutions for critical p-Laplace equations","venue":null,"work_id":"194a5b93-0b9c-44cd-9733-0cf4a7b720b5","year":2016},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.489706Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:d95b034ea36348844916581cd84993f1b1b9e981d0df17fa6638b69682504093","observation_id":"d351c69c-2f6b-47f1-8f8c-bd5618e904bc","resolution":{"observed_at":"2026-08-08T05:06:49.653781Z","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":"2026-08-08T05:06:49.636925Z","title":"A note on the classiﬁcation of positi ve solutions to the critical p-Laplace equation in Rn","venue":null,"work_id":"83853cbc-ac8c-4401-a6c6-5dde8007d786","year":2024},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.492873Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:0c7c258cca53a79a831e656a67d3f0a1634431cbcbd3959b6925aa1fcf4261d0","observation_id":"35df2681-a2e0-47f1-a600-7448a6ef3ef2","resolution":{"observed_at":"2026-08-08T05:06:49.641205Z","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":"2026-08-08T05:06:49.623483Z","title":"On the nonexistence of positive solution to ∆u + aup+1 = 0 on Riemannian manifolds","venue":null,"work_id":"85ca92c1-449b-4b2d-a59f-99b5a09707c0","year":2023},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.496214Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:0855326f5c54fd9db41329f26baa1004c22f0f525b4c7ec8b7074f2aa0d1d315","observation_id":"01b3ef93-726e-4dcc-bdb7-1bdbbd478a71","resolution":{"observed_at":"2026-08-08T05:06:49.628865Z","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":"2026-08-08T05:06:49.609239Z","title":"Harmonic maps from noncompact Rieman nian manifolds with non-negative Ricci curvature outside a compact set","venue":null,"work_id":"6ef1db4d-299c-406b-a603-8137081dc96b","year":1994},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.499552Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:9019914f36b601e8fb6d86806cfd909330a859477aacb3a1ec1e9a010edb77d3","observation_id":"34a60115-7d03-4e44-b689-735ec26eedd3","resolution":{"observed_at":"2026-08-08T05:06:49.613809Z","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":"2026-08-08T05:06:49.596351Z","title":"Y amabe equation on some complete noncomp act manifolds","venue":null,"work_id":"7ed39c89-6da0-4779-acd2-73c11307b345","year":2019},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.503087Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:f0cba41da051dec623c5c8ce10448259bd1fc41b25c59ffc56c1da018b3af82b","observation_id":"0a061cfa-4fce-46e1-8314-a7bf7635ae01","resolution":{"observed_at":"2026-08-08T05:06:49.600178Z","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":"2026-08-08T05:06:49.584404Z","title":"Classiﬁcation of solutions of hig her order conformally invariant equations","venue":null,"work_id":"8ed25793-5865-49ab-93ea-de04adac443a","year":1999},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.506935Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:ceefb24b6a99b50084ddc6f705c051de4d2e92b6d79873f5f14bc66c683b3fe0","observation_id":"7ba2cf67-9805-4206-b3e6-26f758d62c1e","resolution":{"observed_at":"2026-08-08T05:06:49.588473Z","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":"2026-08-08T05:06:49.572164Z","title":"The Gagliardo-Nirenberg inequalities a nd manifolds of non-negative Ricci curvature","venue":null,"work_id":"8b731726-633b-43be-8bb0-b6e70f04b6d6","year":2005},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.510352Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:fdf52f35cac626c89e6f695c867d7eb6913b04b802b965312e294bf4271c171f","observation_id":"fffd6d04-dc0c-4e44-9f19-ffcbd28fe5a8","resolution":{"observed_at":"2026-08-08T05:06:49.575993Z","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":"2026-08-08T05:06:49.560530Z","title":"Uniqueness and non-existence theorems fo r conformally invariant equations","venue":null,"work_id":"f3de5122-47d0-4294-bc9a-5cb8ccb28c52","year":2005},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.513990Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:9e69bee9e729a1bc8d33dacd97b83108350ab811a60fcd2a8a988e9a26246212","observation_id":"ed66b549-a48b-422b-a815-8218b23206a6","resolution":{"observed_at":"2026-08-08T05:06:49.564544Z","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":"2026-08-08T05:06:49.545547Z","title":"Harmonic functions on complete Rieman nian manifolds","venue":null,"work_id":"1ef897cb-7663-4259-915f-06e8bbb3aea3","year":1975},"citing_paper":{"arxiv_id":"2502.08495","last_updated":"2025-03-13T03:03:59Z","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds","version":2},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-08T05:06:49.517590Z"},"links":{"citing_paper":"/paper/2502.08495"},"observation_digest":"sha256:22c8a9fae8db018dad7d9f4668c7005c6d9ff31a0b31093d564bbbe49e6119d5","observation_id":"45dd9ed5-9740-4d75-9582-a2de4ad60d6c","resolution":{"observed_at":"2026-08-08T05:06:49.551655Z","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":"2502.08495","last_updated":"2025-03-13T03:03:59Z","latest_version":2,"primary_category":"math.DG","snapshot_observed_at":"2026-08-10T11:07:13.886246Z","submitted_at":"2025-02-12T15:30:40Z","title":"Critical quasilinear equations on Riemannian manifolds"},"reference_resolution":{"displayed":61,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":2,"verified_exact":0,"verified_fuzzy":59},"total_outbound_references":61},"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 13 August 2026, this Paper Citation Record lists 61 of 61 outbound references and 6 inbound Pith citation observations for arXiv:2502.08495."}