{"as_of":"2026-08-16T07:55:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:4295b66fc593ac49cc0c6ad0b8a910b6c08b1cde1c23658f92a29a762f76c54c","coverage":[{"denominator":26,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":26,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T14:07:59.867961Z","state":"measured"},{"denominator":26,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":26,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/1908.03915/citation-record","integrity":"/paper/1908.03915/integrity","json":"/paper/1908.03915/citation-record.json","paper":"/paper/1908.03915"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:08:00.346220Z","title":null,"venue":null,"work_id":"c2d58eb0-e167-48b5-bf65-b6481d777b93","year":1977},"citing_paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T14:07:59.744828Z"},"links":{"citing_paper":"/paper/1908.03915"},"observation_digest":"sha256:b59aa63d0f9e7f3442310396d519085056ab79015ab0f5926366bdb28d1dfbee","observation_id":"fefd0724-36fe-487b-b1e2-df647b74b11e","resolution":{"observed_at":"2026-08-14T14:08:00.351595Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:08:00.330662Z","title":"Differential Geometry 11 (1976), no","venue":null,"work_id":"abff3e02-9a9b-47a3-83cc-135fdc1730d9","year":1976},"citing_paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T14:07:59.750439Z"},"links":{"citing_paper":"/paper/1908.03915"},"observation_digest":"sha256:0d078a8244dd11b830d25eaedb2e6f559c676375e8e9d75869988d9685c23d53","observation_id":"c2a47e43-55cc-425e-a91a-3853c578f8a0","resolution":{"observed_at":"2026-08-14T14:08:00.335756Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:08:00.313511Z","title":"A., The heat equation with a singular potential , Trans","venue":null,"work_id":"e77171c2-caae-4c3a-958e-dd53592a0280","year":1984},"citing_paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality","version":3},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T14:07:59.755893Z"},"links":{"citing_paper":"/paper/1908.03915"},"observation_digest":"sha256:9a71a8dbdd5d156fa78253b9b5b813f0f91a301b67be7d7039128f9d473e19a8","observation_id":"e89bdb45-20d9-4372-86e7-92a204e358ba","resolution":{"observed_at":"2026-08-14T14:08:00.319326Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:08:00.297383Z","title":"Beckner, W., Pearson, M., On sharp Sobolev embedding and the loga- rithmic Sobolev inequalitiy, Bull","venue":null,"work_id":"42f90763-a12a-45ea-991c-e5f3fac23084","year":1998},"citing_paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality","version":3},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T14:07:59.761109Z"},"links":{"citing_paper":"/paper/1908.03915"},"observation_digest":"sha256:eba9df40666f66531bb32402c84c6b5cfe00d2cf81288494c7875f744d450863","observation_id":"7c79f42a-d612-44c9-bca6-f475f8c4d650","resolution":{"observed_at":"2026-08-14T14:08:00.302439Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:08:00.280399Z","title":null,"venue":null,"work_id":"314300b8-0c79-4504-997f-aab4f457fde7","year":1992},"citing_paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality","version":3},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T14:07:59.766449Z"},"links":{"citing_paper":"/paper/1908.03915"},"observation_digest":"sha256:2c12693b7e57de08b4c999e9bf497c26dd24aff08a0ad13e82f15c768c33ded3","observation_id":"f1e024ff-375d-48b7-80fe-8d5de1ef3462","resolution":{"observed_at":"2026-08-14T14:08:00.284919Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:08:00.264525Z","title":"Brezis, E","venue":null,"work_id":"538f00c1-1f80-4009-bbc2-b1ebcbf55951","year":1983},"citing_paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality","version":3},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T14:07:59.771743Z"},"links":{"citing_paper":"/paper/1908.03915"},"observation_digest":"sha256:3c9e260327b3a0d7fece2ac1e41d27086e4db4ab76d76d80c5b51b69dc49ba6a","observation_id":"81daf2cb-caba-4f31-a07e-e7b95ad712a2","resolution":{"observed_at":"2026-08-14T14:08:00.269544Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:08:00.246824Z","title":"L.,Blow-up solutions of some nonlinear elliptic prob- lems, Rev","venue":null,"work_id":"ceef30a4-d520-45c9-9595-66f72091df5c","year":1997},"citing_paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T14:07:59.777368Z"},"links":{"citing_paper":"/paper/1908.03915"},"observation_digest":"sha256:386374d34c5263c54282a959bd63c448be33f9b8d4260dad7d96e4b2455aceb2","observation_id":"509f4556-1523-42b5-8793-d12ae3c19f39","resolution":{"observed_at":"2026-08-14T14:08:00.253117Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:08:00.231151Z","title":"39 (2013), no","venue":null,"work_id":"3e9c6bd6-779e-47db-95c4-3c66bc34b608","year":2013},"citing_paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T14:07:59.781717Z"},"links":{"citing_paper":"/paper/1908.03915"},"observation_digest":"sha256:2ef38fec19a7e87321303d8085b5387a723e6dd0829e4d7cf2b355a11cec2bd2","observation_id":"9b03fec0-857b-45df-8586-d6a625ad300d","resolution":{"observed_at":"2026-08-14T14:08:00.236046Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:08:00.216117Z","title":"7 (1983), No","venue":null,"work_id":"d3a480b0-42e8-455f-8648-57037a15aca2","year":1983},"citing_paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality","version":3},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T14:07:59.786014Z"},"links":{"citing_paper":"/paper/1908.03915"},"observation_digest":"sha256:1ecaa8bee43b25ed0b08bac02280bfd7e4a49ba93c8e1b2526bf1b97292c01cb","observation_id":"30e33cf4-ccdf-4fff-97a9-f43ff2c35f8a","resolution":{"observed_at":"2026-08-14T14:08:00.220813Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:08:00.200124Z","title":null,"venue":null,"work_id":"96f86c70-df29-4292-b9f7-923027152b3c","year":1992},"citing_paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality","version":3},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T14:07:59.790464Z"},"links":{"citing_paper":"/paper/1908.03915"},"observation_digest":"sha256:22a49734de677efb820a76eba257fa24febc9f1fc4032ff874e7733d4da0e316","observation_id":"fdad2619-5bb7-4b0e-a6b8-a27a7af9d4cf","resolution":{"observed_at":"2026-08-14T14:08:00.205026Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:08:00.182600Z","title":null,"venue":null,"work_id":"83d00c88-c7f6-4f36-ae50-888e75c49161","year":2012},"citing_paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality","version":3},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T14:07:59.795228Z"},"links":{"citing_paper":"/paper/1908.03915"},"observation_digest":"sha256:c6a8d6638cc09fcff4a623bc866c88a59004789ce8dc75da62c5336e0b748501","observation_id":"107db6af-6920-4cee-a677-bcf4d3c0f7ff","resolution":{"observed_at":"2026-08-14T14:08:00.188141Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:08:00.166884Z","title":null,"venue":null,"work_id":"19f43558-2658-4eee-aa6d-b994a24ad97e","year":2019},"citing_paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality","version":3},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T14:07:59.799877Z"},"links":{"citing_paper":"/paper/1908.03915"},"observation_digest":"sha256:8124ab109a9e46679b3db7b713c877e6afc944493a0b641055bf3f442b8793d4","observation_id":"4851df35-e9bf-41ca-9952-13adf76fcc63","resolution":{"observed_at":"2026-08-14T14:08:00.171260Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:08:00.151338Z","title":null,"venue":null,"work_id":"1e383857-9a63-48eb-aeb7-cc88c7a45d93","year":2016},"citing_paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality","version":3},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T14:07:59.804773Z"},"links":{"citing_paper":"/paper/1908.03915"},"observation_digest":"sha256:1c41e33e798f1d0d1369ef3f879dae13d6ff14c067a43e9b71caf085bbcebbb9","observation_id":"34f6a3af-b0c8-4d57-8a17-3fe6debead1a","resolution":{"observed_at":"2026-08-14T14:08:00.156494Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:08:00.134657Z","title":"H., Sharp constants in the Hardy-Littlewood-Sobolev and relat ed inequalities, Ann","venue":null,"work_id":"eee11504-e299-4450-8c29-8131842e61c9","year":1983},"citing_paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality","version":3},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T14:07:59.810026Z"},"links":{"citing_paper":"/paper/1908.03915"},"observation_digest":"sha256:575a398428b9b9e1fa464afe2e2e855308dc78aa0cf5c98af265fe66aae4543e","observation_id":"c69c3901-9f5d-426f-91a1-8593d9a51964","resolution":{"observed_at":"2026-08-14T14:08:00.140148Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:08:00.117244Z","title":null,"venue":null,"work_id":"dcc8baae-cd22-4039-a6fb-f86f5a2b43c5","year":2007},"citing_paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality","version":3},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T14:07:59.814677Z"},"links":{"citing_paper":"/paper/1908.03915"},"observation_digest":"sha256:1b0c8d315327044a4fa95116827d240bfb0bbdda8a200bc28969e5a499517f4d","observation_id":"c271c400-f8e2-4f48-8f8d-8b5bb777e125","resolution":{"observed_at":"2026-08-14T14:08:00.123182Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:08:00.101155Z","title":"Differential Equations 267 (2019), no","venue":null,"work_id":"3d0c9def-8e84-43ca-941b-af65c53786e4","year":2019},"citing_paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality","version":3},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T14:07:59.819411Z"},"links":{"citing_paper":"/paper/1908.03915"},"observation_digest":"sha256:3343389f886c1214a94ec3b959f72e1e4acb68e74be87150eceeeb056ced02c6","observation_id":"66056edc-e1bd-40ae-8140-e8a889f32f6e","resolution":{"observed_at":"2026-08-14T14:08:00.106434Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1911.04105","last_updated":"2019-11-11T06:35:16Z","snapshot_observed_at":"2026-08-06T07:17:23.002165Z","submitted_at":"2019-11-11T06:35:16Z","title":"Two limits on Hardy and Sobolev inequalities","version":1},"cited_work":{"arxiv_id":"1911.04105","doi":null,"metadata_source":"pith","pith_arxiv_id":"1911.04105","snapshot_observed_at":"2026-08-14T14:07:59.935733Z","title":"Two limits on Hardy and Sobolev inequalities","venue":"math.FA","work_id":"8dac489e-cb61-426b-898a-3ad3537713c5","year":2019},"citing_paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality","version":3},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T14:07:59.823971Z"},"links":{"cited_paper":"/paper/1911.04105","citing_paper":"/paper/1908.03915"},"observation_digest":"sha256:2ea2bab5c125628cd871ece0aa761b2750b73e437167028a5be5d8fd94d45788","observation_id":"23ac11e0-7bbc-4155-b71c-a2c463685918","resolution":{"observed_at":"2026-08-14T14:07:59.941508Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1907.09609","last_updated":"2019-07-22T22:21:34Z","snapshot_observed_at":"2026-08-14T16:03:33.036329Z","submitted_at":"2019-07-22T22:21:34Z","title":"Remarks on a limiting case of Hardy type inequalities","version":1},"cited_work":{"arxiv_id":"1907.09609","doi":null,"metadata_source":"pith","pith_arxiv_id":"1907.09609","snapshot_observed_at":"2026-08-14T14:07:59.906651Z","title":"Remarks on a limiting case of Hardy type inequalities","venue":"math.AP","work_id":"4fcacdd7-1855-4eb6-a6bd-d427a64aaa0c","year":2019},"citing_paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality","version":3},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T14:07:59.829258Z"},"links":{"cited_paper":"/paper/1907.09609","citing_paper":"/paper/1908.03915"},"observation_digest":"sha256:5a99e6ffd207f00c5608d657be10865c4bac5a0e0dee088886f3e955be867b05","observation_id":"898a75ba-a8ed-4077-851e-1d56a135bd51","resolution":{"observed_at":"2026-08-14T14:07:59.915626Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:08:00.083891Z","title":null,"venue":null,"work_id":"54321bf0-f9dd-4dc7-a32c-ecf661bc2847","year":2017},"citing_paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality","version":3},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T14:07:59.834510Z"},"links":{"citing_paper":"/paper/1908.03915"},"observation_digest":"sha256:0687e500540a3a8583cc9642688a01816c7ac1b74a15d67d12fc073e9b14a3d9","observation_id":"5b513790-bf2f-4c0b-9e20-11b0a4515806","resolution":{"observed_at":"2026-08-14T14:08:00.089355Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:08:00.066779Z","title":null,"venue":null,"work_id":"c240501a-3265-4e69-a11e-ddb59143ae2d","year":2002},"citing_paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality","version":3},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-14T14:07:59.839198Z"},"links":{"citing_paper":"/paper/1908.03915"},"observation_digest":"sha256:88832e37daefa0804e77580abab66b508df20a71d7cf1d4a781117e63c4aa634","observation_id":"fc846bf0-5f28-4214-9dd3-ef37c13bd1f3","resolution":{"observed_at":"2026-08-14T14:08:00.072336Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:08:00.050565Z","title":"A., Existence of solitary waves in higher dimensions , Comm","venue":null,"work_id":"fdead1cc-914d-418d-bb4b-b3596d0c2fb2","year":1977},"citing_paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality","version":3},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-14T14:07:59.844281Z"},"links":{"citing_paper":"/paper/1908.03915"},"observation_digest":"sha256:29c6de50c8d89fbcb6344eeaa1b5e130c7030a63e8fbfb0fadf4eac750506265","observation_id":"a9ab9c9d-020c-4377-bee6-337aad43821b","resolution":{"observed_at":"2026-08-14T14:08:00.055311Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:08:00.032341Z","title":"Applications to nonlinear partial di ffer- ential equations and Hamiltonian systems","venue":null,"work_id":"7a806624-b41d-4776-9113-fe265f8c98f0","year":2008},"citing_paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality","version":3},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-14T14:07:59.849200Z"},"links":{"citing_paper":"/paper/1908.03915"},"observation_digest":"sha256:cf8b84c1486d8ceb63fc084d29ccc826da2705209853097ff802abd62d281043","observation_id":"2bfb4a57-b079-4173-b2be-c8a536229aae","resolution":{"observed_at":"2026-08-14T14:08:00.038548Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:08:00.011865Z","title":null,"venue":null,"work_id":"f6c1009b-f4b4-4e66-be81-283f45a74783","year":1976},"citing_paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality","version":3},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-14T14:07:59.853548Z"},"links":{"citing_paper":"/paper/1908.03915"},"observation_digest":"sha256:9d67acc24a0141fbfbffda228b5a53a3f5c0c778ed71084767cc933e660c68c4","observation_id":"56720dd7-97de-4ead-a213-187b126024b7","resolution":{"observed_at":"2026-08-14T14:08:00.019166Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:07:59.991020Z","title":"S., On imbeddings into Orlicz spaces and some applications , J","venue":null,"work_id":"276b2715-c8dd-421e-837e-54b7e67d1358","year":1967},"citing_paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality","version":3},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-14T14:07:59.858421Z"},"links":{"citing_paper":"/paper/1908.03915"},"observation_digest":"sha256:827e7e017b5a8396fa7b63d5771d58966429f6557351fd695e804ba667cc51e7","observation_id":"3a8136da-8558-4a11-ae36-d827e268c38b","resolution":{"observed_at":"2026-08-14T14:07:59.996521Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:07:59.971199Z","title":"L., Zuazua, E., The Hardy inequality and asymptotic behaviour of the heat equation with an inverse-square potential , J","venue":null,"work_id":"33e346ff-c1fd-4319-85fa-e642a28bb4f4","year":2000},"citing_paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality","version":3},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-14T14:07:59.863003Z"},"links":{"citing_paper":"/paper/1908.03915"},"observation_digest":"sha256:5926f506c50eeaf085c6368a9d7344526fd6c47f337a548fb3fb7054204c22a9","observation_id":"21051fd6-3c8e-40f0-8be5-a3cf26dcf3b2","resolution":{"observed_at":"2026-08-14T14:07:59.977545Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:07:59.953697Z","title":null,"venue":null,"work_id":"ce7c6ea5-7872-4f32-96fb-7d64dddf048b","year":2010},"citing_paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality","version":3},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-14T14:07:59.867961Z"},"links":{"citing_paper":"/paper/1908.03915"},"observation_digest":"sha256:272e157c87b5f6a60c284699801cbaabee5ff1556a8f103a9aeb903e0f469f9b","observation_id":"20ead201-e5b9-490d-af6f-06a036010f37","resolution":{"observed_at":"2026-08-14T14:07:59.958554Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1908.03915","last_updated":"2020-03-19T03:13:07Z","latest_version":3,"primary_category":"math.AP","snapshot_observed_at":"2026-08-14T13:55:39.202557Z","submitted_at":"2019-08-11T14:36:38Z","title":"Minimization problem associated with an improved Hardy-Sobolev type inequality"},"reference_resolution":{"displayed":26,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":11,"verified_exact":2,"verified_fuzzy":13},"total_outbound_references":26},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:1908.03915."}