{"as_of":"2026-08-23T23:29:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:476cb30189264ae626fa43b7331c4bd03becd12cf2683e9595a717984dd041d9","coverage":[{"denominator":30,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":30,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T14:47:01.714103Z","state":"measured"},{"denominator":31,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":31,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-23T06:30:58.430688+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-09T14:36:37.229570Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-09T14:36:37.757119Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"cited_work":{"arxiv_id":"2412.11808","doi":null,"metadata_source":"pith","pith_arxiv_id":"2412.11808","snapshot_observed_at":"2026-08-09T14:36:37.757119Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","venue":"math.AP","work_id":"12425dad-00f5-42ba-8b05-8f75b7d0392b","year":2024},"citing_paper":{"arxiv_id":"2502.01818","last_updated":"2025-02-03T20:46:29Z","snapshot_observed_at":"2026-08-22T21:56:41.727377Z","submitted_at":"2025-02-03T20:46:29Z","title":"Low regularity analysis of the Zakharov--Kuznetsov equation on $\\mathbb{R} \\times \\mathbb{T}$","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-09T14:36:37.229570Z"},"links":{"cited_paper":"/paper/2412.11808","citing_paper":"/paper/2502.01818"},"observation_digest":"sha256:189593ccded8d36eb57f36db1e6cffd26b3c3d6fa5dd3d14de318411c7418fde","observation_id":"fe0422b7-534e-46b1-94cd-2edadd40d51d","resolution":{"observed_at":"2026-08-09T14:36:37.763080Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2412.11808/citation-record","integrity":"/paper/2412.11808/integrity","json":"/paper/2412.11808/citation-record.json","paper":"/paper/2412.11808"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:47:02.600706Z","title":null,"venue":null,"work_id":"65ef3f42-9ec0-47c0-ad67-228fbe14b4b4","year":2014},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.479103Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:a851c87854f87a633736416e50292d3f07e9bef1cb622f61156320141a728d4e","observation_id":"e9d4c633-9427-4daa-a6df-37172d3f309d","resolution":{"observed_at":"2026-08-11T14:47:02.606491Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:02.562163Z","title":null,"venue":null,"work_id":"0094863f-a0e6-415a-ad76-eec998748c49","year":1993},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.489430Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:6975a5d00c185893ff2e250ab40cf05f004852c65e87d6922c3e449d8f970cdd","observation_id":"ec73b863-36f5-4d60-9324-e15beac60fa1","resolution":{"observed_at":"2026-08-11T14:47:02.572636Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:02.532990Z","title":"Bourgain","venue":null,"work_id":"62e64670-636b-4c21-8fec-618ef30f9d6e","year":1993},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.497740Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:e8dd998db4670acec53be30ee9bbfa9c29d5b8e6149bf438a6038a8fb8be22e3","observation_id":"69bc114b-5452-41f7-b78b-90b945d9ec05","resolution":{"observed_at":"2026-08-11T14:47:02.542469Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:02.505294Z","title":"Bourgain","venue":null,"work_id":"f3e1d8be-f532-4139-85db-e6965104f459","year":1993},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.503498Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:7a78eec7972f0b59db1ac1093b3c18b5fc1bbad41e8b1fdf328d431df8419b63","observation_id":"4f9e71f0-6970-4ac0-bdb9-a7536ae59e01","resolution":{"observed_at":"2026-08-11T14:47:02.513476Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:02.483662Z","title":"Semilinear Schrödinger equations, volume 10 of Courant Lecture Notes in Mathematics","venue":null,"work_id":"a6483e03-e24b-41ce-8047-b81e3dceca28","year":2003},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.509359Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:4bb142d498c9d119f885929e80d6e96ca86134fc8cedabdcb1a47f0e66f49a62","observation_id":"3e8d5588-72f4-47aa-a2b1-c3a99a630099","resolution":{"observed_at":"2026-08-11T14:47:02.491490Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:02.456580Z","title":"W eissler","venue":null,"work_id":"51044987-031b-4b53-827b-a0ac9414d3f9","year":1990},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.516644Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:119564a710810050c5dd077c0927472fa3d06e67e76d5999a40f0f4c98fc65a0","observation_id":"09e7feed-3515-4c7c-b284-af04fd25d6a8","resolution":{"observed_at":"2026-08-11T14:47:02.465795Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:02.432760Z","title":"Sharp local well-posedness and nonlinear smoothing for dispersive equations through frequency-restricted estim ates","venue":null,"work_id":"73d03a16-ee9b-4f44-ad19-9c98b79db260","year":2024},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.523109Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:ca81e29f7a729cbc276a03b752cf5b5b39a5df05a4dabd4e3a610a46bcf8108f","observation_id":"4c5189df-f732-4a50-9cf1-a68e387231ce","resolution":{"observed_at":"2026-08-11T14:47:02.438983Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:02.411038Z","title":"Burak Erdoğan, T","venue":null,"work_id":"9415bf66-c3e2-4d8e-967c-967903df5880","year":2019},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.528540Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:d87bb15d6690d41efe769c8d607135934e1c6422ca29f569d6332957a6e01fdb","observation_id":"50930dad-b541-4716-a70d-cb6bd6aac316","resolution":{"observed_at":"2026-08-11T14:47:02.416239Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:02.392941Z","title":"Burak Erdoğan and Nikolaos Tzirakis","venue":null,"work_id":"6d8ffefc-4e3b-4baf-8602-103dbe88554c","year":2013},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.536620Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:9113282b88622d235ee6c956a63fb000910c939bf5dfe084b0a56e76f7b8de8f","observation_id":"3bcc7b02-2cc4-4783-9b77-9d36e19a1529","resolution":{"observed_at":"2026-08-11T14:47:02.399055Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:02.365434Z","title":"Burak Erdoğan and Nikolaos Tzirakis","venue":null,"work_id":"2fca1cd0-3d96-4d47-a8b9-c96c14b67fc8","year":2016},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.542893Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:87643d1a2ba083e278c2292bb0942815f5ebe5ceb957bfb44a9f8f491231e648","observation_id":"509ed702-9c7a-4d6c-8663-ea63f560b472","resolution":{"observed_at":"2026-08-11T14:47:02.372332Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:02.332229Z","title":"A remark on the modified Zakharov-Kuznet sov equation in three space dimensions","venue":null,"work_id":"4ac58268-24f0-4704-b764-38634e38012c","year":2014},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.549368Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:35a9753be737874cec680fa4011b52e7c4964dadc8be2ab6ea6aa3963a74a10c","observation_id":"df2b08c3-03a1-43b0-b00c-712c1eaa1c1b","resolution":{"observed_at":"2026-08-11T14:47:02.341931Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:02.303510Z","title":"The Fourier restrict ion norm method for the Zakharov-Kuznetsov equation","venue":null,"work_id":"1a3652f3-b44e-48d1-b5d9-f9becc88fbe3","year":2014},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.557511Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:40d42efbaf430908a8b8ee4fe9d4c8453e56f579f01054b58dce8bc861b58707","observation_id":"7eab34f3-93cf-4144-83c4-9dcc4616fcb8","resolution":{"observed_at":"2026-08-11T14:47:02.312016Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:02.281574Z","title":"On the generalized zakharov-kuznetsov equation at critical regularity","venue":null,"work_id":"0868e673-e823-4190-b2df-28a2c338f572","year":2015},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.564644Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:840b0a28843c20febc3bf8b82d1de16bd32c936f1c0985943c9fee0417085d92","observation_id":"1585cc8a-99f8-4197-8de0-3098203b3a40","resolution":{"observed_at":"2026-08-11T14:47:02.288376Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:02.262766Z","title":"The analysis of linear partial differential operators","venue":null,"work_id":"83266556-ff2c-49a7-987f-c4e6d3aa12b5","year":null},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.570668Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:e1fb030a46a33ee6da86f29fb386f0c33346414a62246b3dab425a7b52952faa","observation_id":"9a3da697-d2db-465a-93e3-23eb06c019e0","resolution":{"observed_at":"2026-08-11T14:47:02.269275Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:02.214734Z","title":"Pedro Isaza, L","venue":null,"work_id":"f3a1ee9d-dd28-4491-9e37-84bdb680c7a2","year":2006},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.584761Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:1fa428a77379ab9bb794dd8e473073e41e1f321147152797bb1d8460ef38fd8e","observation_id":"b8af57fb-9542-427b-9d21-8675d10829d6","resolution":{"observed_at":"2026-08-11T14:47:02.220699Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:02.188073Z","title":"Polynomial bound and nonlinear smoothing for the Benjamin-Ono equation on the circle","venue":null,"work_id":"f315458d-3a2d-44d2-8120-2f511c289f65","year":2021},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.597145Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:8efe493d9e7416ade627664a72255ccd7deed3cb12c152adde446537aa732271","observation_id":"4b946ad7-2f84-420f-9017-edd677011a04","resolution":{"observed_at":"2026-08-11T14:47:02.195732Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:02.165847Z","title":"On nonlinear Schrödinger equations","venue":null,"work_id":"6c11b690-7669-4083-a4a9-9efd49e93b32","year":1995},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.604813Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:7ff137b80e88439d13715a3865683194ea41b64b9ac878459f72da0c3fcedfc1","observation_id":"ff5e414f-3ec0-4e8c-8698-64eb4ec222c9","resolution":{"observed_at":"2026-08-11T14:47:02.171632Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:02.136775Z","title":"Kenig, Gustavo Ponce, and Luis Vega","venue":null,"work_id":"6e7c58cd-7d1d-4cc9-b161-2a27eef5d60c","year":1993},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.611689Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:6bf0308dffbd352df4383801bca0853a581f72d5a84955c1c25786df5a831604","observation_id":"25e7a8e5-ae12-404b-8b39-b3c2acc065fe","resolution":{"observed_at":"2026-08-11T14:47:02.147429Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:02.114934Z","title":"A smoothing property for t he L2-critical NLS equations and an application to blowup theory","venue":null,"work_id":"d8cab2c2-6c35-447b-84b8-f8754a91756c","year":2009},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.626617Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:e1f4ee81f5dae70d12fc2392fdc5f1f1162b78617c6e37054c3f43eb4e62d3e2","observation_id":"f1e1e0c9-6a1d-40d4-927a-c4470f8dc035","resolution":{"observed_at":"2026-08-11T14:47:02.121536Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:02.089529Z","title":"W ell-posedness for the Cauchy probl em of the modified Zakharov-Kuznetsov equation","venue":null,"work_id":"e1b9c530-7476-46a7-a08b-f2f62f93f394","year":2022},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.638054Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:7694914cdb1508772925231d5e2a4584e9c19ef709dce3599fe8891c69b0e029","observation_id":"6c134fea-9fed-437a-925d-6561a1324051","resolution":{"observed_at":"2026-08-11T14:47:02.101530Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:02.045485Z","title":"Dispersive blow-up for solutions of the Zakharov-Kuznets ov equation","venue":null,"work_id":"4334a60f-73d8-414a-8110-229f777da8ab","year":2021},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.646189Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:bd204d0283fda56a2b9d36931ac5df2e8c6b0f78f7222e64bc7f9ee1858edf35","observation_id":"2782795d-cfba-466e-b6b1-bb1c12c492a7","resolution":{"observed_at":"2026-08-11T14:47:02.063039Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:02.015297Z","title":"Introduction to nonlinear dispersive equations","venue":null,"work_id":"c2ab1e9a-3d48-472d-bf1f-3d51d87d4dd8","year":2015},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.652355Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:43e3615de3693c208b85dd501a7c63c74ff9401567ebff09b75133b46a06c0ba","observation_id":"75d601f8-7dee-48de-8bd0-82faab28734e","resolution":{"observed_at":"2026-08-11T14:47:02.025154Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:01.983697Z","title":null,"venue":null,"work_id":"7b929067-5b27-49e0-bc37-223a5527b075","year":2017},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.660219Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:afd4623a4e8d748dda93afa179e79d519440a75edd55a233590d0789abf0ff37","observation_id":"41fac9f3-2c21-4558-a648-a693609bdd77","resolution":{"observed_at":"2026-08-11T14:47:01.992476Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:01.950450Z","title":null,"venue":null,"work_id":"434e4db1-784c-4dc4-82c5-49ab29b33887","year":2021},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.667221Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:2dbb0411d75d10286558c8e4a75028d97a48454e32a03f6aeb850433703048ee","observation_id":"62121ad8-1eb2-4ee7-b76a-b3d1955f1dcb","resolution":{"observed_at":"2026-08-11T14:47:01.959430Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:01.906118Z","title":"On the smoothing pro perties of solutions to the modified Korteweg-de Vries equation","venue":null,"work_id":"233296b9-49ec-49d2-a52d-be7f6d35be12","year":1993},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.680740Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:5fdcf7ca880e13f294a1ebf194bbfa0981e292e649dbef6ce1141138a1a67c83","observation_id":"84165ac9-de8b-4302-ab12-75f59606f8be","resolution":{"observed_at":"2026-08-11T14:47:01.915326Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:01.869999Z","title":"Critical point theory and Hamiltonian systems , volume 74 of Applied Mathematical Sciences","venue":null,"work_id":"ad504a1a-ad22-47c6-9267-9c0397639f99","year":1989},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.690230Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:f20631bdd87bf99c3d6a23922a97c04b7ac4d705d8d8f8860c4a1c05ae51338e","observation_id":"212a8847-8624-4c78-afe3-70fd3076a67d","resolution":{"observed_at":"2026-08-11T14:47:01.880911Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:01.839949Z","title":"Solutions of semilinear Schrödinger e quations in H s","venue":null,"work_id":"bc4ee538-5a50-4268-bf8a-62f752c75e9b","year":1997},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.699076Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:b345cf5b579082a6c992eac1890f74f95faa449628f229de2df29d95e583aa85","observation_id":"63b2b9d2-5114-4378-be85-1d251cd9a315","resolution":{"observed_at":"2026-08-11T14:47:01.851842Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:01.810512Z","title":"A note on the Cauchy p roblem for the 2D generalized Zakharov-Kuznetsov equations","venue":null,"work_id":"fa45a2eb-c846-4191-8a89-6126d3baf35c","year":2012},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.706772Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:e206b9c8bd5858e6597f0f43264b41f52077d62759214b13505c32e8a67b8600","observation_id":"9b27a17b-5450-4de5-a359-24ac80a5cd3b","resolution":{"observed_at":"2026-08-11T14:47:01.820688Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:01.783650Z","title":"Nonlinear dispersive equations , volume 106 of CBMS Regional Conference Series in Mathematics","venue":null,"work_id":"bc4e8395-e5ec-4142-a3f3-eefa81b2dafa","year":2006},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.714103Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:6f8d5ac78a179a8e0f7df576e79a7a9cf654f88c6edd78472558e1ead3f15a76","observation_id":"c37877b1-d426-41c1-b46e-c2f35677b33d","resolution":{"observed_at":"2026-08-11T14:47:01.792103Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T14:47:02.236427Z","title":null,"venue":null,"work_id":"5a97005f-6302-4c5c-aacb-e86a1bf217f0","year":1994},"citing_paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities","version":1},"reference_index":2007,"source":"pdf_text","source_observed_at":"2026-08-11T14:47:01.578869Z"},"links":{"citing_paper":"/paper/2412.11808"},"observation_digest":"sha256:c3fc3d1b53094cf120473cba55d02c48b30cf4a3c508fa1573ffe1d1d470e6a2","observation_id":"073b1521-c8ab-4511-ba53-d6b25bcc8ae3","resolution":{"observed_at":"2026-08-11T14:47:02.241944Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.11808","last_updated":"2024-12-16T14:18:02Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-11T14:31:21.218622Z","submitted_at":"2024-12-16T14:18:02Z","title":"Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities"},"reference_resolution":{"displayed":30,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":0,"verified_fuzzy":25},"total_outbound_references":30},"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":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"thesis":"As of 23 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 1 inbound Pith citation observation for arXiv:2412.11808."}