{"as_of":"2026-08-06T03:26:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:136152a5717288a82ac6e5ea9a999c84a1ee8bb787e54f8710c88a9a2ec58619","coverage":[{"denominator":25,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":25,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-27T21:47:43.180587Z","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":"2026-08-05T06:32:48.257954+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":"2026-07-09T05:13:04.941635Z","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":"2026-07-09T05:15:59.160553Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","version":1},"cited_work":{"arxiv_id":"2606.07010","doi":null,"metadata_source":"pith","pith_arxiv_id":"2606.07010","snapshot_observed_at":"2026-07-09T05:15:59.160553Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","venue":"math.AP","work_id":"bbd76ccf-918e-4b71-83b0-1fc5ed410557","year":2026},"citing_paper":{"arxiv_id":"2607.07628","last_updated":"2026-07-08T16:43:59Z","snapshot_observed_at":"2026-08-06T02:28:31.185704Z","submitted_at":"2026-07-08T16:43:59Z","title":"On probabilistic ill-posedness","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-07-09T05:13:04.941635Z"},"links":{"cited_paper":"/paper/2606.07010","citing_paper":"/paper/2607.07628"},"observation_digest":"sha256:d4ee8665f4600d8db82ecc14ecf4468bb2d464d957b3fbf099255bd6b804a56a","observation_id":"d412e87a-1198-435c-8b06-22d5c798b036","resolution":{"observed_at":"2026-07-09T05:15:59.161923Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2606.07010/citation-record","integrity":"/paper/2606.07010/integrity","json":"/paper/2606.07010/citation-record.json","paper":"/paper/2606.07010"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4171/jems/543","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Journal of the European Mathematical Society","work_id":"6a9f1eac-2495-40f4-8f05-92ff8c4e3607","year":2015},"citing_paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-06-27T21:47:43.180587Z"},"links":{"citing_paper":"/paper/2606.07010"},"observation_digest":"sha256:0dc1b1106a21d987dfbcc88b54e2be76da81b867b556dca2cb7138545454ff0a","observation_id":"fa0a999a-c139-46eb-89f6-7e48368550d3","resolution":{"observed_at":"2026-06-27T21:51:18.085387Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1093/imrn/rnz385","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Almost sure local well-posedness for a derivative nonlinear wave equation , volume =","venue":"International Mathematics Research Notices","work_id":"ac8c8f25-bf69-4ab8-a061-f9c9ee236037","year":2021},"citing_paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-06-27T21:47:43.180587Z"},"links":{"citing_paper":"/paper/2606.07010"},"observation_digest":"sha256:9d29109628320fb6e20e77481159a69b385e121a9b81c32c6f38b91ccad72bfa","observation_id":"1c92e43a-3a5b-4b04-96d2-808131a2e896","resolution":{"observed_at":"2026-06-27T21:51:18.110194Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10013-023-00672-w","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"and Yue, Haitian , date-added =","venue":"Vietnam Journal of Mathematics","work_id":"c8cd1ee0-6549-4692-8b8c-9f98e5810147","year":2024},"citing_paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-06-27T21:47:43.180587Z"},"links":{"citing_paper":"/paper/2606.07010"},"observation_digest":"sha256:5007d75452dc15349321e38175927bba16b1f9bcf569e4b4bb081d9515e08f78","observation_id":"4777a718-e18c-403a-8673-b63183166edf","resolution":{"observed_at":"2026-06-27T21:51:18.104075Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.5802/aif.2422","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":", date-added =","venue":"Annales de l’institut Fourier","work_id":"1dfb2f62-4079-422f-b33b-0dbd2487d776","year":2008},"citing_paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-06-27T21:47:43.180587Z"},"links":{"citing_paper":"/paper/2606.07010"},"observation_digest":"sha256:bd2ef23273a369d7f00c7e9088453706a688548c06b2ee0b9a00097f9ada2d5a","observation_id":"52dd43cc-26f4-4fac-bcf6-b1476dfcccc2","resolution":{"observed_at":"2026-06-27T21:51:18.117126Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T21:47:43.180587Z","title":"and L\\\"ofstr\\\"om, J","venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-06-27T21:47:43.180587Z"},"links":{"citing_paper":"/paper/2606.07010"},"observation_digest":"sha256:53fa62413cc5a07dee906dc2d77c874215e7dbe561edca2b5a26880959f4bf68","observation_id":"4340aa07-fca1-41f7-b8ce-e5e35638f2cf","resolution":{"observed_at":"2026-06-27T21:47:43.180587Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00222-004-0388-x","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Inventiones mathematicae","work_id":"d9da4ec0-4976-4ec2-981a-ac979faacff2","year":2005},"citing_paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-06-27T21:47:43.180587Z"},"links":{"citing_paper":"/paper/2606.07010"},"observation_digest":"sha256:c76725c71583c67dd8602d659f9febfed4118a12730c815cc245648c1956b4f9","observation_id":"c31a1d2e-d85b-42ec-adeb-d13241d469db","resolution":{"observed_at":"2026-06-27T21:51:18.104220Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T21:47:43.180587Z","title":"in preparation , title =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-06-27T21:47:43.180587Z"},"links":{"citing_paper":"/paper/2606.07010"},"observation_digest":"sha256:523d216600d4c702b0c94d54c7bb7a3e74e15ed73890928b20cbf7b1ff5331a1","observation_id":"2cedae63-3595-4e02-82db-318a2a1fb707","resolution":{"observed_at":"2026-06-27T21:47:43.180587Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/fms.2020.51","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"and Tzvetkov, N","venue":"Forum of Mathematics Sigma","work_id":"cc7f8765-53c2-48c3-9fd4-032f43bc3946","year":2020},"citing_paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-06-27T21:47:43.180587Z"},"links":{"citing_paper":"/paper/2606.07010"},"observation_digest":"sha256:2f6395296dbfa5b7afc322e46ace56fb3be37d8ee53e5bac7f111d6c61c84abe","observation_id":"92cd3e78-e908-4dea-918c-6e0c78c59e9b","resolution":{"observed_at":"2026-06-27T21:51:18.108203Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2404.18229","last_updated":"2025-06-24T08:50:08Z","snapshot_observed_at":"2026-07-06T18:06:40.922189Z","submitted_at":"2024-04-28T15:48:44Z","title":"Probabilistic well-posedeness for the nonlinear Schr\\\"odinger equation on the $2d$ sphere I: positive regularities","version":2},"cited_work":{"arxiv_id":"2404.18229","doi":null,"metadata_source":"pith","pith_arxiv_id":"2404.18229","snapshot_observed_at":"2026-07-09T05:15:59.153428Z","title":"Probabilistic well-posedeness for the nonlinear Schr\\\"odinger equation on the $2d$ sphere I: positive regularities","venue":"math.AP","work_id":"54427ecd-76d6-4a0c-b9e5-a65a6c8c9b7c","year":2024},"citing_paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-06-27T21:47:43.180587Z"},"links":{"cited_paper":"/paper/2404.18229","citing_paper":"/paper/2606.07010"},"observation_digest":"sha256:6b82af02acbb4811dac73a60b54cd47ff8f48eae5d67a09d2028d7b981162ce2","observation_id":"9e3bd16f-35ac-42be-86bc-84650fabb98f","resolution":{"observed_at":"2026-07-02T18:57:16.756556Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4171/emss/92","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"and Camps, N","venue":"EMS Surveys in Mathematical Sciences","work_id":"f9d54095-d715-4aa2-9da2-3eebe2cb5829","year":2025},"citing_paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-06-27T21:47:43.180587Z"},"links":{"citing_paper":"/paper/2606.07010"},"observation_digest":"sha256:ac24792f6983c6a0823aeba2497395fa4d8d97b3a69ef88b4403b2123ada9cb0","observation_id":"104938cb-ee01-4702-af2b-65fbc1de0a0f","resolution":{"observed_at":"2026-06-27T21:51:18.100468Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf02099556","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":", date-added =","venue":"Communications in Mathematical Physics","work_id":"74db2526-5666-4bfa-a1ce-b476648e5675","year":1996},"citing_paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-06-27T21:47:43.180587Z"},"links":{"citing_paper":"/paper/2606.07010"},"observation_digest":"sha256:9aa5e798ea00cfca113f2cf009d3f5078283c6b80662fe8b67bb3494a7e87761","observation_id":"bbb502e8-d1f4-426c-8b59-1f67b208acbf","resolution":{"observed_at":"2026-06-27T21:51:18.099653Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4171/jems/461","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"and Bulut, A","venue":"Journal of the European Mathematical Society","work_id":"fe5d626b-5a51-4210-b426-93b0cd76a0cc","year":2014},"citing_paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-06-27T21:47:43.180587Z"},"links":{"citing_paper":"/paper/2606.07010"},"observation_digest":"sha256:64daa1ed0a2d768b7ad5a2e22722b6d9095a1b116395497fcd28a3616eae0ded","observation_id":"11fcb3fc-022a-486b-86cb-29a467637fd3","resolution":{"observed_at":"2026-06-27T21:51:18.111998Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jde.2021.01.031","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":", date-added =","venue":"Journal of Differential Equations","work_id":"d7f730a8-17d9-472e-8cd0-cbac0981c622","year":2021},"citing_paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-06-27T21:47:43.180587Z"},"links":{"citing_paper":"/paper/2606.07010"},"observation_digest":"sha256:5a41d738ae4b78268c73de90f5e6cdc3b54d58381dc7cfc23a317621f4e06f3d","observation_id":"da4b9f10-a327-4cd7-aa62-a2f4e41404b3","resolution":{"observed_at":"2026-06-27T21:51:18.115390Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00222-021-01084-8","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Deng, A.R","venue":"Inventiones mathematicae","work_id":"e72adfd2-44dc-4bbc-940b-6fa4d57e0238","year":2022},"citing_paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-06-27T21:47:43.180587Z"},"links":{"citing_paper":"/paper/2606.07010"},"observation_digest":"sha256:d92780e0cee6617f7e83356cfdf3267f1643841edd3a5ca23d3f0f8a63bde6fc","observation_id":"f9a9d3cc-2644-4b8d-822b-81bda024f108","resolution":{"observed_at":"2026-06-27T21:51:18.108385Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-07-14T19:20:19.422928+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-14T19:20:19.422928+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4007/annals.2024.200.2.1","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"and Nahmod, A","venue":"Annals of Mathematics","work_id":"cd5e5f2d-4ca5-4d54-ba5c-d8db50c44267","year":2024},"citing_paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-06-27T21:47:43.180587Z"},"links":{"citing_paper":"/paper/2606.07010"},"observation_digest":"sha256:47e4d97b481a241d1c422451f6e6e0b797c34f023d74dec4d169fb506d6488b0","observation_id":"6a1129f2-b9cd-4430-8dbf-f91d71872f58","resolution":{"observed_at":"2026-06-27T21:51:18.096815Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/pl00005588","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":", date-added =","venue":"Communications in Mathematical Physics","work_id":"d932c6af-dbf3-44a7-a29f-e896bf76c403","year":2001},"citing_paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-06-27T21:47:43.180587Z"},"links":{"citing_paper":"/paper/2606.07010"},"observation_digest":"sha256:4824339c0c2eb7d9e8c78a7f951dcba4eae4941d7b10b85cc0562e953d87243f","observation_id":"f26c8b03-354f-4119-8eef-fa60199d2152","resolution":{"observed_at":"2026-06-27T21:51:18.113723Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1142/s0219891604000032","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":", date-added =","venue":"Journal of Hyperbolic Differential Equations","work_id":"d41bb146-4dc3-4342-a708-c7e5f05f30f1","year":2004},"citing_paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-06-27T21:47:43.180587Z"},"links":{"citing_paper":"/paper/2606.07010"},"observation_digest":"sha256:07bc4e631324ce97158c4cd0ea12c735d22fe6b16a48f99487e3d8459e082ed3","observation_id":"9a373275-5eb4-4777-a5be-30e3ab88b605","resolution":{"observed_at":"2026-06-27T21:51:18.121287Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2512.02250","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-09T05:26:02.049384Z","title":"Kaneshiro,A new proof of the abstract random tensor estimate by Deng, Nahmod, and Yue, arXiv:2512.02250 [math.PR]","venue":null,"work_id":"2767985f-63f7-4dc6-b347-5aad8b529cd0","year":2025},"citing_paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-06-27T21:47:43.180587Z"},"links":{"citing_paper":"/paper/2606.07010"},"observation_digest":"sha256:f74fc164c4d3564a411e3a5a0da8e76e23c09c514b1bc0b4dc28d2af152b45ce","observation_id":"f8ce2871-3909-47ac-a024-1ccd41e2301d","resolution":{"observed_at":"2026-07-02T18:57:16.759039Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.2140/pmp.2025.6.139","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"and Rodnianski, I","venue":"Probability and Mathematical Physics","work_id":"bfcd9497-83dd-49e0-97e9-d61de124d4bd","year":2025},"citing_paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-06-27T21:47:43.180587Z"},"links":{"citing_paper":"/paper/2606.07010"},"observation_digest":"sha256:220d4efff3f8683c80891fe417b346a1c10b99b1b4cacd7b20bd3ff6644022e5","observation_id":"793d49d9-1bb0-40d8-ba72-9e99dfb4d441","resolution":{"observed_at":"2026-06-27T21:51:18.119231Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1155/s1073792804140555","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"and Tsutsumi, Y","venue":"International Mathematics Research Notices","work_id":"3aff4020-f904-43ad-a8c9-02b24ddbd125","year":2004},"citing_paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-06-27T21:47:43.180587Z"},"links":{"citing_paper":"/paper/2606.07010"},"observation_digest":"sha256:2b9e5286586c61f8fcddabdd113a45ec7e1a2e077c71e97c2cbbe6b64674b45c","observation_id":"1d518976-50c4-4fe5-9ae1-6abca109123a","resolution":{"observed_at":"2026-06-27T21:51:18.123130Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-1-4939-7005-6_4","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":", booktitle =","venue":"˜The œIMA volumes in mathematics and its applications","work_id":"bf5ff5b9-a089-4ed0-b750-1fb0e7771fac","year":null},"citing_paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-06-27T21:47:43.180587Z"},"links":{"citing_paper":"/paper/2606.07010"},"observation_digest":"sha256:203a5d556e5331ad1c2ed2c23caa64b647e6e295cabb41f6489883a2e0def0ef","observation_id":"d5451a53-c802-423b-a0c4-37c9209c533b","resolution":{"observed_at":"2026-06-27T21:51:18.117484Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1215/s0012-7094-93-07134-7","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"and Pisier, G","venue":"Duke Mathematical Journal","work_id":"d73a4e31-7a98-4d0d-97e9-c26a0d277fa0","year":1993},"citing_paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-06-27T21:47:43.180587Z"},"links":{"citing_paper":"/paper/2606.07010"},"observation_digest":"sha256:df7946fb01cf6b2a5ea3d84dcd71fa2ff8037b84b30bc063bf95bb3a7dfccb8b","observation_id":"a7d208e5-35b8-4d46-a625-574538e38f2f","resolution":{"observed_at":"2026-06-27T21:51:18.115558Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2509.14861","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-02T18:57:16.760191Z","title":"2025 , bdsk-url-1 =","venue":null,"work_id":"82a8a3ec-009f-43d1-93bd-9c4d3ad0dcd4","year":2025},"citing_paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-06-27T21:47:43.180587Z"},"links":{"citing_paper":"/paper/2606.07010"},"observation_digest":"sha256:33333d254f1a635d9e5cb1f69eb1bee22a49310a8569c475616316c45c2c52f6","observation_id":"6040fa0c-0e25-4b56-bbd6-aeb0923167a6","resolution":{"observed_at":"2026-07-02T18:57:16.761487Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4171/jems/1294","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Gubinelli, H","venue":"Journal of the European Mathematical Society","work_id":"b8b3ccd3-9987-471f-811a-ed7cc87aae2d","year":2024},"citing_paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-06-27T21:47:43.180587Z"},"links":{"citing_paper":"/paper/2606.07010"},"observation_digest":"sha256:71a703de76fa88d47bc5df5bb7942b53d7f9c6ee9527ad7798721a0024431bef","observation_id":"22944948-5044-4664-bcec-80622d58040a","resolution":{"observed_at":"2026-06-27T21:51:18.124801Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-07-14T19:20:20.181621+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-14T19:20:20.181621+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/fmp.2015.2","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"[GK22] G","venue":"Forum of Mathematics Pi","work_id":"5966a1ab-f8de-4a6c-804b-51b413bd6918","year":2015},"citing_paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-06-27T21:47:43.180587Z"},"links":{"citing_paper":"/paper/2606.07010"},"observation_digest":"sha256:2064db994f1cb420bb33e6819d410bcbe35b8089c13d5ca02bdd453fa983c6b6","observation_id":"8cdcbe89-b6c7-487a-8cb9-6e096a1b8716","resolution":{"observed_at":"2026-06-27T21:51:18.113886Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-07-12T03:49:11.824636+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-12T03:49:11.824636+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2606.07010","last_updated":"2026-06-05T07:53:04Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-07-06T23:46:42.693840Z","submitted_at":"2026-06-05T07:53:04Z","title":"Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the $3d$ ball"},"reference_resolution":{"displayed":25,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":2,"verified_exact":23,"verified_fuzzy":0},"total_outbound_references":25},"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":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"thesis":"As of 6 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 1 inbound Pith citation observation for arXiv:2606.07010."}