{"as_of":"2026-08-16T20:20:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:b82ba80bc1cc3e63284593c3c4c8e1e8d600d204b76065227dab491835d75837","coverage":[{"denominator":45,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":45,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T11:46:13.371209Z","state":"measured"},{"denominator":45,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":45,"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/1908.08512/citation-record","integrity":"/paper/1908.08512/integrity","json":"/paper/1908.08512/citation-record.json","paper":"/paper/1908.08512"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:46:14.008536Z","title":"Hyperboloidal similarity coor- dinates and a globally stable blowup profile for supercritic al wave maps","venue":null,"work_id":"b5eaac6b-aa0a-46c5-8ce8-f4e7bdad7c91","year":2017},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.176029Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:38f2c65cc4830262320d4d9847d693a8e1e9def1a9d04a715de737eaa3851896","observation_id":"094bf05b-c985-49a3-b039-be765f9c7ea1","resolution":{"observed_at":"2026-08-14T11:46:14.012756Z","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":"2026-08-14T11:46:13.996504Z","title":"Bourgain and W","venue":null,"work_id":"088f1585-f6a2-424f-a4b2-90878ab90121","year":1997},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.182029Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:7bb8870bcb95afd8e6a0ad438d700ec4465a1a93dc73963b54abfd05242ed1b8","observation_id":"e018a228-a375-47cc-8420-f7f30159bf96","resolution":{"observed_at":"2026-08-14T11:46:14.000609Z","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":"2026-08-14T11:46:13.985124Z","title":null,"venue":null,"work_id":"2369b45a-fc71-4fa6-886f-b93bd7e40bc6","year":2005},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.186653Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:2c79cec3abcf863283faf51def71fd767d36c3dd1600da5605bd24eddb6a18bc","observation_id":"9055b6b5-2570-45aa-9aae-247694fbd77c","resolution":{"observed_at":"2026-08-14T11:46:13.989240Z","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":"2026-08-14T11:46:13.971806Z","title":"Characterization of large energy solutions of the equivariant wave map problem: I","venue":null,"work_id":"1677f991-d810-49bd-b3fe-eb40c83485d9","year":2015},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.192162Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:1449c4d6badfed4e69940a4d9552c1b85ebc1585c9feb09e5e0cf5fbfe0fa9a3","observation_id":"a1170f44-177d-46cd-9c45-6dc19995466a","resolution":{"observed_at":"2026-08-14T11:46:13.976369Z","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":"2026-08-14T11:46:13.960570Z","title":"Universality of blow up profile for small blow up solutions to the energy critical wave map eq uation","venue":null,"work_id":"262a898b-231d-426d-b92f-8baf1bee7951","year":2018},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.196732Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:5b2ea4cacf7867392294a055292e7cfdce1a30a9e92d23c1c03104308fcfad55","observation_id":"52e60d49-647d-41e8-8189-ce02200281ec","resolution":{"observed_at":"2026-08-14T11:46:13.964665Z","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":"2026-08-14T11:46:13.948481Z","title":"Optimal polynomial blow up r ange for critical wave maps","venue":null,"work_id":"3c510575-eb85-4200-be45-f6604b762bba","year":2015},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.201272Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:a87224d2f1415f7d188bb270eebaf2a87e8de76fce6a1463d4ee17b8eb9371aa","observation_id":"e17d2242-bc42-46c3-bfde-b311e9f994d9","resolution":{"observed_at":"2026-08-14T11:46:13.952835Z","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":"2026-08-14T11:46:13.936569Z","title":"Grillakis","venue":null,"work_id":"d5f6e5ea-6ed3-4878-ac1c-cb0803ebd636","year":2017},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.205858Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:07140e9e4aa0e1c5fe1ff3695eb7ce40b15f78ef0d4c67d4e011f01d8dadab52","observation_id":"8622fe17-2bdc-4b66-a9da-fb59137e0337","resolution":{"observed_at":"2026-08-14T11:46:13.940392Z","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":"2026-08-14T11:46:13.923661Z","title":null,"venue":null,"work_id":"16f0ef08-16b1-42de-825c-266e0d0735cf","year":2015},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.209838Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:54104fa44689f8c7aec128afda13d9a3c5a211b2a965aeb529cb971339d303f2","observation_id":"a0a5d2b5-e6ef-47d9-b752-2ad88facb469","resolution":{"observed_at":"2026-08-14T11:46:13.928038Z","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":"2026-08-14T11:46:13.909332Z","title":null,"venue":null,"work_id":"dd7eede2-76fa-4d5a-b39b-3cdc4f4d39a6","year":1923},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.214023Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:179947670b1ca3ec8161a1c24667ec2ba12bcd79c3890868664c427f8debfc52","observation_id":"1f10c97e-ff17-4963-9f18-9293a8c04098","resolution":{"observed_at":"2026-08-14T11:46:13.913480Z","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":"2026-08-14T11:46:13.895817Z","title":null,"venue":null,"work_id":"7a18f7e0-c7c0-41d2-836c-5dfe2cc26a20","year":2017},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.218343Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:91ed44c1f9289b0b5665103adf53db897f2975a55c2e36e04cb9d6f6ec0d6a63","observation_id":"6d9fcab0-d41c-48be-816f-252f6e912f37","resolution":{"observed_at":"2026-08-14T11:46:13.900291Z","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":"2026-08-14T11:46:13.879633Z","title":"Dynamics of strongly interacting unsta ble two-solitons for generalized korteweg-de vries equations","venue":null,"work_id":"36dc6276-4309-45c8-89b7-7ac9582a1e0d","year":2018},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.222300Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:07e1d6a3f28ba0d01055869d2ee6140f6e3a0542a2a6a19e0a80f63875f0c4aa","observation_id":"c7738346-af89-418e-81df-1d63037f5a60","resolution":{"observed_at":"2026-08-14T11:46:13.884620Z","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":"2026-08-14T11:46:13.864569Z","title":"Construction of two-bubble solutions for energy-critical wave equations","venue":null,"work_id":"9ed6fbcb-8006-48c9-8d8a-a2bd3298c8fe","year":2019},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.226646Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:f03aa8632ee5df27bea3bb47bcecd742083c8b4d5585aafd03c9fd304b7b815f","observation_id":"1dbb4efd-3599-42ca-9d68-d5de6944a262","resolution":{"observed_at":"2026-08-14T11:46:13.869182Z","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":"2026-08-14T11:46:13.850640Z","title":"Two-bubble dynamics f or threshold solutions to the wave maps equation","venue":null,"work_id":"88d2daa0-df04-4548-96ad-47cf8d794720","year":2018},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.230609Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:7d764de9c31d0cdeaf325905f9a3836c74a0ab9f1e2a48f20059c74f51fdbadf","observation_id":"f8028775-d755-49f0-8fc3-0719b3712265","resolution":{"observed_at":"2026-08-14T11:46:13.855139Z","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":"2026-08-14T11:46:13.836730Z","title":"Asymptotic decomposition for semilinear wave and equivariant wave map equations","venue":null,"work_id":"f5db79fc-f925-4c2a-aaa1-ae6ef2936bda","year":2017},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.234545Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:06f68cc09df38fa1a6d97dfc8cd8ca04d69dac82fa787820d932b31f58bb02e3","observation_id":"1e7e4d6b-0706-437c-8556-c7ccb933094a","resolution":{"observed_at":"2026-08-14T11:46:13.841261Z","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":"2026-08-14T11:46:13.822047Z","title":"Krieger, W","venue":null,"work_id":"7f25e290-87db-4ea7-9c1e-bc4013a06b3d","year":2008},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.238252Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:66698c0b881e6039a789a9986cd31ca0666149f52dec316916f029a87f64f463","observation_id":"502b809c-bae4-4fbb-9ccb-4a93fd04abaa","resolution":{"observed_at":"2026-08-14T11:46:13.826820Z","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":"2026-08-14T11:46:13.803500Z","title":"On stability of blow up solutions for the critical co- rotational wave maps problem","venue":null,"work_id":"e6bd828a-7a39-4c53-a584-8ce7e0fc2134","year":2018},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.242779Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:8420182ad5a0688df25da2873b68114f643bb27f7ec24d9186e56a3ec7b6cf00","observation_id":"c80e5c96-bb78-4911-84cd-673e73a6bd9d","resolution":{"observed_at":"2026-08-14T11:46:13.808232Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:46:13.246465Z","title":"Manton and P","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.246465Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:f3250532b6c8f1315e71645580ae4cd09eae84c0ae07707c5af3657d03555d37","observation_id":"cee5a5f0-e2aa-4b7e-8103-8082986dbe30","resolution":{"observed_at":"2026-08-14T11:46:13.246465Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:46:13.781360Z","title":null,"venue":null,"work_id":"812d7496-3598-4a1c-b9ec-56346e06f496","year":2005},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.250314Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:2ad730d27aba07f92c950e8b6a04fc5452f5ff18aac92da0a6e401a0175b405d","observation_id":"96e78e89-3ecc-49ef-a01d-a030d034830b","resolution":{"observed_at":"2026-08-14T11:46:13.785442Z","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":"2026-08-14T11:46:13.768266Z","title":"Martel, F","venue":null,"work_id":"01b2c3fb-c19a-4815-8386-5978eafccf4d","year":2014},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.254273Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:572eee0f0f9fc8f9bb3deef0178e305f1e5c19f7da26b9e043bd77ebaf336c06","observation_id":"5c600981-1ab2-4a21-b9b9-0b5eb8f80520","resolution":{"observed_at":"2026-08-14T11:46:13.772568Z","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":"2026-08-14T11:46:13.755077Z","title":"Martel, F","venue":null,"work_id":"30f0dcff-680d-4e32-bf3a-db1f70f36781","year":1925},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.258392Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:adb10ef8b87ad05cb47af8e5dcf349fd020efbae9d9fbc2559f149c5ad4ee076","observation_id":"b0f7cfe9-7f0c-483a-adaa-0a52c6420fcb","resolution":{"observed_at":"2026-08-14T11:46:13.759149Z","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":"2026-08-14T11:46:13.741642Z","title":"Martel, F","venue":null,"work_id":"e267c0c4-3d60-4400-95f8-50eebbbc61ad","year":2015},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.262511Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:ad73dae1190153dfc1e565e36e09aba2c101c081b63e233cf513935b3ae896c7","observation_id":"629c978f-095c-4900-b183-370c53d9c9ad","resolution":{"observed_at":"2026-08-14T11:46:13.745918Z","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":"2026-08-14T11:46:13.727679Z","title":"Blow up and near soliton dynamics for the L2 critical gKdV equation","venue":null,"work_id":"6662ed82-5f14-436f-9bbe-92ab39e1ee82","year":2011},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.266482Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:86b6eb09af7a1a8854fcb0f85ab26566e04ca69f9dcafd1b312713bd5fe3cb6a","observation_id":"dab7c563-076e-4dbe-9944-90410def07a3","resolution":{"observed_at":"2026-08-14T11:46:13.732745Z","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":"2026-08-14T11:46:13.714370Z","title":null,"venue":null,"work_id":"26ece445-bbca-442a-a981-decab4237696","year":2013},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.270477Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:edc250f247bb5138a3d34e1fa3cabe496fefd4df663465066d044f5520d99a44","observation_id":"a2ed8624-56e2-4cdc-9176-6503adb48914","resolution":{"observed_at":"2026-08-14T11:46:13.718478Z","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":"2026-08-14T11:46:13.701413Z","title":"Blow up for the critical generalized Korteweg– de Vries equation","venue":null,"work_id":"b7f277b4-a0f0-45a0-8e5e-23e9910ae962","year":2014},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.274139Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:1829a937f99322bb347f50174f8d02566ee76d7812e47f13fdd4ed10172e222d","observation_id":"f336b449-c0b7-44c5-bbd6-09204a717f82","resolution":{"observed_at":"2026-08-14T11:46:13.705627Z","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":"2026-08-14T11:46:13.686698Z","title":"Blow up for the critical gKdV equation","venue":null,"work_id":"5166635f-f0df-4809-9fb4-c435a0633e14","year":1925},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.277996Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:bcb403452f37d2c32433be838dfab3c23d344a0a3c4579b2f0db639ba9cd0a27","observation_id":"ceee7f49-e6b1-4bd7-96a9-fa875fa0ef11","resolution":{"observed_at":"2026-08-14T11:46:13.691479Z","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":"2026-08-14T11:46:13.672468Z","title":"Blow up for the critical gKdV equation III: exotic regimes","venue":null,"work_id":"4a450d09-7c47-45c8-bdcc-86028fb373f0","year":2015},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.282215Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:41aa271f8ec719f3480460aabb970877a5ef2c6128fff2d5def641caba6e0173","observation_id":"56062c91-c668-41ff-b688-6690f781cd75","resolution":{"observed_at":"2026-08-14T11:46:13.676789Z","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":"2026-08-14T11:46:13.659099Z","title":null,"venue":null,"work_id":"dd5b9013-f9df-44f6-aed6-cf014d53e6d3","year":1990},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.286573Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:9e3c1a4708989d48967972ec173be327f67d3f0bfb058ceaa4a83a7497f52493","observation_id":"5eaacbc9-3805-4721-ba56-a31fa9154d68","resolution":{"observed_at":"2026-08-14T11:46:13.663577Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:46:13.290764Z","title":null,"venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.290764Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:b6fae2d3fbac3dbe575652bfcb62ccf5900f2bd6d0898fe8271ef1ba5bddf144","observation_id":"4bbe6042-d55c-444f-aa8a-5ef087342506","resolution":{"observed_at":"2026-08-14T11:46:13.290764Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:46:13.635773Z","title":"Merle and P","venue":null,"work_id":"93c62d3a-4a58-4077-b33b-95198413d070","year":2003},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.295060Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:6ab0c56dba2635a0a46a603cb5f84ba966dc66598a81a41d682110e417c15a98","observation_id":"7ed97a5c-449a-4762-93da-d12157399a00","resolution":{"observed_at":"2026-08-14T11:46:13.640026Z","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":"2026-08-14T11:46:13.622413Z","title":"Merle and P","venue":null,"work_id":"4ea4ddb9-d105-4e4d-baa6-a67048f1910c","year":2005},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.300030Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:e9cc8c1657f0594a7ee278c58c894e8a57711070d6b6614825f942525c982799","observation_id":"42abe450-9791-4110-b18e-5231644d6136","resolution":{"observed_at":"2026-08-14T11:46:13.626772Z","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":"2026-08-14T11:46:13.608211Z","title":"Merle, P","venue":null,"work_id":"252b7da8-5b63-4e8f-8808-2d2e124de026","year":2013},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.305775Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:02ce22c5e3f275833e58f3a97bd981555295e28b306583d5272b40e76bd59885","observation_id":"05c94171-c11b-47ab-b005-616ce88776ce","resolution":{"observed_at":"2026-08-14T11:46:13.613248Z","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":"2026-08-14T11:46:13.594523Z","title":"On universality of blow -up profile for L2 critical nonlinear Schr¨ odinger equation.Invent","venue":null,"work_id":"d50abc2d-b1e8-4eee-aebb-624873d04168","year":2004},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.310032Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:f83cfd86bcdf8a3993d7cdb86c905ad99abea4bdbd25ff5a96a7ca09c1451ccd","observation_id":"01a8a28b-ecf2-4064-803d-2dba652f00a9","resolution":{"observed_at":"2026-08-14T11:46:13.598937Z","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":"2026-08-14T11:46:13.580581Z","title":"The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schr¨ odinger equation.Ann","venue":null,"work_id":"8ba90e95-10c0-46f9-b30d-b272792231f4","year":2005},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.314105Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:09b08fe05de5accd1a38b254ebe8280b8d06952a520e6d7ae6f181ec1ff17dfd","observation_id":"5498c318-9f26-49f8-bb28-212575a09e24","resolution":{"observed_at":"2026-08-14T11:46:13.585122Z","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":"2026-08-14T11:46:13.565870Z","title":"Profiles and quantizati on of the blow up mass for critical nonlinear Schr¨ odinger equation.Comm","venue":null,"work_id":"18e7c255-c793-406c-90ce-aaa5022e1d73","year":2005},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.318744Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:6bac298146915936176c157b82da6edce9084f126c35c53a0b2cffaa36f4644c","observation_id":"d1cda535-210f-4c07-94a6-605dfd911938","resolution":{"observed_at":"2026-08-14T11:46:13.570488Z","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":"2026-08-14T11:46:13.550846Z","title":"On a sharp lower bound on the blow-up rate for the L2 critical nonlinear Schr¨ odinger equation.J","venue":null,"work_id":"8cca887c-b5b4-4409-a5d8-74ac9c9deac4","year":2006},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.323901Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:baddeea9516d445686eca0523fd51890493d2dd97bf46047a53513f48afc4e91","observation_id":"12025a94-2514-42a1-9769-03bfebd619b9","resolution":{"observed_at":"2026-08-14T11:46:13.555602Z","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":"2026-08-14T11:46:13.536950Z","title":"Rapha¨ el and I","venue":null,"work_id":"2ca0b7d3-fbec-4eff-a5f5-ca36ee9595ae","year":2012},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.328774Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:11e48792748f706d410deec93e15a710b5634bae1c0cd8669e1cb6f9a7a561db","observation_id":"3a429d97-dd97-4e68-b067-2ce93dc3de48","resolution":{"observed_at":"2026-08-14T11:46:13.540995Z","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":"2026-08-14T11:46:13.522945Z","title":"Rapha¨ el and J","venue":null,"work_id":"1a8c7362-8e43-4a24-a658-ae3f9afa2614","year":2011},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.333753Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:0f3983872cd90956da123fac06e6cecb81b82cc6f105f7728d988cd8b19d7aad","observation_id":"2f18e794-9aa9-40aa-affc-d8f65329b0ac","resolution":{"observed_at":"2026-08-14T11:46:13.527626Z","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":"2026-08-14T11:46:13.507920Z","title":"Rodnianski and J","venue":null,"work_id":"a5846e4b-cf50-41a9-b2e9-1fb5d18c0452","year":2010},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.338295Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:5e6832763eede5a08f176c88bac34b665a99ff317c252087ebbe9a3cd61e80df","observation_id":"df73d9dc-1796-4e47-b122-ee852fc04086","resolution":{"observed_at":"2026-08-14T11:46:13.512921Z","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":"2026-08-14T11:46:13.493345Z","title":"Threshold dynamics for corotational wave maps","venue":null,"work_id":"ea43e004-6afc-483d-95d1-11f070df6649","year":2018},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.343276Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:5b7eb119c1207440f3b1ba89b8cc08e2726c68bd83b35bfbc64e7d3f2a66eeda","observation_id":"2add3d54-9be2-4300-8959-891f4399e97c","resolution":{"observed_at":"2026-08-14T11:46:13.498160Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:46:13.348073Z","title":"Shatah and M","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.348073Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:40fad2a17617e42b8cd664840ee9ba145132e7b3d8a3a77fd10a2ea33a63360a","observation_id":"0757b0ce-1101-4638-97aa-537d09105406","resolution":{"observed_at":"2026-08-14T11:46:13.348073Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:46:13.464373Z","title":"Shatah and A","venue":null,"work_id":"72b1755e-3dfa-4f68-95c8-ebe3ada9fe31","year":1994},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.352892Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:97005b9fbbcf8e79adce2bc1547a6c7eeb7efa7d352f0426c9f8f1c828c8f06d","observation_id":"6fc42649-63fb-4f04-b583-6c2bbba1a7f0","resolution":{"observed_at":"2026-08-14T11:46:13.468908Z","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":"2026-08-14T11:46:13.450549Z","title":null,"venue":null,"work_id":"f44630b6-ca59-4b89-9b44-ec54c04ba33a","year":2003},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.357969Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:744128614eb61a78a10b178bcddadf96b8843d1d71eb50124ea8ea2e3bbd76fd","observation_id":"6e90f623-0cfb-4875-86d7-36767665f914","resolution":{"observed_at":"2026-08-14T11:46:13.454957Z","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":"2026-08-14T11:46:13.435093Z","title":"Uniqueness for critical nonlinear wav e equations and wave maps via the energy inequality","venue":null,"work_id":"6361e9c7-35b1-4b2d-865e-a12a3cf50e96","year":1999},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.362649Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:08f772f9c926de644843769b8bf28a017179a51cbce5cb974c6109c53a05f03f","observation_id":"dc01b435-cd39-493a-b43b-9e5037257a9e","resolution":{"observed_at":"2026-08-14T11:46:13.440172Z","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":"2026-08-14T11:46:13.419892Z","title":"Reverse bubbling and nonuniqueness in t he harmonic map flow","venue":null,"work_id":"aa7ebd27-de68-45e6-81c0-255c1153d8ea","year":2002},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.366781Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:a0bc0f01dfff2839b81cd474e20899883979226af9e0117887150fa8469f3e44","observation_id":"5256b8a8-ca57-4e5c-a27d-a76a24104586","resolution":{"observed_at":"2026-08-14T11:46:13.425358Z","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":"2026-08-14T11:46:13.403333Z","title":null,"venue":null,"work_id":"0def664b-4249-45b1-aa4f-b5bdc0cf81b8","year":2013},"citing_paper":{"arxiv_id":"1908.08512","last_updated":"2019-08-22T17:39:23Z","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-14T11:46:13.371209Z"},"links":{"citing_paper":"/paper/1908.08512"},"observation_digest":"sha256:279a17bb319d08782a6e47f8b86a5cd21b53c1003b245107c40d77d1c378ae77","observation_id":"e530545a-727d-49d1-a8e7-4a0b9f81362f","resolution":{"observed_at":"2026-08-14T11:46:13.409482Z","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":"1908.08512","last_updated":"2019-08-22T17:39:23Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-16T08:17:48.556401Z","submitted_at":"2019-08-22T17:39:23Z","title":"Dynamics of Bubbling Wave Maps with Prescribed Radiation"},"reference_resolution":{"displayed":45,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":12,"verified_exact":0,"verified_fuzzy":33},"total_outbound_references":45},"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 45 of 45 outbound references and 0 inbound Pith citation observations for arXiv:1908.08512."}