{"as_of":"2026-08-22T23:13:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c4a12625227c0ae87f4953bb5ab74b9d0020ba2aed968fe1da967cdac85e711c","coverage":[{"denominator":23,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":23,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T00:52:08.438132Z","state":"measured"},{"denominator":23,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":23,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-22T06:32:14.747728+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/2608.11553/citation-record","integrity":"/paper/2608.11553/integrity","json":"/paper/2608.11553/citation-record.json","paper":"/paper/2608.11553"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:52:08.327618Z","title":"Albritton, E","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.11553","last_updated":"2026-08-12T01:40:31Z","snapshot_observed_at":"2026-08-20T01:45:42.364588Z","submitted_at":"2026-08-12T01:40:31Z","title":"Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-16T00:52:08.327618Z"},"links":{"citing_paper":"/paper/2608.11553"},"observation_digest":"sha256:678bc8ab9e3e007bb100d8bb524128ad5e9e0ee72b178e4da5ab445d30141716","observation_id":"0ccb9a86-ac6c-40a9-8f96-a99784224dfd","resolution":{"observed_at":"2026-08-16T00:52:08.327618Z","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":"10.7494/opmath.202606031","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:52:08.666269Z","title":"Beir˜ ao da Veiga and J","venue":null,"work_id":"bf9cf4ed-b873-4fab-bd1d-4d17a4d7e0b5","year":2026},"citing_paper":{"arxiv_id":"2608.11553","last_updated":"2026-08-12T01:40:31Z","snapshot_observed_at":"2026-08-20T01:45:42.364588Z","submitted_at":"2026-08-12T01:40:31Z","title":"Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-16T00:52:08.333126Z"},"links":{"citing_paper":"/paper/2608.11553"},"observation_digest":"sha256:8930ca816afdae4ebd52636a28d52f1faddf43169e5889ebb02a0351e972e8d3","observation_id":"c080c8df-255b-43da-8c8a-0814196a1472","resolution":{"observed_at":"2026-08-16T00:52:08.670493Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.3934/dcds.2017081","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:52:08.652144Z","title":null,"venue":null,"work_id":"67695d7f-dea7-4261-b877-7de9f184e890","year":2017},"citing_paper":{"arxiv_id":"2608.11553","last_updated":"2026-08-12T01:40:31Z","snapshot_observed_at":"2026-08-20T01:45:42.364588Z","submitted_at":"2026-08-12T01:40:31Z","title":"Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-16T00:52:08.338196Z"},"links":{"citing_paper":"/paper/2608.11553"},"observation_digest":"sha256:51e6900aeab0d741cbc38306787f850a22061bbbc6133009602e02900dd787db","observation_id":"0bfee954-258f-4ca6-ad37-9b693e646537","resolution":{"observed_at":"2026-08-16T00:52:08.656270Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1093/imrn/rnn016","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:52:08.638031Z","title":null,"venue":null,"work_id":"f71ac668-4a47-4150-a86c-2c22b1d3fe4f","year":2008},"citing_paper":{"arxiv_id":"2608.11553","last_updated":"2026-08-12T01:40:31Z","snapshot_observed_at":"2026-08-20T01:45:42.364588Z","submitted_at":"2026-08-12T01:40:31Z","title":"Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-16T00:52:08.343303Z"},"links":{"citing_paper":"/paper/2608.11553"},"observation_digest":"sha256:9c25d55ffce45c9343213c087ccca75303586018b71fd388ea98f5dde0abbe2c","observation_id":"c1a3ddeb-3e37-4302-a3c9-ab8729e042f0","resolution":{"observed_at":"2026-08-16T00:52:08.642343Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1080/03605300902793956","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:52:08.622080Z","title":null,"venue":null,"work_id":"44b1e47d-a639-4a69-af87-210bfd42fb6e","year":2009},"citing_paper":{"arxiv_id":"2608.11553","last_updated":"2026-08-12T01:40:31Z","snapshot_observed_at":"2026-08-20T01:45:42.364588Z","submitted_at":"2026-08-12T01:40:31Z","title":"Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-16T00:52:08.348714Z"},"links":{"citing_paper":"/paper/2608.11553"},"observation_digest":"sha256:982d26dabbc2d248754390cffe8570c48acacd285ee3a297f7ca3ad2320ad379","observation_id":"20553a10-c61f-471f-97d3-4138ac962533","resolution":{"observed_at":"2026-08-16T00:52:08.626978Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T00:52:08.353582Z","title":"Escauriaza, G","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2608.11553","last_updated":"2026-08-12T01:40:31Z","snapshot_observed_at":"2026-08-20T01:45:42.364588Z","submitted_at":"2026-08-12T01:40:31Z","title":"Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-16T00:52:08.353582Z"},"links":{"citing_paper":"/paper/2608.11553"},"observation_digest":"sha256:21e2de92108bc679830782784f4d5211e469ea9f8e6b62a91167a0a7772f6cbd","observation_id":"b4463d8b-a3e2-43e2-8e7d-e7b1bd075e34","resolution":{"observed_at":"2026-08-16T00:52:08.353582Z","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/s00021-011-0078-6","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-18T11:03:46.223893Z","title":"Farwig, H","venue":"Journal of Mathematical Fluid Mechanics","work_id":"43e6175b-57fa-4fb1-942d-62854c7b640a","year":2012},"citing_paper":{"arxiv_id":"2608.11553","last_updated":"2026-08-12T01:40:31Z","snapshot_observed_at":"2026-08-20T01:45:42.364588Z","submitted_at":"2026-08-12T01:40:31Z","title":"Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-16T00:52:08.359155Z"},"links":{"citing_paper":"/paper/2608.11553"},"observation_digest":"sha256:f085e335a2cb4df55a1980f129a41d4ff0fae7523ec17cc31052e6beaba0059b","observation_id":"79a0511d-ce2f-454c-96d5-7a908f1eff4c","resolution":{"observed_at":"2026-08-16T00:52:08.601177Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1070/sm1982v043n02abeh002447","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:52:08.579644Z","title":null,"venue":null,"work_id":"27c85efb-590d-494a-bbd8-e071980fcd7e","year":1982},"citing_paper":{"arxiv_id":"2608.11553","last_updated":"2026-08-12T01:40:31Z","snapshot_observed_at":"2026-08-20T01:45:42.364588Z","submitted_at":"2026-08-12T01:40:31Z","title":"Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-16T00:52:08.363862Z"},"links":{"citing_paper":"/paper/2608.11553"},"observation_digest":"sha256:3dda9f5e40f52843a654fe70379e40641d1a6d2886e1f3bd95095b592494646f","observation_id":"e5fcac2d-cd51-4041-a319-c29afa19d213","resolution":{"observed_at":"2026-08-16T00:52:08.584801Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T00:52:08.981337Z","title":null,"venue":null,"work_id":"5700bcea-2703-4953-a04a-57ca0c85a0de","year":2000},"citing_paper":{"arxiv_id":"2608.11553","last_updated":"2026-08-12T01:40:31Z","snapshot_observed_at":"2026-08-20T01:45:42.364588Z","submitted_at":"2026-08-12T01:40:31Z","title":"Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-16T00:52:08.368682Z"},"links":{"citing_paper":"/paper/2608.11553"},"observation_digest":"sha256:937382174018197ec34c57906363df56d8109df970e16f29ad9f798ce3e7ee81","observation_id":"625caa14-908c-4850-bd46-29393e403b81","resolution":{"observed_at":"2026-08-16T00:52:08.986252Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2606.15189","last_updated":"2026-08-15T18:40:02Z","snapshot_observed_at":"2026-08-20T23:09:37.855933Z","submitted_at":"2026-06-13T08:34:21Z","title":"Blow-up and uniqueness of Leray-Hopf solutions to forced Navier-Stokes equations","version":4},"cited_work":{"arxiv_id":"2606.15189","doi":null,"metadata_source":"pith","pith_arxiv_id":"2606.15189","snapshot_observed_at":"2026-08-16T00:52:08.878053Z","title":"Blow-up and uniqueness of Leray-Hopf solutions to forced Navier-Stokes equations","venue":"math.AP","work_id":"2ad06e10-2806-4c8d-915c-fba6ba3fce11","year":2026},"citing_paper":{"arxiv_id":"2608.11553","last_updated":"2026-08-12T01:40:31Z","snapshot_observed_at":"2026-08-20T01:45:42.364588Z","submitted_at":"2026-08-12T01:40:31Z","title":"Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-16T00:52:08.373537Z"},"links":{"cited_paper":"/paper/2606.15189","citing_paper":"/paper/2608.11553"},"observation_digest":"sha256:e891a19a80148ac1ab1368ca61232e23c3682c3449c8d527d08d918b95550cfd","observation_id":"ad8f1383-4506-4d94-94ca-21282382c0b9","resolution":{"observed_at":"2026-08-16T00:52:08.886263Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T00:52:08.378555Z","title":"Giga,Solutions for semilinear parabolic equations in Lp and regularity of weak solutions of the Navier–Stokes system, J","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2608.11553","last_updated":"2026-08-12T01:40:31Z","snapshot_observed_at":"2026-08-20T01:45:42.364588Z","submitted_at":"2026-08-12T01:40:31Z","title":"Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-16T00:52:08.378555Z"},"links":{"citing_paper":"/paper/2608.11553"},"observation_digest":"sha256:da55e68022872c020cb7065b932aabbf9d0eeac77d941dd4031ea7b279f1956e","observation_id":"9d884a22-f41a-4fc8-a162-7c5399c4ed47","resolution":{"observed_at":"2026-08-16T00:52:08.378555Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-16T00:52:08.963560Z","title":"Hopf, ¨Uber die Anfangswertaufgabe f¨ ur die hydrodynamischen Grundgleichungen, Math","venue":null,"work_id":"e93befe6-bc1a-4fbf-bf91-901c0038944f","year":1951},"citing_paper":{"arxiv_id":"2608.11553","last_updated":"2026-08-12T01:40:31Z","snapshot_observed_at":"2026-08-20T01:45:42.364588Z","submitted_at":"2026-08-12T01:40:31Z","title":"Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-16T00:52:08.383686Z"},"links":{"citing_paper":"/paper/2608.11553"},"observation_digest":"sha256:4c513cae42b1c76c2f4173aee395b642527bbca91b3fe11c42f9f472edb2f206","observation_id":"697146c3-2910-40f7-a677-473f18876e8d","resolution":{"observed_at":"2026-08-16T00:52:08.969461Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s11511-009-","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:52:08.553198Z","title":null,"venue":null,"work_id":"1f6c77c4-b943-494f-b1f4-dd72d827f8ab","year":2009},"citing_paper":{"arxiv_id":"2608.11553","last_updated":"2026-08-12T01:40:31Z","snapshot_observed_at":"2026-08-20T01:45:42.364588Z","submitted_at":"2026-08-12T01:40:31Z","title":"Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-16T00:52:08.388644Z"},"links":{"citing_paper":"/paper/2608.11553"},"observation_digest":"sha256:8734684a029719086a88f47071b3b04126c8d1da657504e229ae387f3d92b54c","observation_id":"762c0e63-4843-402f-a40e-b76725b91112","resolution":{"observed_at":"2026-08-16T00:52:08.558193Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1524/anly.1996.16.3.255","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:52:08.536595Z","title":"Kozono and H","venue":null,"work_id":"34dbd01a-64d2-47b7-bf23-0c4a0a17e265","year":1996},"citing_paper":{"arxiv_id":"2608.11553","last_updated":"2026-08-12T01:40:31Z","snapshot_observed_at":"2026-08-20T01:45:42.364588Z","submitted_at":"2026-08-12T01:40:31Z","title":"Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-16T00:52:08.393436Z"},"links":{"citing_paper":"/paper/2608.11553"},"observation_digest":"sha256:365c636c78b850e1b60a38e744870252ea53da007ff4cf7de2f79d40b025c1d9","observation_id":"dc9b16a0-aeac-4521-9f05-6c6fc0ffc8be","resolution":{"observed_at":"2026-08-16T00:52:08.541994Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T00:52:08.946439Z","title":null,"venue":null,"work_id":"75febc4c-9992-40f6-966a-90a545d732c9","year":1969},"citing_paper":{"arxiv_id":"2608.11553","last_updated":"2026-08-12T01:40:31Z","snapshot_observed_at":"2026-08-20T01:45:42.364588Z","submitted_at":"2026-08-12T01:40:31Z","title":"Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-16T00:52:08.398453Z"},"links":{"citing_paper":"/paper/2608.11553"},"observation_digest":"sha256:f393c66ec188842e0dfbb868a611aa064225f8c72a563405b88d01fa981d328b","observation_id":"f0b4c0a2-70d2-4b2b-8892-ca358af964e8","resolution":{"observed_at":"2026-08-16T00:52:08.951615Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T00:52:08.403269Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.11553","last_updated":"2026-08-12T01:40:31Z","snapshot_observed_at":"2026-08-20T01:45:42.364588Z","submitted_at":"2026-08-12T01:40:31Z","title":"Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-16T00:52:08.403269Z"},"links":{"citing_paper":"/paper/2608.11553"},"observation_digest":"sha256:97b6f5a03a0ad968af502de122379daa4ab69f67aafa1a93d5c88ea87ff5577b","observation_id":"e73c386c-8736-4b77-a622-675a1b05dfaf","resolution":{"observed_at":"2026-08-16T00:52:08.403269Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:52:08.408026Z","title":"Leray,Sur le mouvement d’un liquide visqueux emplissant l’espace, Acta Math.63(1934), no","venue":null,"work_id":null,"year":1934},"citing_paper":{"arxiv_id":"2608.11553","last_updated":"2026-08-12T01:40:31Z","snapshot_observed_at":"2026-08-20T01:45:42.364588Z","submitted_at":"2026-08-12T01:40:31Z","title":"Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-16T00:52:08.408026Z"},"links":{"citing_paper":"/paper/2608.11553"},"observation_digest":"sha256:73a5c3360cc4c1aac6b6c1b72d0778ac5f5d64a61c026914b727dc1b12fe6d50","observation_id":"469aec9d-a40f-4333-9501-d64ae575727c","resolution":{"observed_at":"2026-08-16T00:52:08.408026Z","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/bf02551584","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-18T11:03:46.223893Z","title":"Neˇ cas, M","venue":"Acta Mathematica","work_id":"840ac451-9d7c-4c20-9d49-9f0166505be0","year":1996},"citing_paper":{"arxiv_id":"2608.11553","last_updated":"2026-08-12T01:40:31Z","snapshot_observed_at":"2026-08-20T01:45:42.364588Z","submitted_at":"2026-08-12T01:40:31Z","title":"Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-16T00:52:08.413175Z"},"links":{"citing_paper":"/paper/2608.11553"},"observation_digest":"sha256:f9eb9f395b6cb7974a80bef09b5b25a201da19b519fcb32030c4637478e50d74","observation_id":"7b730eb2-8e5d-45b0-b2a9-59b350a00bea","resolution":{"observed_at":"2026-08-16T00:52:08.512820Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jde.2016.02.026","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:52:08.489507Z","title":"Pan,Regularity of solutions to axisymmetric Navier–Stokes equations with a slightly supercritical condition, J","venue":null,"work_id":"90427efa-50a4-4619-b30d-229822da0edb","year":2016},"citing_paper":{"arxiv_id":"2608.11553","last_updated":"2026-08-12T01:40:31Z","snapshot_observed_at":"2026-08-20T01:45:42.364588Z","submitted_at":"2026-08-12T01:40:31Z","title":"Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-16T00:52:08.417876Z"},"links":{"citing_paper":"/paper/2608.11553"},"observation_digest":"sha256:dc06136c510efd431eadc5b282a49a375a84c011b39cb2b713e74be557c15d57","observation_id":"86d8f844-aa8a-46e7-9f37-2ba21c1875ec","resolution":{"observed_at":"2026-08-16T00:52:08.496018Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T00:52:08.929391Z","title":"Serrin,The initial value problem for the Navier–Stokes equations, in: Nonlinear Problems (Proc","venue":null,"work_id":"7df3fa7d-e75f-45af-ba57-3cfce3f2de17","year":1962},"citing_paper":{"arxiv_id":"2608.11553","last_updated":"2026-08-12T01:40:31Z","snapshot_observed_at":"2026-08-20T01:45:42.364588Z","submitted_at":"2026-08-12T01:40:31Z","title":"Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-16T00:52:08.423105Z"},"links":{"citing_paper":"/paper/2608.11553"},"observation_digest":"sha256:aa7aec1d328c0f93fc60c5b3b02858162b543872e972dcce862ccdfb98e99a52","observation_id":"91ae162a-777a-422e-9cdd-f86354b10f33","resolution":{"observed_at":"2026-08-16T00:52:08.935074Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T00:52:08.912682Z","title":"Sohr,The Navier–Stokes Equations: An Elementary Functional Analytic Approach, Birkh¨ auser Advanced Texts, Birkh¨ auser, Basel, 2001","venue":null,"work_id":"442b70b7-be6b-4256-b10d-4fa625e4c525","year":2001},"citing_paper":{"arxiv_id":"2608.11553","last_updated":"2026-08-12T01:40:31Z","snapshot_observed_at":"2026-08-20T01:45:42.364588Z","submitted_at":"2026-08-12T01:40:31Z","title":"Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-16T00:52:08.428143Z"},"links":{"citing_paper":"/paper/2608.11553"},"observation_digest":"sha256:f288ab9f601f7e680433815fb02e2ddf41c8c17bc346d590a00b09cd2c294b79","observation_id":"0097e3f6-80d4-4187-941a-f9a0eb8a40de","resolution":{"observed_at":"2026-08-16T00:52:08.917382Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T00:52:08.897571Z","title":null,"venue":null,"work_id":"92d1d562-e712-4c40-9489-284200cc21a2","year":1973},"citing_paper":{"arxiv_id":"2608.11553","last_updated":"2026-08-12T01:40:31Z","snapshot_observed_at":"2026-08-20T01:45:42.364588Z","submitted_at":"2026-08-12T01:40:31Z","title":"Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-16T00:52:08.432714Z"},"links":{"citing_paper":"/paper/2608.11553"},"observation_digest":"sha256:eb682123b23b1c808c86c116d83afa5909a6467f265244c923d0c57e4f12bbb7","observation_id":"544d8c0b-4855-4a0c-8175-c04d3b526d62","resolution":{"observed_at":"2026-08-16T00:52:08.902198Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4208/jms.v58n4.25.02","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:52:08.471583Z","title":null,"venue":null,"work_id":"3d1dd709-1b2e-481b-86e7-361c3bf5f235","year":2025},"citing_paper":{"arxiv_id":"2608.11553","last_updated":"2026-08-12T01:40:31Z","snapshot_observed_at":"2026-08-20T01:45:42.364588Z","submitted_at":"2026-08-12T01:40:31Z","title":"Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-16T00:52:08.438132Z"},"links":{"citing_paper":"/paper/2608.11553"},"observation_digest":"sha256:2fddc196fba0b89f42bb2111ef893d896c380f19216d40c3ceb160624dd629b8","observation_id":"f0a6905b-cf44-458d-bcb6-290090b603b1","resolution":{"observed_at":"2026-08-16T00:52:08.477434Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2608.11553","last_updated":"2026-08-12T01:40:31Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-20T01:45:42.364588Z","submitted_at":"2026-08-12T01:40:31Z","title":"Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges"},"reference_resolution":{"displayed":23,"state_counts":{"malformed_identifier":2,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":7,"verified_exact":11,"verified_fuzzy":3},"total_outbound_references":23},"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":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"thesis":"As of 22 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 0 inbound Pith citation observations for arXiv:2608.11553."}