{"as_of":"2026-08-12T21:42:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:3170b654641eb75ea2baba6f31b20f9caf6eb04c64ff9647ddfed07f2c49c30f","coverage":[{"denominator":65,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":65,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T15:51:21.160293Z","state":"measured"},{"denominator":67,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":67,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T21:22:41.913031Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-11T07:26:02.562240Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"cited_work":{"arxiv_id":"2412.10725","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2412.10725","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Qin and J","venue":null,"work_id":"08b57c15-226a-459f-b999-c078fada79bb","year":2024},"citing_paper":{"arxiv_id":"2604.09546","last_updated":"2026-04-10T17:59:11Z","snapshot_observed_at":"2026-07-06T22:58:25.877654Z","submitted_at":"2026-04-10T17:59:11Z","title":"Clustered vortex helices with compactly supported cross-sectional vorticity in the 3D Euler equations","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-05-10T17:11:04.356713Z"},"links":{"cited_paper":"/paper/2412.10725","citing_paper":"/paper/2604.09546"},"observation_digest":"sha256:2b438dcbc899162866cdca1be4cd2cc6eab68ea3b42591b8dd8476c231414a89","observation_id":"47675cfc-29e5-47bc-8fcf-e7b08146761d","resolution":{"observed_at":"2026-05-11T07:26:02.564811Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.10725","snapshot_observed_at":"2026-08-01T21:22:41.913031Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.16141","last_updated":"2026-07-17T17:22:07Z","snapshot_observed_at":"2026-08-09T19:38:27.045995Z","submitted_at":"2026-07-17T17:22:07Z","title":"Piecewise smooth stationary Euler flows with support in a neighborhood of a helix","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-01T21:22:41.913031Z"},"links":{"cited_paper":"/paper/2412.10725","citing_paper":"/paper/2607.16141"},"observation_digest":"sha256:a7409fb0e57a3229cd55b84f9a193f0707ca5b9f1a3b846cfd9c2a311929d8dc","observation_id":"cb938f55-b31d-48d2-b914-d20c0b91ca19","resolution":{"observed_at":"2026-08-01T21:22:41.913031Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2412.10725/citation-record","integrity":"/paper/2412.10725/integrity","json":"/paper/2412.10725/citation-record.json","paper":"/paper/2412.10725"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:51:22.772055Z","title":"Abe, Existence of vortex rings in Beltrami flows","venue":null,"work_id":"cfb8a707-b72d-483c-88d7-dcbfcc741012","year":2022},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.597701Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:0dc081bcde569f27e3d08bcff3d43ae57de0ec741bccf6b1ff40f896e89e53f8","observation_id":"3f7b576e-8468-4585-b5b4-4fca9dcdea37","resolution":{"observed_at":"2026-08-11T15:51:22.778422Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.750837Z","title":"Abidi and S","venue":null,"work_id":"9b38fe83-893b-4780-a2de-33425eaf71e8","year":2016},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.606117Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:e615ff84d8da3416d892511675b44a178d2fe759b74f30dfbf01afca7f873e3f","observation_id":"75b3fdc7-bdc4-4e04-ac1c-97aa71f80b05","resolution":{"observed_at":"2026-08-11T15:51:22.757491Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.726897Z","title":null,"venue":null,"work_id":"f57023c4-b8f5-4d5a-bd32-e932ecfe0681","year":2022},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.613228Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:9fde4f0f5b2a123efc09418de2142a340bef8f984bdae70dd7b33fac8544c055","observation_id":"e79b38ef-83b8-4c3f-b908-20c54df6075e","resolution":{"observed_at":"2026-08-11T15:51:22.734698Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.708727Z","title":"Arms and F.R","venue":null,"work_id":"19bfa4e6-75af-48fa-aa1d-2342a3d0eba5","year":1965},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.623851Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:9e57517f6bb92394b2687a2ff1f60d2797f75c285fc7576a93665aac7314ac25","observation_id":"643f9e99-5ed2-4198-b1fe-5469119ef4d4","resolution":{"observed_at":"2026-08-11T15:51:22.714510Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.689530Z","title":"Bronzi, M.C","venue":null,"work_id":"f8b0ea0d-7f3b-438d-9101-c843869acf44","year":2015},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.633326Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:5beaf9dbbf3d972ee5404749dd6db76458a9048d238a54d389c7b6b2ffc5d458","observation_id":"0ec2e97a-bfdf-47c9-826b-19979d47ee27","resolution":{"observed_at":"2026-08-11T15:51:22.696157Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.667710Z","title":"Burchard and Y","venue":null,"work_id":"bdbd74c3-b8d8-46f9-b282-dd52b3dab9d1","year":2004},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.652737Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:d5f196ec026fc80ccfa386e916dcf581f470c87465d856745bcef65e9e8c729e","observation_id":"675ca8bd-c7a2-464d-a659-a74dd7099458","resolution":{"observed_at":"2026-08-11T15:51:22.672703Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.648519Z","title":"Caffarelli and A","venue":null,"work_id":"b0cc07f7-c730-4cb4-a58d-289d97b9bff0","year":1980},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.667406Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:e728dfc2f9cd140c642abebbeb5cbfe9c9a77f004ad91a85a7b16c1d448e0c1e","observation_id":"5484b2ca-6033-4047-aba1-1efd506a9582","resolution":{"observed_at":"2026-08-11T15:51:22.655169Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.630603Z","title":null,"venue":null,"work_id":"2b332475-c8a3-48b8-a575-023b59da7099","year":2024},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.673848Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:27e4f524103bc901fc9d35aa4fbdfc49f36a596bc72c8cd7e56240f8a6f5017b","observation_id":"a3e46abe-6879-4518-9967-151200c06cdb","resolution":{"observed_at":"2026-08-11T15:51:22.635756Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.611091Z","title":"Cao and S","venue":null,"work_id":"a2d374b8-65a1-48d3-a41a-3f2ba3a55836","year":2023},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.684074Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:adf25c9fec1fe9d6a03c50a74898fc99724598d866b6015db44f21bdedce3ff7","observation_id":"b24188f5-c8c0-42ba-b6e1-441d18b38656","resolution":{"observed_at":"2026-08-11T15:51:22.617293Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.588533Z","title":null,"venue":null,"work_id":"7a58d82b-2bd4-42b3-9270-dfec90a89511","year":null},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.693669Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:bd540010024c81f58a8552b7701c881b1655124a7fc2a4e69a05f085614e244d","observation_id":"cba2a55b-c181-47e9-92af-c0c88b3a58b9","resolution":{"observed_at":"2026-08-11T15:51:22.594475Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.561560Z","title":null,"venue":null,"work_id":"078da99f-6fb8-4729-8211-a830e9b18859","year":2014},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.699406Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:392a518abb960104454ed35acb88eaa53e36083af1be7b652be617c7a76c3cbd","observation_id":"3e065482-6824-4ad0-b36d-886bfc40afc5","resolution":{"observed_at":"2026-08-11T15:51:22.570988Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.540455Z","title":null,"venue":null,"work_id":"620f5a3f-9d0b-4562-ab72-05b8c4fb39f0","year":2015},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.709209Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:8f5da36c3e17bd3d1379d4a141d91f10d5a4edfc535ac9602d79d34ec46e2d09","observation_id":"3ac3fa03-70df-4188-a34a-6c9a17821a6e","resolution":{"observed_at":"2026-08-11T15:51:22.547256Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.520631Z","title":"Cao and J","venue":null,"work_id":"c4e0fde6-b204-4027-b51f-2a5ac84c33f9","year":2023},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.717675Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:4b81285710de2f72deef110fa18551f7afe0720c16c22b1264f2de2bf1481edf","observation_id":"4528135e-fd43-40db-80a5-b49a4240f85c","resolution":{"observed_at":"2026-08-11T15:51:22.525851Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.499099Z","title":"Cao and J","venue":null,"work_id":"f25931a4-9303-42c7-96ed-d842777d6431","year":2024},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.726946Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:b8eb82957dc44f73007d9739a78570d68ee53886d256ed72fc6764c47ee515e2","observation_id":"c62ef2d4-9200-459d-a24b-ba8a0684e271","resolution":{"observed_at":"2026-08-11T15:51:22.505395Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.477383Z","title":null,"venue":null,"work_id":"9043e87a-0276-4bab-a94b-514567fa01bf","year":2022},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.735753Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:52a2dc1dc2cb9296866d9de1493fcf8b75ca893e6ba0e2d2a6ff4edb456ecb76","observation_id":"81d7f330-9413-43a0-a33f-b06eb239ac56","resolution":{"observed_at":"2026-08-11T15:51:22.484558Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.456227Z","title":"Cao and W","venue":null,"work_id":"e140156f-b9cd-4aa1-b38f-569c86eb63ce","year":null},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.745061Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:1328d68f128e4c677b36cfe06c32e7b5b71bcc95c1c7b05548bc89ab32aa7676","observation_id":"c34f53d2-29b8-42f1-9966-1ece108e3524","resolution":{"observed_at":"2026-08-11T15:51:22.463595Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.434826Z","title":"Chiron, Vortex helices for the Gross-Pitaevskii equ ation, J","venue":null,"work_id":"0b4a5ce4-548e-448d-87ee-d886d13867d1","year":2005},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.762444Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:3f6b650694c0d086b9a2e5b4bdee3fda307537c1372570654e3545e861637b5f","observation_id":"182cf44f-a8aa-4d98-8266-4f9c4de422d2","resolution":{"observed_at":"2026-08-11T15:51:22.440764Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.413002Z","title":"Da Rios, Sul moto d’un liquido indefinito con un filet to vorticoso di forma qualunque, Rendiconti del Circolo Matematico di Palermo (1884-1940) , 22 (1906), no","venue":null,"work_id":"65beabb2-86dc-4126-85be-d4d9b4afb905","year":1906},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.769665Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:2e1bf1e3fdb713dce21b42875cd0055a0b1a182454fa0d504fdd622c5cc1fd14","observation_id":"593598d9-1918-4c3a-920c-e67832ef4e41","resolution":{"observed_at":"2026-08-11T15:51:22.418692Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.395634Z","title":"Dávila, M","venue":null,"work_id":"0fb858ec-c872-4587-b3c0-b3d6d20d719c","year":2022},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.775886Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:3cdcf1594a598043dc1e1dd1152fbeb1e13019991867d77f69dee338bfe0f77d","observation_id":"97b25b4a-32d4-454c-9ed5-2b2e2e8dbf13","resolution":{"observed_at":"2026-08-11T15:51:22.400501Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.375930Z","title":"Dávila, M","venue":null,"work_id":"b9364346-23b5-44e3-91ca-3740ab0e1436","year":2022},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.782782Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:ef3a49b5aa524c3de7099e404324b49aa622acb1da0dc5fb1cf2a3f3fa74c81f","observation_id":"5095f6c2-5ba8-4bf0-9fd7-5ac7b9002a7e","resolution":{"observed_at":"2026-08-11T15:51:22.381343Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.356096Z","title":"D ´avila, M","venue":null,"work_id":"8ec2a612-deb8-4539-a317-79562fcf8ad2","year":2020},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.790736Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:c216397255a12c8c641b7b4c88dbb41bc11eab338ecd2a35892c6227eef312c4","observation_id":"bc23e761-b934-4352-aafc-e2f7159ca0cd","resolution":{"observed_at":"2026-08-11T15:51:22.361950Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.333593Z","title":"D ´avila, M","venue":null,"work_id":"924690a7-194b-4a73-9bb3-fb18ff8ac795","year":2022},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.799610Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:102f2b12dfd70b6b39f63b1c87062db03883ae74e14cf5f9410cd67a8badbfb7","observation_id":"5f7b1370-9f4e-4fb3-9e48-f8b997fec958","resolution":{"observed_at":"2026-08-11T15:51:22.340085Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.312455Z","title":"de Valeriola and J","venue":null,"work_id":"026b90d8-2a9e-4346-9897-466a67e28b1a","year":2013},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.810282Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:1e715c94be8c61e9a85b0a3f524c71dbaad7b799f2975c98ed2e3a1b5e5e8a3e","observation_id":"7bc9771d-b8ec-41b9-8d48-ba9df7c0c9b9","resolution":{"observed_at":"2026-08-11T15:51:22.317890Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.291769Z","title":"Dutrifoy, Existence globale en temps de solutions h ´elico¨idales des ´equations d’Euler, C","venue":null,"work_id":"862f6c3b-c8ce-45e8-ad47-bb8a266f8233","year":1999},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.817153Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:6db91bbe91c9ec72bcc3741ad0c013da1e6493278b61d259e9c36e3ef77b2da5","observation_id":"a5b564c1-5ae4-4a4d-bb67-3f5f8de8f05f","resolution":{"observed_at":"2026-08-11T15:51:22.299036Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.271524Z","title":"Enciso and D","venue":null,"work_id":"caa4fdc7-8e46-4788-961d-46f22da46c6a","year":2015},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.827471Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:f023bde29f5a00940b18f8c2093ad4e99c40fb31af5efcc465c5b696332a7dd0","observation_id":"3534e963-4418-4a20-88f4-9417bae5aeaa","resolution":{"observed_at":"2026-08-11T15:51:22.278366Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.248676Z","title":"Enciso and D","venue":null,"work_id":"9203ae83-2df3-4619-a1e5-2d7fa663b214","year":2015},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.836385Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:1c429b473cc1cb608904f249d8e2761d8890afa35ceaaf6b8dd26182c1bc8d24","observation_id":"5cffc3ad-c8f3-4e46-872a-ed2431423e9d","resolution":{"observed_at":"2026-08-11T15:51:22.257529Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.224497Z","title":"Ettinger and E.S","venue":null,"work_id":"f689085c-0aa5-4a25-b5b8-022c7f82a83e","year":2009},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.843286Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:8436b6b5411dfc0b900bf995d3d2bac3272817a972f3d72dff88fbcbd4dac56f","observation_id":"8b09f7e9-3929-4dcd-8a9f-6d6367cd21c8","resolution":{"observed_at":"2026-08-11T15:51:22.231456Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.198042Z","title":"Fraenkel, On steady vortex rings of small cross-se ction in an ideal fluid, Proc","venue":null,"work_id":"60590533-61d8-4fe8-8572-65f4162aa611","year":1970},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.852395Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:9e095294b7463f41c7c57f28269a1d60a7ff0ebe5b941826ab9c364e9c9d75c0","observation_id":"5a37c0a4-3342-48e5-a23a-f2d25d099c5b","resolution":{"observed_at":"2026-08-11T15:51:22.210969Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.172541Z","title":"Fraenkel, Examples of steady vortex rings of small cross-section in an ideal fluid, J","venue":null,"work_id":"0e6378e7-65ce-4885-8b03-00557beecda2","year":1972},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.860394Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:53b6e9e3f99704a034617d083f630ffe3d1624b350670aab85ac6db3146928d8","observation_id":"bf4b065e-698c-496c-a930-cf69f0f56d9e","resolution":{"observed_at":"2026-08-11T15:51:22.180088Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.146290Z","title":"Fraenkel and M.S","venue":null,"work_id":"dd13839e-d80e-4af4-a18a-2ada06abb1e3","year":1974},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.868315Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:3788667a84a93180c0bd2a01a52aab6b452f72047b8c065d45c2b11f871cd754","observation_id":"b74dfbaa-cd51-4938-b0a1-cc4397393f34","resolution":{"observed_at":"2026-08-11T15:51:22.152772Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.120223Z","title":"Friedman and B","venue":null,"work_id":"3fb0c036-7598-4b04-b829-ce03b3f2c7de","year":1981},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.878377Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:3eea6f75bba3dbde7bbcabdafa5f889b6ad9d78f326f7a9cb0661ff314698531","observation_id":"bbda96a6-befe-4843-9de5-01d23ac922ce","resolution":{"observed_at":"2026-08-11T15:51:22.126636Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.100623Z","title":"Fukumoto and T","venue":null,"work_id":"d943cfc2-056f-4964-9fc9-ced86ab8f28e","year":1991},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.883748Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:a37c739d1e669078ad4b20caeba4c737e84eb0ee1bf328bc51a37dbfb6076962","observation_id":"703a6e0f-810b-4ab7-a42a-09c6f207797f","resolution":{"observed_at":"2026-08-11T15:51:22.106232Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.076443Z","title":"García, Vortex patches choreography for active scal ar equations, J","venue":null,"work_id":"404a431a-c311-4d2f-ba38-e2860e3fe3db","year":2021},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.892263Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:14648bc13a910b445ac43ff790d59886838a3be153606a53395a33a9be5db3f2","observation_id":"2330b43f-427d-40e3-a674-81dd96f8922d","resolution":{"observed_at":"2026-08-11T15:51:22.087367Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.047114Z","title":"García, Kármán vortex street in incompressible fluid models, Nonlinearity, 33 (2020), no","venue":null,"work_id":"50bdd010-6d40-4efe-a8d1-c22c1bc580ce","year":2020},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.899169Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:d1646c7523b8b7902e765cab73d0cfea2a2f0f73c2c3b5f878e10655df0fd43c","observation_id":"5d9e3be1-1da4-4828-a76c-e36bfce10776","resolution":{"observed_at":"2026-08-11T15:51:22.058653Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:22.017829Z","title":"Gilbarg and N.S","venue":null,"work_id":"524d1655-66d0-450c-a496-c4f535563ba3","year":2001},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.908449Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:c020a0f87c8cbd76ebf8dbda16b8180d93934564db0718c7f43d92d0bc5ba6c7","observation_id":"648a433f-573b-49d9-ae46-f8fbb89f73ae","resolution":{"observed_at":"2026-08-11T15:51:22.024787Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.986310Z","title":"Guerra and M","venue":null,"work_id":"6becfe6b-b94c-4926-b8b1-e27519974346","year":null},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.917875Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:079250d247e4b0f984f0907c7d6bc3bd4163548f388f0f9b0e6186d6a79b5926","observation_id":"c30ed00f-71a6-4db6-b8d9-d72b101c015f","resolution":{"observed_at":"2026-08-11T15:51:21.994310Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.960787Z","title":"Guo and L","venue":null,"work_id":"5f778495-cc18-4cff-b09b-14e4b5f9ae4e","year":2025},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.924994Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:2d3addc39fa462de400bae5b693434ad67aa5d9272b27aad611b9451394f851c","observation_id":"e409f5c9-2408-45ff-94e2-49aaa2ab9863","resolution":{"observed_at":"2026-08-11T15:51:21.966855Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.927628Z","title":"Hassainia and M.H","venue":null,"work_id":"5c959ab2-e5f1-430b-9755-506f264fed3d","year":2022},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.931819Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:228af4682dfd1e4d115272c8a3fdbf55e9fc5e8c3ce70ccead068db71c00f6f5","observation_id":"a3f27379-cb68-4314-a916-999aeecd0710","resolution":{"observed_at":"2026-08-11T15:51:21.936601Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.884516Z","title":"Hassainia and T","venue":null,"work_id":"705ec1e3-3060-402a-879f-bc30e8ebdcc6","year":2021},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.939889Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:210cbbc5df175bacc6ccc242e4bc8db528cdd67d9b782b7e549fdc09191c74aa","observation_id":"8af6714f-c2da-4b50-9d2a-5bebb6383e3f","resolution":{"observed_at":"2026-08-11T15:51:21.893116Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.860481Z","title":"Helmholtz, On integrals of the hydrodynamics equati ons which express vortex motion, J","venue":null,"work_id":"5397fcae-d410-4394-a656-d960a78dedf6","year":null},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.945907Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:9aab0b883c6bab37f98d3b748e268aa6cb22d4c42a87a15e547e6cd6512b6d1a","observation_id":"7ce9ecb4-18b1-4d61-9978-21ab1ba7c370","resolution":{"observed_at":"2026-08-11T15:51:21.868115Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.831986Z","title":"Hmidi and J","venue":null,"work_id":"eb97bc89-5ed2-4fd9-ba77-35d20006e1d3","year":2017},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.956583Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:72667e3d49d97285dd3be9bf26ce6779624298792b4a517938d6a2ef62db340c","observation_id":"8e1980a3-75f6-41ce-814a-d1f5dacb9dbb","resolution":{"observed_at":"2026-08-11T15:51:21.841531Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.811349Z","title":"Jerrard and C","venue":null,"work_id":"0189ee99-232b-441a-a5ff-136a6ff71f96","year":2017},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.964257Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:657789574195874666b4aa02ebb3901c99c55c5a50125af168694805729f90ab","observation_id":"09d09287-7754-43dc-a71e-02b7cac8f62f","resolution":{"observed_at":"2026-08-11T15:51:21.817359Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.783753Z","title":"Jerrard and D","venue":null,"work_id":"3ac6edb6-14de-4d08-a3b4-f7d5b8264d04","year":2015},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.970203Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:64727c6dc7846908d6d01a8a7adb9e3b71792be0e465ef055e3ec961d0422525","observation_id":"4d00e98a-02d1-4a5c-8e51-c87986ecafd7","resolution":{"observed_at":"2026-08-11T15:51:21.793002Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.756497Z","title":null,"venue":null,"work_id":"ccac52a5-3364-421e-bb57-b018ab5eb2d7","year":2017},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.977471Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:0fbb94bbed0c91a4903391732f10822b60cef81e17eaac00893b776b8870aeb2","observation_id":"526e3867-afb6-46b3-9cfe-ba4395084e5b","resolution":{"observed_at":"2026-08-11T15:51:21.765856Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.728074Z","title":"Jiu, M.C","venue":null,"work_id":"f89baeff-8578-4247-a1dd-d5f4bafd999a","year":2018},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:20.990037Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:4f2979506669608dc01f6eed3ab6b7ca07db54f8ee0ce01fed1b49616b86c628","observation_id":"7ef4a5e8-229f-4bcd-90ee-4936d328d7bd","resolution":{"observed_at":"2026-08-11T15:51:21.738176Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.691912Z","title":"Keener, Knotted vortex filaments in an ideal fluid, J","venue":null,"work_id":"f6f2ed68-7b14-4b6e-a82b-95dd35cf4a2a","year":1990},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:21.000292Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:69d7a4348cbc0ce96c8a8b71abbbd74c06b4cfb88512a1dc904480ed81624b10","observation_id":"77881854-2483-485b-a10a-0373a0f619bc","resolution":{"observed_at":"2026-08-11T15:51:21.699396Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.668689Z","title":"Lamb, Hydrodynamics, Cambridge Mathematical Libra ry, 6th edn","venue":null,"work_id":"8fd146fa-b01a-4517-ad4d-d1103aaf58df","year":1932},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:21.005503Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:936f4d6bd90579f7c6a3a88e5791d966d23a329b30804d4a07be38b07f7a8c7c","observation_id":"cced223b-d346-4f1a-985e-134bf079b3b6","resolution":{"observed_at":"2026-08-11T15:51:21.675150Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.641710Z","title":"Levi-Civita, Sull’attrazione esercitata da una lin ea materiale in punti prossimi alla linea stessa, Rend","venue":null,"work_id":"6f6ae1c8-e402-4b93-8ca3-2d3fdf79b5d3","year":1908},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:21.011855Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:967c0e61520471a9bfa800ebeaa1cf3c777cfd7b046b5a2e51231363d9adfcf6","observation_id":"6955dba2-3adc-4fa0-b8c3-3ddd641b5e1b","resolution":{"observed_at":"2026-08-11T15:51:21.648805Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.615866Z","title":"Levi-Civita, Attrazione newtoniana dei tubi sottil i e vortici filiformi, Annali della Scuola Normale Superiore di Pisa - Classe di Scienze Ser","venue":null,"work_id":"ef5c3415-f79b-4def-a037-c5b1d6c386aa","year":1932},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:21.019183Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:c404181203975186713e1faf894db4e1b08ff0327e0701fe23870e64cf7bfb14","observation_id":"278f4e0c-7bd9-4321-90ff-7543bf8ceebb","resolution":{"observed_at":"2026-08-11T15:51:21.624686Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.590321Z","title":"Lieb and M","venue":null,"work_id":"72a2522f-b93a-47f0-b31e-2735b5c06605","year":2001},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:21.027225Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:7d0d3fce9335cf91f2556f189fa562670df63d1719578a643e078f091546e6c0","observation_id":"8bacc3d9-307b-49f1-83b6-ada7d1e7ba74","resolution":{"observed_at":"2026-08-11T15:51:21.599215Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.553150Z","title":"Lopes Filho, A.L","venue":null,"work_id":"d05e2f0a-1c4e-4029-9f1a-eeeaf97769fd","year":2014},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:21.035606Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:b613692671595767320f7f43acb3efe4d58d74d0d01978aa4e3d8ea021c5d692","observation_id":"2121c286-c5b7-4f97-934d-81b8d9c81648","resolution":{"observed_at":"2026-08-11T15:51:21.569291Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.525807Z","title":"Majda and A","venue":null,"work_id":"cb6e50df-82d0-4194-a109-da1d7421ffd0","year":2002},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:21.044804Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:357c2527490af3af20d4f1fe5aed30acb372425576fef87e6ff0b805a1072d18","observation_id":"074f799c-056e-4235-99d0-5fc2a38107c2","resolution":{"observed_at":"2026-08-11T15:51:21.532861Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.502384Z","title":"Moore and P.G","venue":null,"work_id":"4167cdf8-4ee8-4263-a986-d2e18f4a7e30","year":1972},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:21.051612Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:d29a08bf13f28fdc87393f5a145fd37f3bb811832274a7e872a21c437c4d4520","observation_id":"5331e529-089d-48a6-a85f-2b38fca81898","resolution":{"observed_at":"2026-08-11T15:51:21.509171Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.476133Z","title":"Ni, On the existence of global vortex rings, J","venue":null,"work_id":"c1e365fb-6700-4173-9409-3ef1a1d4cb23","year":1980},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:21.059310Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:1eebcfb3017bd576e21047aac935128f6b876481f009bbf365414b35716e22ef","observation_id":"19142633-bc1a-4bad-99c4-fb60d94e0ae0","resolution":{"observed_at":"2026-08-11T15:51:21.484809Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.452297Z","title":"Norbury, A steady vortex ring close to Hill’s spheric al vortex, Proc","venue":null,"work_id":"10685a20-aec8-4a05-a901-2a12c2564b85","year":1972},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:21.069053Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:247212e024200e988f1759f189cb4bb2679b5589882bebce72ca23877d2c845a","observation_id":"b51b0356-7221-4b92-a520-68e6027fa8b9","resolution":{"observed_at":"2026-08-11T15:51:21.459568Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.432265Z","title":"Ricca, Rediscovery of da rios equations, Nature, 352 (1991), no","venue":null,"work_id":"8dd3487c-765d-4fa9-a3dc-94797c92589d","year":1991},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:21.074909Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:7cee082942bc54113e49ba83b4fb03ccf07a2ddffe258d0df8551ec69561784c","observation_id":"48301c54-7017-4ce4-84ee-62b59b04b486","resolution":{"observed_at":"2026-08-11T15:51:21.438237Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.410728Z","title":"Ricca, The contributions of Da Rios and Levi-Civit a to asymptotic potential theory and vortex filament dynamics, Fluid dyn","venue":null,"work_id":"d1054a00-e3d0-40a6-a8c7-fe5f8234ac7a","year":1996},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:21.081413Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:c54bcb711da941dc9461260b278dc82861620ce8c05200f3ff50bb80b600736c","observation_id":"db94ef02-278f-4899-ae93-c5959ffb1aeb","resolution":{"observed_at":"2026-08-11T15:51:21.417427Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.390471Z","title":"Saffman, Vortex dynamics, Cambridge Monographs on Mechanics and Applied Mathematics, Cambridge University Press, New York, (1992)","venue":null,"work_id":"8d90027e-9fcf-4b34-a5dd-f60e6ec0b387","year":1992},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:21.087049Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:6778d7957ae8e7af65e19d68ec9e3c5e633c20b889e5b61363fb585991bddf8e","observation_id":"7466d56d-30b6-48e9-be27-64d029f6331a","resolution":{"observed_at":"2026-08-11T15:51:21.396829Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.360466Z","title":"Smets and J","venue":null,"work_id":"80c8ac71-6a7f-4cf8-a9b6-d30e2f67e92f","year":2010},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:21.095924Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:b4d62c97dfeb9f02d8f4df77f8d4aa247f02349be6aa7185fc8e16e9b5674d0b","observation_id":"adb12bee-7c9e-41fc-966a-221f0979e2dd","resolution":{"observed_at":"2026-08-11T15:51:21.373210Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.339279Z","title":"Thomson (Lord Kelvin), Vortex statics, Proc","venue":null,"work_id":"5db7a15b-b868-46d5-93da-f10b205200d0","year":null},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:21.105405Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:0195c014f52110dd4288ff2ffae5e30f919c77297790d0cbeefff8bacdd84dc8","observation_id":"9a97c231-97ad-436c-a504-8c6479c13132","resolution":{"observed_at":"2026-08-11T15:51:21.345691Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.315916Z","title":"Thomson (Lord Kelvin), Mathematical and Physical Pa pers, IV., Cambridge, (1910)","venue":null,"work_id":"48b9bd7a-e95e-468c-83b8-9e538508e610","year":1910},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:21.111875Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:0e3a397ceb0e696e263a55b2e9bc0929e29168837ee7472cf072955446cb4169","observation_id":"2cfc44ec-ddff-4f1e-af91-fe8baaedb921","resolution":{"observed_at":"2026-08-11T15:51:21.322946Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.295887Z","title":"Turkington, On steady vortex flow in two dimensions","venue":null,"work_id":"81a924a9-d339-471c-be7c-967855806bbe","year":1983},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:21.127609Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:ec2c5f52fed2396ca5fa0142b9ea623dacfcb66760d158f51a5e6e5850afb13c","observation_id":"06448ef7-b9df-4e94-ab99-4d1c4fb1e229","resolution":{"observed_at":"2026-08-11T15:51:21.302460Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.271232Z","title":"Turkington, Vortex rings with swirl: axisymmetric s olutions of the Euler equations with nonzero helicity, SIAM J","venue":null,"work_id":"80b9a241-254f-4e5e-b437-449d2712c91b","year":1989},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:21.142756Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:db1dda277b61834538456bc4b3dd7a2820769efd7b4894df685d2b4900f386fc","observation_id":"39142dcf-b358-47af-b9ea-86035b0c3a4f","resolution":{"observed_at":"2026-08-11T15:51:21.278533Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.250826Z","title":"Wei and J","venue":null,"work_id":"ad0ea465-e26e-4174-b2bc-55b68fa6d683","year":2016},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:21.153857Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:38463425c705ecf0e8c787e0265de83c93baffbdc7d67c3e25cd48eb546a6828","observation_id":"b085210d-8a27-42d3-ba84-eb988e95053d","resolution":{"observed_at":"2026-08-11T15:51:21.257370Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-11T15:51:21.220815Z","title":"Yang, Global vortex rings and asymptotic behaviour, Nonlinear Anal., 25 (1995), no","venue":null,"work_id":"bd79a4b7-60c8-4188-ae08-c27ccbfda01c","year":1995},"citing_paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-11T15:51:21.160293Z"},"links":{"citing_paper":"/paper/2412.10725"},"observation_digest":"sha256:c6be4648d6af68e21e1db5e74209e3f834afc7a4e0fe7aeefd47c7ae2f8ba1cf","observation_id":"b26cc4cb-4913-4d76-b554-fda038f28863","resolution":{"observed_at":"2026-08-11T15:51:21.228627Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.10725","last_updated":"2024-12-14T07:49:25Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-11T23:25:57.034762Z","submitted_at":"2024-12-14T07:49:25Z","title":"On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl"},"reference_resolution":{"displayed":65,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":7,"verified_exact":0,"verified_fuzzy":58},"total_outbound_references":65},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 65 of 65 outbound references and 2 inbound Pith citation observations for arXiv:2412.10725."}