{"as_of":"2026-08-19T11:35:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:541b3668bd1b3cb3098062a92662c9d4813ab5331c7fe5bcd250a25c3b557b41","coverage":[{"denominator":47,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":47,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T10:36:39.973345Z","state":"measured"},{"denominator":48,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":48,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-19T06:32:44.657259+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T11:10:36.594396Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-16T11:10:36.808551Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"cited_work":{"arxiv_id":"2412.16532","doi":null,"metadata_source":"pith","pith_arxiv_id":"2412.16532","snapshot_observed_at":"2026-08-16T11:10:36.808551Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","venue":"math.AP","work_id":"ad1ee049-2867-4380-a8d7-787c17d84a10","year":2024},"citing_paper":{"arxiv_id":"2504.16687","last_updated":"2025-04-30T11:01:32Z","snapshot_observed_at":"2026-08-18T00:47:32.093046Z","submitted_at":"2025-04-23T13:16:04Z","title":"Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations","version":2},"reference_index":114,"source":"pdf_text","source_observed_at":"2026-08-16T11:10:36.594396Z"},"links":{"cited_paper":"/paper/2412.16532","citing_paper":"/paper/2504.16687"},"observation_digest":"sha256:47968485f5ebe78d4b9ae14061412ff09337211db6cb4cfdc7e0b4c293a457fe","observation_id":"42e69a6f-6df1-42f6-9c12-391b6f7ba2f7","resolution":{"observed_at":"2026-08-16T11:10:36.813877Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2412.16532/citation-record","integrity":"/paper/2412.16532/integrity","json":"/paper/2412.16532/citation-record.json","paper":"/paper/2412.16532"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T10:36:41.065700Z","title":"Albritton, E","venue":null,"work_id":"6e93c523-e9bb-4a30-b161-62dab07fb6d4","year":2022},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.706480Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:6dd6f912b62b3b5b7f252f2111a54ce91f59b109548edbf2a0cb9f8e66d917c5","observation_id":"7ef7f224-9033-4838-a2c0-1e1e14347eb7","resolution":{"observed_at":"2026-08-11T10:36:41.070515Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:41.048865Z","title":"Albritton, E","venue":null,"work_id":"5e2149f0-577e-46a4-8f87-35943119b297","year":2023},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.712447Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:1e81013d06e786c374e2a03d23b91e4a46e718b77d8dad23ffb460c2ce902d19","observation_id":"f9244f6f-8e86-4dd7-8144-a806552233c6","resolution":{"observed_at":"2026-08-11T10:36:41.054196Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:41.031245Z","title":"Albritton and M","venue":null,"work_id":"aab1b9a1-0176-4d71-b2de-286368a2879b","year":2023},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.717455Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:8dd7e1d7be6af6212ad85821118c36cf188cfa4925643af80ba83fcd33b76045","observation_id":"ede2bfc9-d529-443e-983b-7d61d1b536c6","resolution":{"observed_at":"2026-08-11T10:36:41.036497Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:41.012847Z","title":"Bahouri, J.-Y","venue":null,"work_id":"a216a166-bb4f-4f28-90ad-25134acb799b","year":2011},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.722800Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:e40646be87aabf643aa0f01b07a931dcaa5726da6fcd846234b48e0b76164408","observation_id":"bc902ce3-e054-4ce1-b9cc-8d9ab0c33979","resolution":{"observed_at":"2026-08-11T10:36:41.018557Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2412.08622","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T10:36:40.296529Z","title":null,"venue":null,"work_id":"093e27ae-c6c7-435e-a87c-f805e30e8245","year":2024},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.727653Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:abefc5dfc86b9feed51512742fa5dae643486d9d33e52b8ce664980b9f2ff502","observation_id":"fbbbfeb1-41d8-4ea2-ad1a-5191a545ad33","resolution":{"observed_at":"2026-08-11T10:36:40.306090Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.992467Z","title":"Bru` e and C","venue":null,"work_id":"ae0143ed-579b-48f1-af92-89fac00f4bf3","year":2023},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.732430Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:00629f6345ab048f34720f5ba00caec60d15fb97d65cd0a085f0e7d4740b59d0","observation_id":"c054c256-97b3-4ae7-9606-160523317b1c","resolution":{"observed_at":"2026-08-11T10:36:40.999911Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2309.09753","last_updated":"2024-04-07T06:53:39Z","snapshot_observed_at":"2026-08-17T19:10:39.413595Z","submitted_at":"2023-09-18T13:28:03Z","title":"Non-uniqueness in law of Leray solutions to 3D forced stochastic Navier-Stokes equations","version":2},"cited_work":{"arxiv_id":"2309.09753","doi":null,"metadata_source":"pith","pith_arxiv_id":"2309.09753","snapshot_observed_at":"2026-08-11T10:36:40.124948Z","title":"Non-uniqueness in law of Leray solutions to 3D forced stochastic Navier-Stokes equations","venue":"math.PR","work_id":"2c8cf19e-3622-4214-8932-7e755de34983","year":2023},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.738080Z"},"links":{"cited_paper":"/paper/2309.09753","citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:7d831ce65ca0d07bdedd59188bfde0d7862cfac32f95a6374f812d3e8ccc1dca","observation_id":"66ed2cfa-0ff4-4605-94df-656c708ff71c","resolution":{"observed_at":"2026-08-11T10:36:40.131154Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.971573Z","title":"Buckmaster, M","venue":null,"work_id":"fec7e9d4-a602-479b-b10b-6178591e8aef","year":2022},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.744066Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:9b67f95e7304e6a65ee2b2bb069ba493c015cc25e33e0edc59dab4f3de02771b","observation_id":"cc72c4ec-271f-4f5d-b671-170f9a312ac6","resolution":{"observed_at":"2026-08-11T10:36:40.976967Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.951536Z","title":"Buckmaster, C","venue":null,"work_id":"a6501434-7ed5-4366-889b-f3243a2a0914","year":2015},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.749301Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:7d25f26479c295faf0a375efe8d003d52c7f240877334b8cc64ff6ec43b07066","observation_id":"b72c5466-3191-4614-9838-c48b73758e6e","resolution":{"observed_at":"2026-08-11T10:36:40.958092Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.933055Z","title":"Buckmaster, C","venue":null,"work_id":"91ecd0ae-f441-4ea7-bd1e-e91de53d1525","year":2019},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.754799Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:03e2975b71fa99e2326b769a7bc933c86aa5f3c805be2eb51d5728341b1c780b","observation_id":"a2edbdcb-1709-4616-8d70-5edf3599c27b","resolution":{"observed_at":"2026-08-11T10:36:40.938833Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.915928Z","title":"Buckmaster and V","venue":null,"work_id":"eb49445b-5836-40d8-8895-1e6f20e382f5","year":2019},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.760381Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:8741720c1986934e394c91bfed31336eaa564072564a0245190b95ac1881d63a","observation_id":"68becbbc-938d-4e4f-adcc-6ff742b93686","resolution":{"observed_at":"2026-08-11T10:36:40.920998Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.897930Z","title":"Colombo, C","venue":null,"work_id":"3d83e2d4-1d07-42d5-83a3-10296b319a31","year":2018},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.766182Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:56824e3485602e22aebaa9eab45f5b442726106b03b8a76bb58bcf583ec62800","observation_id":"8b2cc98f-a860-47ee-913b-8ac5a8a8cd5f","resolution":{"observed_at":"2026-08-11T10:36:40.903672Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.880902Z","title":null,"venue":null,"work_id":"9592723c-1e05-41b1-b9dc-0409e9884bc7","year":2021},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.771826Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:68e01399510e00b14650941def701b7ec0113544232aee207951b85fa24f95a5","observation_id":"5af76b24-c4f0-4189-b1bc-6919ddae353f","resolution":{"observed_at":"2026-08-11T10:36:40.886075Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.863323Z","title":"De Lellis and L","venue":null,"work_id":"4e57b559-0d4e-4c6c-8795-eb39022e8d34","year":2013},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.780058Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:7e999f43acdf82e8e2c862a1aae20df9fe2bef788442950b8e967ea0f79c0762","observation_id":"f15b2a87-86db-4065-b362-308f7c82029a","resolution":{"observed_at":"2026-08-11T10:36:40.868756Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.841529Z","title":null,"venue":null,"work_id":"265275e7-5504-493c-ab8b-3d364f9db7b7","year":2019},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.786442Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:11d3f9d93a0db0e1c56cf3ddb66fff53603a41608945c32d8fa1386703c10484","observation_id":"0d2f3fe8-8566-420c-8f74-ccb402bbb26a","resolution":{"observed_at":"2026-08-11T10:36:40.850499Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.820119Z","title":"Debussche, M","venue":null,"work_id":"fe7b1fe4-f0f7-4a93-9dc0-257381bf2a9e","year":1916},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.792862Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:c5254da9681cdca5edbad49011c86fa504c6166b1e342eb385c08ad1d51e94ea","observation_id":"cb380904-233c-402b-93a6-abfa4934906a","resolution":{"observed_at":"2026-08-11T10:36:40.826962Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.801527Z","title":"Debussche and U","venue":null,"work_id":"9606ae80-6fb6-489e-8892-c4efde4cd17a","year":2024},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.799941Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:761b657aa403ce0cf0a7b241dea5c19077543392db65229c1ddd5190eba66312","observation_id":"a59cc0ab-3c42-4c28-9777-53c8ede185f0","resolution":{"observed_at":"2026-08-11T10:36:40.807191Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.780735Z","title":"Flandoli, M","venue":null,"work_id":"c109c3e1-00cd-428f-a5cf-ccb381e5f724","year":2022},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.807036Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:dc72ba5733b0e5980013bcf94b901c9a5634cacbe6a1baca33576be14b65521d","observation_id":"32f41359-da01-4fec-a40f-4ec71af3d30a","resolution":{"observed_at":"2026-08-11T10:36:40.787325Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.760476Z","title":"Flandoli and D","venue":null,"work_id":"0de0dedd-dd0d-4e7a-a5f2-c127e83dade6","year":2021},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.815379Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:62a6536a03b0fcbe6fac2258e6a844384963227bc0391f51cf6d26d5167fae21","observation_id":"585a4778-510a-4576-a38e-4222b7f61ab2","resolution":{"observed_at":"2026-08-11T10:36:40.767554Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.743185Z","title":"Flandoli and U","venue":null,"work_id":"22601484-c303-42b2-b39f-43a63713b129","year":2022},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.821571Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:ed5f68df1bd60c9ea53c584ea4595c73930bd38459c508fa0f0186024af23432","observation_id":"d401a2f9-6e10-49a1-a58a-b84d39305976","resolution":{"observed_at":"2026-08-11T10:36:40.748846Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.723869Z","title":null,"venue":null,"work_id":"c71cc183-8ea2-4aa6-b53a-f250f1c768ba","year":2020},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.827585Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:f0bc09b7f3dcc66d7c3d6d3c070dee28396789eace41c99b69c353447f3bc597","observation_id":"d6555d76-2a18-40ad-a044-8a96f69cc412","resolution":{"observed_at":"2026-08-11T10:36:40.730261Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.705309Z","title":null,"venue":null,"work_id":"1bb36c76-45ef-4e43-8193-46f1f24be193","year":2023},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.833480Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:66b805767fbda6fe111017e66b25374611a602c06d9563dc35d19eb683cfe3c0","observation_id":"8360f242-b741-4eeb-9566-730f96705061","resolution":{"observed_at":"2026-08-11T10:36:40.710971Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.685633Z","title":"Hofmanov´ a, T","venue":null,"work_id":"32f6f8e8-7e94-488d-a707-9ad1406fe1d4","year":2023},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.839391Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:8b4593f2a0c231bd421961f1cc137d19d34a42440ade3998bc4ae507413fcbe0","observation_id":"4a871c4c-286a-4d59-a9b1-8be053d25d5e","resolution":{"observed_at":"2026-08-11T10:36:40.691893Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.669121Z","title":"Hofmanov´ a, R","venue":null,"work_id":"fd074e3a-e5a0-4a51-b883-5286ef5bd633","year":2023},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.844583Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:60d727b1a35f4062d5a11d93396da8a4419183ec439418bd401500f1f30b77f5","observation_id":"8cfec387-0651-40fa-8a18-75133623b264","resolution":{"observed_at":"2026-08-11T10:36:40.674319Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.651857Z","title":"Hofmanov´ a, R","venue":null,"work_id":"7d5b6ffe-24c8-4f00-867f-b152c17a28c0","year":2023},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.849197Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:08e901f21838c97645d92d8cbb0c1e6e7968eb7dd7227a55fe8f83289e58f2f1","observation_id":"d4532f5d-5c63-4456-a889-abeebdb306b1","resolution":{"observed_at":"2026-08-11T10:36:40.657125Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.632516Z","title":"Hofmanov´ a, R","venue":null,"work_id":"03613934-4ac2-4296-b22d-d5f9626bbb6d","year":2023},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.853682Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:93dbc624b935a2f6499218d9829f8a394de561df874112508b191afeb979fae3","observation_id":"a501cde7-1dd9-4aa9-9117-bbde352a31ec","resolution":{"observed_at":"2026-08-11T10:36:40.639200Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2208.08290","last_updated":"2024-07-18T08:02:33Z","snapshot_observed_at":"2026-08-18T10:14:53.595794Z","submitted_at":"2022-08-17T13:37:03Z","title":"Non-unique ergodicity for deterministic and stochastic 3D Navier--Stokes and Euler equations","version":2},"cited_work":{"arxiv_id":"2208.08290","doi":null,"metadata_source":"pith","pith_arxiv_id":"2208.08290","snapshot_observed_at":"2026-08-11T10:36:40.096385Z","title":"Non-unique ergodicity for deterministic and stochastic 3D Navier--Stokes and Euler equations","venue":"math.PR","work_id":"bff7ccba-8ac0-4154-9918-ee553ae22868","year":2022},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.858352Z"},"links":{"cited_paper":"/paper/2208.08290","citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:5324dfbdcf7625361704a747322eeb3243405aab0302c4195ddd42f95bb6e2fc","observation_id":"c5aa2814-d327-4252-986c-6c211eb8709e","resolution":{"observed_at":"2026-08-11T10:36:40.104323Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2309.03668","last_updated":"2024-09-10T07:15:48Z","snapshot_observed_at":"2026-08-16T15:02:32.836409Z","submitted_at":"2023-09-07T12:12:31Z","title":"Non-uniqueness of Leray-Hopf solutions for stochastic forced Navier-Stokes equations","version":2},"cited_work":{"arxiv_id":"2309.03668","doi":null,"metadata_source":"pith","pith_arxiv_id":"2309.03668","snapshot_observed_at":"2026-08-11T10:36:40.064886Z","title":"Non-uniqueness of Leray-Hopf solutions for stochastic forced Navier-Stokes equations","venue":"math.PR","work_id":"75b13eb3-0b9d-4f5b-867d-151631ded84a","year":2023},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.864928Z"},"links":{"cited_paper":"/paper/2309.03668","citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:2aea5ecc4eae86d883f62543709e6dcf44d55c8245c8f9e963acc1c8e2112a51","observation_id":"4834bb8a-9b23-484a-9def-9dc27f2cb071","resolution":{"observed_at":"2026-08-11T10:36:40.071253Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.615223Z","title":"Hyt¨ onen, J","venue":null,"work_id":"62c2086f-cba4-4855-8211-a34ed4f3cac1","year":2011},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.871955Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:dfd5b7dd78fb13a574ca4e3a488b51ef39b7b6bd8d4cf820042b89bcc04f443d","observation_id":"cfe04571-306d-4a2c-bbdb-f97f25ac761c","resolution":{"observed_at":"2026-08-11T10:36:40.620597Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.598169Z","title":null,"venue":null,"work_id":"e79701ba-3d8b-4ee4-a215-58f55fcba06e","year":2018},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.878009Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:659696cf32eae98651f2ac06d08c53b07a72f89df8665880b5b2d40f769cacbf","observation_id":"8520a96d-840a-4e62-9be4-89b016f1185e","resolution":{"observed_at":"2026-08-11T10:36:40.603412Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.580937Z","title":null,"venue":null,"work_id":"c9617500-a242-4728-9289-7917b21e779f","year":1990},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.883739Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:f3bdd117c5e4e927678811423a33c89bf7212b69ef1c8bb92cbcc6bf62d2c569","observation_id":"c52687c6-e130-4dcb-971b-6f9476754771","resolution":{"observed_at":"2026-08-11T10:36:40.586103Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.563493Z","title":"Lellis and L","venue":null,"work_id":"68f8de88-f497-40c2-bff6-f181f64aa8ac","year":2014},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.889120Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:d81ccb4130a0c49404af28f5fdd1c9816f8ef279b763288d47633ca31ac96e5d","observation_id":"1dfbc3a9-3c4f-4071-9861-6ede230ea3d4","resolution":{"observed_at":"2026-08-11T10:36:40.569058Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.546009Z","title":null,"venue":null,"work_id":"e6a49acb-349c-49f9-a03b-abd621a915b2","year":1934},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.894260Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:ac3185da1db6a73234490fb71dd70bd9d39883248db90aa60135070784770c9f","observation_id":"90ef1b11-4ca5-4c94-a252-8ad8e3a0513f","resolution":{"observed_at":"2026-08-11T10:36:40.551676Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.529051Z","title":null,"venue":null,"work_id":"8ea1ecc1-94c6-49e0-a1c1-b62038e1dea0","year":1969},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.899848Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:1ca2cef5f8349bcdf09d325bcc439e4db0cccc8fab4fa84d57efd56c75b6a882","observation_id":"0a5ca3ad-c61e-463e-bec8-ce272365c7e5","resolution":{"observed_at":"2026-08-11T10:36:40.534365Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.511578Z","title":null,"venue":null,"work_id":"1df36e82-5779-4b7a-bcd7-3be86ae7b6ab","year":2018},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.905226Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:e3e90e6f3e746f6fde90ec5bc0f457dfbfe6c4ef6943f0982cef07e1a9a596dd","observation_id":"cbf6a548-105f-479f-beea-28c31a3aae92","resolution":{"observed_at":"2026-08-11T10:36:40.516935Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.494667Z","title":"Luo and P","venue":null,"work_id":"ac2570be-6e3e-4c01-b267-7cb2b7c08b4e","year":2020},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.912356Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:224e23340e75855710516f2753f5b7482c57d4d14849e26fb77153f85beb7e0e","observation_id":"359396b2-7a2a-4322-9bdf-c7411124bd7e","resolution":{"observed_at":"2026-08-11T10:36:40.500107Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.478751Z","title":"Luo and E","venue":null,"work_id":"985d5db9-8ef9-4514-a249-ed15da32df68","year":2020},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.918074Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:c5d0f670ecb47e677bd62957f362ef154dccba2d18019c8581fc63f6c234af35","observation_id":"ca9df203-379a-43ff-bd63-1a41afe5d665","resolution":{"observed_at":"2026-08-11T10:36:40.483816Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.462502Z","title":"Mourrat and H","venue":null,"work_id":"74723d2a-1016-40c2-80b8-802ef54ee2cb","year":2017},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.924061Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:688920a985d8b77893d4ec07169d966a063ef86f844be3ecbb5d29c7bbb62962","observation_id":"f8223967-1ea3-4c0f-926a-ff0b278289b3","resolution":{"observed_at":"2026-08-11T10:36:40.467896Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.444062Z","title":"Pappalettera","venue":null,"work_id":"c9a1201b-8883-4aac-a968-568c79704d40","year":2024},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.929062Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:0e1430a00a3f07554ecfbb44a6a906ddaeec462ac3a2841a50a12da259a51198","observation_id":"66ff9d80-0d34-45c8-ba35-5ef562679fd9","resolution":{"observed_at":"2026-08-11T10:36:40.450102Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.426979Z","title":"Rehmeier and A","venue":null,"work_id":"b15bae0f-160b-4cc4-a213-52490b96bdd5","year":2023},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.934031Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:d88847297f6742b48bb54f4fc22c7f625fe90f98afda31d89ecd7986420c08cd","observation_id":"afe9c713-d21b-416b-b2b2-073f0b13f04e","resolution":{"observed_at":"2026-08-11T10:36:40.432512Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.410305Z","title":"Roncal and P","venue":null,"work_id":"aa14663c-6244-4a6b-9584-54e4652f9073","year":2016},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.939931Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:9620ee7b03976d71051ecd000688eb978367e510ecb32832ddb4226d57e8b8b6","observation_id":"f27c6106-8859-4bfa-8574-3944e4d940ec","resolution":{"observed_at":"2026-08-11T10:36:40.415398Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.393294Z","title":null,"venue":null,"work_id":"2b503665-f3ae-4e16-87c7-ff4096a704dc","year":2019},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.945310Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:4682fa2b170588db2b72b3a5cd4a91804098657a00c2fee0ea7ef8d0a3b8b190","observation_id":"fabb5412-f623-4d0a-a6da-5d87e49a3b7a","resolution":{"observed_at":"2026-08-11T10:36:40.398498Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.375598Z","title":"Schmeisser and H","venue":null,"work_id":"e0ef2f2a-221e-4547-b1d2-8d7e5b0e0a52","year":1987},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.950659Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:2f4bfb0ade19824e89387e4f20856ad6b571693916375aa68ac23167c7c46d1a","observation_id":"fbb07014-1897-4bc6-a054-97712b0c9caf","resolution":{"observed_at":"2026-08-11T10:36:40.380767Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.358098Z","title":null,"venue":null,"work_id":"c868990c-3042-4475-93ac-11ba58fd3e5b","year":2009},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.956336Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:b9f62d4d83266975003603cdce8e3c3976426287d021ad7762539826b025d358","observation_id":"1579dade-a94a-4ea5-a406-d8a04eafe377","resolution":{"observed_at":"2026-08-11T10:36:40.363670Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2104.10294","last_updated":"2021-04-21T00:40:52Z","snapshot_observed_at":"2026-08-18T07:12:32.346730Z","submitted_at":"2021-04-21T00:40:52Z","title":"Non-uniqueness in law of three-dimensional Navier-Stokes equations diffused via a fractional Laplacian with power less than one half","version":1},"cited_work":{"arxiv_id":"2104.10294","doi":null,"metadata_source":"pith","pith_arxiv_id":"2104.10294","snapshot_observed_at":"2026-08-11T10:36:40.023521Z","title":"Non-uniqueness in law of three-dimensional Navier-Stokes equations diffused via a fractional Laplacian with power less than one half","venue":"math.PR","work_id":"82a43cf9-c99d-413e-b701-d96c87d574c6","year":2021},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.962571Z"},"links":{"cited_paper":"/paper/2104.10294","citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:72716b5cd2ce4b4316190a512753d3aca7accb257ac02841f33a78325c519f98","observation_id":"d061cb39-af80-4c1d-b5fc-e63ec1b78bbf","resolution":{"observed_at":"2026-08-11T10:36:40.033125Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.340137Z","title":"Nonuniqueness in law for two-dimensional Navier–St okes equations with diffusion weaker than a full Laplacian","venue":null,"work_id":"0f2e6c3f-9e55-462b-80a8-b665bbb72c1c","year":2022},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.968114Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:80198fe2604ea4d1c16f4aee882c23fa8748addc205574c07d799ac0fd5a409c","observation_id":"fd7abd08-ed87-437e-93fe-9fa58b67166f","resolution":{"observed_at":"2026-08-11T10:36:40.345836Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T10:36:40.321200Z","title":"Yamazaki","venue":null,"work_id":"d9a4a7ef-7dbd-4311-af06-180a214b0f81","year":2022},"citing_paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-11T10:36:39.973345Z"},"links":{"citing_paper":"/paper/2412.16532"},"observation_digest":"sha256:a26a273597ecf8a31280b54eff63eaf8670a9331d21e41247e03ef1d5126cb47","observation_id":"9196af12-4828-429b-ad29-735da122f2f4","resolution":{"observed_at":"2026-08-11T10:36:40.327545Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.16532","last_updated":"2024-12-21T08:19:14Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-18T00:31:25.728526Z","submitted_at":"2024-12-21T08:19:14Z","title":"Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise"},"reference_resolution":{"displayed":47,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":11,"verified_exact":5,"verified_fuzzy":31},"total_outbound_references":47},"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":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 1 inbound Pith citation observation for arXiv:2412.16532."}