{"as_of":"2026-08-12T15:18:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c39c14921731ac1906baedb689d1ca1bcd064b050cf152370c8ef77ee8ce9df6","coverage":[{"denominator":33,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":33,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T12:58:18.956660Z","state":"measured"},{"denominator":34,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":34,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+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":"2026-08-07T11:10:18.245485Z","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":"2026-08-07T11:10:18.465510Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"cited_work":{"arxiv_id":"2505.23391","doi":null,"metadata_source":"pith","pith_arxiv_id":"2505.23391","snapshot_observed_at":"2026-08-07T11:10:18.465510Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","venue":"math.AP","work_id":"ae992cff-ddbd-421c-bf9b-6ba55bb71169","year":2025},"citing_paper":{"arxiv_id":"2506.03679","last_updated":"2025-06-04T08:10:45Z","snapshot_observed_at":"2026-08-07T10:55:13.512946Z","submitted_at":"2025-06-04T08:10:45Z","title":"Transition threshold of Couette flow for 2D Boussinesq equations","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T11:10:18.245485Z"},"links":{"cited_paper":"/paper/2505.23391","citing_paper":"/paper/2506.03679"},"observation_digest":"sha256:5eefda8219f0c62da2759cb219a75a83fafcb0ad7cedf541e1c4a9042d2508b3","observation_id":"a7ae98e5-466f-407e-874b-53c0dac1d801","resolution":{"observed_at":"2026-08-07T11:10:18.469787Z","resolver_source":"local_arxiv","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"}}],"links":{"evidence":"/evidence","html":"/paper/2505.23391/citation-record","integrity":"/paper/2505.23391/integrity","json":"/paper/2505.23391/citation-record.json","paper":"/paper/2505.23391"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:58:23.373443Z","title":"Nonlinear inviscid damping and shear-buoyancy instability in the two-dimensional B oussinesq equations","venue":null,"work_id":"44acc0f5-92b0-431b-a43a-5e1d61f773b5","year":2023},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:17.190864Z"},"links":{"citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:bb507b70502c6e2de1a23d94b9e298acd4fabdb8bedae5c70a7d15b1833980d1","observation_id":"da8b734c-8836-4fa9-b2da-f7fedd28bed7","resolution":{"observed_at":"2026-08-07T12:58:23.425456Z","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":"2026-08-07T12:58:23.256413Z","title":"On the stability threshold for the 3 D C ouette flow in S obolev regularity","venue":null,"work_id":"bd2e4d0d-4bed-4a5d-b2d3-02126af8765f","year":2017},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:17.248506Z"},"links":{"citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:3e61b4cae67238a658e1680120ad4f27554926463acb5f8700fdf24c59c549f7","observation_id":"2ff7ef1f-f7ed-4e94-8e22-0e62f0bdc8f8","resolution":{"observed_at":"2026-08-07T12:58:23.301844Z","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":"2026-08-07T12:58:23.099558Z","title":"Inviscid damping and the asymptotic stability of planar shear flows in the 2 D E uler equations","venue":null,"work_id":"73cd5ed3-90b4-4dd2-a485-8afce7b65cbb","year":2015},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:17.322416Z"},"links":{"citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:075e89f7db5ea432291b02f25c4b681cbeb04c425a862bc1794e3d519611a435","observation_id":"3934b28f-1475-4c58-b910-12205cfd6bea","resolution":{"observed_at":"2026-08-07T12:58:23.169142Z","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":"2026-08-07T12:58:22.888745Z","title":"Inviscid damping and the asymptotic stability of planar shear flows in the 2d E uler equations","venue":null,"work_id":"b0ba85dc-e447-4fe3-9559-036fa8672514","year":2015},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:17.373044Z"},"links":{"citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:eb54a80ca6b5a917da44fed5e42eef58ea32762389473f8bb00302150776e645","observation_id":"7693c4ed-5ac1-41ce-bab8-be1d51635167","resolution":{"observed_at":"2026-08-07T12:58:23.006550Z","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":"2026-08-07T12:58:22.666184Z","title":"Enhanced dissipation and inviscid damping in the inviscid limit of the N avier- S tokes equations near the 2D C ouette flow","venue":null,"work_id":"cf054981-b20c-4384-a7e8-ca7a0b62a0e7","year":2016},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:17.414396Z"},"links":{"citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:db62676d4690f17e5e0dfb4e07cce843ed8168f22879a139c6bdfd16e8255362","observation_id":"7b7f2c3c-6e22-438a-ab81-5cccd96c24b5","resolution":{"observed_at":"2026-08-07T12:58:22.819639Z","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":{"arxiv_id":"2410.22804","last_updated":"2024-10-30T08:32:09Z","snapshot_observed_at":"2026-08-10T04:19:43.755594Z","submitted_at":"2024-10-30T08:32:09Z","title":"Large norm inflation of the current in the viscous, non-resistive magnetohydrodynamics equations","version":1},"cited_work":{"arxiv_id":"2410.22804","doi":null,"metadata_source":"pith","pith_arxiv_id":"2410.22804","snapshot_observed_at":"2026-08-07T12:58:19.557811Z","title":"Large norm inflation of the current in the viscous, non-resistive magnetohydrodynamics equations","venue":"math.AP","work_id":"9af3c838-5bf1-4546-8a3b-30a9ea4608fb","year":2024},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:17.465090Z"},"links":{"cited_paper":"/paper/2410.22804","citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:02e0f772e697d40d8b9de26533f194b622eb950ccd71923a7ca987d10f1f835e","observation_id":"4f85cea9-e9ac-4211-b222-31046d9e6410","resolution":{"observed_at":"2026-08-07T12:58:19.596260Z","resolver_source":"local_arxiv","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:58:22.415033Z","title":"Long-time instability of the C ouette flow in low G evrey spaces","venue":null,"work_id":"6ab08d19-9d42-449c-a394-88b00953174e","year":2023},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:17.523577Z"},"links":{"citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:7dde110f28ebdc78eeea4563b1fdcc2864b044413090c09e5f9adcdc373615fa","observation_id":"3ba923ac-c2d2-4efe-b0a1-57adfe344378","resolution":{"observed_at":"2026-08-07T12:58:22.496529Z","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":"2026-08-07T12:58:22.229925Z","title":"Stability threshold of the 2D C ouette flow in a homogeneous magnetic field using symmetric variables","venue":null,"work_id":"eeafda9b-4aea-4520-9c4b-03ccf2b1c988","year":2024},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:17.578033Z"},"links":{"citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:968eedd85458aad8ea9ea02e86255d32401e2bee4d47a2ed03a7f59af19c62fc","observation_id":"54fc2177-653b-484b-b2df-e4f8de847013","resolution":{"observed_at":"2026-08-07T12:58:22.295267Z","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":"2026-08-07T12:58:22.047081Z","title":"Echo chains as a linear mechanism: Norm inflation, modified exponents and asymptotics","venue":null,"work_id":"aef06c45-a357-4ec7-b307-124465754332","year":2021},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:17.633630Z"},"links":{"citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:1daee45a50c7a72721bcc58287e9c4a466484f85e2398737ed104baaa96cb9aa","observation_id":"379e9925-968a-47b5-b37b-e8dc7b50fed7","resolution":{"observed_at":"2026-08-07T12:58:22.127599Z","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":"2026-08-07T12:58:21.939881Z","title":"Stability threshold of couette flow for 2D MHD equations in the S obolev space","venue":null,"work_id":"f29fc8d4-0c89-465f-9263-badadadd8cd7","year":2025},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:17.692437Z"},"links":{"citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:ba732cba191849365c8fa0d84a5f33c6d6582bb901157b7aa94a2ff8cc325681","observation_id":"95a49ac2-a7f7-4b7d-899c-ae563a3f85c3","resolution":{"observed_at":"2026-08-07T12:58:21.985743Z","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":{"arxiv_id":"2410.21835","last_updated":"2025-04-02T11:21:32Z","snapshot_observed_at":"2026-07-06T19:41:24.411424Z","submitted_at":"2024-10-29T07:58:06Z","title":"Ideal Magnetohydrodynamics Around Couette Flow: Long Time Stability and Vorticity-Current Instability","version":2},"cited_work":{"arxiv_id":"2410.21835","doi":null,"metadata_source":"pith","pith_arxiv_id":"2410.21835","snapshot_observed_at":"2026-08-07T12:58:19.476888Z","title":"Ideal Magnetohydrodynamics Around Couette Flow: Long Time Stability and Vorticity-Current Instability","venue":"math.AP","work_id":"d6371bed-a93f-40a6-8468-1f5d5210590a","year":2024},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:17.752927Z"},"links":{"cited_paper":"/paper/2410.21835","citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:6474a408dd5197ee6c46da7667c6f01eb4dd90681b6e9258ac6b87abfb199640","observation_id":"6e466708-7506-431c-a44a-28d31b913273","resolution":{"observed_at":"2026-08-07T12:58:19.511407Z","resolver_source":"local_arxiv","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":"2401.12548","last_updated":"2024-01-23T08:13:08Z","snapshot_observed_at":"2026-07-06T17:19:14.478786Z","submitted_at":"2024-01-23T08:13:08Z","title":"Sobolev Stability for the 2D MHD Equations in the Non-Resistive Limit","version":1},"cited_work":{"arxiv_id":"2401.12548","doi":null,"metadata_source":"pith","pith_arxiv_id":"2401.12548","snapshot_observed_at":"2026-08-07T12:58:19.355270Z","title":"Sobolev Stability for the 2D MHD Equations in the Non-Resistive Limit","venue":"math.AP","work_id":"78855e63-4781-411e-882e-6846327b2824","year":2024},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:17.814591Z"},"links":{"cited_paper":"/paper/2401.12548","citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:752ca2be9335d2bd4d1202ded8d5508f021e1e62b08ea84e4bef137b82496df2","observation_id":"7236ae81-2f86-44e9-9518-6412284d783b","resolution":{"observed_at":"2026-08-07T12:58:19.405553Z","resolver_source":"local_arxiv","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:58:21.834628Z","title":"On echoes in magnetohydrodynamics with magnetic dissipation","venue":null,"work_id":"6d094c0e-19ec-4e50-8635-a2dfbab70451","year":2023},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:17.872075Z"},"links":{"citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:bb8eca20cedbe535058f29fb86d01ec13423e888341ce94d40de6f419a0a4fa7","observation_id":"7f4e1a0e-fb13-4c4b-ba11-4907c7864d0f","resolution":{"observed_at":"2026-08-07T12:58:21.886145Z","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":"2026-08-07T12:58:21.627398Z","title":"On the S obolev stability threshold for the 2D MHD equations with horizontal magnetic dissipation","venue":null,"work_id":"85d6a377-b125-45da-9bf3-3ac9a0e9d03e","year":2025},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:17.928371Z"},"links":{"citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:d8d4c0cad0d7b551830c2cf429746c5e03fdd4dafcdf58dfad5a636064ff3085","observation_id":"d98f1b10-2396-4fde-b4f3-07f2c1acd810","resolution":{"observed_at":"2026-08-07T12:58:21.680978Z","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":"2026-08-07T12:58:21.522160Z","title":"On the S obolev stability threshold of 3D C ouette flow in a uniform magnetic field","venue":null,"work_id":"1d2044a1-6ba7-4a73-b933-6a8d2c6776e3","year":2020},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:17.980306Z"},"links":{"citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:e4c102e09b4f119157c53c8091c1176f46339951a79c71fd8cc2db27e464fed7","observation_id":"dbe47dee-14a6-4ec8-9ea4-5cd00feeb46b","resolution":{"observed_at":"2026-08-07T12:58:21.553873Z","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":{"arxiv_id":"2208.14898","last_updated":"2022-08-31T14:42:28Z","snapshot_observed_at":"2026-07-06T13:47:32.907485Z","submitted_at":"2022-08-31T14:42:28Z","title":"Asymptotic stability of two-dimensional Couette flow in a viscous fluid","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2208.14898","snapshot_observed_at":"2026-08-07T12:58:18.039987Z","title":"Asymptotic stability of two-dimensional C ouette flow in a viscous fluid","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:18.039987Z"},"links":{"cited_paper":"/paper/2208.14898","citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:e20816b100466845cff76f8ab6caebebc9678ad95d713c613ba2651b101061ae","observation_id":"14cb7191-6215-431a-9dcb-c7dc57df9d1b","resolution":{"observed_at":"2026-08-07T12:58:18.039987Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:58:21.286120Z","title":"Stability of C ouette flow for 2D B oussinesq system without thermal diffusivity","venue":null,"work_id":"3cf0e417-d23b-4b97-96d4-794a1b887c31","year":2022},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:18.095752Z"},"links":{"citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:d919cd43ffa1b8af8c3383518aa4134f82901b5e85026d1beade9fa48bea15d3","observation_id":"cd1fea8d-e541-491c-b53f-409d2dfc68f2","resolution":{"observed_at":"2026-08-07T12:58:21.421166Z","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":"2026-08-07T12:58:21.097904Z","title":"Stability threshold of two-dimensional C ouette flow in S obolev spaces","venue":null,"work_id":"33af7a7d-0294-4a30-8759-206768c6d159","year":2022},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:18.158714Z"},"links":{"citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:ecc1507bca17138f9056b8f4ba57be8cf80393682c42bf45efe85a3139a7bd99","observation_id":"398f4946-99d9-4dfd-9d40-25ffa1ecd35f","resolution":{"observed_at":"2026-08-07T12:58:21.183021Z","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":"2026-08-07T12:58:20.920024Z","title":"Asymptotic stability for two-dimensional B oussinesq systems around the C ouette flow in a finite channel","venue":null,"work_id":"d8b678df-248e-49dc-b875-4aa29b2835f0","year":2023},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:18.218082Z"},"links":{"citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:b2986fd8b2aabb223f4b3f95501ba80a6858e1a570d7dcf37a5edd3e5d984708","observation_id":"599af26e-de68-4dc2-a71c-2efbdaaa1d2c","resolution":{"observed_at":"2026-08-07T12:58:20.972370Z","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":{"arxiv_id":"2409.16216","last_updated":"2024-09-24T16:21:48Z","snapshot_observed_at":"2026-07-06T19:21:16.524383Z","submitted_at":"2024-09-24T16:21:48Z","title":"Improved stability threshold of the Two-Dimensional Couette flow for Navier-Stokes-Boussinesq Systems via quasi-linearization","version":1},"cited_work":{"arxiv_id":"2409.16216","doi":null,"metadata_source":"pith","pith_arxiv_id":"2409.16216","snapshot_observed_at":"2026-08-07T12:58:19.242488Z","title":"Improved stability threshold of the Two-Dimensional Couette flow for Navier-Stokes-Boussinesq Systems via quasi-linearization","venue":"math.AP","work_id":"02764cd5-6732-4d00-a1ac-32df1e49443d","year":2024},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:18.275340Z"},"links":{"cited_paper":"/paper/2409.16216","citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:aa74d75cf91f5f768c170fcc4d6f1ff1d725c5e0120a1c8ab84b281f647c9875","observation_id":"8c7876f5-0f6a-46d4-861a-180d1633d63e","resolution":{"observed_at":"2026-08-07T12:58:19.272438Z","resolver_source":"local_arxiv","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:58:20.713576Z","title":null,"venue":null,"work_id":"865f41ad-8b3d-4e8a-9576-a78d29271bed","year":null},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:18.320204Z"},"links":{"citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:c59994905096dfcff039a873a78657be32991a07f46d1f7b4c2c959f55870f3c","observation_id":"b8a36ff7-6c72-48dc-b706-5a7e548bd242","resolution":{"observed_at":"2026-08-07T12:58:20.823173Z","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":"2026-08-07T12:58:20.540136Z","title":"Stability threshold of C ouette flow for the 3D MHD equations","venue":null,"work_id":"5d1ebd8f-26ec-4c67-84a4-91b2f279ed0a","year":2025},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:18.371305Z"},"links":{"citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:bf461df0f15882ec98d95e8743f5100ba6c794887d81fee760e900dae0d0c71e","observation_id":"ce1d1998-3b67-46b7-bbe4-595cc031b9ce","resolution":{"observed_at":"2026-08-07T12:58:20.576485Z","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":"2026-08-07T12:58:20.455565Z","title":"Stability and transition in shear flows","venue":null,"work_id":"2c8acd9f-f806-4d4b-8ca0-89d287cdf5e4","year":2002},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:18.428175Z"},"links":{"citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:06756e7d1521b7c6ee1309622bb09819745a3854496d098b6c05d4e49abc23b2","observation_id":"6f93d3d5-1990-4d88-a89d-ee90d9d6323c","resolution":{"observed_at":"2026-08-07T12:58:20.496408Z","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":{"arxiv_id":"2505.19822","last_updated":"2025-09-10T15:34:13Z","snapshot_observed_at":"2026-08-07T14:03:22.192855Z","submitted_at":"2025-05-26T11:00:11Z","title":"The stability threshold for 3D MHD equations around Couette with rationally aligned magnetic field","version":3},"cited_work":{"arxiv_id":"2505.19822","doi":null,"metadata_source":"pith","pith_arxiv_id":"2505.19822","snapshot_observed_at":"2026-08-07T12:58:19.128558Z","title":"The stability threshold for 3D MHD equations around Couette with rationally aligned magnetic field","venue":"math.AP","work_id":"7f078a43-21b8-4e7e-bfb9-fc4bab327e76","year":2025},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:18.486009Z"},"links":{"cited_paper":"/paper/2505.19822","citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:14b5dc784635101fe9670164d6b3d04b630785924ab8faa657c815cd9269ca8f","observation_id":"f3b9fe7f-a8aa-429b-8482-1278d68f28b0","resolution":{"observed_at":"2026-08-07T12:58:19.175981Z","resolver_source":"local_arxiv","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:58:20.344104Z","title":"Nonlinear enhanced dissipation and inviscid damping for the 2D C ouette flow","venue":null,"work_id":"78e96f32-2b5d-4d80-bf18-e78364d17026","year":2023},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:18.537859Z"},"links":{"citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:927ede866c56d1a0be903907e97413466dc00a3e84660a43ef55d556049d1275","observation_id":"2e2036f6-5b87-4105-b6fb-f58bfb66fd18","resolution":{"observed_at":"2026-08-07T12:58:20.411612Z","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":{"arxiv_id":"2410.20404","last_updated":"2024-10-27T10:32:47Z","snapshot_observed_at":"2026-08-09T13:08:33.715970Z","submitted_at":"2024-10-27T10:32:47Z","title":"The stability threshold for 2D MHD equations around Couette with general viscosity and magnetic resistivity","version":1},"cited_work":{"arxiv_id":"2410.20404","doi":null,"metadata_source":"pith","pith_arxiv_id":"2410.20404","snapshot_observed_at":"2026-08-07T12:58:19.034644Z","title":"The stability threshold for 2D MHD equations around Couette with general viscosity and magnetic resistivity","venue":"math.AP","work_id":"452d5809-96fa-4053-bde6-72776b722146","year":2024},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:18.585554Z"},"links":{"cited_paper":"/paper/2410.20404","citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:de0ee767014d420c891914a8cb1a35a88b245180667398e92b3a6697cc71c5c8","observation_id":"8910039d-7598-4dd5-8a2f-b5cf07fedbce","resolution":{"observed_at":"2026-08-07T12:58:19.062221Z","resolver_source":"local_arxiv","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:58:20.186063Z","title":"Linear inviscid damping for C ouette flow in stratified fluid","venue":null,"work_id":"62d97ce8-3bc3-471e-9edc-46e8bf02da3a","year":2018},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:18.635143Z"},"links":{"citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:50e9a1167cfd7e84c07b30fe74dc81bf98cdcb8bfac5a0747ef2ba6515d8765e","observation_id":"0dfc430f-a01c-40b7-bef6-ac8f80977258","resolution":{"observed_at":"2026-08-07T12:58:20.254043Z","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":"2026-08-07T12:58:20.112693Z","title":"On enhanced dissipation for the B oussinesq equations","venue":null,"work_id":"f40960a3-8cad-4fab-8308-5473a276d55a","year":2021},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:18.693091Z"},"links":{"citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:bafbea4579521d071e1534ffb8ac5288a4f8677a6c76a3e61cf52bf003ab224b","observation_id":"8d28b75b-5dfe-4f8a-a1fa-4128caf9d47e","resolution":{"observed_at":"2026-08-07T12:58:20.139850Z","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":"2026-08-07T12:58:20.020123Z","title":"On the B oussinesq equations with non-monotone temperature profiles","venue":null,"work_id":"73c92e46-4a03-49ef-a518-28cc70ff0fa3","year":2021},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:18.732629Z"},"links":{"citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:5563f67110017d83ee0982c612cf1ad7ec952391e23c16c43a495b6b033c208f","observation_id":"af6c5cda-e701-46c4-b6fd-e95475846114","resolution":{"observed_at":"2026-08-07T12:58:20.071588Z","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":"2026-08-07T12:58:19.841053Z","title":"On echo chains in the linearized B oussinesq equations around traveling waves","venue":null,"work_id":"3029e0e4-8a81-4d91-b66e-5ddf0fda1239","year":2023},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:18.780148Z"},"links":{"citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:176dd03609784d035536aff4d93c73f6b6cf789f2364d1f45d941684121865c9","observation_id":"4fc2731f-2228-400a-800b-ae26fc269af1","resolution":{"observed_at":"2026-08-07T12:58:19.911265Z","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":"2026-08-07T12:58:19.793923Z","title":"Stability threshold of the C ouette flow for N avier-- S tokes B oussinesq system with L arge R ichardson number","venue":null,"work_id":"b7181266-854a-48a1-819a-96d2bb6fe1d8","year":2023},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:18.838604Z"},"links":{"citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:83eb34f65dc7471221e15b93dcf9e268c673e2151e3b1554d511e253bda2fb3c","observation_id":"3927fc7d-8950-4247-ac6c-d350b9e12c9c","resolution":{"observed_at":"2026-08-07T12:58:19.813958Z","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":"2026-08-07T12:58:19.749369Z","title":"Stability threshold of C ouette flow for 2D B oussinesq equations in S obolev spaces","venue":null,"work_id":"d12c6425-5d2e-4371-ba19-1ec137fef901","year":2023},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:18.895123Z"},"links":{"citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:c220fbf408b32aebc4aee48362df76346823c200df06fe4207a5d19ccd4e4a8c","observation_id":"51f63329-1827-4371-a04c-077fff908fc6","resolution":{"observed_at":"2026-08-07T12:58:19.780521Z","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":"2026-08-07T12:58:19.659115Z","title":"Asymptotic stability of C ouette flow in a strong uniform magnetic field for the E uler- MHD system","venue":null,"work_id":"dc6bea4c-14be-4b95-b314-8150a8ed4b59","year":2024},"citing_paper":{"arxiv_id":"2505.23391","last_updated":"2025-05-29T12:23:33Z","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-07T12:58:18.956660Z"},"links":{"citing_paper":"/paper/2505.23391"},"observation_digest":"sha256:bcc478be40890dcfc22d5d82cfb29ee70c591691cd0a0a408243cc47d631c96a","observation_id":"e528940d-6cf1-4942-a91e-243e69358e49","resolution":{"observed_at":"2026-08-07T12:58:19.699538Z","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":"2505.23391","last_updated":"2025-05-29T12:23:33Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-07T12:44:24.058343Z","submitted_at":"2025-05-29T12:23:33Z","title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow"},"reference_resolution":{"displayed":33,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":2,"verified_exact":6,"verified_fuzzy":25},"total_outbound_references":33},"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 33 of 33 outbound references and 1 inbound Pith citation observation for arXiv:2505.23391."}