{"as_of":"2026-08-17T10:09:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:126d20d27e99eaeb64cdb2327461f8d5c8835922fc1e1f65e0ece6f86eb9f2be","coverage":[{"denominator":45,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":45,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T23:11:14.908033Z","state":"measured"},{"denominator":47,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":47,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-17T06:30:58.91139+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T16:56:45.717395Z","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":"2026-07-02T10:16:51.661442Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"cited_work":{"arxiv_id":"2505.05430","doi":null,"metadata_source":"pith","pith_arxiv_id":"2505.05430","snapshot_observed_at":"2026-07-02T10:16:51.661442Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","venue":"math.AP","work_id":"fe45f579-3a5b-4c43-a3cf-6b7f6181a03c","year":2025},"citing_paper":{"arxiv_id":"2607.00450","last_updated":"2026-07-01T05:08:38Z","snapshot_observed_at":"2026-08-10T03:45:08.376761Z","submitted_at":"2026-07-01T05:08:38Z","title":"A rigidity result for the 3D capillary liquid drop with constant vorticity","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-07-02T10:10:01.205825Z"},"links":{"cited_paper":"/paper/2505.05430","citing_paper":"/paper/2607.00450"},"observation_digest":"sha256:fd8b8494cf4d48d65ebc4ac627c394bc319a0d9b3fccc93023b36e7c48e8bd03","observation_id":"106a1752-6937-4748-a3f4-c85143ec65a6","resolution":{"observed_at":"2026-07-02T10:16:51.663090Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.05430","snapshot_observed_at":"2026-08-01T16:56:45.717395Z","title":"Pasquali , Two-dimensional water waves with constant vorticity and general bottom topography, preprint, arXiv:2505.05430","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.17844","last_updated":"2026-07-20T11:39:13Z","snapshot_observed_at":"2026-08-07T09:37:55.346310Z","submitted_at":"2026-07-20T11:39:13Z","title":"Rigidity for capillary liquid drops of nearly circular section with constant vorticity","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-01T16:56:45.717395Z"},"links":{"cited_paper":"/paper/2505.05430","citing_paper":"/paper/2607.17844"},"observation_digest":"sha256:e3067e85dddf579a68aff56c14c891aa41f957f1ccdd115b96fe424f48a218e7","observation_id":"2ca4a6a8-acc0-48f6-8309-dd345766f17c","resolution":{"observed_at":"2026-08-01T16:56:45.717395Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2505.05430/citation-record","integrity":"/paper/2505.05430/integrity","json":"/paper/2505.05430/citation-record.json","paper":"/paper/2505.05430"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.674219Z","title":"Gravity capillary standing water waves","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.674219Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:1f74ff102cda0284e48fb83a0640eb3242518fc3f5a1b1416215379b50b04de5","observation_id":"11cda1a9-9ca1-43b1-94ba-b060b33be2de","resolution":{"observed_at":"2026-08-15T23:11:14.674219Z","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":"2026-08-15T23:11:15.512158Z","title":"Control of water waves","venue":null,"work_id":"56d70f5f-35ae-4fd1-a44c-e051d4e8c4d9","year":2018},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.679829Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:a94eb1ea8bd75b970501b8774645d7e27dea0692c4391549f2366d7ca5efa524","observation_id":"6d570fcc-2c3c-49d1-a0d6-613142bbbff8","resolution":{"observed_at":"2026-08-15T23:11:15.517231Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.685736Z","title":"On the water-wave equations with surface tension","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.685736Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:f3092be50f6dceecccbde975239547857df33bf48091eaf75658347a740b7864","observation_id":"13b4809c-f9c2-466f-934e-71c1f6671b4c","resolution":{"observed_at":"2026-08-15T23:11:14.685736Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.691329Z","title":"On the Cauchy problem for gravity water waves","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.691329Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:bf795e3c5f1d21cf696018f1e31ba3bd82656d36a9e70a958ca22eecccd66086","observation_id":"a2444cab-55d6-4cdc-bb3b-727afac39dbe","resolution":{"observed_at":"2026-08-15T23:11:14.691329Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.697284Z","title":"Cauchy theory for the gravity water waves system with non-localized initial data","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.697284Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:0d0088ddbf10f48ae894dab13f8311881840409e6c2f36886864ff701c3eeb25","observation_id":"048a01d5-5dd0-4624-b475-19890aba074b","resolution":{"observed_at":"2026-08-15T23:11:14.697284Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.702760Z","title":"Sobolev estimates for two dimensional gravity water waves","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.702760Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:eb88a3c89971938841c06e0766e8a27ad369ab368183d53bf9af06f4f21acbbe","observation_id":"0ad7b555-714b-48a4-8c89-10b17b6a094c","resolution":{"observed_at":"2026-08-15T23:11:14.702760Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.709303Z","title":"Two-dimensional gravity waves at low regularity II: Global solutions","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.709303Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:f9f9e8ca95a55cf1a58c6c585cec447827fad13053c452adcbb4bc92ed2cd84c","observation_id":"fc57d66e-5f41-4770-ad93-adf9f5ed4824","resolution":{"observed_at":"2026-08-15T23:11:14.709303Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.714468Z","title":"Paralinearization of the Dirichlet to Neumann operator, and regularity of three-dimensional water waves","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.714468Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:207edc53e53d14278bf6dd1f9f2076d7285f885ec85a1472adf065f80142bce2","observation_id":"bf075457-c617-4c1e-bce5-ea09f98c7231","resolution":{"observed_at":"2026-08-15T23:11:14.714468Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.720504Z","title":"Time quasi-periodic gravity water waves in finite depth","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.720504Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:797254532e1e0a4b4c6646e5ef8e6de5a9d787f2f5778096158aa61e40e8d721","observation_id":"379995ec-3a65-4aa0-b4df-817e873f7afb","resolution":{"observed_at":"2026-08-15T23:11:14.720504Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.14353","last_updated":"2025-07-24T12:20:26Z","snapshot_observed_at":"2026-08-16T12:58:43.154042Z","submitted_at":"2025-01-24T09:29:42Z","title":"Bifurcation of gravity-capillary Stokes waves with constant vorticity","version":2},"cited_work":{"arxiv_id":"2501.14353","doi":null,"metadata_source":"pith","pith_arxiv_id":"2501.14353","snapshot_observed_at":"2026-08-15T23:11:14.992896Z","title":"Bifurcation of gravity-capillary Stokes waves with constant vorticity","venue":"math.AP","work_id":"59153b0a-3588-4b51-82c4-93b606baad0e","year":2025},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.725565Z"},"links":{"cited_paper":"/paper/2501.14353","citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:2dfde51ab92c3bc63ec9eec36d8854aa55433151b69cd65794b3736c284b3b2e","observation_id":"c253a444-a348-4193-8f2e-ea8c608bf5b1","resolution":{"observed_at":"2026-08-15T23:11:14.999059Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.731804Z","title":"Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.731804Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:28db6d18677a2192ad9e514c8e6a4406d8264ede1c5e2153548ed1cf6d43cfa1","observation_id":"c85df4b4-9966-4c58-aa57-224e85cb9835","resolution":{"observed_at":"2026-08-15T23:11:14.731804Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.737098Z","title":"Traveling quasi-periodic water waves with constant vorticity","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.737098Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:6f7f997b0e026abe5b0b7cccb2a934f440d42f71f45f7b1f1c7dc14f6beb7eb3","observation_id":"f2c1bc97-fa54-48d0-a18c-32fed593a99a","resolution":{"observed_at":"2026-08-15T23:11:14.737098Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.742074Z","title":"Pure gravity traveling quasi-periodic water waves with constant vorticity","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.742074Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:4e537246d7f7f15eca47959ed08cdc101e514854252174be09233737e23e8cb7","observation_id":"d41fa163-f294-42a5-9670-917470f01325","resolution":{"observed_at":"2026-08-15T23:11:14.742074Z","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":"2026-08-15T23:11:15.382104Z","title":"Hamiltonian birkhoff normal form for gravity-capillary water waves with constant vorticity: almost global existence","venue":null,"work_id":"6e303508-66d8-4b36-8715-065d7f65c363","year":2024},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.746978Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:659f2bb5845d4293f40570924aa0f017a17ef3bd8e406120766c1ad8419d9370","observation_id":"7d2f164e-8b56-4129-83b9-dcf20002684d","resolution":{"observed_at":"2026-08-15T23:11:15.387148Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T23:11:15.365000Z","title":"On the analyticity of the dirichlet--neumann operator and stokes waves","venue":null,"work_id":"68e53f89-5de7-4ac9-b4c5-af21360edfb5","year":2022},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.752056Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:8632cd54447317e0a69a7886af193efbc4201620f7ba7e81e7e679e8df923830","observation_id":"b2dae80b-ce13-40c5-b9c7-b91df0187a40","resolution":{"observed_at":"2026-08-15T23:11:15.370186Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T23:11:15.348241Z","title":"Analytic theory of global bifurcation: an introduction , volume 9","venue":null,"work_id":"0601854b-132c-451e-ac58-700c6765beb4","year":2003},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.757189Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:106b3b5e2dafd898d3c5932a587d00054974cb191558c302f1360da2c1d47b9a","observation_id":"6aa0a1ea-9982-4bb7-b9ee-20d7d14d7d5e","resolution":{"observed_at":"2026-08-15T23:11:15.353434Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T23:11:15.332011Z","title":"Hamiltonian long--wave expansions for water waves over a rough bottom","venue":null,"work_id":"65b9588f-2b85-44bc-a5a2-6b1e6ddde62c","year":2005},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.762979Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:a0f615dbcdde00bd3e76564febf12cb6ad145d3a46feadeea8b411c357cf7c48","observation_id":"b51e0bd2-8ec6-4580-bf7e-a0a4cb08e52d","resolution":{"observed_at":"2026-08-15T23:11:15.337206Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T23:11:15.314272Z","title":"Nearly-Hamiltonian Structure for Water Waves with Constant Vorticity","venue":null,"work_id":"ce400133-a2d3-498f-8a18-6a51c674032e","year":2007},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.768355Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:762511ab8f61f2cf75e8f5479bbe803d3b8839cdf503cab861006391d3467b94","observation_id":"984589f1-3be4-4fb3-a892-f6aca45feac8","resolution":{"observed_at":"2026-08-15T23:11:15.319534Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.773190Z","title":"Well-posedness and shallow-water stability for a new Hamiltonian formulation of the water waves equations with vorticity","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.773190Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:8798e2f4de471bc2c236cfd24e540366de5e41d6ce8e5a08a5ef23eddc80788c","observation_id":"55ec907f-36b0-445f-914b-12751b85e0e3","resolution":{"observed_at":"2026-08-15T23:11:14.773190Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.778411Z","title":"Numerical simulation of gravity waves","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.778411Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:bd348186cd50d84ebe082afee8e735db8b515c1234d9c5aed403a22afd7ffcc6","observation_id":"b1610840-6aa2-4e1e-be53-7f4f66b2859a","resolution":{"observed_at":"2026-08-15T23:11:14.778411Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.783430Z","title":"Exact steady periodic water waves with vorticity","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.783430Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:da2dd300c59d3712dcacec289ac79d14efbb24ca7a455c3eb53d4dcd97749c61","observation_id":"4162cbb4-350b-4fe8-bef2-85b1a303d274","resolution":{"observed_at":"2026-08-15T23:11:14.783430Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.788451Z","title":"Well-posedness of the free-surface incompressible Euler equations with or without surface tension","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.788451Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:fa0937eac76468c8c5adf0676c6ce64956a4fe9fce5689e24e39580687a47043","observation_id":"b360a92b-0dcb-402f-b61e-314810df1aae","resolution":{"observed_at":"2026-08-15T23:11:14.788451Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.793308Z","title":"Smooth stationary water waves with exponentially localized vorticity","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.793308Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:b64406d9a295876843597a1b3907acfac7f741ba42a08a6ac6e6981b17c69d8c","observation_id":"bd57bb4e-baeb-4ca5-ac10-f546e36cf2bc","resolution":{"observed_at":"2026-08-15T23:11:14.793308Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.798285Z","title":"Quasi-periodic traveling waves on an infinitely deep perfect fluid under gravity , volume 295","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.798285Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:ce7882706b2ee73df645d77e63cee319aa2ef86faedad2a98a97d892c352e471","observation_id":"57c27bc3-d38d-453c-92bb-7a9e6ce72a95","resolution":{"observed_at":"2026-08-15T23:11:14.798285Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.803804Z","title":"Theorie der wellen","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.803804Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:3dc7ff772144b9823cbd5fac149eca723948ee865101f62d02de2420788ffda3","observation_id":"e5b382c7-a129-4998-84ed-308805bc9214","resolution":{"observed_at":"2026-08-15T23:11:14.803804Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.809610Z","title":"A variational formulation for steady surface water waves on a Beltrami flow","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.809610Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:a4eb56c5abffeff1fb834da9fc2730ccf0d6e92bd0fe54aa25ad588c4be939f2","observation_id":"897ea7f6-0015-4f3f-9d15-0a32993eb6c8","resolution":{"observed_at":"2026-08-15T23:11:14.809610Z","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":"2026-08-15T23:11:15.208132Z","title":"Analytical Study of a generalised Dirichlet-Neumann operator and application to three-dimensional water waves on Beltrami flows","venue":null,"work_id":"71b5e650-997d-4886-9f53-29df9848831c","year":2024},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.816103Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:97b51f8d40a7c3323a137b4eebd3f7bbe97db073aa0a776abffdf5884fa83686","observation_id":"0c1a20ff-0559-46a6-8e39-5a936400508e","resolution":{"observed_at":"2026-08-15T23:11:15.213368Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T23:11:15.190000Z","title":"A mathematical analysis of tsunami generation in shallow water due to seabed deformation","venue":null,"work_id":"f23bebd6-8db3-4e21-ae0d-ec26e792a919","year":2011},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.822113Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:513b39b59b780329156b8b1b0db56078b59055a9a7fa78c304088c052d658548","observation_id":"5f9ceac6-af50-460f-8879-66037784565a","resolution":{"observed_at":"2026-08-15T23:11:15.195758Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.827282Z","title":"Global solutions for the gravity water waves system in 2d","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.827282Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:268aa4f3ade687f966864ef8f6355858eedc48a217a0ed3b009f0a359cc5b91f","observation_id":"0e817944-656f-4704-b944-cfdf30333aed","resolution":{"observed_at":"2026-08-15T23:11:14.827282Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.832096Z","title":"Standing waves on an infinitely deep perfect fluid under gravity","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.832096Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:5c4a41daca5e60487d7cdb707f93ce432f3abec99827336a06aef22fe4d932b0","observation_id":"ad785994-c0f3-4c80-963e-0e13d4da0301","resolution":{"observed_at":"2026-08-15T23:11:14.832096Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2309.05625","last_updated":"2025-03-26T11:53:33Z","snapshot_observed_at":"2026-08-16T15:01:39.085032Z","submitted_at":"2023-09-11T17:13:35Z","title":"Sharp Hadamard local well-posedness, enhanced uniqueness and pointwise continuation criterion for the incompressible free boundary Euler equations","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2309.05625","snapshot_observed_at":"2026-08-15T23:11:14.837103Z","title":"Sharp Hadamard local well-posedness, enhanced uniqueness and pointwise continuation criterion for the incompressible free boundary Euler equations","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.837103Z"},"links":{"cited_paper":"/paper/2309.05625","citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:c2f504f494656d8d1bfa72328ead04bf0fdab9c2f0a24cb53bf7b20b2e79e1e9","observation_id":"6e20d281-83dc-48aa-9893-0e0ffd5bc92b","resolution":{"observed_at":"2026-08-15T23:11:14.837103Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.842194Z","title":"Two-dimensional gravity water waves with constant vorticity, I: Cubic lifespan","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.842194Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:9173c31b5ae92a1ae9814de144d3fe8097a4ee7137dd961de40b429b9429c519","observation_id":"0b340ea8-d58e-48fa-b0b0-7f761d03f67b","resolution":{"observed_at":"2026-08-15T23:11:14.842194Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.847019Z","title":"Well-posedness of the water-waves equations","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.847019Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:6edee855d35e7ecf0004df6a95c7118bdc4041a3c5f0233e2d444863ba1a5188","observation_id":"be8b2250-cf86-4670-9eb4-a56723615dd1","resolution":{"observed_at":"2026-08-15T23:11:14.847019Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.851897Z","title":"The water waves problem: mathematical analysis and asymptotics , volume 188","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.851897Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:6d1d060a4be9d6a1414c64b1331f800386c8f39cd140d160829423b240864358","observation_id":"f86bd031-8a4b-4748-8a1c-dca9fa8ece66","resolution":{"observed_at":"2026-08-15T23:11:14.851897Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.856956Z","title":"D \\'e termination rigoureuse des ondes permanentes d'ampleur finie","venue":null,"work_id":null,"year":1925},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.856956Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:5851aad2920a8d259a7350ca98359eba2898f86840850ebb9cbe658531bdbd9e","observation_id":"ef01285a-a51f-4574-acc0-506bce54f684","resolution":{"observed_at":"2026-08-15T23:11:14.856956Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.862145Z","title":"Paradifferential Calculus and Application to the Cauchy Problem for Nonlinear Systems","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.862145Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:d3de7ce6e7f9153d3d1ea47ce6a51f6609b2cb05336dba7e3facd7cda2b133bd","observation_id":"aca6ff13-aee8-4f56-b2c2-117117b4e9b3","resolution":{"observed_at":"2026-08-15T23:11:14.862145Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.09370","last_updated":"2025-07-11T15:38:48Z","snapshot_observed_at":"2026-08-07T21:42:00.794620Z","submitted_at":"2025-02-13T14:36:36Z","title":"Analytical study of a generalized Dirichlet-Neumann operator for three-dimensional water waves with vorticity","version":2},"cited_work":{"arxiv_id":"2502.09370","doi":null,"metadata_source":"pith","pith_arxiv_id":"2502.09370","snapshot_observed_at":"2026-08-15T23:11:14.947611Z","title":"Analytical study of a generalized Dirichlet-Neumann operator for three-dimensional water waves with vorticity","venue":"math.AP","work_id":"9cf596e1-b7e4-4218-aeac-021e32304e12","year":2025},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.867103Z"},"links":{"cited_paper":"/paper/2502.09370","citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:8b2bcb57c6e83a94367078d5b78c10aee4322fc86158bd4b13240c72f5eaa911","observation_id":"dc6f4b1c-ab70-494a-baa5-f81138dd994f","resolution":{"observed_at":"2026-08-15T23:11:14.954950Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.872326Z","title":"On the theory of oscillatory waves","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.872326Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:9515d5919aec5766e32e24ba0c0807a6ea06dc435db0f3554a7317b2a81e6f72","observation_id":"2374db69-ad81-47d1-8162-c0e6c9903ce6","resolution":{"observed_at":"2026-08-15T23:11:14.872326Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.877349Z","title":"Local well-posedness for fluid interface problems","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.877349Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:7478af124049d0d3e430f4d7058b03b5317fcdb94b9ff02b43eee9f4902dc4ac","observation_id":"39c433a3-e46e-4a77-945e-1d567c72879c","resolution":{"observed_at":"2026-08-15T23:11:14.877349Z","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":"2026-08-15T23:11:15.072102Z","title":"Partial differential equations I: Basic Theory , volume 115","venue":null,"work_id":"f238a66b-4883-41f6-9760-8c03b2c2f154","year":2011},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.882128Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:8a222b7f14abc84d54245870f9fbd530befd1e9427f7f4e3a115ec20b61e3558","observation_id":"00c55a42-1810-44ff-ba79-3e24e9a03d01","resolution":{"observed_at":"2026-08-15T23:11:15.077395Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.887254Z","title":"Steady periodic capillary-gravity waves with vorticity","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.887254Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:159860d498708e9463b9eef71ff8ba857dbfcd90442b092de60647a6129b296b","observation_id":"d9497eab-53a7-40e6-b0d1-7819be07ef6e","resolution":{"observed_at":"2026-08-15T23:11:14.887254Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.891977Z","title":"A Hamiltonian formulation of water waves with constant vorticity","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.891977Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:a344ccb69b0e12cdfb74129aeb73299dd2df4067128e114269d15f7b55228cf9","observation_id":"aa603acc-f211-49c4-a4f1-66948da2e82a","resolution":{"observed_at":"2026-08-15T23:11:14.891977Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.896862Z","title":"Almost global wellposedness of the 2-D full water wave problem","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.896862Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:779c66fb5c4ba236e1cfffa4941e42123403e321a0a13385bd3dcae7345bd0f5","observation_id":"f962a819-94dd-4b09-86af-c0bb220dc4d5","resolution":{"observed_at":"2026-08-15T23:11:14.896862Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T23:11:14.902785Z","title":"Global bifurcation of capillary-gravity water waves with overhanging profiles and arbitrary vorticity","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.902785Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:a3f342fd32058d89e0dd737cf4f16bf5870ac2d1898ccc1d48e79a18c69b1fd1","observation_id":"22160bb2-f05e-42be-95c7-18ae4bb7d823","resolution":{"observed_at":"2026-08-15T23:11:14.902785Z","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":"2026-08-15T23:11:15.011305Z","title":"Local well-posedness and break-down criterion of the incompressible Euler equations with free boundary , volume 270","venue":null,"work_id":"273148c1-3970-436c-b7f8-5fb331b4e5c9","year":2021},"citing_paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography","version":4},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-15T23:11:14.908033Z"},"links":{"citing_paper":"/paper/2505.05430"},"observation_digest":"sha256:5df60213efb8b5fb67a433ae1a278d9cba4158c88ebf442f986565921582ecfe","observation_id":"7afab9e1-003d-4697-99f8-0f2d45332e63","resolution":{"observed_at":"2026-08-15T23:11:15.016723Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.05430","last_updated":"2026-07-07T13:50:49Z","latest_version":4,"primary_category":"math.AP","snapshot_observed_at":"2026-08-15T23:01:30.156296Z","submitted_at":"2025-05-08T17:20:33Z","title":"Two-dimensional water waves with constant vorticity and general bottom topography"},"reference_resolution":{"displayed":45,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":33,"verified_exact":2,"verified_fuzzy":10},"total_outbound_references":45},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"thesis":"As of 17 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 2 inbound Pith citation observations for arXiv:2505.05430."}