{"as_of":"2026-08-14T11:42:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:d31383f601be7f7955968659dcc46b58dc04e80dbeadffd9b9ed43fa7c0e51fe","coverage":[{"denominator":71,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":71,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T05:47:16.929573Z","state":"measured"},{"denominator":71,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":71,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2608.06314/citation-record","integrity":"/paper/2608.06314/integrity","json":"/paper/2608.06314/citation-record.json","paper":"/paper/2608.06314"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:47:30.239422Z","title":"Alvarez-Samaniego and D","venue":null,"work_id":"f878212b-4ca5-419a-b760-df61bf0caa66","year":2008},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:11.931516Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:cf152b112b7a2420b5eb0397f1d5a8ca121579c40bbff5ba9e5fed452914a652","observation_id":"a17c1820-caf1-44eb-994c-d3cef1e2fb4d","resolution":{"observed_at":"2026-08-07T05:47:30.302022Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:30.069787Z","title":null,"venue":null,"work_id":"50605cde-f7a3-4842-814e-bf935a82a36d","year":1995},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:12.015612Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:fd859a2a96edb335bd0b4c882698944327d34fc22f4da9a88eb0d2bdcc8d4b06","observation_id":"f1a8436f-b91a-4602-9436-d799451f178d","resolution":{"observed_at":"2026-08-07T05:47:30.176988Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:29.915246Z","title":"Baldi, M","venue":null,"work_id":"b4bc9061-7339-4878-b0a1-3bd2fd30ad21","year":2018},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:12.096692Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:b806fe388a2a2d2fd4a15e012eec39a4b5932af72e07462284dec56e3cd82420","observation_id":"8a786675-e262-45d3-bd74-e67d467397ed","resolution":{"observed_at":"2026-08-07T05:47:29.990913Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:29.752678Z","title":null,"venue":null,"work_id":"e8599303-9031-435f-bbc9-5376155ae3de","year":1954},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:12.160600Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:9c4d1c5d87b6acbb0a2c371a97a29655a4b0d1108bce6ad8c880e717119b8721","observation_id":"b8fb88b0-8f65-4783-a434-eb40f5e42743","resolution":{"observed_at":"2026-08-07T05:47:29.814953Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:29.498391Z","title":"Berti, L","venue":null,"work_id":"e87aef2d-6fc5-4cbc-8e7f-d47414a5d04d","year":2021},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:12.257120Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:1e7661c7ea7a469f054a6a7871503af9623a3aa31dfe14c12a69cc55b3d79131","observation_id":"945b67e0-42ea-4581-a4db-a4047820488b","resolution":{"observed_at":"2026-08-07T05:47:29.608016Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:29.234229Z","title":"Benjamin and T.J","venue":null,"work_id":"49c09d63-706e-44e2-8710-23fd9c1b4421","year":1997},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:12.343462Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:4d0390230f64bffd7c6764cf1ddb8ad634e6c9e690230def06c22386721cd793","observation_id":"5ef9ef14-5388-4091-b9ea-38dcdbaec414","resolution":{"observed_at":"2026-08-07T05:47:29.319429Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:28.995657Z","title":"Benjamin and T.J","venue":null,"work_id":"45348cd9-13db-4253-8675-babb3e7dcee2","year":1997},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:12.412565Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:c93eebfe77baadfb67a9bcb0844f97bed1444426f76c3d3eb94489a4b01c7320","observation_id":"ae513e85-de12-45e9-a24e-7a2fa1102c7f","resolution":{"observed_at":"2026-08-07T05:47:29.126057Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:12.521594Z","title":null,"venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:12.521594Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:b3685fb48e44126293c5927126537bfc412661b427eab2b893823b1d93cd5939","observation_id":"8e483d12-ae16-4dfe-ae50-d45d65a088b5","resolution":{"observed_at":"2026-08-07T05:47:12.521594Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:47:28.803410Z","title":"Camassa, G","venue":null,"work_id":"a5774dd3-1868-4905-9a30-731a2898b226","year":2021},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:12.591765Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:3bd56d7fad6863b7a66092935f19fbdba96432433bd105b31b38d40a80cd8ae1","observation_id":"d700656c-408a-4ce4-bc22-07e981b29b1a","resolution":{"observed_at":"2026-08-07T05:47:28.914068Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"0811.06011","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:47:18.721482Z","title":"Canning Gregory and D.P","venue":null,"work_id":"1ae50a81-5186-4bef-a644-c7c9ebdb96fe","year":2012},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:12.654552Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:ba3c066b0f533cd534e1153f10340f28ea5591508ace1d9c7f9db0c511f53a0d","observation_id":"3b0b5271-3806-4aa3-844c-a4338284e53b","resolution":{"observed_at":"2026-08-07T05:47:18.832649Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:28.645984Z","title":"Choi and R","venue":null,"work_id":"cb294931-3496-402e-a673-633775e312df","year":1996},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:12.710325Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:58afc2ca82262f3b3f612ae2610af8b5090ab6c91a9631c7d81e97d292f44e0e","observation_id":"a8c87fd2-bc6e-469b-ac62-00605b77e954","resolution":{"observed_at":"2026-08-07T05:47:28.687472Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:28.514532Z","title":"Choi and R","venue":null,"work_id":"090a6c03-b4f4-4569-a291-bb909bf85967","year":1999},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:12.796084Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:028ebdbed0980b8569f4af71077a3ae92211cae01d9e1c868bb994a706e02434","observation_id":"08b0dce7-ff19-4b00-975a-1a8d05b199c8","resolution":{"observed_at":"2026-08-07T05:47:28.588407Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/jfm.2022.830","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Clamond, Explicit Dirichlet-Neumann operator for water waves","venue":"Journal of Fluid Mechanics","work_id":"66517c90-d555-4f7c-bce4-7c767b57bb1e","year":2022},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:12.862124Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:ee9a357268e68f1977dade07c1fb3ffca70be40d88a9771b63afa16ba4f72dde","observation_id":"b5ff6df3-899d-497c-8b77-8672f0257334","resolution":{"observed_at":"2026-08-07T05:47:17.676114Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1611.06581","last_updated":"2016-11-20T20:05:50Z","snapshot_observed_at":"2026-07-06T05:19:23.158124Z","submitted_at":"2016-11-20T20:05:50Z","title":"The Dynamics of Flat Surface Internal Geophysical Waves with Currents","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1611.06581","snapshot_observed_at":"2026-08-07T05:47:12.944135Z","title":"Compelli, R","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:12.944135Z"},"links":{"cited_paper":"/paper/1611.06581","citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:be68bf99e61b1f463cd73a6b761979db6516882b6ca85d2293e804f3f2db613a","observation_id":"7f7fe0ac-01a7-4158-9f94-547a3c7cbfe2","resolution":{"observed_at":"2026-08-07T05:47:12.944135Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1708.06791","last_updated":"2017-08-22T19:27:41Z","snapshot_observed_at":"2026-07-06T05:56:18.481069Z","submitted_at":"2017-08-22T19:27:41Z","title":"Hamiltonian models for the propagation of irrotational surface gravity waves over a variable bottom","version":1},"cited_work":{"arxiv_id":"1708.06791","doi":null,"metadata_source":"pith","pith_arxiv_id":"1708.06791","snapshot_observed_at":"2026-08-07T05:47:18.451947Z","title":"Hamiltonian models for the propagation of irrotational surface gravity waves over a variable bottom","venue":"physics.flu-dyn","work_id":"6d7cd471-969c-4b21-8d69-b38ffbf804ec","year":2017},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:13.006166Z"},"links":{"cited_paper":"/paper/1708.06791","citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:c87e43d0348a9b3ff3926d3d351114eb2a1daf9c51ebdfd49c0d11cdae883c99","observation_id":"eda18f36-50ae-44e7-86cc-b39d8d9470b0","resolution":{"observed_at":"2026-08-07T05:47:18.530763Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1811.03140","last_updated":"2018-11-07T20:54:11Z","snapshot_observed_at":"2026-07-06T07:13:21.130146Z","submitted_at":"2018-11-07T20:54:11Z","title":"Surface waves over currents and uneven bottom","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1811.03140","snapshot_observed_at":"2026-08-07T05:47:13.131314Z","title":"Compelli, R","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:13.131314Z"},"links":{"cited_paper":"/paper/1811.03140","citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:c3ad8e425739fda8efc434bc549e5e36e5fb8bc8f21f1126c5c68cfa739ea407","observation_id":"3f4c5bcf-c03c-417d-abfe-242e38493297","resolution":{"observed_at":"2026-08-07T05:47:13.131314Z","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":"2026-08-07T05:47:28.342503Z","title":"Constantin, Some three-dimensional nonlinear equatorial flows, J","venue":null,"work_id":"44d066ad-c031-4cd6-8f50-70d4987a1043","year":2013},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:13.215092Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:35a2272aecaf8a4388cd59261aa46d2ec23fec8eeeb9c413af827b3c664aae8f","observation_id":"fccb5fcd-226a-459d-9c42-4490bbb7761b","resolution":{"observed_at":"2026-08-07T05:47:28.428731Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:28.204654Z","title":"Constantin, Some nonlinear, equatorially trapped, nonhydrostatic internal geophysical waves, J","venue":null,"work_id":"3c19de4d-12a9-4644-a6b9-4e05ce9df4f8","year":2014},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:13.259383Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:847506cbc0a964f82d290fac751dfe9aea0e5879af652febe0d397020c8724dc","observation_id":"430cb0d4-4ea7-4f35-84aa-9080123b9418","resolution":{"observed_at":"2026-08-07T05:47:28.266203Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:13.297971Z","title":"Constantin and R.I","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:13.297971Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:24458a06fb735757d73bb523965f1f589ec6c89d6464f6151e0ba4a3c3a7d22f","observation_id":"98aa3291-250a-47f7-9534-0708c9cb2e02","resolution":{"observed_at":"2026-08-07T05:47:13.297971Z","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":"2026-08-07T05:47:13.379545Z","title":"Constantin, R","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:13.379545Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:608e5e01e1d20c558d292615a4ee24e1a3edaad7f19a55120f2064403944a247","observation_id":"7a3642bb-2b36-40de-95c5-4e4cea33bc12","resolution":{"observed_at":"2026-08-07T05:47:13.379545Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"math-ph/0610014","last_updated":"2006-10-06T11:35:15Z","snapshot_observed_at":"2026-07-07T06:16:50.870997Z","submitted_at":"2006-10-06T11:35:15Z","title":"Nearly-Hamiltonian Structure for Water Waves with Constant Vorticity","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"math-ph/0610014","snapshot_observed_at":"2026-08-07T05:47:13.447541Z","title":"Constantin, R","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:13.447541Z"},"links":{"cited_paper":"/paper/math-ph/0610014","citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:451d5668676d36868be1a482b80fcb37aff5bc89c8f7e1ee2d3e8a652b186108","observation_id":"8e26c6b0-a220-4180-a4dd-f65915583d70","resolution":{"observed_at":"2026-08-07T05:47:13.447541Z","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":"2026-08-07T05:47:27.963350Z","title":"Constantin and R","venue":null,"work_id":"9e38c9a2-3e46-4a44-b4aa-606a970b508c","year":2015},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:13.509941Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:d6cda986fe55075eef6e3dec5b0116a3083e292a1e050b814912763aa07bebf2","observation_id":"630275ce-651d-4630-aeb0-2c60fa52f209","resolution":{"observed_at":"2026-08-07T05:47:28.061841Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:27.716945Z","title":"Constantin and R.S","venue":null,"work_id":"43d87ce8-486e-4edd-b704-7616f7bc7a85","year":2017},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:13.544515Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:360f197784251667a93bf4d3bc8cdc300505260170611814edb35ea61adaf6c9","observation_id":"6b7da186-ec81-4fbd-aa06-3b9208c55ddc","resolution":{"observed_at":"2026-08-07T05:47:27.836544Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:27.482093Z","title":"Cotter, D.D","venue":null,"work_id":"250e01bf-a1a5-41ab-93d2-03f7395d2a41","year":2010},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:13.619184Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:011acf05cd63edc9d9c9fe4bf9e0ab2cba9e8be14025f67906a63533f639446f","observation_id":"b63f6e10-4607-479f-89b7-1cce6c1c622f","resolution":{"observed_at":"2026-08-07T05:47:27.568334Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:27.195022Z","title":"Craig, P","venue":null,"work_id":"0f0af05f-8813-406d-bfba-b2c0e98ba52b","year":2005},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:13.672961Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:6e389239803948dc22a39a0f49ca6f45b1f87696e4544c495e66356d942ec4d1","observation_id":"f5cce23a-ddb0-4d32-8aae-8b959a52c9a8","resolution":{"observed_at":"2026-08-07T05:47:27.294077Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:26.986264Z","title":"Craig, P","venue":null,"work_id":"df6ba0b1-65e8-429f-8eae-36da45cb5405","year":2005},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:13.728677Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:f6ec75dea1c9f3d3eb40546baa2e2644fd3ee69837d836be0a7193421e2b4691","observation_id":"7120abeb-762a-4457-b1d7-75a78ba47a30","resolution":{"observed_at":"2026-08-07T05:47:27.053611Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:26.729485Z","title":"Craig, P","venue":null,"work_id":"daf059ac-8559-4253-b51c-eb92f82d7a2e","year":2012},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:13.789360Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:741a1c76015014a64333f316f8158c8191cc16f690ec23be48474b991f8f7d57","observation_id":"37ecadbb-761f-4e13-888b-719273627227","resolution":{"observed_at":"2026-08-07T05:47:26.834218Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:26.398304Z","title":"Craig, P","venue":null,"work_id":"91c8773d-77c5-4dc3-bca0-87ede6740169","year":2015},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:13.822734Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:1fe6dd9b3b59049a97d26a4a9a14a9f74da765501eb790855ce20fe57906dfe0","observation_id":"b2f20c69-d9a5-4ba6-be31-1ca98add96e2","resolution":{"observed_at":"2026-08-07T05:47:26.528231Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:26.337919Z","title":"Craig, P","venue":null,"work_id":"57752cf6-3993-4e64-b90d-d1d9d83a7296","year":2011},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:13.870711Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:364c0ed0670c52092991eec372234fdb62294bc6419cd5aff7e61fe4139fea9d","observation_id":"eb96d905-f4f2-47b7-b019-97ffa686d2b0","resolution":{"observed_at":"2026-08-07T05:47:26.357209Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:13.913613Z","title":"Craig, C","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:13.913613Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:dcf4276e801fdf7aa2178033a78d62c8079902b3e9d2b1c2e8713aaad53c288c","observation_id":"e1975391-f6f0-4008-a545-8072f9535afa","resolution":{"observed_at":"2026-08-07T05:47:13.913613Z","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":"2026-08-07T05:47:26.269302Z","title":"Cushman-Roisin and J.-M","venue":null,"work_id":"eb3658a8-c2e0-4d41-8d15-77c332c29ad4","year":2011},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:13.961371Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:205e54e7fcbadaf8775f8dd8b22e1e5f09f95868025fc68c7430f58c2a8074f0","observation_id":"aa88004d-b77b-4dec-8e8f-9bebdbb371ad","resolution":{"observed_at":"2026-08-07T05:47:26.292793Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:26.186612Z","title":"Evans,Partial Differential Equations, Graduate Studies in Mathematics, AMS, Rhode Island, 2010","venue":null,"work_id":"d506d88a-c53f-4609-8d49-49da2821d02e","year":2010},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:14.021432Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:66c25313071b2194fe053a492a4042b3ca609204b44d59a4b764d3caae69dbda","observation_id":"438d992b-03bc-46dd-abf4-9f8921ae55ff","resolution":{"observed_at":"2026-08-07T05:47:26.209496Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:26.101379Z","title":"Escher, P","venue":null,"work_id":"bb4f9734-abc7-4c03-8b19-d7c28171b170","year":2020},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:14.082540Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:6d06bc401418ebf213114d0767923a393e4cc813859f3901e1db77261782e541","observation_id":"cbe0e062-0c0d-4930-b6a2-ab55637c1b7c","resolution":{"observed_at":"2026-08-07T05:47:26.148689Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:25.940770Z","title":"Fedorov and J.N","venue":null,"work_id":"e47a95f9-b655-40b7-a1f2-c8314fcc2735","year":2009},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:14.126653Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:3ec783fd2f16835eecc465c35f85408f13dd6996773d92d5d2b9d117ad68318c","observation_id":"b03710a0-a4af-4832-a93d-62cc7bcdedda","resolution":{"observed_at":"2026-08-07T05:47:26.047308Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:25.581794Z","title":"Gill.Atmosphere–Ocean Dynamics","venue":null,"work_id":"918be477-4805-4b0d-94d9-69cbe5e73189","year":1982},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:14.173975Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:8b5f230baa75a926df432b7fe27f6627ae53bf6ad7ec62f75ed6ee20211b555b","observation_id":"6dd5a840-f946-466b-98a4-1a8009a24881","resolution":{"observed_at":"2026-08-07T05:47:25.783424Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:25.241477Z","title":null,"venue":null,"work_id":"f3940748-fdf8-4d26-8f7c-96d3825a7685","year":null},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:14.242050Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:808c14665aa1e2aba731b6691fabd70a9142b852db86f00c5d815e6272154c9e","observation_id":"48521cd1-6f01-417b-87fb-bde369ba534c","resolution":{"observed_at":"2026-08-07T05:47:25.418177Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:24.937939Z","title":"Grimshaw, C","venue":null,"work_id":"e7d5d4bd-d156-4e09-a41e-b7ee02913b5c","year":2014},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:14.282142Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:24e4d0d4ded48c42af7d0e8e2e5be7fdc87f7ba4aa95b309285d01e9b60ddcfe","observation_id":"f96c052b-34c0-4f04-bb5c-0564b61cfbcd","resolution":{"observed_at":"2026-08-07T05:47:25.087954Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:24.511365Z","title":"Guyenne, A high-order spectral method for nonlinear water waves in the presence of a linear shear current, Computers & Fluids 154 (2017) 224–235","venue":null,"work_id":"e4c10d34-a825-48e0-82e4-3193826929e2","year":2017},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:14.313074Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:6ec518485172ed539de6346e2860b3187425df22e8abba93bad6bda0f23ad860","observation_id":"44aab4dc-8a0e-4ca1-9d11-e03fa0b22293","resolution":{"observed_at":"2026-08-07T05:47:24.714623Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jcp.2016.05.055","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Guyenne, E","venue":"Journal of Computational Physics","work_id":"5e498f3c-f2ea-40e9-8559-585fab3c1491","year":2016},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:14.381429Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:0be34d084a4c5a8fb50581f31a11fdb1a0a5284b9371dfeaac5fa1893d7751a7","observation_id":"6a23aa2f-3d34-4094-b382-be9d1e69837d","resolution":{"observed_at":"2026-08-07T05:47:17.398453Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:24.170660Z","title":"Henry and G","venue":null,"work_id":"0da17d51-2e27-4941-a942-211f7e73b579","year":2022},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:14.426879Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:31820317601cb8e952e9740aa02658154f88f1774428469b772a5a1877365441","observation_id":"721ed36a-c0c9-4bff-8aea-a6a1ce8ff964","resolution":{"observed_at":"2026-08-07T05:47:24.311332Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:23.833973Z","title":null,"venue":null,"work_id":"0b591c33-7c58-4256-9d55-d0b20ff7deb8","year":null},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:14.479474Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:d89c0d9aeb967d0c46fbc845e1a2e86dd05f1f4427c18374f4afd0ddd7259e73","observation_id":"ef46c5b9-4c79-412c-8e75-f5069b936c06","resolution":{"observed_at":"2026-08-07T05:47:24.020131Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2203.02590","last_updated":"2022-03-04T22:20:24Z","snapshot_observed_at":"2026-08-13T16:29:13.085416Z","submitted_at":"2022-03-04T22:20:24Z","title":"Hamiltonian approach to modelling interfacial internal waves over variable bottom","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2203.02590","snapshot_observed_at":"2026-08-07T05:47:14.544970Z","title":"Ivanov, C.I","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:14.544970Z"},"links":{"cited_paper":"/paper/2203.02590","citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:e0bf133466541192f63166ef46dc95456f5f441274cc3875290c3e3402b15c7b","observation_id":"6fd4fe0e-4fbd-4e02-b085-dcaa312facdc","resolution":{"observed_at":"2026-08-07T05:47:14.544970Z","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":"2026-08-07T05:47:23.574194Z","title":"Ivanov and C.I","venue":null,"work_id":"cea0511a-a5ca-4daa-bd86-85647116bccd","year":null},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:14.591422Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:607eaff7196eb1ebc5b82ecac12d723da69afceb42619b3fe89cabdbc05ebd94","observation_id":"c30ff484-06f1-4dc8-a472-c1df703704d8","resolution":{"observed_at":"2026-08-07T05:47:23.700592Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:23.227366Z","title":"Kakutani and N","venue":null,"work_id":"e1bd0e02-325d-4379-8590-727866b3be76","year":1978},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:14.654197Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:4b7feb8771a4c4a088fa97be3ad89f891b2c8ce80a5888c1c2b6252ff1573fd9","observation_id":"32b519aa-2479-4378-aa2d-83fc9e9d2cce","resolution":{"observed_at":"2026-08-07T05:47:23.365107Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:22.901766Z","title":"Kessler and M.J","venue":null,"work_id":"7d911fe8-3020-4297-ab1a-35504aefe85c","year":1995},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:14.743544Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:f34c541a0e467b6ec61e2b19d436c674ae98771aa42ecf440c846415f2620f64","observation_id":"8b99fe1d-acf4-488f-b629-40e0d439ff26","resolution":{"observed_at":"2026-08-07T05:47:23.039016Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/jfm.2016.510","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Kodaira, T","venue":"Journal of Fluid Mechanics","work_id":"f9eac40a-ab3a-43da-befa-1ffc8ced4d05","year":2016},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:14.790987Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:78a6341a8e3cf1cccdc8aa23f13cd73f8359768d55bd432c578fe07b24f50bd1","observation_id":"a67be6a7-eae7-4973-9e77-6e9d57e193b5","resolution":{"observed_at":"2026-08-07T05:47:17.252035Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:22.629336Z","title":"Lamb,Hydrodynamics, 6 ed., Cambridge University Press, Cambridge, 1932","venue":null,"work_id":"057dfe75-ffb6-48e9-a42f-1da31fb0ad4e","year":1932},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:14.886007Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:5bbcd7688d804aa78cf13f7e13b4a4b66d8bb906e76e087e74cea1402f6a05ba","observation_id":"5cf667c5-5cc1-4fee-86aa-b3acf083a5e5","resolution":{"observed_at":"2026-08-07T05:47:22.739687Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:22.479756Z","title":"Lannes, Well-posedness of the water-waves equations, J","venue":null,"work_id":"2599d608-9d5b-4429-bd44-49d098757fab","year":null},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:14.985480Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:445917f5284c41b9d9cee4c35eae504df8e3db8c6e9039befd82b8430d274f21","observation_id":"dfcf95f3-e5a3-49e1-9ba5-e25ff586a137","resolution":{"observed_at":"2026-08-07T05:47:22.527561Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:22.316563Z","title":"Marshall and R","venue":null,"work_id":"c37c2607-b91f-41de-a372-217d21f0b8f5","year":2016},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:15.080147Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:29c14f95b8dd4cf2c1b87b1068c44a2d8df8081638a59f3c45235cfd6823b868","observation_id":"6c07689f-1c82-4ac8-a3df-73321f8e71e0","resolution":{"observed_at":"2026-08-07T05:47:22.361210Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:22.197886Z","title":null,"venue":null,"work_id":"ea23c046-1177-4a60-9188-8795eef9f995","year":2021},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:15.130219Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:a371838bd68537c899aa5e0f97afdfb910b2f437e2e690243eaa7e6bf70d7a98","observation_id":"29b5e82b-9e3d-4df1-b0d6-b88124270a56","resolution":{"observed_at":"2026-08-07T05:47:22.239864Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:22.058230Z","title":"Massel,Internal gravity waves in the shallow seas, Springer International Publishing, Switzerland, 2015","venue":null,"work_id":"f2a3e31b-ed69-4b4b-85a1-91ec878697b9","year":2015},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:15.258790Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:b36f2675e47cdd2f93b3c681d7f1fb66d42a29ef928201c3883cd97b1fef1743","observation_id":"b3fe2534-9f76-4036-9d95-4a36c79c82bc","resolution":{"observed_at":"2026-08-07T05:47:22.120012Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:21.899104Z","title":"Matioc, Steady internal water waves with a critical layer bounded by the wave surface, J","venue":null,"work_id":"aaacab85-1cce-4a2e-9d10-8e9bd9711b4d","year":2012},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:15.346665Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:05a6cd4b80015d9a914c33a617c706b3cb25e3f5f3e81a21123cd83a952207f5","observation_id":"3201a11a-1a7c-420a-bece-f4634b904ac2","resolution":{"observed_at":"2026-08-07T05:47:21.974423Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1111/sapm.12266","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"de Melo Vir ´ ıssimo, P.A","venue":"Studies in Applied Mathematics","work_id":"ce52e73d-c51c-462d-9323-6edaa0b9bc46","year":2019},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:15.451331Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:7af22452fd68896e5ac6316f56fd46f7c99da65d2c86174eb48fe6630a51bc33","observation_id":"ace61a53-c4fb-48be-b512-b7b8904886b7","resolution":{"observed_at":"2026-08-07T05:47:17.135479Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:21.767347Z","title":"Nachbin, A three-dimensional Dirichlet-to-Neumann operator for water waves over topog- raphy, J","venue":null,"work_id":"69d52d80-0dbb-4dd8-955b-35cc27bcb614","year":2018},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:15.537950Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:e3204f092a356b724c5c8c72a323e0a9b9d4ba3249aa0d7088167684ab02392c","observation_id":"09eda2e7-7243-463a-a541-00a5ddb7c88b","resolution":{"observed_at":"2026-08-07T05:47:21.794131Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:21.573330Z","title":null,"venue":null,"work_id":"9fab6dff-40d0-40b7-9070-d9fdf5eeb49e","year":1993},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:15.606747Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:ea00ec58fbb5d6ef0ae08e600f12635288c0b7b29e0519a2c8228fa49208f0fd","observation_id":"39314608-3953-4ed5-8e91-80133ba65f96","resolution":{"observed_at":"2026-08-07T05:47:21.676482Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:21.439901Z","title":"Ostrovsky and K.R","venue":null,"work_id":"241e8eb1-9b05-4755-a8ec-d5df90cfb6b6","year":2019},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:15.747414Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:9eb9241a17e8195e6fdc0d3d86d3b89cc973183bf5cab1de2ecf1e1512f94589","observation_id":"f240483a-99ef-4cba-84a2-9ab49ac05acf","resolution":{"observed_at":"2026-08-07T05:47:21.481951Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:21.293951Z","title":"shallow water","venue":null,"work_id":"e9497a6d-450d-4da3-a0c3-2eaeec45d524","year":1979},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:15.851294Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:54047e974554b93cba514b372af69797fbb3dfaea05609ea088c932a3962b50a","observation_id":"b23506a1-9c0b-41e9-91d7-2f1b2bb40ccc","resolution":{"observed_at":"2026-08-07T05:47:21.350541Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.02009","last_updated":"2022-06-13T20:54:04Z","snapshot_observed_at":"2026-08-13T19:38:31.305482Z","submitted_at":"2021-08-02T19:29:59Z","title":"Isolation Intervals of the Real Roots of the Parametric Cubic Equation and Improved Complete Root Classification","version":3},"cited_work":{"arxiv_id":"2108.02009","doi":null,"metadata_source":"pith","pith_arxiv_id":"2108.02009","snapshot_observed_at":"2026-08-07T05:47:18.002869Z","title":"Isolation Intervals of the Real Roots of the Parametric Cubic Equation and Improved Complete Root Classification","venue":"math.GM","work_id":"8ebb454e-f043-418b-b8d9-c2b38eb69401","year":2021},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:15.915823Z"},"links":{"cited_paper":"/paper/2108.02009","citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:4f62ab731f687a9c010853489f053cb4d2444a7c2aaad82cfcf34a3f2f387d0c","observation_id":"eafaf748-1d54-4400-ab63-bd496613de08","resolution":{"observed_at":"2026-08-07T05:47:18.088504Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2107.01847","last_updated":"2022-06-11T19:17:28Z","snapshot_observed_at":"2026-08-13T12:55:31.450513Z","submitted_at":"2021-07-05T08:05:03Z","title":"The Siebeck-Marden-Northshield Theorem and the Real Roots of the Symbolic Cubic Equation","version":2},"cited_work":{"arxiv_id":"2107.01847","doi":null,"metadata_source":"pith","pith_arxiv_id":"2107.01847","snapshot_observed_at":"2026-08-07T05:47:17.831613Z","title":"The Siebeck-Marden-Northshield Theorem and the Real Roots of the Symbolic Cubic Equation","venue":"math.GM","work_id":"86716021-8f3a-4bf7-a484-02c3bde6db90","year":2021},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:16.006147Z"},"links":{"cited_paper":"/paper/2107.01847","citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:b93632bd5567c4c702a29a52a4a0bf24d9d799b4ea83e7b56bab701afd9f5338","observation_id":"668a538e-7ba3-404b-8203-a172c7c433bd","resolution":{"observed_at":"2026-08-07T05:47:17.906756Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:21.122719Z","title":"Rahman and G","venue":null,"work_id":"c89ed830-8b9c-4601-89a2-47b1bcbb576e","year":2002},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:16.113725Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:38c0d9272b95d01d48a852c30ea4d8ab99913c1c73a4800a3cd4d7a81123efa7","observation_id":"11049fd3-e0c3-45b8-9d8e-3001b44ae146","resolution":{"observed_at":"2026-08-07T05:47:21.201443Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:20.906771Z","title":"Ratliff, Genuine nonlinearity and its connection to the modified Korteweg–de Vries equa- tion in phase dynamics, Nonlinearity 35 (2022) 30-65","venue":null,"work_id":"c03aa614-56cc-4ddc-b0d7-aabf34e08602","year":2022},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:16.198116Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:f9c4aa657ee8806634c2156daa47ddcc37ce84d35e8c4bd1af92dd88be4b7005","observation_id":"20d02b72-5f32-483e-a621-bb4efc258674","resolution":{"observed_at":"2026-08-07T05:47:21.049038Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:20.612967Z","title":"Reed and B","venue":null,"work_id":"c28ca4d4-88c5-4b9f-b1fa-0e4095460a6e","year":1975},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:16.266765Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:075458bcdfacd9f7826382b631ed63c4c67bc0bcf0d34b440eeade940befdca9","observation_id":"d5c954f0-d148-41a8-b9b3-f4afd28abf0d","resolution":{"observed_at":"2026-08-07T05:47:20.755110Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:20.327976Z","title":"Shintani and M","venue":null,"work_id":"2bb2bb46-4fae-4f60-b5f4-ed0497946b9e","year":2001},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:16.386142Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:76157075df6caac288b2715f906c7961195d630064647a4b67d6c29b35432b0b","observation_id":"29fe098e-eb0a-4f51-9e97-5a066b049118","resolution":{"observed_at":"2026-08-07T05:47:20.468651Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:19.974982Z","title":"Simmons, M.-H","venue":null,"work_id":"a69fa300-4adf-4b1c-b5ca-175da4739d8f","year":2011},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:16.510032Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:fc40dd76d6b4b02d48655373226c61642de82cef3ebbaa0c2295880795d5c06b","observation_id":"495c8701-e707-466b-997b-3e9308e2a3f1","resolution":{"observed_at":"2026-08-07T05:47:20.082564Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:19.808969Z","title":null,"venue":null,"work_id":"37921930-21d9-4479-a867-8a2f2d0e360f","year":2010},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:16.564265Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:a1a218556b2ae6d081060d886258c193bbd43cb8d45270693076378700899532","observation_id":"5e3e7421-6c6e-4afe-9557-8352f802b467","resolution":{"observed_at":"2026-08-07T05:47:19.895555Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:19.698063Z","title":"Vallis,Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circula- tion, Cambridge University Press, 2017","venue":null,"work_id":"f445be94-5120-4e0c-bd70-d9c6a7ce1950","year":2017},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:16.633582Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:31caa6786a30a3ec7fc3f845e620b9b8f78bf3963f66bb248f7b6f4386bc6f95","observation_id":"10e00bf3-2a7e-4035-8c7b-9aafaf43d346","resolution":{"observed_at":"2026-08-07T05:47:19.742643Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:19.553040Z","title":"Whitham,Linear and nonlinear waves, 1999, Wiley","venue":null,"work_id":"354a6e0b-addb-4728-8902-c89ea517505c","year":1999},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:16.673140Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:f3fd601895b5d0cd0714aefd968fdd81d8cc5b9acf1868ed27e9580c4111de04","observation_id":"12368097-a383-4a19-8a63-26a820c532a3","resolution":{"observed_at":"2026-08-07T05:47:19.620715Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:19.420514Z","title":"Wahl´ en, A Hamiltonian formulation of water waves with constant vorticity, Lett","venue":null,"work_id":"bd5c4010-7cd6-46ff-9e59-539ee6d4fcd1","year":2007},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:16.707975Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:056540282745c1b7a7269c2a4e62b321393162fa779bc09cdccc406793f8b457","observation_id":"9176cfd5-d967-44ff-87bf-ee2c4a4bebc3","resolution":{"observed_at":"2026-08-07T05:47:19.465140Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:19.274208Z","title":"Wahl´ en, Hamiltonian long-wave approximations of water waves with constant vorticity, Phys","venue":null,"work_id":"1ae65ca1-99ed-4254-b15e-5fa33f28906f","year":2008},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:16.794662Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:c0dc48beb01589bed97f9ba77f95970d5cf0bda936525005c7dc1590f681e3a9","observation_id":"5f50a117-a711-410f-911a-e3e90b80d6a3","resolution":{"observed_at":"2026-08-07T05:47:19.324950Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:19.088816Z","title":"Yih,Stratified flows, Academic Press, 1980","venue":null,"work_id":"0be673d7-1d7d-42ab-b7cc-6504aa4d7eb9","year":1980},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:16.881380Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:dfc0b6bbd832609cb7724c91572c431d140c2f330349075ff14d70a3fba0d070","observation_id":"1952d3a9-e554-401a-aaff-0a108ba64ec7","resolution":{"observed_at":"2026-08-07T05:47:19.145629Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:47:18.943198Z","title":"Zakharov, Stability of periodic waves of finite amplitude on the surface of a deep fluid, J","venue":null,"work_id":"aed34457-a9b6-45ac-a97e-afc6714b3d0a","year":1968},"citing_paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:16.929573Z"},"links":{"citing_paper":"/paper/2608.06314"},"observation_digest":"sha256:e2a9f7de488be088bad16643b61b2b4543cd566dfdb30ca529be6c054468df7d","observation_id":"e3767aab-0fa6-4d05-9e16-ab15ccc40115","resolution":{"observed_at":"2026-08-07T05:47:19.012557Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2608.06314","last_updated":"2026-08-06T17:28:13Z","latest_version":1,"primary_category":"physics.flu-dyn","snapshot_observed_at":"2026-08-09T23:13:16.640692Z","submitted_at":"2026-08-06T17:28:13Z","title":"Three-layer water flows: Dirichlet-Neumann operators and approximations"},"reference_resolution":{"displayed":71,"state_counts":{"malformed_identifier":2,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":14,"verified_exact":7,"verified_fuzzy":47},"total_outbound_references":71},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 71 of 71 outbound references and 0 inbound Pith citation observations for arXiv:2608.06314."}