{"as_of":"2026-08-16T15:43:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:770c3ecd6753907454c392f4ba6307b98f0ea35423d071ee431d82a42000cd3c","coverage":[{"denominator":55,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":55,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T13:00:33.331620Z","state":"measured"},{"denominator":55,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":55,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+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/1908.06144/citation-record","integrity":"/paper/1908.06144/integrity","json":"/paper/1908.06144/citation-record.json","paper":"/paper/1908.06144"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:00:34.394421Z","title":"Whitham modu lation theory for (2 +1)-dimensional equations of Kadomtsev-Petviashvili type","venue":null,"work_id":"ed75d77e-17e3-49e8-8e79-0a0f97e9f427","year":2018},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:32.982010Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:aac52e4395cfcc4bccf52897bd6c51fb81e8dc7450472783d89f0e535fed85a6","observation_id":"d26ca84e-4426-4236-aae4-f2f2e0cff5ca","resolution":{"observed_at":"2026-08-14T13:00:34.400578Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:34.377954Z","title":"Whitham modulat ion theory for the Kadomtsev- Petviashvili equation","venue":null,"work_id":"a204ba19-4f6b-41b7-b0cb-1c4245e3283f","year":2017},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:32.996830Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:99c0ec68000e915c9532853e7ef4a5ad72bd487b225e8d3b2d9234082634bdb5","observation_id":"98130ade-0158-4db9-885a-5fba242520dd","resolution":{"observed_at":"2026-08-14T13:00:34.383168Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:34.360047Z","title":"Whitham modulat ion theory for the two-dimensional Benjamin-Ono equation","venue":null,"work_id":"d7804ac9-538e-4bd3-9d3c-d0aabf568fa0","year":2017},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.003055Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:73b7cb28d645cc338970d0547c4aa870be1f75cbd4847636b70c4dff17fbbb95","observation_id":"63a5ec69-bf93-4b52-82da-7a397c8dbdf9","resolution":{"observed_at":"2026-08-14T13:00:34.366296Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:34.341514Z","title":null,"venue":null,"work_id":"50340eb9-49ae-4a11-aa2c-1c4d2a48de4d","year":1991},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.009017Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:5f5411687ef45a058b84da118e73624658f06c2a1fdf5dd4fe2dc3fd2a054f0c","observation_id":"537ffa23-b949-4255-b3ec-fe79eacbe86d","resolution":{"observed_at":"2026-08-14T13:00:34.346371Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:34.326360Z","title":null,"venue":null,"work_id":"863a0659-4815-4971-ad7a-f2d16436aec4","year":1981},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.014312Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:47c9717e6d498ed392a40d3b334e6e33c85e8061d4d4d2078b894b6751a55e13","observation_id":"8319e070-d351-449f-bd78-4843bba658a6","resolution":{"observed_at":"2026-08-14T13:00:34.331346Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:34.310666Z","title":null,"venue":null,"work_id":"d9a1f0e5-f7ee-454c-975f-2b18fbd5f73b","year":1994},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.021324Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:c17e383de4dd1790bfbabcc5fe5c8df806a16d5db8a0b0238b5f662d97af106d","observation_id":"2fec2da7-bfeb-4016-842b-054e2d78946a","resolution":{"observed_at":"2026-08-14T13:00:34.315578Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:34.294425Z","title":"Line soliton interactions of the Kadomtse v-Petviashvili equation","venue":null,"work_id":"8ea17df3-ed26-4ec4-907a-5d4cf3ae4765","year":2007},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.028652Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:c2fb463350f593e3d4115b65cd9bae3ba8a3a60e7d4ae651107087eef83708fd","observation_id":"f1ec603c-9305-4cb1-8356-76f02b8bbb05","resolution":{"observed_at":"2026-08-14T13:00:34.300229Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:34.278081Z","title":"Soliton solutions of th e Kadomtsev-Petviashvili II equation","venue":null,"work_id":"37b998d1-dfb6-4b15-8ceb-552ad29265cd","year":2006},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.034265Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:f9e7a99535aaa0e5639eb746463a90fb2422f2705b1043859969af5d5ea58c9b","observation_id":"87969e72-d7d9-41a1-b78c-06e6427d23cc","resolution":{"observed_at":"2026-08-14T13:00:34.283712Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:34.260023Z","title":"On a family of solutions of the Kadomtsev-Petviashvili equation which also satisfy the Toda lattice hierarchy","venue":null,"work_id":"45244851-8196-47e0-ad3f-e14171b688a8","year":2003},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.041033Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:907c085c6381382cda029b4f5fe1cb43f87777db8ffc4d595118486063026d7c","observation_id":"564f6f62-37be-47d0-abca-7e0968ce77f3","resolution":{"observed_at":"2026-08-14T13:00:34.266345Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:34.240931Z","title":"Soli ton interactions of the Kadomtsev- Petviashvili equation and the generation of large-amplitu de water waves","venue":null,"work_id":"02a46ef3-e278-4188-9439-eae0710fdb91","year":2009},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.048030Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:7670535e9aa658d1a60a36411327430c7c6e3daf745b96cdc358c137dcb6dc3c","observation_id":"28a1d749-9bba-4943-b81c-f26081eca937","resolution":{"observed_at":"2026-08-14T13:00:34.248952Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:34.223380Z","title":null,"venue":null,"work_id":"f402196d-099a-4631-a5f0-8d6af0571e5e","year":1990},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.055238Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:4f8d789618047c99568e23dce30ad4dfe84661e7325afed95a726a987fc4570d","observation_id":"68687bd3-29f4-4a47-9803-8674e518436b","resolution":{"observed_at":"2026-08-14T13:00:34.229021Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:34.206876Z","title":"Towards an inverse scattering theory for non-decaying potentials of the heat equation","venue":null,"work_id":"32d92bae-415c-4118-94c3-91ba3607e202","year":2001},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.061445Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:a6d718c212764e5e10a1e8ac783032f79e0c5affedcd932e6d7fcb5d7aa056cc","observation_id":"5b3a87ec-1de2-4d47-ad8f-69a25382830b","resolution":{"observed_at":"2026-08-14T13:00:34.212200Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:34.191202Z","title":"Extended resolvent and inverse scattering with an application to KPI","venue":null,"work_id":"2006ba8f-c9e1-460a-bbfa-ff178400287e","year":2003},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.067484Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:9155fc71d128485d3bade8856eb18332e760beb1b402642cc00d81b29bb20bc1","observation_id":"b201351b-2ea4-411a-ba9e-9719f7bda584","resolution":{"observed_at":"2026-08-14T13:00:34.196119Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:34.173322Z","title":"Building an extended resolvent of the heat operator via twisting transformations","venue":null,"work_id":"8bc5845b-9268-42af-86dc-4d0a3b1cc3f1","year":2009},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.073481Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:a1b40407da3ccacda3ca8b5c6ac29eff98e1c533792595cd82c5d0b88edb899e","observation_id":"afef4a8b-1636-4a7a-828b-5028d7b8695c","resolution":{"observed_at":"2026-08-14T13:00:34.178733Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:34.156302Z","title":"On the equivalence of di ﬀerent approaches for generating multisoliton solutions of the KPII equation s","venue":null,"work_id":"11f58ecf-f81a-4d2d-ae08-0bebce99274d","year":2010},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.079141Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:7716f01bf5d40423bd5c6ef280252bf816b0418295445d8808df33bb35313584","observation_id":"fda1fed2-7e04-43cc-b81c-e1859b870130","resolution":{"observed_at":"2026-08-14T13:00:34.161947Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:34.139571Z","title":"Mach reﬂection for the two dime nsional Burgers equation","venue":null,"work_id":"8ca38cd6-183e-4a46-a909-39282c576565","year":1992},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.086164Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:bbd30d1f77836624296b19ef89e66fae20528e58fbbb6233f4ab15d9f37182a0","observation_id":"54160447-bbad-418c-9242-06fd235ee377","resolution":{"observed_at":"2026-08-14T13:00:34.145301Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1812.06593","last_updated":"2019-06-27T13:14:41Z","snapshot_observed_at":"2026-08-14T17:43:57.825165Z","submitted_at":"2018-12-13T19:06:59Z","title":"Interaction of linear modulated waves and unsteady dispersive hydrodynamic states with application to shallow water waves","version":2},"cited_work":{"arxiv_id":"1812.06593","doi":null,"metadata_source":"pith","pith_arxiv_id":"1812.06593","snapshot_observed_at":"2026-08-14T13:00:33.377492Z","title":"Interaction of linear modulated waves and unsteady dispersive hydrodynamic states with application to shallow water waves","venue":"nlin.PS","work_id":"ec10c72a-503d-4adb-b178-b164aa3a902d","year":2018},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.091961Z"},"links":{"cited_paper":"/paper/1812.06593","citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:cb8765b17b666c20d7a6bcbe54907178dd527a3833d6beb13914a683cd13801e","observation_id":"62b400aa-15c3-48af-8261-fc6741920ac2","resolution":{"observed_at":"2026-08-14T13:00:33.386286Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:34.123592Z","title":"Stability for systems of conservation l aws in several space dimensions","venue":null,"work_id":"ac95b8b5-0078-4b5e-9f9c-e15da4b5d7a9","year":1995},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.098665Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:0000fd2d0b3d1a617d26d18047ad91ed3fec1ca17373d31d8708af11cbc619b4","observation_id":"e947f51c-e443-4b98-ac01-2e0bad2b7b08","resolution":{"observed_at":"2026-08-14T13:00:34.128870Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:34.106907Z","title":null,"venue":null,"work_id":"3f6aee44-56d2-487a-88bc-d4b2ddc9e867","year":2000},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.103507Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:10be09c04539b943cf35785f6ce039247c11b31f3045e2739998e17dba85a66f","observation_id":"c029b8b6-e969-421d-8ada-ec237b0783ec","resolution":{"observed_at":"2026-08-14T13:00:34.112079Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:34.087793Z","title":"Analytic solution of the two-dimensiona l Korteweg-de Vries equation,","venue":null,"work_id":"dfca209b-a04f-47ea-a5e9-d3be587d9f25","year":1974},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.108780Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:d0ed09efe15896f431deb9c64cca3aec34fe50aa9abf2da83fd3d254a02b0f4f","observation_id":"a272dc57-6cc1-4e5e-acb7-45e7b04d1414","resolution":{"observed_at":"2026-08-14T13:00:34.093993Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:34.071068Z","title":"Dispersive shock waves and mod ulation theory","venue":null,"work_id":"0370298c-e2a8-4b09-9328-c11777d16874","year":2016},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.114091Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:5b2b8c35af3340ac6d512947c2e14a4834210d3a5d0eb06ef7ec28879208c95c","observation_id":"b82764ab-f735-4f7b-89c9-933811815080","resolution":{"observed_at":"2026-08-14T13:00:34.076038Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:34.043258Z","title":"The characte rization of two-component (2 +1)- dimensional integrable systems of hydrodynamic type","venue":null,"work_id":"dd1ffb69-3e6c-403c-a4fe-17ec22046e35","year":2004},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.119277Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:27b3abfd97a057833d12ee95e580d4e9ad9c7c54d009696db05d15f6feb9feff","observation_id":"2e01ff15-9cd9-41e9-a875-e3b188f15036","resolution":{"observed_at":"2026-08-14T13:00:34.049340Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:34.025749Z","title":"On the integr ability of (2 +1)-dimensional quasilinear systems","venue":null,"work_id":"98fc2073-dc80-4705-860c-990fbef43231","year":2004},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.124767Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:e2a7d05da5d560c5144f03fb507478cd3e0919f016a207fb7ca862668e92649a","observation_id":"759b9850-478a-4409-a30e-67b99d202914","resolution":{"observed_at":"2026-08-14T13:00:34.031019Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:34.003155Z","title":"The Haantjes tensor and double waves for multi- dimensional systems of hydrodynamic type: a necessary cond ition for integrability","venue":null,"work_id":"b42c39ae-3a27-494d-ba52-e6bdb3ea5712","year":2006},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.130867Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:99c727e5f88ed675d945921fb211e1efed0774640ecdb5347dbaa16c536b5b3b","observation_id":"245d603f-b125-45e2-8791-6b37baebaf15","resolution":{"observed_at":"2026-08-14T13:00:34.009251Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.984495Z","title":"Dispersive deformations of hydrodynamic reductions of (2 +1)-D dispersionless integrable systems","venue":null,"work_id":"192487e5-ea1f-42c1-9bc9-f074d4ee5cf9","year":2009},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.136634Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:273fb9d682e139dcd8fcc9bbaa9cb65d54ba7e05286c4647f0f1f8590f246397","observation_id":"b5c664e2-02c6-4473-8ed0-7a17e8973c06","resolution":{"observed_at":"2026-08-14T13:00:33.990334Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.963843Z","title":"Uniqueness for multidimensi onal hyperbolic systems with commuting Jacobians","venue":null,"work_id":"427e442e-c456-44b3-93be-ca7f971f1186","year":2006},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.145087Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:2181051defc2373c2df3a4fd433eeeb445856e1e776c052e43abc1a4e6097fa1","observation_id":"5ca09c5a-79ab-403e-a03f-e84006e63a2b","resolution":{"observed_at":"2026-08-14T13:00:33.971531Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.943136Z","title":"Reductions of the Benney eq uations","venue":null,"work_id":"22c44016-3fc2-42ac-ba6d-fda782e2f14f","year":1996},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.151427Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:1615df3837c75602515decceb8fb6e427897c018dc811c90af740b2c841ec68f","observation_id":"b0d4d8dc-44c0-4e8c-b990-754e05e4881d","resolution":{"observed_at":"2026-08-14T13:00:33.950248Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.920944Z","title":"Numerical study of the Kadomtsev-Petviashvili equation and dispersive shock waves","venue":null,"work_id":"b55195ac-7fba-437a-9100-8206f31f11e3","year":2018},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.158271Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:f4851cc3c4e9a639da23ebe8c552cd40528db478d84bbec83757251dabee58cf","observation_id":"207d5e62-0d19-4b06-b132-a414cc05be4f","resolution":{"observed_at":"2026-08-14T13:00:33.927261Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.902901Z","title":"On Xm-forming sets of eigenvectors","venue":null,"work_id":"4194aead-6bd7-443e-8a19-020072f245ff","year":1955},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.165369Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:3b344645cf2cb852c545394e3ae9345490f2589d13858d40061dcacec13cc11a","observation_id":"f63aa326-6c1c-431a-b35b-19b3fcae8ddd","resolution":{"observed_at":"2026-08-14T13:00:33.908469Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.880576Z","title":"Wronskian structure s of solitons for soliton equations","venue":null,"work_id":"a592e4b6-4904-4e9f-b9e6-99ab724cb1ee","year":1988},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.172557Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:7e1ef65d495b969e55eef7c5d64f6ba287d36d0d45ebee28b2ba67dd6bf4a519","observation_id":"220daba7-21d6-4988-83c0-6a78aafa1e5b","resolution":{"observed_at":"2026-08-14T13:00:33.888762Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.862662Z","title":"Infeld and G","venue":null,"work_id":"69836a61-5071-428e-bca6-198c0e373125","year":2000},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.178736Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:220dbfc22ce2e21dd6410c81c1da622428ec962a6797feb79ee111e74d71850f","observation_id":"058545e6-b795-45b6-b5e2-f2d497bfd67a","resolution":{"observed_at":"2026-08-14T13:00:33.868760Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.844966Z","title":"On the stabilit y of solitary waves in weakly dispersive media","venue":null,"work_id":"fc4a441b-fbe4-4a8a-b602-c71706ebe82f","year":1970},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.185964Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:3bc4370746a8b062a31de221450617458d8177aab55e00caab86fdbf5c6b34d7","observation_id":"6da71e84-4717-46cf-a851-c7d6a213a05e","resolution":{"observed_at":"2026-08-14T13:00:33.850507Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.827111Z","title":"On exact solutions of nonlinear acoustic equations","venue":null,"work_id":"3d4b3639-93f2-40ce-9a36-7785af1647bd","year":2016},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.192742Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:1163b8539919439f535619dccdb22f0597fc62b03295ebf8b51f570a496c7d6a","observation_id":"408e45d1-7079-40dc-bbdb-e36d5c1a17a5","resolution":{"observed_at":"2026-08-14T13:00:33.832870Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.810516Z","title":"Numerical study of the KP equat ion for non-periodic waves","venue":null,"work_id":"5ecf25ff-fda0-4565-89de-e86adb27697e","year":2012},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.198490Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:a8f060a8889dd4fd695c21f871f14cd0cf4792c2e8714eabbdb45285ee490cb0","observation_id":"9252ff69-b7e7-4cef-9f92-418f8e8493ea","resolution":{"observed_at":"2026-08-14T13:00:33.815776Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.794622Z","title":"Self-similar solutions of two-dimensio nal conservation laws","venue":null,"work_id":"3b494e05-4a47-4cfa-a69b-424eb59dc7a9","year":2004},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.205181Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:1e76291f3b6fd0747d232a03c26cc8170b5f45fdd640b58dae8b8f6660a2fce3","observation_id":"37a0fde8-10e4-4e8e-9ad6-fae9052feaa4","resolution":{"observed_at":"2026-08-14T13:00:33.799628Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.776121Z","title":"Numerical study of oscillatory regimes in the Kadomtsev- Petviashvili equation","venue":null,"work_id":"02d7e1e9-6835-49d4-b1e6-4a80866348a1","year":2007},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.210605Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:313a6c5cc9a08bad4c7ded61067cb9e314f9991bd625e9d0e7dcc279d8cd8f84","observation_id":"e833b619-7364-45bd-b6bb-cf57d70d6ff2","resolution":{"observed_at":"2026-08-14T13:00:33.782123Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.757411Z","title":"Y oung diagrams and N-soliton solutions of the KP equation,","venue":null,"work_id":"7b967c3d-7d33-4105-ac75-ffac14605377","year":2004},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.215482Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:6f22481ed997438512956b6a29e9d2d359a3fa44eb67abf069e7c493eca3168d","observation_id":"416c53f6-5c00-4bb8-b83d-a1fbda9041b3","resolution":{"observed_at":"2026-08-14T13:00:33.763111Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.739599Z","title":"A method for solving the dispersionless KP e quation and its exact solutions","venue":null,"work_id":"43f0d655-0387-422c-a823-64c4bb1ed72d","year":1988},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.222208Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:c9c73e84e5afc9fbe5c22117dded8e3d2dc8968b174c08154e4a44d549602117","observation_id":"566d318c-0c43-410c-8388-c99d5f376000","resolution":{"observed_at":"2026-08-14T13:00:33.745727Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.722603Z","title":"A method for solving the dispe rsionless KP equation and its exact solutions. II","venue":null,"work_id":"a7bbe426-d328-426c-a444-20dddbf1f1d4","year":1989},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.229617Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:0222ae8da93d1d8aed61fc2d0b48a1d92873e8a0f0138744e26f266eafb4a606","observation_id":"37b632c6-4ee7-47ff-ae47-8d4c6c54f5f4","resolution":{"observed_at":"2026-08-14T13:00:33.727792Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.704784Z","title":"KP solitons, total positi vity, and cluster algebras","venue":null,"work_id":"5ae4079c-bc7a-4c23-91b4-e2bbf38ff7ad","year":2011},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.234940Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:e71ef790b4ac9d20ef9b55ea3687c95b34b89d266926f325e3ad894f0cabe642","observation_id":"940d2a74-4a44-4017-9c8f-7a1e053651da","resolution":{"observed_at":"2026-08-14T13:00:33.711257Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.685274Z","title":null,"venue":null,"work_id":"ca980062-d6b0-4c9b-b46c-63816182011b","year":1993},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.240907Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:b60697ec6f47d176482a8ed4bff5eedbd39aacc9bf7e04878de2e1ffbf9c9286","observation_id":"605e541b-2914-4dcc-b8dd-5ab3ebbff663","resolution":{"observed_at":"2026-08-14T13:00:33.691353Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.666429Z","title":"Quasiconformal mappings and solutions of the dispersionless KP hierarchy","venue":null,"work_id":"1f797891-729c-4d1b-8c39-83a641d2316f","year":2002},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.247307Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:23c3b2752cf94cf27992282fba12e9c7810cc322dfdc0fcbcd9b1b25bd250806","observation_id":"862e5b54-d3b1-4a34-ba22-958acaf91047","resolution":{"observed_at":"2026-08-14T13:00:33.672250Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.649961Z","title":"Method of averaging for two-dimensio nal “integrable","venue":null,"work_id":"e44e78c8-acfe-4116-94e0-8b0e9feb3b8c","year":1988},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.252737Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:b1fb75a9e5dee80335dee2225ca482bcae162fbbbcc8f68c6e650f02a083b316","observation_id":"006e1993-86a1-47b2-b6c0-2f00c9097daa","resolution":{"observed_at":"2026-08-14T13:00:33.655495Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.633935Z","title":"Solitonic dispersive hydrodynamics: Theory and observation","venue":null,"work_id":"389ef8f7-dece-466c-99d1-6f4116b3241b","year":2018},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.259596Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:2bc596aef878c1a4a62ca48c987ce70a7ee73c79fe1b5b4001e856913d031721","observation_id":"1502bdae-e312-47cc-8c2f-0ce5c46a2868","resolution":{"observed_at":"2026-08-14T13:00:33.639210Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.616301Z","title":"The Cauchy problem on th e plane for the dispersionless Kadomtsev-Petviashvili equation","venue":null,"work_id":"75f9e072-a5db-4817-879a-38cc32b4429a","year":2006},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.271759Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:3b9068d5abd0e4b2e439b780d729fe6da7ad16bc92dc1a4ef0894fed5e811c12","observation_id":"b77fe4d0-3d96-429b-93e1-dff5eaaee0f5","resolution":{"observed_at":"2026-08-14T13:00:33.622453Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.599609Z","title":"On the solutions of the d KP equation: the nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions a nd wave breaking","venue":null,"work_id":"4a26bff3-5164-49e9-aba6-e7609d16df42","year":2008},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.279133Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:258d8500eac87836049e11084471826612f3b85a0b3639965107969098d115b1","observation_id":"af701b2e-5490-412a-8512-a66612567d13","resolution":{"observed_at":"2026-08-14T13:00:33.604892Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.582229Z","title":"Solvable vector nonlin ear Riemann problems, exact implicit solutions of dispersionless PDEs and wave breaking","venue":null,"work_id":"b8ecfe89-73ef-4b5c-bb46-f785ea6c18e3","year":2011},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.288241Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:57f1b7cc270b1edb922281be706c127045b8bab153137d21242dd496e6ebb32c","observation_id":"1c141789-9fce-4bb0-8921-afb8efd73349","resolution":{"observed_at":"2026-08-14T13:00:33.587440Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.560620Z","title":"An N soliton resonance solution for the KP equation: interactio n with change of form and velocity","venue":null,"work_id":"f0cd5689-f516-4486-b334-7c7b0ac74e49","year":2002},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.293622Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:0aad4af47a1f9f8d0a410774eb1d51e70cc39af0c7b0edd2f4bd6a722b08a0a8","observation_id":"78878ef0-9f53-4ac8-8f1b-1e62e539bf7f","resolution":{"observed_at":"2026-08-14T13:00:33.568897Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.541224Z","title":null,"venue":null,"work_id":"e15b0bef-2a82-4847-a594-e091df96fd1b","year":2015},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.298980Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:777e2071efcdce471dfb21879849ad235cdef105d8972294bb64ad59f39baeb9","observation_id":"19150624-d09c-4e14-9352-dbcab293e7ce","resolution":{"observed_at":"2026-08-14T13:00:33.547475Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.522168Z","title":"Novikov, S","venue":null,"work_id":"0bd11779-c957-4013-8df5-8a19b1d53f26","year":1984},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.303893Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:6ba713d1e89d0e90ca97d3e88c7b4667a4b42a5867f5dbd2552eb2791734da73","observation_id":"f0316bb0-ccee-4cfe-baef-53b40cc3ea88","resolution":{"observed_at":"2026-08-14T13:00:33.527211Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.502446Z","title":null,"venue":null,"work_id":"8108f236-b4d8-4d6f-a09a-e1f6a36b4a1e","year":2010},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.309216Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:8b31be06f2f67591c7c92126e5c4605c11a8eba381a3ab9b981930b44e35cfd8","observation_id":"a26b2cc8-b832-41ca-9884-e0d786c766fb","resolution":{"observed_at":"2026-08-14T13:00:33.508235Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.482281Z","title":"Classiﬁcation of integrable hydrodynam ic chains and generating functions of conservation laws","venue":null,"work_id":"4c095a0f-84eb-4c43-a9d9-66751894c538","year":2006},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.314740Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:53548492581c469fcdf952c411223706032ad323c6e9a893b52c78389cdb60ca","observation_id":"1a50cb4d-6c91-4e38-aba8-3724f71c00ea","resolution":{"observed_at":"2026-08-14T13:00:33.489441Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.460734Z","title":"Integrability of the Gibbons-Tsarev sys tem","venue":null,"work_id":"b288b416-b3d4-4539-9a6d-9617e45db8cb","year":2006},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.319893Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:e7c2c25109bc73000a9c69ab1130d20c5ffac69763f2b063cbbc9c5bbd2f8817","observation_id":"15816fd3-91d8-4f4d-b9da-c1cb01cdb8e9","resolution":{"observed_at":"2026-08-14T13:00:33.466753Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.433837Z","title":"Non-linear dispersive waves","venue":null,"work_id":"3b4051e5-dabe-468a-a12c-cbeb3130ac23","year":1965},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.325212Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:5b7653c3039e0df807a7d87f8baefa88ee213ec9b78f7ddfd42083f74b3ff8f0","observation_id":"39ddb7ee-a561-4b83-a37a-d2596b6cd813","resolution":{"observed_at":"2026-08-14T13:00:33.445809Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:00:33.409350Z","title":null,"venue":null,"work_id":"84d4f1cb-ed76-4a8a-9151-caf2dbdc2c0f","year":1974},"citing_paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations","version":2},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-14T13:00:33.331620Z"},"links":{"citing_paper":"/paper/1908.06144"},"observation_digest":"sha256:a848e1fbbb56e9aa06a444fb7eb429397b1bde784c0eece278f928f83ba7ab18","observation_id":"e6e84160-79dc-4315-954a-7eeae7553772","resolution":{"observed_at":"2026-08-14T13:00:33.415325Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1908.06144","last_updated":"2020-03-24T21:12:58Z","latest_version":2,"primary_category":"nlin.SI","snapshot_observed_at":"2026-08-16T09:34:40.295122Z","submitted_at":"2019-08-16T19:47:28Z","title":"Integrability, exact reductions and special solutions of the KP-Whitham equations"},"reference_resolution":{"displayed":55,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":9,"verified_exact":1,"verified_fuzzy":45},"total_outbound_references":55},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 55 of 55 outbound references and 0 inbound Pith citation observations for arXiv:1908.06144."}