{"as_of":"2026-08-13T22:28:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:41b759d3b94df7136cd4314279d17cf4245ae4784e305818c2b0b86fa8944dd8","coverage":[{"denominator":28,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":28,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T05:47:37.106484Z","state":"measured"},{"denominator":29,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":29,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T05:56:11.264679Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-07T05:56:11.286073Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"cited_work":{"arxiv_id":"2506.07246","doi":null,"metadata_source":"pith","pith_arxiv_id":"2506.07246","snapshot_observed_at":"2026-08-07T05:56:11.286073Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","venue":"math.AP","work_id":"de097ee4-b36f-4856-8538-5598162062fb","year":2025},"citing_paper":{"arxiv_id":"2506.08046","last_updated":"2025-07-13T02:58:30Z","snapshot_observed_at":"2026-08-08T18:24:54.458667Z","submitted_at":"2025-06-08T05:57:18Z","title":"Solvability of the Korteweg-de Vries equation under meromorphic initial conditions by quadrature","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T05:56:11.264679Z"},"links":{"cited_paper":"/paper/2506.07246","citing_paper":"/paper/2506.08046"},"observation_digest":"sha256:f817590eef76d41cb820c40f707c0697e378b7f06be8832438d13a0fb67356ba","observation_id":"0f2d8248-f4df-4b42-bd62-741229c9d543","resolution":{"observed_at":"2026-08-07T05:56:11.290976Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2506.07246/citation-record","integrity":"/paper/2506.07246/integrity","json":"/paper/2506.07246/citation-record.json","paper":"/paper/2506.07246"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:47:37.497677Z","title":"Ablowitz, Nonlinear Dispersive Waves: Asymptotic Analysis and Solit ons, Cambridge University Press, Cambridge, 2011","venue":null,"work_id":"7946b26d-b321-4017-b336-e24dbd1e28ac","year":2011},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:34.809935Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:3823e56a556618dce5ad607be2ff06d94ee5188724611de504520280edaf6151","observation_id":"181f91ce-aff5-4733-83eb-99a462312c43","resolution":{"observed_at":"2026-08-07T05:47:37.501751Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T05:47:37.485246Z","title":"Ablowitz and A.S","venue":null,"work_id":"006972a7-933d-47de-b8c0-312a43a53ac8","year":2003},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:34.877651Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:99e0277dd2dab8ddb657bc567838f3baa84219063879b6873ac72483128fb9e8","observation_id":"2ced7a69-70ba-483f-b996-315c781f6a19","resolution":{"observed_at":"2026-08-07T05:47:37.489332Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T05:47:37.471203Z","title":"Ablowitz, B","venue":null,"work_id":"bef948cd-4a3c-4d03-82ce-2c0dd05fd515","year":2004},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:34.925744Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:9939963700d0f3bc3782de84d2c2c422f7cffeeab4809e65c1461536100dc2c5","observation_id":"4bf2e649-ac68-4466-9c2d-c283cc66deba","resolution":{"observed_at":"2026-08-07T05:47:37.475557Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T05:47:37.457401Z","title":"Ablowitz and H","venue":null,"work_id":"7fde1a4e-4995-4c3a-b5c8-101edeb735f0","year":1981},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:35.041546Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:9d45eff8547a80808f4bcba4b2593da531d507f5aaf9e4d57dd7ec42df9ebfcb","observation_id":"b4c39795-5703-4cfb-a857-935956db790a","resolution":{"observed_at":"2026-08-07T05:47:37.461194Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T05:47:37.444822Z","title":"Balser, Formal Power Series and Linear Systems of Meromorphic Ordin ary Differential Equations Springer, New York, 2000","venue":null,"work_id":"4f56b156-ee23-49ba-b95d-f077588ab988","year":2000},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:35.098713Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:e81dd4349ac8047915df96beec86da3e4a1651b6f3ebb720f4a8d2205f0f8c7c","observation_id":"20880083-3063-4204-8dde-301056cd855b","resolution":{"observed_at":"2026-08-07T05:47:37.449079Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T05:47:37.430440Z","title":"Beutler, Positon solutions of the sine-Gordon equati on, J","venue":null,"work_id":"eac8aaa3-15ba-4439-b271-a59cfbba072b","year":1993},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:35.207436Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:947fe9a458891b5b2b528afe3656f0d89def49bb59d3ef7e7aa694b5b0cc299b","observation_id":"d1cb9135-f7c4-4160-b96d-ec9a5c5e3e95","resolution":{"observed_at":"2026-08-07T05:47:37.435339Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T05:47:37.416660Z","title":"Clarkson, Special polynomials associated with rat ional solutions of the defocusing non- linear Schr¨ odinger equation and the fourth Painlev´ e equation, European J","venue":null,"work_id":"544ae049-9060-4ca5-8b7d-c4deed565941","year":2006},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:35.261047Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:c5f2355e1f8468641afe7df58cf74b4fe1caa1fbe6447d24f043d5f49aa5bad7","observation_id":"28a5a1a0-07f4-4fcd-90b4-e3b15e0fc50d","resolution":{"observed_at":"2026-08-07T05:47:37.420958Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T05:47:37.403059Z","title":"Clarkson, Special polynomials associated with rat ional solutions of the Painlev´ e equa- tions and applications to soliton equations, Comput","venue":null,"work_id":"8b659704-55ac-4ead-8859-ee96f0f32a01","year":2006},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:35.389537Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:6743861c6a42d31240962abaf51401b9075e83885d6ae1094149420cdd53ed44","observation_id":"de74960e-83fc-4f1b-b521-ef64afa0abf5","resolution":{"observed_at":"2026-08-07T05:47:37.407843Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T05:47:35.449436Z","title":"Coddington and N","venue":null,"work_id":null,"year":1955},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:35.449436Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:52adac9021c4b2d451c6c61124e86293dcddb785c66e2287ef8f31e265aeaa1b","observation_id":"b96163a9-8246-4d41-aa94-95ed95f432dd","resolution":{"observed_at":"2026-08-07T05:47:35.449436Z","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":"2026-08-07T05:47:37.381221Z","title":"Crespo and Z","venue":null,"work_id":"f6c41b35-891e-4542-93a9-b276df2a7c3e","year":2011},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:35.575821Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:f545952a1265a8c0578c5a3dc40aa33e5bb35ce167bd2b030e778e030c43f290","observation_id":"99c357f9-d4a2-457f-ae97-0ad86d35d674","resolution":{"observed_at":"2026-08-07T05:47:37.385089Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T05:47:37.368324Z","title":"Hane, Crum transformation and rational solutio ns of the non-focusing nonlinear Schr¨ odinger equation,J","venue":null,"work_id":"c1087ff6-fdaf-4548-82f9-b4739c8a2b2c","year":1997},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:35.657910Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:c1a2d17f62d8c5da2bd2f5c4ad3610bda9973799a9b639c3aab25c91027eb1a4","observation_id":"46261079-fa80-4cb4-acd8-76e1fbd0ed78","resolution":{"observed_at":"2026-08-07T05:47:37.372586Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T05:47:37.354890Z","title":"Jaworski and J","venue":null,"work_id":"146a0c20-c151-433a-9a53-847991697368","year":1995},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:35.703421Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:fa8643974b3bee12c65acb25de98d516537a3fc9ebc65807c838c7f8cdff9a57","observation_id":"533b9dd0-5b9c-4889-b4a7-0e4167b4558b","resolution":{"observed_at":"2026-08-07T05:47:37.359792Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T05:47:37.342098Z","title":"Kovacic, An algorithm for solving second order lin ear homogeneous differential equations, J","venue":null,"work_id":"f0de080c-5115-4c5e-91c3-fcd9f5ba3bf3","year":1986},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:35.772394Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:b345b11613a32303985245386db6ec90a3efba1350f30e18a02e95ef53cbcf39","observation_id":"2115d359-0726-48b0-885a-87c3655a7699","resolution":{"observed_at":"2026-08-07T05:47:37.346456Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T05:47:37.328904Z","title":"Loday-Richaud, Stokes phenomenon, multisummabili ty and differential Galois groups, Ann","venue":null,"work_id":"278c2db9-1e18-4409-9f9f-495012e76657","year":1994},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:35.775886Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:bd2a88a990f4741b470908d8ce24b01c511f84f620de7fa64ca572153a4ea413","observation_id":"9d6f6ee8-7631-44cc-9187-3849c68e046c","resolution":{"observed_at":"2026-08-07T05:47:37.333510Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T05:47:37.315987Z","title":"Mitschi anhd D","venue":null,"work_id":"024b2776-7d59-42dd-82ae-5f1d4805e7c6","year":2016},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:35.904757Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:c6ac4de73f472ecdf85c75ff7e6f505466045589ca40364992b312a2f9306f3e","observation_id":"e58dafe3-2681-42f5-859c-8e91e6546586","resolution":{"observed_at":"2026-08-07T05:47:37.319828Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T05:47:37.302675Z","title":"Morales-Ruiz, Differential Galois Theory and Non-Integrability of Hamilt onian Systems Birkh¨ auser, Basel,1999","venue":null,"work_id":"536947dc-a1da-4fce-bb72-58440480c2c0","year":1999},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:35.982512Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:71dddee4f42cc0a482cd3cdc6eef508298b6cd399110cf6d99a17819fa0aa509","observation_id":"1da8b90b-4486-4bc4-83d4-9eb72a92a3a8","resolution":{"observed_at":"2026-08-07T05:47:37.307272Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T05:47:37.290544Z","title":"Nakamura and R","venue":null,"work_id":"49a1b819-408e-4c5a-8a72-07cabe7361e5","year":1985},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:36.107988Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:eeeec85359a523c75435e7dde5a4f5af4f6ba9b48e528898d0fd1773ea0515c6","observation_id":"4604af38-119a-4df6-aa24-01c0e62e33b9","resolution":{"observed_at":"2026-08-07T05:47:37.294416Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T05:47:37.277297Z","title":"Ohmiya, The inverse scattering problem for the Dirac operator and the modified Korteweg- de Vries equation, Osaka J","venue":null,"work_id":"dced715f-f4fc-41ce-a768-06b5a3e0e8ab","year":1979},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:36.255711Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:77cf81b68293e9850cee5dcfd07cf3929d4ce03066a9eaca3cd49979b06cacc9","observation_id":"d46f0e5a-c7f9-4344-964e-5ff0dfa03111","resolution":{"observed_at":"2026-08-07T05:47:37.281840Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T05:47:37.264896Z","title":"van der Put and M","venue":null,"work_id":"2dccce8e-12ab-4dc9-8966-add1cc0412d1","year":2003},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:36.421020Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:5822444afa81ff14d46816cee6a7279da36744a3c5afc27904a517df65e028f8","observation_id":"103b998e-cf7e-4432-bc99-f5befb8ba71b","resolution":{"observed_at":"2026-08-07T05:47:37.269104Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T05:47:37.251907Z","title":"Ramis and J","venue":null,"work_id":"4c38600a-25cb-4b32-89bc-963ff56c2587","year":1990},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:36.563507Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:dd77fb75443ced972065bef411e2b73ab0c9eb746522ea92bc1b6c677e4e67a4","observation_id":"a7c494fa-5913-497f-977c-283424cf1441","resolution":{"observed_at":"2026-08-07T05:47:37.255679Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T05:47:37.239634Z","title":"Rasinariu, U","venue":null,"work_id":"80a09820-0c07-4189-9d91-09371440da1f","year":1996},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:36.698732Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:4b5b3b78e1c46e7b5af4827a3ea0a230c86d5b100ade8eedf36004c84c8d594b","observation_id":"844bb04b-5e3f-43b7-b150-d8bb6fe37e7d","resolution":{"observed_at":"2026-08-07T05:47:37.243410Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T05:47:37.225893Z","title":"Singer, Introduction to the Galois theory of linear d ifferential equations, in Algebraic Theory of Differential Equations , M.A.H","venue":null,"work_id":"48b26d55-2123-4c60-8c1c-fa5a59094dfa","year":2009},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:36.860254Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:21d1ac6f81c6c8e263747fd4607828e51fcb87caa1e868d9a1eacccda35e9302","observation_id":"eccd3c5f-2337-4ebe-b4e0-f335d2af37ca","resolution":{"observed_at":"2026-08-07T05:47:37.230781Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T05:47:37.210768Z","title":"Stahlhofen, Positons of the modified Korteweg de Vr ies equation, Ann","venue":null,"work_id":"79256e6b-7968-42c2-b947-3397c026182a","year":1992},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:36.983488Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:78693a5ab921ab460f397706a594241a9858f085d76ffc2e09fe7018aebb9ba7","observation_id":"5b2f2139-8e60-4d50-b9b9-d207c02521c7","resolution":{"observed_at":"2026-08-07T05:47:37.215638Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T05:47:37.196357Z","title":"W u and T","venue":null,"work_id":"fe0446d7-fff0-4f21-8cd9-a20c16bf1962","year":2007},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:37.081632Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:fb2ded28108f9217430374b68342345b3c0dba45a81d055a162ee29590c4a7f6","observation_id":"a36b140a-3038-4b52-b34c-12b2aa30eceb","resolution":{"observed_at":"2026-08-07T05:47:37.201954Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T05:47:37.182309Z","title":null,"venue":null,"work_id":"27d619ed-3e3f-4ecc-b956-f4667c0c5f5e","year":2008},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:37.095545Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:5e27210cc2e174e78bd1f74ff5f4daf9c1a870c45bd32e0aeff24ef3bb2fd8cf","observation_id":"e7047b43-6cc8-4a44-9770-0b753c8b6e59","resolution":{"observed_at":"2026-08-07T05:47:37.186415Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T05:47:37.168783Z","title":"Yagasaki, Integrability of the Zakharov-Shabat sys tems by quadrature, Comm","venue":null,"work_id":"efcc15db-c22f-4026-a7fe-d3c1f91de473","year":2023},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:37.099397Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:46d92d41c255651f219ba87b610addb5708a4fa98c52ebe2d5308eb6866704e4","observation_id":"f320d726-739e-4bc1-9f12-75e68fb552a8","resolution":{"observed_at":"2026-08-07T05:47:37.173056Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2506.08046","last_updated":"2025-07-13T02:58:30Z","snapshot_observed_at":"2026-08-08T18:24:54.458667Z","submitted_at":"2025-06-08T05:57:18Z","title":"Solvability of the Korteweg-de Vries equation under meromorphic initial conditions by quadrature","version":2},"cited_work":{"arxiv_id":"2506.08046","doi":null,"metadata_source":"pith","pith_arxiv_id":"2506.08046","snapshot_observed_at":"2026-08-07T05:47:37.139846Z","title":"Solvability of the Korteweg-de Vries equation under meromorphic initial conditions by quadrature","venue":"math.AP","work_id":"2a25321a-0334-4ae2-ac89-a63a44277f82","year":2025},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:37.102458Z"},"links":{"cited_paper":"/paper/2506.08046","citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:4d7b2e1fe6e7640747bc821de17fc2c431fe74934e39db95e4f38bf822a03297","observation_id":"4ea3da99-00d3-42fa-bab3-8c7cfca02dd0","resolution":{"observed_at":"2026-08-07T05:47:37.146213Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T05:47:37.155932Z","title":"Zakharov and A.B","venue":null,"work_id":"95f211ff-6ca3-4ad3-b134-1e3f81757a09","year":1973},"citing_paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T05:47:37.106484Z"},"links":{"citing_paper":"/paper/2506.07246"},"observation_digest":"sha256:d6f7cd5673219f64a667dde9740c4dbf960d4b90f885ccc75194b87a97374ac2","observation_id":"b859b985-eec8-4f4c-ac7f-e2bcee1e7f67","resolution":{"observed_at":"2026-08-07T05:47:37.159796Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.07246","last_updated":"2025-07-13T07:59:18Z","latest_version":2,"primary_category":"math.AP","snapshot_observed_at":"2026-08-07T05:35:47.990111Z","submitted_at":"2025-06-08T18:04:21Z","title":"Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature"},"reference_resolution":{"displayed":28,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":2,"verified_exact":1,"verified_fuzzy":25},"total_outbound_references":28},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 1 inbound Pith citation observation for arXiv:2506.07246."}