{"as_of":"2026-08-19T01:59:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:220271016bdd889bd2ed9d35024b363fb915c7e81ebed73ba0d81f3e84f0d787","coverage":[{"denominator":43,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":43,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T22:43:45.606436Z","state":"measured"},{"denominator":43,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":43,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+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/2505.06768/citation-record","integrity":"/paper/2505.06768/integrity","json":"/paper/2505.06768/citation-record.json","paper":"/paper/2505.06768"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:43:48.867518Z","title":null,"venue":null,"work_id":"fb1b8724-b6fc-4b68-9322-86008cfa8b6c","year":2013},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:44.890864Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:e58b1eccfaef8d44a7cf6b9177c6a0ca936d44a953149cdf92cb7f55608a3841","observation_id":"ec7c97f0-3a43-440f-ba1d-adb7901b72a6","resolution":{"observed_at":"2026-08-15T22:43:48.988455Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:48.842596Z","title":null,"venue":null,"work_id":"c053d2b7-5a99-49c3-8fbf-65fe3ff862d6","year":2015},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:44.968673Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:175b575f9606855e641d4ea540c6c93918ae20970a7a36780fbb9f19debec3e5","observation_id":"ab60eb19-b333-46e8-bf8a-c870690aabd0","resolution":{"observed_at":"2026-08-15T22:43:48.850275Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:48.650215Z","title":"Bambusi, T","venue":null,"work_id":"75c91f2a-e0ff-4094-b27f-2a684b6c8997","year":2015},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.024275Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:7294f408c1468da0915c2512a5c01e86bd46b4e25934bb94c37560470df30453","observation_id":"f1640f1d-ab6b-4060-8a04-d6cafa986723","resolution":{"observed_at":"2026-08-15T22:43:48.748785Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:48.631486Z","title":null,"venue":null,"work_id":"d3e07da2-5656-4ad2-919f-b8fbf193c1d5","year":2012},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.075231Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:c1198265676acd3d59428375628a2aa360115a4e82021e5eb4a7d40cc6c74eb9","observation_id":"0094a2a5-b121-4e46-9feb-0bbf7fd51a5d","resolution":{"observed_at":"2026-08-15T22:43:48.637038Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:48.611936Z","title":"Biondini and Y","venue":null,"work_id":"7180dc83-c17b-4532-b6e1-7b3ea47bb8f3","year":2003},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.118262Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:18cfeb123d618c9a7193e6517e4743f400ced3f2e0a6805e77800be8deabc4bb","observation_id":"b71a68d0-3661-470f-801e-0138f29ff9c8","resolution":{"observed_at":"2026-08-15T22:43:48.617311Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:48.454733Z","title":"Biondini and D","venue":null,"work_id":"5ecf8d1e-aa79-467f-8976-622c1eb95980","year":2010},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.174031Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:8f8c9305bc4491bf0546c85a32a278eddf5378532022d2b93027770627be5e14","observation_id":"0cbe6b2c-4180-4d5b-9d17-44784c30e624","resolution":{"observed_at":"2026-08-15T22:43:48.513493Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:48.431123Z","title":null,"venue":null,"work_id":"1b26632b-c8ce-4770-a741-002593c4d36f","year":1985},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.181274Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:27a1372774aaebbd845557ee9a2f9a5e7597cb9834a45248b4265bccc5e9a905","observation_id":"a37a2249-c7e5-4459-bc35-b1d26e473b6e","resolution":{"observed_at":"2026-08-15T22:43:48.439319Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:48.409131Z","title":"Contreras and D","venue":null,"work_id":"bd5a572f-549b-4a5f-853c-a18d113bb97c","year":2014},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.188576Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:84919646104276d77385ce28c3dddb5ad8bccb649e39d305bc667a41ed333bf3","observation_id":"e776385b-f312-4273-9970-7bacf344c273","resolution":{"observed_at":"2026-08-15T22:43:48.416137Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:48.196545Z","title":"Contreras, D","venue":null,"work_id":"846327b9-0342-4a21-a32e-1d980dfaa46a","year":2016},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.194052Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:961d75122dae0f3acc26ab6dd3ccf96c7d5761eea02319a8d0fdd82c1055b706","observation_id":"ce2d5fef-b0ed-46d5-8761-4b5775af0586","resolution":{"observed_at":"2026-08-15T22:43:48.277155Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:48.161058Z","title":"Flaschka , On the Toda lattice","venue":null,"work_id":"914c51aa-87f5-4c66-8a4b-c6a38b3c3a34","year":1974},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.200871Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:6e45956690adfe081b444a9a93a6c6c635585c22d7dfec9ad1a5f3c97f4846a8","observation_id":"4c612ee9-e5ad-446f-ae61-0420f39e9990","resolution":{"observed_at":"2026-08-15T22:43:48.169148Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:48.138512Z","title":"Friesecke and R","venue":null,"work_id":"8a0c2edd-3853-4301-a7c1-89f3b1eae0fa","year":2002},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.206937Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:c84852d70586397d004f0979a89c695ec073dfe6114bfd6b3aed52db3418782a","observation_id":"49d735e7-814c-4f08-b476-321ce220802f","resolution":{"observed_at":"2026-08-15T22:43:48.146054Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:48.077641Z","title":"Friesecke and R","venue":null,"work_id":"fe1c8706-4a19-4446-a96e-75ff5771786a","year":2004},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.215468Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:ceca8cdff754fd291f63b3336abb2fcd072dbbe25a9182024417f7542928124b","observation_id":"516a210e-90ed-4a41-90f1-78a2811d8dfe","resolution":{"observed_at":"2026-08-15T22:43:48.110828Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:48.043685Z","title":"Geyer, Y","venue":null,"work_id":"e05758fa-e8fc-4d9a-9f93-4867f56b51ef","year":2024},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.224592Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:7539a3d52078ed607d67e40ba8fe343756d53a83ca98210f32ae60b6d4da202a","observation_id":"3a8f3eec-1c74-4037-b08b-00fbb5fb5c20","resolution":{"observed_at":"2026-08-15T22:43:48.049128Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:48.025981Z","title":"Hadac, S","venue":null,"work_id":"dd42687c-a356-4fea-a113-5f64fb1a8739","year":2009},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.230873Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:2a77dcd5584b42be417b27e45a871f2b24ee391720218a46757cfddda5721b51","observation_id":"14913c4b-3ba4-4fb6-8dc7-9ab2bd063fe7","resolution":{"observed_at":"2026-08-15T22:43:48.031895Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:48.007053Z","title":"Hirota , The direct method in soliton theory","venue":null,"work_id":"6953ff01-2787-4013-87b7-62572bce6008","year":2004},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.239753Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:77d29c835d19a4711d018292ac6d0f67f577100b3f7d7fb6a7c2973b57cbed05","observation_id":"5afd7c68-4852-477f-a504-877a8f582a72","resolution":{"observed_at":"2026-08-15T22:43:48.013516Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:47.951390Z","title":"Hristov and D","venue":null,"work_id":"f377808b-fa09-4e94-bf73-802965dd4957","year":2022},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.246472Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:0ea7dc9c9bc281a2dbd456aaf19b83d704ce704de48c44190c869d903611f175","observation_id":"ab780658-dea4-4be3-bae8-00889c85e78a","resolution":{"observed_at":"2026-08-15T22:43:47.991362Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:47.883059Z","title":"Koch and D","venue":null,"work_id":"d835e526-7f2c-4fa6-b16f-2b88bbbb2bd7","year":2024},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.253255Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:8ffa93f0686e65ad7d3f2d5a95c63c207bc396f6ab4a521450f4d0fd8926210b","observation_id":"27af74fc-2eb1-47eb-a6e0-33c4410e4ab9","resolution":{"observed_at":"2026-08-15T22:43:47.889141Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:47.857620Z","title":"Kr\\\"uger and G","venue":null,"work_id":"8f760d62-1f22-4441-9dbf-0f52cbeb4fff","year":2009},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.265928Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:1a5c01b31a12b9b4d783090111e3db8c6e5a6f042260f4e22bfae60d1c06d130","observation_id":"2589c57e-00db-47b4-961d-58ff47e91089","resolution":{"observed_at":"2026-08-15T22:43:47.866420Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:47.644144Z","title":"Kr\\\"uger and G","venue":null,"work_id":"97df7af7-06b2-48a4-8c5f-285d0b1dcef5","year":2009},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.272765Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:cc80a5961e3fca38237aa3334b58e97a5f006ff44d502fb41fc26e3f6cb1f045","observation_id":"157082c5-d08c-44ef-8325-78726af38588","resolution":{"observed_at":"2026-08-15T22:43:47.757730Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:47.626769Z","title":"Liu and J","venue":null,"work_id":"66d7ec6a-c54c-42d9-98ee-2275bfc5cf30","year":2018},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.279010Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:19d4af7f77ec284c7f12f245a3e3869975c07bc143c46746449ddfbcfce52cbc","observation_id":"53e8d1b2-f107-4d25-8732-415de1bd8031","resolution":{"observed_at":"2026-08-15T22:43:47.632332Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:47.608637Z","title":"Liu and J","venue":null,"work_id":"46fa1e37-698f-4a3a-acbe-8375ec2334da","year":2019},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.283479Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:9739661b5778c0c1785309f55373c2d6f1ba47fc2f094c6533cac3ebe6a8e4ba","observation_id":"3f75bdfb-bbbe-4f08-95b4-cd79a9971383","resolution":{"observed_at":"2026-08-15T22:43:47.614125Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:47.493784Z","title":null,"venue":null,"work_id":"605b0199-a4a8-44eb-9398-d4d91f05a845","year":2024},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.288952Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:0b3ded7061ac815f3f8590988880eb3734023e20cae19826f2f0dd36d4e8c0d5","observation_id":"59ae2a34-7381-4176-b193-c3e593aa5c60","resolution":{"observed_at":"2026-08-15T22:43:47.560549Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:47.471748Z","title":"Merle and L","venue":null,"work_id":"66386c28-1845-4e3f-b074-468c7d781367","year":2003},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.295598Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:5e259ebee4fe43979d0105466b34f7ec23c5203fce5992c9ec36fcf09e1b1b77","observation_id":"b85cb113-0f9f-47b9-86f6-312fb0b03843","resolution":{"observed_at":"2026-08-15T22:43:47.478949Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:47.409656Z","title":null,"venue":null,"work_id":"4f0640d7-e6c8-48f6-a56d-a0bde296d8f5","year":1981},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.300568Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:d921407cfa4c26dfa55b0814d6c20e50d5801e3d8948f872c476abe764698950","observation_id":"030b4be3-4ee9-4023-adcd-5eee9f78e743","resolution":{"observed_at":"2026-08-15T22:43:47.454798Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:47.215058Z","title":"Mizumachi , Asymptotic stability of lattice solitons in the energy space, Comm","venue":null,"work_id":"6863612d-6c89-4abf-be2f-5f95384375f5","year":2009},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.305540Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:9cb7ca05da632ebd1bb4a15d1d09f75eba152da8c720fdebc0dc817cd2e9f617","observation_id":"d0122298-0c7e-4035-b1b1-5ac11300d26c","resolution":{"observed_at":"2026-08-15T22:43:47.310022Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:47.193405Z","title":"Mizumachi , Asymptotic stability of N -solitary waves of the FPU lattices, Arch","venue":null,"work_id":"3dbe80ec-365a-47d5-8e32-9494e0337d3f","year":2013},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.312158Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:0d3b1c5f827816e0451cb4bfb3fed314f7642232e2e4c104dc9293931061302a","observation_id":"1fd8ece6-38b9-48f3-85fc-a847aa50348d","resolution":{"observed_at":"2026-08-15T22:43:47.199048Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:47.178488Z","title":"Mizumachi , Stability of line solitons for the KP-II equation in ^2 , Mem","venue":null,"work_id":"bfd0a6ff-c8a6-4487-8d72-8e3335c152bc","year":2015},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.318821Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:43bda90153ab9aaf7bb25d93f51792903e48cd4fb9cef79573babca254674bdf","observation_id":"10891d71-7218-4583-9b19-e2dc83ed1172","resolution":{"observed_at":"2026-08-15T22:43:47.183600Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:47.119456Z","title":"Mizumachi , Stability of line solitons for the KP-II equation in R^2","venue":null,"work_id":"d2195caa-2d68-40b8-8cc5-47aab3448486","year":2018},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.361875Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:65602b0e0e5b61dbffb89603690add1d9689f7c6e96ce81d5c67e6b0cbcd78e4","observation_id":"c0fdd851-e909-4d9f-b6ef-c457b11f1a1a","resolution":{"observed_at":"2026-08-15T22:43:47.167233Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:47.043522Z","title":"Mizumachi , The phase shift of line solitons for the KP-II equation , in Nonlinear dispersive partial differential equations and inverse scattering , 433--495, Fields Inst","venue":null,"work_id":"b31fce45-3e0b-40e6-8474-539da58e37c3","year":2019},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.435850Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:64e90f9927ca33aa6b2396ec29e4a7726182d38a946ec428a6aa989c900944ec","observation_id":"a9fef832-f7dc-4105-9c7f-df4006172bb3","resolution":{"observed_at":"2026-08-15T22:43:47.050213Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:46.849135Z","title":"Mizumachi , Linear stability of elastic-line solitons for the KP-II equation","venue":null,"work_id":"dd4a2532-4d71-4f3c-9ed0-939c66154b70","year":null},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.476421Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:e2afc647fca9630b38011acac3588515804a95c52270ab2f16386141a62af7f2","observation_id":"e571ff4a-5ab4-4952-8663-323d1f33fd65","resolution":{"observed_at":"2026-08-15T22:43:46.946166Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:46.827121Z","title":"Mizumachi and R","venue":null,"work_id":"7ed14e2b-0fd3-452d-8640-5d728eba018c","year":2008},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.501662Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:62740b810876cbafe3acf575645552f3006c775077cd98fe1603475ab1aa8959","observation_id":"dc95581b-9794-46c9-9604-638d2676f4d0","resolution":{"observed_at":"2026-08-15T22:43:46.833305Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:46.809778Z","title":"Mizumachi and D","venue":null,"work_id":"500b6923-7e7a-4a69-a288-d5882b350d6c","year":2012},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.512860Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:118d0d26d226a01b2c29ffcca98c5fbb253054d9b8a151b170b2ed8ac9c00ece","observation_id":"3ed3a91e-7441-4d3d-bacd-0992e48ebef0","resolution":{"observed_at":"2026-08-15T22:43:46.814242Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:46.612799Z","title":"Mizumachi and Y","venue":null,"work_id":"9e5a81f4-f462-40f9-9cd0-d17e04c49a71","year":2017},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.521699Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:ad05d02eec7b06f3607174544943b664f4621565dc0aa023800314500687467a","observation_id":"8fa48c0a-50ae-4524-97e3-53b3d77914e1","resolution":{"observed_at":"2026-08-15T22:43:46.736027Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:46.503253Z","title":"Mizumachi and Y","venue":null,"work_id":"b80ef864-5c53-4b4c-a2b1-7dbb24ecb0c9","year":2020},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.544323Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:67c90f00aae27d1478cf3b175fb80af516937ef9e91a0e867fe25fee71303b82","observation_id":"2b927756-b8d5-455c-8d93-b95318062fbe","resolution":{"observed_at":"2026-08-15T22:43:46.509540Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:46.464979Z","title":"Mizumachi and N","venue":null,"work_id":"85343613-6a4c-4bf8-bac0-baaafa398d19","year":2012},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.561152Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:46940998b6d74c3d3f4a7cf165cde0588aed09ec4e48f3a1de8949549954a972","observation_id":"2e4cd5fc-3b49-4aad-8a00-44e10dbc9445","resolution":{"observed_at":"2026-08-15T22:43:46.483941Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:46.225011Z","title":null,"venue":null,"work_id":"cb7996c1-a8b6-438c-bd3b-62046a33d8a3","year":1994},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.566637Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:fdf9cde6c223924b5df9091a7e37941cea7b151397ace1986d5c98f015a09813","observation_id":"351b81cc-c157-4dc2-9a7b-d89d532c66ec","resolution":{"observed_at":"2026-08-15T22:43:46.390184Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:46.093840Z","title":null,"venue":null,"work_id":"09248034-8954-4684-9d6d-ad8d24b42d1f","year":2023},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.572170Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:40c63f533849894e3b9776c5e1f404a175093211c99cc60b4bc73514b3264ea9","observation_id":"3e98616c-5e7d-4b7f-a802-b3e04552d412","resolution":{"observed_at":"2026-08-15T22:43:46.210633Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.12530","last_updated":"2024-12-17T04:40:56Z","snapshot_observed_at":"2026-08-16T05:05:47.068130Z","submitted_at":"2024-12-17T04:40:56Z","title":"On the B\\\"acklund transform and the stability of the line soliton of the KP-II equation on $\\mathbb R^2$","version":1},"cited_work":{"arxiv_id":"2412.12530","doi":null,"metadata_source":"pith","pith_arxiv_id":"2412.12530","snapshot_observed_at":"2026-08-15T22:43:45.679148Z","title":"On the B\\\"acklund transform and the stability of the line soliton of the KP-II equation on $\\mathbb R^2$","venue":"math.AP","work_id":"81fa4e55-07b1-42c8-9de2-fbeec35ee7bd","year":2024},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.577460Z"},"links":{"cited_paper":"/paper/2412.12530","citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:fd91c6b42143073060fe9955137d351bf08e359f10cdc567eb22fdb9160ec9ae","observation_id":"ec80656f-e01b-4144-96e1-b42335f68feb","resolution":{"observed_at":"2026-08-15T22:43:45.684635Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.11115","last_updated":"2024-02-16T22:40:15Z","snapshot_observed_at":"2026-08-17T18:11:09.856128Z","submitted_at":"2024-02-16T22:40:15Z","title":"Transverse linear stability of one-dimensional solitary gravity water waves","version":1},"cited_work":{"arxiv_id":"2402.11115","doi":null,"metadata_source":"pith","pith_arxiv_id":"2402.11115","snapshot_observed_at":"2026-08-15T22:43:45.653227Z","title":"Transverse linear stability of one-dimensional solitary gravity water waves","venue":"math.AP","work_id":"24b4fd58-e201-4c2b-84f2-bfff11a6df49","year":2024},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.583485Z"},"links":{"cited_paper":"/paper/2402.11115","citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:d9a3974fdf262b21e206e51659c2c4722fcf27ff8ba5c4662c8690519d4741df","observation_id":"3893b37d-9a0f-45f3-aca4-c7e02596ca19","resolution":{"observed_at":"2026-08-15T22:43:45.660811Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:45.975439Z","title":"Toda , Nonlinear waves and solitons , translated from the Japanese, Mathematics and its Applications (Japanese Series), 5, Kluwer Acad","venue":null,"work_id":"41574c34-e2cb-4de2-8e70-9e27f445430b","year":1989},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.590370Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:0caca083a1c7be5e18b2805ec80bd534e6ce9b5363f8a0ec67896e6eb2594261","observation_id":"e65e07df-7994-4a01-bec4-36e3848e0ab4","resolution":{"observed_at":"2026-08-15T22:43:45.982868Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:45.779963Z","title":"Toda , Wave Propagation in Anharmonic Lattices, Journal of the Physical Society of Japan 23 (1967), 501--506","venue":null,"work_id":"6abb7e0c-e812-4107-9bf8-2f2c8e44f667","year":1967},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.595774Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:eabc30a288f5cc4f5ee909844db2d1a8611fa60b0cd55cbda908a400ac7b6e52","observation_id":"eea699ed-88ee-4ff6-95bf-c5a2173b67c6","resolution":{"observed_at":"2026-08-15T22:43:45.912804Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:45.720840Z","title":"Toda and M","venue":null,"work_id":"7c93afc3-a42e-4318-ae71-2c5d41964b62","year":1975},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.600987Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:52fd9bd6a1dc351b7019860c2ff9da211ea895a9f55555d8dd7a046639ec3ce5","observation_id":"ce8a1af2-24e4-4462-b377-afa6daaeb3e6","resolution":{"observed_at":"2026-08-15T22:43:45.726430Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T22:43:45.699473Z","title":"Ueno and K","venue":null,"work_id":"801b0a03-c745-4512-9380-96865f35932a","year":1984},"citing_paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-15T22:43:45.606436Z"},"links":{"citing_paper":"/paper/2505.06768"},"observation_digest":"sha256:ad0aba085a03b68e70dcc0153c1a30c00f8eff1aaf430435c14e72b3d5e0215f","observation_id":"fda3359b-e05e-461b-90e5-e5a0e0aa49c6","resolution":{"observed_at":"2026-08-15T22:43:45.705864Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.06768","last_updated":"2025-05-10T22:16:57Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-15T22:31:20.668536Z","submitted_at":"2025-05-10T22:16:57Z","title":"Transverse linear stability of line solitons for 2D Toda"},"reference_resolution":{"displayed":43,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":8,"verified_exact":2,"verified_fuzzy":33},"total_outbound_references":43},"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":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 0 inbound Pith citation observations for arXiv:2505.06768."}