{"as_of":"2026-08-16T14:50:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c96f305825f622d46e027381b0b172577cda80f0a6aad75b09f360ca6908c546","coverage":[{"denominator":29,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":29,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T17:19:09.994047Z","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":"2026-08-16T06:30:59.297886+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2411.12868/citation-record","integrity":"/paper/2411.12868/integrity","json":"/paper/2411.12868/citation-record.json","paper":"/paper/2411.12868"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:19:10.276377Z","title":"Ampatzoglou, Global well-posedness of the inhomogeneous kinetic wave eq uation near vacuum , Kinet","venue":null,"work_id":"349a37b1-f03d-4722-bc84-cd19a31cfc4e","year":2024},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.905733Z"},"links":{"citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:2e3df38524c898b6715304f477c0e73418f7991941bcda66574ab2fb77cd4a91","observation_id":"bc9e6384-b044-42f6-830b-966d7eb1158d","resolution":{"observed_at":"2026-08-12T17:19:10.280139Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:19:10.266190Z","title":"Ampatzoglou, C","venue":null,"work_id":"a40e9455-dce9-49ba-80d0-bb61c514125b","year":2024},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.909666Z"},"links":{"citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:4b666da2e48053379fdea6718c6d966e52c1c999ca2dea6e98646c531d128e2c","observation_id":"e653061c-c186-424f-90f4-3a9a73d3cd16","resolution":{"observed_at":"2026-08-12T17:19:10.269625Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.03984","last_updated":"2024-05-07T03:48:24Z","snapshot_observed_at":"2026-08-16T13:54:50.543942Z","submitted_at":"2024-05-07T03:48:24Z","title":"Inhomogeneous wave kinetic equation and its hierarchy in polynomially weighted $L^\\infty$ spaces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.03984","snapshot_observed_at":"2026-08-12T17:19:09.912936Z","title":"Ampatzoglou, J.K","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.912936Z"},"links":{"cited_paper":"/paper/2405.03984","citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:c2351f7cbedcde7e87b09a2f1b07a8fce52c795d0eba4d513b493887f2a7b148","observation_id":"35ac0d07-c0ed-468b-a57e-eb50fc688502","resolution":{"observed_at":"2026-08-12T17:19:09.912936Z","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":"2026-08-12T17:19:10.256009Z","title":"Ampatzoglou, T","venue":null,"work_id":"7edd2e82-fa9c-4c6e-aa4e-26cd03f9df2f","year":2024},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.916577Z"},"links":{"citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:fc0ff7ba5b8a83172a0408d94e01d7ae253512e58c71a7edb445d38ecde3fd49","observation_id":"92edeece-bd30-4996-873f-8d84efe56c08","resolution":{"observed_at":"2026-08-12T17:19:10.259342Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:19:10.246405Z","title":"B´ enyi, T","venue":null,"work_id":"01c594a7-d60c-45ce-8c45-deda9af7ec77","year":2013},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.919371Z"},"links":{"citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:47cd0c7c8555e14338acfcad3f0f05689280eb27b179fb8adc0c4e42b2a0c151","observation_id":"65fc449d-196a-45fc-b3ba-2f37c96257a9","resolution":{"observed_at":"2026-08-12T17:19:10.249655Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:19:10.236720Z","title":"Buckmaster, P","venue":null,"work_id":"dcd13f59-8b54-4e4e-a7ce-43524a8e4725","year":2021},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.922362Z"},"links":{"citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:632e9e2787c437ba638c9b329b8ff58ab9bd4d784b7e3ab46d8e875924542d80","observation_id":"999562f7-d72d-44f5-8cab-8d65120c2257","resolution":{"observed_at":"2026-08-12T17:19:10.240019Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:19:10.227873Z","title":null,"venue":null,"work_id":"ff97d53c-bc29-4edf-abfd-769d32518229","year":null},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.925518Z"},"links":{"citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:3e7467b7fc719370fe23028a731fa4720f8c478eb2b1c6fa59d02461f6d7d7c4","observation_id":"10226612-5af5-4e79-b47a-884392f27535","resolution":{"observed_at":"2026-08-12T17:19:10.230894Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:19:10.219302Z","title":"Collot, H","venue":null,"work_id":"b42ad047-84e9-4bf4-a0fb-b1b4c61d4ec3","year":2024},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.928173Z"},"links":{"citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:093114f12b8820a0aeeed75adc0fdac4fb4123fc5b1bf553cf61aad4d2d2ecdb","observation_id":"c7ff3142-6b1e-4130-a297-d44eec9dccf6","resolution":{"observed_at":"2026-08-12T17:19:10.222084Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1912.10368","last_updated":"2021-02-18T09:22:39Z","snapshot_observed_at":"2026-08-11T17:46:56.343865Z","submitted_at":"2019-12-22T01:23:32Z","title":"On the derivation of the homogeneous kinetic wave equation","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1912.10368","snapshot_observed_at":"2026-08-12T17:19:09.930981Z","title":"Collot, P","venue":null,"work_id":null,"year":1912},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.930981Z"},"links":{"cited_paper":"/paper/1912.10368","citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:5cc29953049047c429a6c519301b25fcbd15c88252741d38316917ffd1d2648a","observation_id":"ed9ea232-555a-4fb3-818e-10929dfdea30","resolution":{"observed_at":"2026-08-12T17:19:09.930981Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2007.03508","last_updated":"2020-07-07T14:43:53Z","snapshot_observed_at":"2026-08-11T17:46:53.203889Z","submitted_at":"2020-07-07T14:43:53Z","title":"Derivation of the homogeneous kinetic wave equation: longer time scales","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2007.03508","snapshot_observed_at":"2026-08-12T17:19:09.933915Z","title":"Collot, P","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.933915Z"},"links":{"cited_paper":"/paper/2007.03508","citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:4bc11058d342485f3e32da1c1ec7a8197fce3a92040f650b3703040f55facf19","observation_id":"4facf370-44ba-4b4e-988f-eeea43886c4b","resolution":{"observed_at":"2026-08-12T17:19:09.933915Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:19:09.936651Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.936651Z"},"links":{"citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:cbc07736c5bce29c82156946c1669bef6419f348095f60a13e4d4990aec84742","observation_id":"01f783a7-f517-44a6-bbe6-7841c79bc2ef","resolution":{"observed_at":"2026-08-12T17:19:09.936651Z","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":"2026-08-12T17:19:10.204570Z","title":null,"venue":null,"work_id":"bef99548-d64f-4657-b5bb-a84b6b9f73a8","year":2023},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.939517Z"},"links":{"citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:1fba3c1d460b02b9dc39743f4266832573e093660b9820575551bdc62f1b3891","observation_id":"aad43dac-fd6a-4fe8-b678-c4a4b3094320","resolution":{"observed_at":"2026-08-12T17:19:10.207615Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2311.10082","last_updated":"2024-04-07T02:58:23Z","snapshot_observed_at":"2026-08-16T14:42:35.547225Z","submitted_at":"2023-11-16T18:38:22Z","title":"Long time justification of wave turbulence theory","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.10082","snapshot_observed_at":"2026-08-12T17:19:09.942116Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.942116Z"},"links":{"cited_paper":"/paper/2311.10082","citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:87391f690cd76b8638f396dd4ec97854bb86807bdb227284b56c290c98c29227","observation_id":"b422bc37-06ac-43d7-ba84-868e7dbb528f","resolution":{"observed_at":"2026-08-12T17:19:09.942116Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2408.07818","last_updated":"2025-07-18T22:31:34Z","snapshot_observed_at":"2026-08-16T13:26:23.456948Z","submitted_at":"2024-08-14T21:14:18Z","title":"Long time derivation of the Boltzmann equation from hard sphere dynamics","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2408.07818","snapshot_observed_at":"2026-08-12T17:19:09.945063Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.945063Z"},"links":{"cited_paper":"/paper/2408.07818","citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:fa3eaa2c537d46fb782cf650819d1085cbb6907a91491122ba49dc793ced2f16","observation_id":"79df889f-7501-456a-a619-54bf28fb90cb","resolution":{"observed_at":"2026-08-12T17:19:09.945063Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2406.05280","last_updated":"2024-06-07T22:20:32Z","snapshot_observed_at":"2026-08-16T13:45:00.556894Z","submitted_at":"2024-06-07T22:20:32Z","title":"Instability of singular equilibria of a wave kinetic equation","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2406.05280","snapshot_observed_at":"2026-08-12T17:19:09.948519Z","title":"Escobedo, A","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.948519Z"},"links":{"cited_paper":"/paper/2406.05280","citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:22daa957295c842011cce36b3d0f1cd767479c01fa8635335b1f84cbb4b5509f","observation_id":"17972ffc-c192-47c2-b551-662fb759918e","resolution":{"observed_at":"2026-08-12T17:19:09.948519Z","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":"2026-08-12T17:19:10.195727Z","title":"Escobedo, J.J.L","venue":null,"work_id":"aa8db6c4-6e58-4c0d-a8f2-5d4e381241a3","year":2015},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.951814Z"},"links":{"citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:9b36d9cd34b5e85a9a6485ba65b30734d17d607deb717b3a1af90f4c6e213ee9","observation_id":"b07017f0-d031-40c3-bcc3-c06aaf5d8049","resolution":{"observed_at":"2026-08-12T17:19:10.198601Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:19:10.187237Z","title":"Faou, Linearized Wave Turbulence Convergence Results for Three- Wave Systems , Volume 378, pages 807–849, (2020)","venue":null,"work_id":"e9999800-60c4-478b-9789-fe78da7d61ce","year":2020},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.955017Z"},"links":{"citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:dcdff0c9e76e13554c3a88d26531faa88b11087e548e155ae67bc10bb665d8a5","observation_id":"d9e61155-2f04-49bc-9fb5-138d27e05879","resolution":{"observed_at":"2026-08-12T17:19:10.190216Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:19:10.178063Z","title":"Germain, A","venue":null,"work_id":"40971da4-607f-404c-8aea-9e67f5a2d121","year":2020},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.958688Z"},"links":{"citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:d01c776baa73ec275309188a555d832a549d09d3ca9c037e2c890edc2c10c98a","observation_id":"76b85ba8-4470-481f-b9b3-319b43fcac47","resolution":{"observed_at":"2026-08-12T17:19:10.181256Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2310.11893","last_updated":"2023-10-18T11:25:23Z","snapshot_observed_at":"2026-08-13T05:46:56.039244Z","submitted_at":"2023-10-18T11:25:23Z","title":"Local Well-posedness for the Kinetic MMT Model","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2310.11893","snapshot_observed_at":"2026-08-12T17:19:09.961902Z","title":"Germain, J","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.961902Z"},"links":{"cited_paper":"/paper/2310.11893","citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:a26fee392f35280c98eaee7534de0981681389ec8a35190f4f1b5f14bc31e16d","observation_id":"4319834c-f4de-475b-acde-209270f1b8c2","resolution":{"observed_at":"2026-08-12T17:19:09.961902Z","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":"2026-08-12T17:19:10.168113Z","title":null,"venue":null,"work_id":"c6dd0245-82c5-4a8e-9c65-164086bd8631","year":2024},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.965192Z"},"links":{"citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:6fbc8a04495690736d04292b95e4faeae0b8a74d787084a0c1e0c8794eedac86","observation_id":"b5cfae7f-f2a3-4892-a4a5-72b7eb238891","resolution":{"observed_at":"2026-08-12T17:19:10.171905Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2210.17445","last_updated":"2022-11-08T14:54:43Z","snapshot_observed_at":"2026-08-13T13:52:53.145141Z","submitted_at":"2022-10-31T16:15:18Z","title":"On the wave turbulence theory for a stochastic KdV type equation -- Generalization for the inhomogeneous kinetic limit","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2210.17445","snapshot_observed_at":"2026-08-12T17:19:09.968756Z","title":"Hannani, M","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.968756Z"},"links":{"cited_paper":"/paper/2210.17445","citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:60737c9a29cc193cb6e45f6b9fd7fbbe8558fa627254bca5b07d4e7c927ef042","observation_id":"1e766306-f7ce-43f2-a71c-4f1915f0de17","resolution":{"observed_at":"2026-08-12T17:19:09.968756Z","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":"2026-08-12T17:19:10.157561Z","title":"Kenig, G","venue":null,"work_id":"9e051779-bce3-45c3-a994-2cd39fda381c","year":1993},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.972417Z"},"links":{"citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:a7b83b849e940ffb45181b6d1dd066ea0406a8b3faab033dcf6db7c4f57d3565","observation_id":"82bf1852-3965-43b0-a429-5d87c5d23c83","resolution":{"observed_at":"2026-08-12T17:19:10.161315Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:19:10.147333Z","title":"Kenig, G","venue":null,"work_id":"8aef31a9-1121-4c54-94a8-748274c68ae0","year":1998},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.975453Z"},"links":{"citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:fbfe88c6969e7b589881bfbc0a2e3a1a06e3e8eae29bab2c4ccd572258552532","observation_id":"5227e09f-dd3a-457e-b938-e1c76b67a4b9","resolution":{"observed_at":"2026-08-12T17:19:10.150644Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2204.06148","last_updated":"2022-06-16T04:15:00Z","snapshot_observed_at":"2026-08-14T08:38:30.164949Z","submitted_at":"2022-04-13T03:01:53Z","title":"Almost sharp wave kinetic theory of multidimensional KdV type equations with $d\\ge 3$","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2204.06148","snapshot_observed_at":"2026-08-12T17:19:09.978497Z","title":"Ma, Almost sharp wave kinetic theory of multidimensional KdV ty pe equations with d ≥ 3, Preprint: arXiv:2204.06148 (2022)","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.978497Z"},"links":{"cited_paper":"/paper/2204.06148","citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:eb5fbb27f728471836791c89d99c3dc6411e967965aabb37956b3e855cf866c4","observation_id":"1e1ed722-6247-4edd-9c11-9a171d7304b5","resolution":{"observed_at":"2026-08-12T17:19:09.978497Z","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":"2026-08-12T17:19:10.137485Z","title":"Majda, D.W","venue":null,"work_id":"9658b1e8-2984-4d8d-a7a3-51fb1387bfcc","year":1997},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.981730Z"},"links":{"citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:3803b10bac68c5d224fb309bda1a2391d870db80be1cb18a5210e00ab6fad521","observation_id":"421341bc-4e42-464a-af9b-3906990e7c52","resolution":{"observed_at":"2026-08-12T17:19:10.140871Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:19:10.127170Z","title":"Menegaki, L2-stability near equilibrium for the 4 waves kinetic equatio n, Kinet","venue":null,"work_id":"4b156e95-31cf-4b4c-9833-b71c27be12d7","year":2024},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.984734Z"},"links":{"citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:7bfdae264ed5f376e6d148102e159913253e2bb14e6cb19f9b40bcbf6614d1c9","observation_id":"48270fc9-1d43-4615-9909-c72aa465a6f4","resolution":{"observed_at":"2026-08-12T17:19:10.130692Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:19:10.116339Z","title":"Nazarenko, Wave turbulence, Lecture Notes in Physics, 825","venue":null,"work_id":"014d39c3-519a-4e1a-8706-31418a140d0c","year":2011},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.987925Z"},"links":{"citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:ad6c9b530040f54653abc31e08ae618236e62faa23bc1cab64bbf30fc6bbfac1","observation_id":"f7f2056a-9b19-4397-b745-57d2e8dadffb","resolution":{"observed_at":"2026-08-12T17:19:10.120694Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2106.09819","last_updated":"2024-02-12T16:01:04Z","snapshot_observed_at":"2026-08-13T19:01:12.073901Z","submitted_at":"2021-06-17T21:14:07Z","title":"On the wave turbulence theory for a stochastic KdV type equation","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2106.09819","snapshot_observed_at":"2026-08-12T17:19:09.991268Z","title":"Staﬃlani, M.-B","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.991268Z"},"links":{"cited_paper":"/paper/2106.09819","citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:a8f70964179a19da87fb35ec1bc3dfcae03b0f383427c2272c2c086030ce837f","observation_id":"51816929-6540-4c17-a4bd-0dc88501a9a5","resolution":{"observed_at":"2026-08-12T17:19:09.991268Z","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":"2026-08-12T17:19:10.106343Z","title":null,"venue":null,"work_id":"618accd3-bf4c-4180-9cd1-94bbc618ea23","year":2022},"citing_paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-12T17:19:09.994047Z"},"links":{"citing_paper":"/paper/2411.12868"},"observation_digest":"sha256:69641199abe46e0f57850d9dfd1ea887ce8a7d01d4aefeacb7fb1c7b95616e6d","observation_id":"265cb9de-8c35-4425-b48a-a0026e75d05f","resolution":{"observed_at":"2026-08-12T17:19:10.110112Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2411.12868","last_updated":"2024-11-21T15:18:15Z","latest_version":2,"primary_category":"math.AP","snapshot_observed_at":"2026-08-14T08:01:52.848539Z","submitted_at":"2024-11-19T21:24:31Z","title":"On the ill-posedness of kinetic wave equations"},"reference_resolution":{"displayed":29,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":15,"verified_exact":0,"verified_fuzzy":14},"total_outbound_references":29},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 0 inbound Pith citation observations for arXiv:2411.12868."}