{"as_of":"2026-08-08T18:47:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ffbfe7759162ac9d2e72efb84cd8f85dd7ef2b57391f9092333a68a55b3c2f09","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":5,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":5,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":5,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":5,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T15:07:56.958854Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-23T00:25:14.261168Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2007.03508","last_updated":"2020-07-07T14:43:53Z","snapshot_observed_at":"2026-08-04T19:50:43.861011Z","submitted_at":"2020-07-07T14:43:53Z","title":"Derivation of the homogeneous kinetic wave equation: longer time scales","version":1},"cited_work":{"arxiv_id":"2007.03508","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2007.03508","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Collot and P","venue":null,"work_id":"bb89f86c-f754-400f-b874-7339c12a50bc","year":2007},"citing_paper":{"arxiv_id":"2503.12805","last_updated":"2026-04-18T19:08:32Z","snapshot_observed_at":"2026-07-06T20:53:41.124209Z","submitted_at":"2025-03-17T04:21:47Z","title":"A fast Fourier spectral method for wave kinetic equation","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-23T00:24:50.580597Z"},"links":{"cited_paper":"/paper/2007.03508","citing_paper":"/paper/2503.12805"},"observation_digest":"sha256:f6c6d61b334ef00e24d8333b1e04286d66756c08daebcfd0e56922b7ee2d5e7d","observation_id":"96a15b23-f0f6-427c-8cc2-187fc5b750e3","resolution":{"observed_at":"2026-05-23T00:25:14.268769Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2007.03508","last_updated":"2020-07-07T14:43:53Z","snapshot_observed_at":"2026-08-04T19:50:43.861011Z","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":"2026-08-07T15:07:56.958854Z","title":"Collot, P","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2505.16488","last_updated":"2025-06-03T18:18:32Z","snapshot_observed_at":"2026-08-07T14:57:55.951486Z","submitted_at":"2025-05-22T10:13:52Z","title":"Kinetic approximation for equations of discrete turbulence in the subcritical case","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T15:07:56.958854Z"},"links":{"cited_paper":"/paper/2007.03508","citing_paper":"/paper/2505.16488"},"observation_digest":"sha256:7e591d900ca0ce06b0293d0411faf68b4318e1f01e9fcea62d3e1d2c382f39b8","observation_id":"37dcce12-31f0-46c3-81b3-435a4781baca","resolution":{"observed_at":"2026-08-07T15:07:56.958854Z","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":"2026-08-04T19:50:43.861011Z","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":"2026-08-07T11:22:21.714487Z","title":"Derivation of the homogeneous kinetic wave equation: longer time scales","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2506.02948","last_updated":"2025-06-12T16:12:56Z","snapshot_observed_at":"2026-08-08T04:33:56.777251Z","submitted_at":"2025-06-03T14:44:43Z","title":"Rigorous Derivation of the Wave Kinetic Equation for $\\beta$-FPUT System","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-07T11:22:21.714487Z"},"links":{"cited_paper":"/paper/2007.03508","citing_paper":"/paper/2506.02948"},"observation_digest":"sha256:696630326d4e511cf2282e7caf5baa62eadfeb323cef96bcb62c882e3399329c","observation_id":"1f546b0d-d157-43d3-91be-6231c6cae5ae","resolution":{"observed_at":"2026-08-07T11:22:21.714487Z","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":"2026-08-04T19:50:43.861011Z","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":"2026-08-05T11:48:18.331931Z","title":"Collot, P","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2509.02344","last_updated":"2025-09-02T14:11:42Z","snapshot_observed_at":"2026-08-06T18:41:55.860297Z","submitted_at":"2025-09-02T14:11:42Z","title":"Probabilistic well-posedness of dispersive PDEs beyond variance blowup I: Benjamin-Bona-Mahony equation","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-05T11:48:18.331931Z"},"links":{"cited_paper":"/paper/2007.03508","citing_paper":"/paper/2509.02344"},"observation_digest":"sha256:6fc70bd6c112b1b4b83ad27134a1c7d6e9e0763777256901eda5da70b5122232","observation_id":"c015ca85-a311-442a-89ed-3f70d0f23584","resolution":{"observed_at":"2026-08-05T11:48:18.331931Z","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":"2026-08-04T19:50:43.861011Z","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":"2026-08-03T21:34:28.007256Z","title":"Collot, P","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2511.15587","last_updated":"2026-06-09T22:59:43Z","snapshot_observed_at":"2026-08-08T04:33:57.788064Z","submitted_at":"2025-11-19T16:18:56Z","title":"On the optimal local well-posedness of the wave kinetic equation in $L^r$","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-03T21:34:28.007256Z"},"links":{"cited_paper":"/paper/2007.03508","citing_paper":"/paper/2511.15587"},"observation_digest":"sha256:6595eb771f7fe47004414c5dc6092aeb1192022cfe6595d6337aa0d73e00c8d8","observation_id":"49e52229-4c6f-4752-bea2-0fea38f1adde","resolution":{"observed_at":"2026-08-03T21:34:28.007256Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2007.03508/citation-record","integrity":"/paper/2007.03508/integrity","json":"/paper/2007.03508/citation-record.json","paper":"/paper/2007.03508"},"outbound":[],"paper":{"arxiv_id":"2007.03508","last_updated":"2020-07-07T14:43:53Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-04T19:50:43.861011Z","submitted_at":"2020-07-07T14:43:53Z","title":"Derivation of the homogeneous kinetic wave equation: longer time scales"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 5 inbound Pith citation observations for arXiv:2007.03508."}