{"as_of":"2026-08-09T02:34:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:104b70c88ce7fabef05e1f20c92e7b6286095ac69b4b14c80ed795d947246535","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":6,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":6,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":6,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":6,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T15:07:59.923177Z","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":"2026-06-30T14:24:45.271586Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2106.09819","last_updated":"2024-02-12T16:01:04Z","snapshot_observed_at":"2026-07-06T11:20:32.533833Z","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":"2026-08-07T15:07:59.923177Z","title":"Staffilani and M.-B","venue":null,"work_id":null,"year":2021},"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":32,"source":"pdf_text","source_observed_at":"2026-08-07T15:07:59.923177Z"},"links":{"cited_paper":"/paper/2106.09819","citing_paper":"/paper/2505.16488"},"observation_digest":"sha256:327a77e2276a0e067995517b05937b83177db0900e86dff1cf1ed007c83ef292","observation_id":"cecc1506-ba7b-4557-ba3e-a0a8f9ae4346","resolution":{"observed_at":"2026-08-07T15:07:59.923177Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2106.09819","last_updated":"2024-02-12T16:01:04Z","snapshot_observed_at":"2026-07-06T11:20:32.533833Z","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":"2026-08-04T09:35:07.350634Z","title":"Staffilani, and M","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2510.15159","last_updated":"2026-07-29T08:56:38Z","snapshot_observed_at":"2026-08-08T12:33:21.710195Z","submitted_at":"2025-10-16T21:39:25Z","title":"Rogue waves and large deviations for 2D pure gravity deep water waves","version":4},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-04T09:35:07.350634Z"},"links":{"cited_paper":"/paper/2106.09819","citing_paper":"/paper/2510.15159"},"observation_digest":"sha256:28579f6e6b5377768e3fcca51d14d537f8a91447247f385abbba52093aa1652e","observation_id":"f3dfb7d6-8524-4d22-a2ab-860fb9fa4951","resolution":{"observed_at":"2026-08-04T09:35:07.350634Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2106.09819","last_updated":"2024-02-12T16:01:04Z","snapshot_observed_at":"2026-07-06T11:20:32.533833Z","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":"2106.09819","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2106.09819","snapshot_observed_at":"2026-06-30T14:24:45.271586Z","title":"Staffilani and M.-B","venue":null,"work_id":"bca7a21c-bb47-4a4a-b523-c03aefc542bf","year":2021},"citing_paper":{"arxiv_id":"2512.17777","last_updated":"2026-04-30T09:23:58Z","snapshot_observed_at":"2026-07-06T22:39:33.919723Z","submitted_at":"2025-12-19T16:48:13Z","title":"Irreversible thermalization vs reversible dynamics mediated by anomalous correlators: Wave turbulence theory and experiments in optical fibers","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-05-16T20:38:13.295736Z"},"links":{"cited_paper":"/paper/2106.09819","citing_paper":"/paper/2512.17777"},"observation_digest":"sha256:06d999b0057f8789ebae8e8f22ea54522d1e06122dd351d93bf0ce0034c2d14d","observation_id":"786b4e46-0c05-4987-8989-2b54f4adcbb0","resolution":{"observed_at":"2026-05-16T20:38:24.494406Z","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":"2106.09819","last_updated":"2024-02-12T16:01:04Z","snapshot_observed_at":"2026-07-06T11:20:32.533833Z","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":"2106.09819","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2106.09819","snapshot_observed_at":"2026-06-30T14:24:45.271586Z","title":"Staffilani and M.-B","venue":null,"work_id":"bca7a21c-bb47-4a4a-b523-c03aefc542bf","year":2021},"citing_paper":{"arxiv_id":"2604.12118","last_updated":"2026-04-13T22:53:31Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-13T22:53:31Z","title":"Weakly turbulent dynamics on Schwarzschild-AdS black hole spacetimes","version":1},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-05-10T15:24:11.775563Z"},"links":{"cited_paper":"/paper/2106.09819","citing_paper":"/paper/2604.12118"},"observation_digest":"sha256:4c5c02e3d0f656c51c33da3b9736ba766f8625767c3826819eaf7290e3e7cc20","observation_id":"9d24ff31-ad79-42ea-997d-2ad11921d1ea","resolution":{"observed_at":"2026-05-11T10:36:07.564698Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"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":"2106.09819","last_updated":"2024-02-12T16:01:04Z","snapshot_observed_at":"2026-07-06T11:20:32.533833Z","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":"2106.09819","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2106.09819","snapshot_observed_at":"2026-06-30T14:24:45.271586Z","title":"Staffilani and M.-B","venue":null,"work_id":"bca7a21c-bb47-4a4a-b523-c03aefc542bf","year":2021},"citing_paper":{"arxiv_id":"2605.24268","last_updated":"2026-05-22T22:40:40Z","snapshot_observed_at":"2026-08-06T11:52:00.466239Z","submitted_at":"2026-05-22T22:40:40Z","title":"Resonant interactions in the $\\alpha$-FPUT lattice with site-dependent coefficients","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-06-30T14:15:18.210031Z"},"links":{"cited_paper":"/paper/2106.09819","citing_paper":"/paper/2605.24268"},"observation_digest":"sha256:e610989052c3e5f6cca979da6f612a6149c0851d19834c27bc44e0fd0e411ad6","observation_id":"42ba00f7-f4ab-4328-ac1e-a63e915ea69f","resolution":{"observed_at":"2026-06-30T14:24:45.273816Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"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":"2106.09819","last_updated":"2024-02-12T16:01:04Z","snapshot_observed_at":"2026-07-06T11:20:32.533833Z","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":"2106.09819","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2106.09819","snapshot_observed_at":"2026-06-30T14:24:45.271586Z","title":"Staffilani and M.-B","venue":null,"work_id":"bca7a21c-bb47-4a4a-b523-c03aefc542bf","year":2021},"citing_paper":{"arxiv_id":"2605.29265","last_updated":"2026-05-28T02:34:13Z","snapshot_observed_at":"2026-07-06T23:38:41.516603Z","submitted_at":"2026-05-28T02:34:13Z","title":"Complex-valued modified Zakharov Kuznetsov equation","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-06-29T07:06:53.709262Z"},"links":{"cited_paper":"/paper/2106.09819","citing_paper":"/paper/2605.29265"},"observation_digest":"sha256:a0bcb3905aeccc5110bfafb84f1f94568bdb0f159801cc1ff74c8ad12f010fce","observation_id":"3782a315-6e56-4512-9efc-6bf0687888a2","resolution":{"observed_at":"2026-06-29T07:13:16.724563Z","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"}}],"links":{"evidence":"/evidence","html":"/paper/2106.09819/citation-record","integrity":"/paper/2106.09819/integrity","json":"/paper/2106.09819/citation-record.json","paper":"/paper/2106.09819"},"outbound":[],"paper":{"arxiv_id":"2106.09819","last_updated":"2024-02-12T16:01:04Z","latest_version":5,"primary_category":"math.AP","snapshot_observed_at":"2026-07-06T11:20:32.533833Z","submitted_at":"2021-06-17T21:14:07Z","title":"On the wave turbulence theory for a stochastic KdV type equation"},"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 9 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 6 inbound Pith citation observations for arXiv:2106.09819."}