{"as_of":"2026-08-10T00:46:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:076bfcca78731447070833db3833e35ab2947ac7d4deb9dd42eff517e5a8b9b0","coverage":[{"denominator":45,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":45,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T15:18:18.010837Z","state":"measured"},{"denominator":46,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":46,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T13:05:34.338623Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-07T13:05:35.531549Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"cited_work":{"arxiv_id":"2505.16018","doi":null,"metadata_source":"pith","pith_arxiv_id":"2505.16018","snapshot_observed_at":"2026-08-07T13:05:35.531549Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","venue":"math.PR","work_id":"57b3f9a6-f273-4240-8d2e-2a46c225452f","year":2025},"citing_paper":{"arxiv_id":"2505.22903","last_updated":"2025-06-20T20:06:33Z","snapshot_observed_at":"2026-08-07T12:55:32.949866Z","submitted_at":"2025-05-28T22:09:54Z","title":"Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T13:05:34.338623Z"},"links":{"cited_paper":"/paper/2505.16018","citing_paper":"/paper/2505.22903"},"observation_digest":"sha256:9a38eef116da91df28ddbe9864ad954bc372fc0faf0188ad0cbdc11fef39d542","observation_id":"47bfcb98-9868-4702-8597-941b5eda3261","resolution":{"observed_at":"2026-08-07T13:05:35.586814Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2505.16018/citation-record","integrity":"/paper/2505.16018/integrity","json":"/paper/2505.16018/citation-record.json","paper":"/paper/2505.16018"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:18:25.354147Z","title":null,"venue":null,"work_id":"c7087e78-ca51-4f65-95e1-d2747aec9525","year":2012},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:14.042874Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:5b1c74ea490292e54f067fe6e1c669308da1626e8e573a64964f6baf781096f1","observation_id":"d6ba1045-78f3-49bb-9d27-ded05c1dfa26","resolution":{"observed_at":"2026-08-07T15:18:25.492136Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:25.214773Z","title":null,"venue":null,"work_id":"e8c6a553-1e35-4ee5-b607-20b43a80ea60","year":2024},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:14.076226Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:3f60b69ab97bd5c6e316b1c21eab1125d17f2f06c094e11c7e9ba6ac03113a3b","observation_id":"71d49dc9-8131-4c01-a629-40b7fb7e0533","resolution":{"observed_at":"2026-08-07T15:18:25.306688Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.16592","last_updated":"2024-07-23T15:49:03Z","snapshot_observed_at":"2026-08-05T06:06:44.401637Z","submitted_at":"2024-07-23T15:49:03Z","title":"Existence of stationary measures for partially damped SDEs with generic, Euler-type nonlinearities","version":1},"cited_work":{"arxiv_id":"2407.16592","doi":null,"metadata_source":"pith","pith_arxiv_id":"2407.16592","snapshot_observed_at":"2026-08-07T15:18:18.312107Z","title":"Existence of stationary measures for partially damped SDEs with generic, Euler-type nonlinearities","venue":"math.PR","work_id":"4a6886d3-1575-4bd9-aa7d-42d9467f30b2","year":2024},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:14.161978Z"},"links":{"cited_paper":"/paper/2407.16592","citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:f0a0b0dc0cf6a8687f5dd16f96d3b0d3e94771d22fc4125fb52e751b5f585e54","observation_id":"e969fb24-6f60-4906-a836-b5e48d603920","resolution":{"observed_at":"2026-08-07T15:18:18.385923Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:25.075851Z","title":"1, 241–303","venue":null,"work_id":"c2bd1fa7-a116-44b5-92c1-3b74a667f56c","year":2022},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:14.243584Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:e87608eb204ce67599b7b4b4fe0e4baaa7c0d9d8151ff2fc78360fb3c2d9c583","observation_id":"e42af9f8-dc63-4724-bff9-1eb5bf25e69a","resolution":{"observed_at":"2026-08-07T15:18:25.130567Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:24.857320Z","title":"1, 101–178","venue":null,"work_id":"dd5c5b7b-7717-426e-9aa2-c9316830ee21","year":2024},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:14.288654Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:21454e9bc4ed766d243ca0d7d2b456b3ceae720c5454efb4082b60df03cacf63","observation_id":"1d2cd144-73a2-4b28-8c36-2caed45dc2b6","resolution":{"observed_at":"2026-08-07T15:18:24.913111Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:24.714389Z","title":"1, 47–92","venue":null,"work_id":"b2838113-f4b5-4757-a01c-5f6cefc18235","year":1994},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:14.356723Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:69343c611e4bf0423affc3a0d1f6bd4779243ac5ad574bbc64d88b4433d2470d","observation_id":"3f7aca5c-9740-452b-b030-743e7771f811","resolution":{"observed_at":"2026-08-07T15:18:24.767478Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:24.534752Z","title":"Buckmaster, P","venue":null,"work_id":"9c3ab6e1-a222-4831-a13d-4e9495e14540","year":2021},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:14.415785Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:28c06f03423cd1ffb6a5613b94ebdbb5d349d006661200197ed62f931b1e9a34","observation_id":"6e6e56bc-8eed-447d-be1c-f680c8670987","resolution":{"observed_at":"2026-08-07T15:18:24.652930Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2404.16817","last_updated":"2026-07-31T19:45:00Z","snapshot_observed_at":"2026-08-08T04:34:14.898521Z","submitted_at":"2024-04-25T17:57:58Z","title":"Modified scattering for the cubic Schr\\\"odinger equation on Diophantine waveguides","version":3},"cited_work":{"arxiv_id":"2404.16817","doi":null,"metadata_source":"pith","pith_arxiv_id":"2404.16817","snapshot_observed_at":"2026-08-07T15:18:18.151250Z","title":"Modified scattering for the cubic Schr\\\"odinger equation on Diophantine waveguides","venue":"math.AP","work_id":"4af78331-6bb2-44b7-8e67-45239a17556a","year":2024},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:14.477902Z"},"links":{"cited_paper":"/paper/2404.16817","citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:910951ef6bcd03735adb7bd096db818b3ee6b2ebb4f2436ac6bab5cfe53312c4","observation_id":"7c44c90d-e962-4a40-ac42-04a69f804abe","resolution":{"observed_at":"2026-08-07T15:18:18.229385Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:24.274197Z","title":"1, 012210","venue":null,"work_id":"9adf2ca5-ab79-4faa-b34c-f440a1e5deff","year":2025},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:14.566330Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:7d70f1c9ffef2ef02935d46fa3f4dce53273bfff378e2aad6ea6273919ef4c52","observation_id":"d1f6b5a9-741e-4dcc-9039-a671a7136622","resolution":{"observed_at":"2026-08-07T15:18:24.314761Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:24.157232Z","title":null,"venue":null,"work_id":"bf841796-6d7b-422d-b79d-732c9bd70e95","year":2024},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:14.667044Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:47c524cfdf3e60fb3d09f3f80ff7bb33b261fefaab1a03138de122c129a3019b","observation_id":"34aaae27-ba01-481d-ba91-27d70c2b2bcc","resolution":{"observed_at":"2026-08-07T15:18:24.223581Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:23.966604Z","title":"Pi 9 (2021)","venue":null,"work_id":"1adbdc22-3164-4c2c-914e-5db9c97461d3","year":2021},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:14.753911Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:39467c21d71b679f368316b6e17cb8055cc45dc81eccc74f82a118d767b17511","observation_id":"231ba27c-9418-4946-a0be-59c8350f8a0f","resolution":{"observed_at":"2026-08-07T15:18:24.051867Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:23.849347Z","title":null,"venue":null,"work_id":"83c64eeb-93e4-4acc-bc51-b392eb393e00","year":2023},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:14.831836Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:431c75abb9f5eb7cf93cba1dda54e9bd7c5e51978547f98196939c3da36f1e72","observation_id":"2e518309-c44e-49a2-ab76-81e3f2f462ed","resolution":{"observed_at":"2026-08-07T15:18:23.925479Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:23.696504Z","title":null,"venue":null,"work_id":"2ec7f042-4f7c-491d-bdc7-5c6a6ff095a8","year":2023},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:14.941793Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:782ba3f0e1c93f95192f6ca657a2927aaa4614d85a50152ffacc0d9d4b668dac","observation_id":"62147045-3d02-4b15-8405-3198d50835bc","resolution":{"observed_at":"2026-08-07T15:18:23.750657Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2311.10082","last_updated":"2024-04-07T02:58:23Z","snapshot_observed_at":"2026-08-08T04:33:29.885988Z","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":"2026-08-07T15:18:15.041927Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:15.041927Z"},"links":{"cited_paper":"/paper/2311.10082","citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:d16a0f4496bd4dcff6a657779128d75355d7e4fbfe88c275dbbae9ce7f842f5e","observation_id":"af071add-d747-47fe-bb8e-db7a01f6e404","resolution":{"observed_at":"2026-08-07T15:18:15.041927Z","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":"2026-08-07T15:18:23.605069Z","title":"3, 439–461","venue":null,"work_id":"197a6129-e567-45bc-b528-cae272cc4ccd","year":2007},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:15.146236Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:e9b856ea77348de226be00fb945c75711b2bb148acef5b0dc6be74f49329a97d","observation_id":"ca0850cc-9635-4835-9c5a-29d5f9ab1410","resolution":{"observed_at":"2026-08-07T15:18:23.639264Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:23.348401Z","title":null,"venue":null,"work_id":"978cfaf0-f478-4607-a060-19b02d88df7e","year":1999},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:15.216708Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:e5281011bca10f15f3406e1c412dcae020db33a2bac156af9ebe350a54624a79","observation_id":"059d17b2-b978-4f43-9f14-6db1f6bb8939","resolution":{"observed_at":"2026-08-07T15:18:23.485478Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:23.185734Z","title":"1, 237–267","venue":null,"work_id":"416fe645-4ac0-4b37-99a8-b33f12fe6988","year":2006},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:15.275839Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:a05da4be3b46d59ce047d8a8cb857bd5619cde7de8b52e70f2641c171315cae2","observation_id":"a6e8d7cf-4857-4563-a9af-ee4fa6c69daa","resolution":{"observed_at":"2026-08-07T15:18:23.247221Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:23.008660Z","title":null,"venue":null,"work_id":"39884175-3aa9-489d-b27f-4faa26de0b85","year":1999},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:15.353274Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:9e824882082977edb5054ea5f2fc0e91e5b30c412ea1ea00c51bc0a3aeb65b21","observation_id":"692863f1-4217-4c7e-8205-96a3ebcb8c91","resolution":{"observed_at":"2026-08-07T15:18:23.131098Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:18:15.410673Z","title":"19, American Mathematical Society, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:15.410673Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:b1fef32a75bbb83d4407dbff8ffd2e79052c9bd60cd992ebf40c6276cabf6758","observation_id":"80c16d07-09f1-4a4b-b421-464133c742e8","resolution":{"observed_at":"2026-08-07T15:18:15.410673Z","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":"2026-08-07T15:18:22.828902Z","title":"260, Springer Science & Business Media, 2012","venue":null,"work_id":"5e530945-74ce-4293-a6d7-43ceed586dbe","year":2012},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:15.498409Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:999f4512a4e1dbdf5013a7cd7870f64cca050d9ec80f1eed6cf091083c4dcc6e","observation_id":"10425c79-b285-4c71-80da-d097031f39b0","resolution":{"observed_at":"2026-08-07T15:18:22.908145Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:22.647575Z","title":"109, Princeton university press, 1985","venue":null,"work_id":"32467156-002c-4e7a-8536-4cc24e00446d","year":1985},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:15.597174Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:acefc28172b7d0cbb351eb3de801f44f437358e2f2fbc858a9915a31598072af","observation_id":"0f244c3f-8a09-4e3c-be5e-ce7a96b2050d","resolution":{"observed_at":"2026-08-07T15:18:22.737373Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2409.01507","last_updated":"2024-09-03T00:15:44Z","snapshot_observed_at":"2026-07-06T19:09:27.758765Z","submitted_at":"2024-09-03T00:15:44Z","title":"Stability of Rayleigh-Jeans equilibria in the kinetic FPU equation","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.01507","snapshot_observed_at":"2026-08-07T15:18:15.684692Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:15.684692Z"},"links":{"cited_paper":"/paper/2409.01507","citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:4a309cd9ecc4c4fe37bfcb203288f47aff12d267757a924b154077927975207f","observation_id":"d829b1a5-39f7-409a-ab66-779c68d5566a","resolution":{"observed_at":"2026-08-07T15:18:15.684692Z","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":"2026-08-07T15:18:22.473155Z","title":"220 (2022)","venue":null,"work_id":"d0855286-48f9-4db3-b4b8-379d337204c0","year":2022},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:15.770671Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:73a176b4e2d6b98c85485edb9638927ab0ae9c6e7db47938f68203607060ec99","observation_id":"fe81a8ad-44ff-467e-b683-74f81dcfb204","resolution":{"observed_at":"2026-08-07T15:18:22.539726Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:22.326152Z","title":null,"venue":null,"work_id":"83173cc4-7b59-4476-8c65-2bf8c8e421cd","year":2010},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:15.880859Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:50809b4b0ec458da1273c53154c992cbf31eb5c52f18e55ac7c81c2b7488c4b9","observation_id":"29b1d641-5a5b-49ba-a905-3a3937538dcb","resolution":{"observed_at":"2026-08-07T15:18:22.405432Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:22.152424Z","title":null,"venue":null,"work_id":"c49bc410-02ff-4c3b-9bcc-c941a64377e2","year":2006},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:15.992488Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:b3b2d8593536cc23ccff9f971a8ffd7a4b61f5c0bb2f0055fd58f325a85694af","observation_id":"aa11112f-12a2-445a-98e3-959e7cf71150","resolution":{"observed_at":"2026-08-07T15:18:22.232286Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:21.978092Z","title":"Pi 3 (2015)","venue":null,"work_id":"1e2c368a-8896-41a5-8719-be8df460f357","year":2015},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:16.102741Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:81aefbda19a94988a10e8734e409b806de6eacad1544f845aa515811f536f348","observation_id":"cefcbb12-c8c5-44a4-ac95-52e3b1ce623a","resolution":{"observed_at":"2026-08-07T15:18:22.071264Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:21.825745Z","title":"3, 1893–1942","venue":null,"work_id":"cac25600-f4da-4917-af76-fc2c242bea68","year":2018},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:16.189761Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:c852fb45bbdf07122680bdf8e69e25d2fb4252b8fdc43d69ea864913d1919b6c","observation_id":"8943ec6f-1e24-497b-82df-6ca32b4f1b76","resolution":{"observed_at":"2026-08-07T15:18:21.903425Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:21.624903Z","title":null,"venue":null,"work_id":"0bc9fa53-1a07-454b-8a87-09b7b1e4b0e6","year":2015},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:16.286503Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:d2174c76686e49a4c20791d43820ad5872e41610a998373a14780319cc220c31","observation_id":"5384784e-3930-4524-a454-955fef33791f","resolution":{"observed_at":"2026-08-07T15:18:21.731970Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:21.364439Z","title":null,"venue":null,"work_id":"7ade9796-0e5c-4065-a9a0-01faa3269070","year":2023},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:16.399333Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:29b1cdfbe13e391c638b458b29133bee76119b776b98f1e2fb0915241a6418f2","observation_id":"1897439f-06b0-4e86-b2e4-2436c716fb70","resolution":{"observed_at":"2026-08-07T15:18:21.476743Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:21.206023Z","title":"4, 1712–1730","venue":null,"work_id":"9e865d9f-308a-468b-9775-a3c9f3f29dbc","year":2015},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:16.493313Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:0f8a76c2c8576222d5c2d7706a3ea2c5765a0ac0e2944f8cf789ebc365670aa3","observation_id":"40f61c03-6815-4fc0-9710-6fef012ecd77","resolution":{"observed_at":"2026-08-07T15:18:21.276674Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:21.051898Z","title":"Staffilani H","venue":null,"work_id":"09aa2f46-8da5-44ff-a9a0-6fe69a25ce47","year":2010},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:16.616056Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:767dcb26992248ef9c94ff826c970c752aa205b7402af68a63f8bd346c22cd7c","observation_id":"1c9156c6-a8fa-4315-8386-5708f3a2b582","resolution":{"observed_at":"2026-08-07T15:18:21.088120Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:20.935794Z","title":"132, Springer Science & Business Media, 2013","venue":null,"work_id":"327eb246-8288-4ab3-9e3f-502c98228686","year":2013},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:16.714826Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:2f16ff6f6ed9d3ba4511e9c031fe4d156e6c757175cb1d19ae16b08484cb158c","observation_id":"8b080f3c-05c1-42cc-bfb4-0c12604b3f14","resolution":{"observed_at":"2026-08-07T15:18:20.986102Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:20.781097Z","title":"1, 304–362","venue":null,"work_id":"d1dd8f92-84e7-4291-a702-14c024040e2a","year":2003},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:16.800372Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:a93bcce17dca76b009a06805f43c71fb23f825a0a2d8c4473a961b3f85f9223b","observation_id":"1f5795eb-764b-40db-9f1d-2add08c5632b","resolution":{"observed_at":"2026-08-07T15:18:20.843529Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:20.616626Z","title":", Electronic Communications in Probability [electronic only] 10 (2005), 61–123","venue":null,"work_id":"13afe6fa-0614-4a80-a839-ee5a0ae702c1","year":2005},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:16.895619Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:9d5160f3f541e0896f95a18ca7412aed9e8b7b833d7c172aca6ecdce7274c99e","observation_id":"3617bc75-2851-4f6d-935f-460d584a23e1","resolution":{"observed_at":"2026-08-07T15:18:20.672000Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:20.469685Z","title":null,"venue":null,"work_id":"20d67bd9-780b-4de8-a7be-84960b040ef5","year":2003},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:16.975323Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:c692621b86fc6dd828c9bc99f75d5f621449a49ded3e1aa011a694b41a901906","observation_id":"876608ec-7d62-4fb0-8a48-4f8eb34a88f3","resolution":{"observed_at":"2026-08-07T15:18:20.526743Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:20.265953Z","title":"9, 1777–1811","venue":null,"work_id":"d8f42df0-a212-48d3-b01e-ce88f4f43761","year":2016},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:17.078855Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:4f1a051afbb8446762210d06cdf7772d5ea2e47c3ae29ca2ab43039f4d91dff7","observation_id":"0470b8b8-ae0b-4140-ad24-9c1a3f856e26","resolution":{"observed_at":"2026-08-07T15:18:20.379379Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:20.056594Z","title":"3, 639–660","venue":null,"work_id":"04b498b2-f3e7-462a-b283-2f0816c044c2","year":2002},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:17.140202Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:9fdfecd2208cb50f261ca6ba799709b4294777bb92372f028971d7174ec6852f","observation_id":"09f1fa24-a9b4-49f2-b0a0-566222526720","resolution":{"observed_at":"2026-08-07T15:18:20.149026Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:19.878286Z","title":"2, 185–232","venue":null,"work_id":"e56bfa29-cee6-4f6e-a6b1-5f388e0f7c9f","year":2002},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:17.204069Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:7031b8808b292bfc6312150a95cf40bb2f240c3bc09a243e6f7c201b957b39c6","observation_id":"72e9d4c9-467f-4791-bfd9-7ff90d641e6f","resolution":{"observed_at":"2026-08-07T15:18:19.941982Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:19.747053Z","title":"1, 189–220","venue":null,"work_id":"907843d1-be54-4e03-8bd6-5c26052301fc","year":2007},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:17.307517Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:52d1c28fdced724db1ca443179aa544076160ab946989d5893e5cc21d8523288","observation_id":"350147d0-a9e5-429a-b5b1-ad5a2b8690fe","resolution":{"observed_at":"2026-08-07T15:18:19.827319Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:19.554204Z","title":null,"venue":null,"work_id":"a302878f-d3d7-460a-87ea-fac0cd28641a","year":2012},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:17.403518Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:0c72253b8496c298b63c23eacc1d547ae396dc7722b681ffa254c3dcf7130b56","observation_id":"f7e3f435-d3a5-4730-a1c6-b632feaa30b7","resolution":{"observed_at":"2026-08-07T15:18:19.641850Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:19.381808Z","title":null,"venue":null,"work_id":"d6979cec-0bf8-4bdd-b267-02f712d028ec","year":2011},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:17.526504Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:c6cbd49d3214172bd0f48f2ee857a07103143904ec81f5e0c524cd0d0b463ed2","observation_id":"8adf91d2-21b5-4c51-8470-e520eda918b4","resolution":{"observed_at":"2026-08-07T15:18:19.498524Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:19.201148Z","title":null,"venue":null,"work_id":"eb8ceff9-99e7-48e8-84be-4d9f475ae119","year":2002},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:17.638783Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:4ea8598fe52df18573684d7d805f4b2e4bd34c47ae38583ae34c1c2ff1f27727","observation_id":"c593b9eb-c34c-4fb6-91d9-9e00fefa8616","resolution":{"observed_at":"2026-08-07T15:18:19.294242Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:18.998803Z","title":null,"venue":null,"work_id":"6c893f62-4150-49da-ba38-0c0b4ec21657","year":1971},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:17.760859Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:5224c575020f4823a0d75016d29ec1545f859ae1390b0bdf55e8d63acd84abd9","observation_id":"870f4a49-88fd-4a99-8cb0-9df4400a955a","resolution":{"observed_at":"2026-08-07T15:18:19.114918Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:18.759438Z","title":"112, Cambridge University Press, 2008","venue":null,"work_id":"2c8744af-25e8-4f6f-ab04-30131521e4ae","year":2008},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:17.852865Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:5a443a596d1e55db488f2dd152f2f5ccf0d9e7f4823d28a1587103d654d5bb8e","observation_id":"e6d951b9-ab70-43de-a9fc-aca5b4800cc0","resolution":{"observed_at":"2026-08-07T15:18:18.870804Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T15:18:18.536646Z","title":null,"venue":null,"work_id":"8f6752c5-1763-4ab1-9dc8-2b738dd7c2aa","year":2012},"citing_paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-07T15:18:18.010837Z"},"links":{"citing_paper":"/paper/2505.16018"},"observation_digest":"sha256:f48da1c0073b666f680d8f017fc946e983aadb96b128368a3c1e90cbc4b7b430","observation_id":"df63e826-2549-480a-909e-2845096bd503","resolution":{"observed_at":"2026-08-07T15:18:18.610248Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.16018","last_updated":"2025-05-21T21:01:54Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-08T04:33:54.078347Z","submitted_at":"2025-05-21T21:01:54Z","title":"Non-equilibrium steady state for a three-mode energy cascade model"},"reference_resolution":{"displayed":45,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":20,"verified_exact":2,"verified_fuzzy":23},"total_outbound_references":45},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 1 inbound Pith citation observation for arXiv:2505.16018."}