{"as_of":"2026-08-18T06:11:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5c7557b116481b47a84363c454ad1bd8f475f451bcb1378dd339ac68c064d05d","coverage":[{"denominator":23,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":23,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T06:01:42.245250Z","state":"measured"},{"denominator":25,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":25,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-17T06:30:58.91139+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T16:15:24.409451Z","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":"2026-08-15T16:15:24.935558Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2506.06947","last_updated":"2025-06-23T07:50:22Z","snapshot_observed_at":"2026-08-10T00:22:56.770830Z","submitted_at":"2025-06-07T23:00:33Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","version":2},"cited_work":{"arxiv_id":"2506.06947","doi":null,"metadata_source":"pith","pith_arxiv_id":"2506.06947","snapshot_observed_at":"2026-08-15T16:15:24.935558Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","venue":"math.PR","work_id":"e0ea4c1c-6883-4919-a5a9-873859dc81ec","year":2025},"citing_paper":{"arxiv_id":"2509.10211","last_updated":"2025-09-12T12:57:07Z","snapshot_observed_at":"2026-08-15T15:54:59.914903Z","submitted_at":"2025-09-12T12:57:07Z","title":"Anomalous dissipation and regularization in isotropic Gaussian turbulence","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-15T16:15:24.409451Z"},"links":{"cited_paper":"/paper/2506.06947","citing_paper":"/paper/2509.10211"},"observation_digest":"sha256:fce772a41f1494da9fc8ee232e95163d780e7d77f9cf96122eed58f11b99a959","observation_id":"288c6c6e-5eca-40b8-9c66-5ad2a90e9568","resolution":{"observed_at":"2026-08-15T16:15:24.940976Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2506.06947","last_updated":"2025-06-23T07:50:22Z","snapshot_observed_at":"2026-08-10T00:22:56.770830Z","submitted_at":"2025-06-07T23:00:33Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.06947","snapshot_observed_at":"2026-07-30T12:53:43.309603Z","title":"arXiv:2506.06947 , primaryClass=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.27044","last_updated":"2026-08-06T10:45:20Z","snapshot_observed_at":"2026-08-09T23:09:59.762663Z","submitted_at":"2026-07-29T15:34:52Z","title":"Failure of the Weak Sard property without Anomalous Dissipation","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-07-30T12:53:43.309603Z"},"links":{"cited_paper":"/paper/2506.06947","citing_paper":"/paper/2607.27044"},"observation_digest":"sha256:87f4534f4e1e0cf1f477ee5652ba9be09bed97162ad53fe65a21180550bfe101","observation_id":"1071d3dc-8e91-4415-ae24-2358c699e66f","resolution":{"observed_at":"2026-07-30T12:53:43.309603Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2506.06947/citation-record","integrity":"/paper/2506.06947/integrity","json":"/paper/2506.06947/citation-record.json","paper":"/paper/2506.06947"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2308.03216","last_updated":"2024-07-29T10:12:22Z","snapshot_observed_at":"2026-08-16T15:10:26.625874Z","submitted_at":"2023-08-06T22:03:25Z","title":"Existence and uniqueness by Kraichnan noise for 2D Euler equations with unbounded vorticity","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2308.03216","snapshot_observed_at":"2026-08-07T06:01:42.174096Z","title":"Existence and uniqueness by Kraichnan noise for 2D Euler equations with unbounded vorticity.arXiv 2308.03216,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.06947","last_updated":"2025-06-23T07:50:22Z","snapshot_observed_at":"2026-08-10T00:22:56.770830Z","submitted_at":"2025-06-07T23:00:33Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T06:01:42.174096Z"},"links":{"cited_paper":"/paper/2308.03216","citing_paper":"/paper/2506.06947"},"observation_digest":"sha256:99d14b3789535e13b2f27a5b8c523bc4664f652b37e5c449d87046fecb791df9","observation_id":"f6253d49-c1dd-4626-abe6-96fc30580f79","resolution":{"observed_at":"2026-08-07T06:01:42.174096Z","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":"2026-08-07T06:01:42.699654Z","title":"Large deviations for fast transport stochastic RDEs with applica- tions to the exit problem.The Annals of Applied Probability, 29(4):1993–2032,","venue":null,"work_id":"48c72513-c179-4380-a6c4-1fe65957b4e0","year":1993},"citing_paper":{"arxiv_id":"2506.06947","last_updated":"2025-06-23T07:50:22Z","snapshot_observed_at":"2026-08-10T00:22:56.770830Z","submitted_at":"2025-06-07T23:00:33Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T06:01:42.179975Z"},"links":{"citing_paper":"/paper/2506.06947"},"observation_digest":"sha256:1c48ef3d67c27a723d76398e4c01744cfb2def5ea78bd424ff5af95c963ebbb1","observation_id":"167fa4ad-5d3a-43f8-a821-cf7faa00a638","resolution":{"observed_at":"2026-08-07T06:01:42.706121Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T06:01:42.680399Z","title":null,"venue":null,"work_id":"7e95d18a-22a0-4027-999a-06b7f4c9fcad","year":1985},"citing_paper":{"arxiv_id":"2506.06947","last_updated":"2025-06-23T07:50:22Z","snapshot_observed_at":"2026-08-10T00:22:56.770830Z","submitted_at":"2025-06-07T23:00:33Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T06:01:42.190099Z"},"links":{"citing_paper":"/paper/2506.06947"},"observation_digest":"sha256:8285561eb04efa6fe0ce1bde38f8153ed9b161d18ca950109a5372b38d563ce4","observation_id":"40bb8003-a6a8-41cc-95d5-4a9aa3e5fff5","resolution":{"observed_at":"2026-08-07T06:01:42.686017Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2503.22905","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T06:01:42.391477Z","title":"On the zero-noise limit for SDE’s singular at the initial time.arXiv preprint arXiv:2503.22905,","venue":null,"work_id":"d0994d11-ee4a-45f1-b62d-b3b1bd935e8a","year":null},"citing_paper":{"arxiv_id":"2506.06947","last_updated":"2025-06-23T07:50:22Z","snapshot_observed_at":"2026-08-10T00:22:56.770830Z","submitted_at":"2025-06-07T23:00:33Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T06:01:42.229731Z"},"links":{"citing_paper":"/paper/2506.06947"},"observation_digest":"sha256:6edb6136d47ac61718e70eb56bc079ae1325fc19ab3ad528c61a4e9dfcc507c7","observation_id":"2150e6cb-bdbf-46bc-9503-1bc844b6e547","resolution":{"observed_at":"2026-08-07T06:01:42.401492Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1805.09426","last_updated":"2018-05-23T21:07:32Z","snapshot_observed_at":"2026-08-14T19:11:48.082037Z","submitted_at":"2018-05-23T21:07:32Z","title":"Instability and non-uniqueness in the Cauchy problem for the Euler equations of an ideal incompressible fluid. Part I","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1805.09426","snapshot_observed_at":"2026-08-07T06:01:42.240139Z","title":"Instability and non-uniqueness in the Cauchy problem for the Euler equations of an ideal incompressible fluid","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.06947","last_updated":"2025-06-23T07:50:22Z","snapshot_observed_at":"2026-08-10T00:22:56.770830Z","submitted_at":"2025-06-07T23:00:33Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","version":2},"reference_index":1981,"source":"pdf_text","source_observed_at":"2026-08-07T06:01:42.240139Z"},"links":{"cited_paper":"/paper/1805.09426","citing_paper":"/paper/2506.06947"},"observation_digest":"sha256:ad307cf93da253b47b47852975d6889cc7838ae5b586f1a9ad06452640d1303b","observation_id":"6a0bac57-5b29-4e7c-a5c1-3c47df364abf","resolution":{"observed_at":"2026-08-07T06:01:42.240139Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1909.08702","last_updated":"2019-09-18T20:54:10Z","snapshot_observed_at":"2026-08-10T00:23:39.892391Z","submitted_at":"2019-09-18T20:54:10Z","title":"Zero noise limit for multidimensional SDEs driven by a pointy gradient","version":1},"cited_work":{"arxiv_id":"1909.08702","doi":null,"metadata_source":"pith","pith_arxiv_id":"1909.08702","snapshot_observed_at":"2026-08-07T06:01:42.494269Z","title":"Zero noise limit for multidimensional SDEs driven by a pointy gradient","venue":"math.PR","work_id":"088589fc-f82c-48e6-9cdd-599588b59899","year":2019},"citing_paper":{"arxiv_id":"2506.06947","last_updated":"2025-06-23T07:50:22Z","snapshot_observed_at":"2026-08-10T00:22:56.770830Z","submitted_at":"2025-06-07T23:00:33Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","version":2},"reference_index":1989,"source":"pdf_text","source_observed_at":"2026-08-07T06:01:42.184835Z"},"links":{"cited_paper":"/paper/1909.08702","citing_paper":"/paper/2506.06947"},"observation_digest":"sha256:b08459a991ebc1fb9546d7c8123bf9b58059b3eb433c14f3fd005d4db07fb981","observation_id":"17bd23ed-f858-4ff0-9e71-8e6b6ab9eb38","resolution":{"observed_at":"2026-08-07T06:01:42.499963Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T06:01:42.665711Z","title":"Springer, Heidelberg,","venue":null,"work_id":"2c3336db-ea56-4b56-a947-0d1057a22957","year":2015},"citing_paper":{"arxiv_id":"2506.06947","last_updated":"2025-06-23T07:50:22Z","snapshot_observed_at":"2026-08-10T00:22:56.770830Z","submitted_at":"2025-06-07T23:00:33Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","version":2},"reference_index":1995,"source":"pdf_text","source_observed_at":"2026-08-07T06:01:42.195433Z"},"links":{"citing_paper":"/paper/2506.06947"},"observation_digest":"sha256:528360a70f0cda10dbfa3eaae456ce4de607a20fd2a4faf6aed6b4919600e389","observation_id":"675f7e2e-7b5e-41f3-96f3-68975a282e08","resolution":{"observed_at":"2026-08-07T06:01:42.670235Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2305.08761","last_updated":"2024-04-15T19:32:09Z","snapshot_observed_at":"2026-08-16T15:32:59.042635Z","submitted_at":"2023-05-15T16:20:15Z","title":"Weak well-posedness by transport noise for a class of 2D fluid dynamics equations","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2305.08761","snapshot_observed_at":"2026-08-07T06:01:42.213869Z","title":"Weak well-posedness by transport noise for a class of 2D fluid dynamics equations.arXiv 2305.08761,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.06947","last_updated":"2025-06-23T07:50:22Z","snapshot_observed_at":"2026-08-10T00:22:56.770830Z","submitted_at":"2025-06-07T23:00:33Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","version":2},"reference_index":1996,"source":"pdf_text","source_observed_at":"2026-08-07T06:01:42.213869Z"},"links":{"cited_paper":"/paper/2305.08761","citing_paper":"/paper/2506.06947"},"observation_digest":"sha256:6060135690d0f28c8c75c86f8e1b5b656a14ad3928494598f7ee9d952c3cd0dd","observation_id":"4bdd6014-2f30-4f25-88fc-524c76c382ea","resolution":{"observed_at":"2026-08-07T06:01:42.213869Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2504.19153","last_updated":"2025-04-29T08:32:41Z","snapshot_observed_at":"2026-08-16T05:57:58.743202Z","submitted_at":"2025-04-27T08:12:02Z","title":"Strong Uniqueness by Kraichnan Transport Noise for the 2D Boussinesq Equations with Zero Viscosity","version":2},"cited_work":{"arxiv_id":"2504.19153","doi":null,"metadata_source":"pith","pith_arxiv_id":"2504.19153","snapshot_observed_at":"2026-08-07T06:01:42.419059Z","title":"Strong Uniqueness by Kraichnan Transport Noise for the 2D Boussinesq Equations with Zero Viscosity","venue":"math.PR","work_id":"53368c5f-e53b-4912-9f8f-258f0a2fe2e9","year":2025},"citing_paper":{"arxiv_id":"2506.06947","last_updated":"2025-06-23T07:50:22Z","snapshot_observed_at":"2026-08-10T00:22:56.770830Z","submitted_at":"2025-06-07T23:00:33Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","version":2},"reference_index":1998,"source":"pdf_text","source_observed_at":"2026-08-07T06:01:42.218793Z"},"links":{"cited_paper":"/paper/2504.19153","citing_paper":"/paper/2506.06947"},"observation_digest":"sha256:9008430a7416b62f9727b8c0a5d003db9e63b06f030bd388e6192eb84103cd19","observation_id":"2290af0f-8877-4efd-8569-6210da0f8d36","resolution":{"observed_at":"2026-08-07T06:01:42.424187Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.16668","last_updated":"2026-06-21T20:11:59Z","snapshot_observed_at":"2026-08-16T13:31:40.945117Z","submitted_at":"2024-07-23T17:35:25Z","title":"Anomalous Regularization in Kraichnan's Passive Scalar Model","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.16668","snapshot_observed_at":"2026-08-07T06:01:42.209057Z","title":"Anomalous regularization in Kraichnan’s passive scalar model.arXiv 2407.16668,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.06947","last_updated":"2025-06-23T07:50:22Z","snapshot_observed_at":"2026-08-10T00:22:56.770830Z","submitted_at":"2025-06-07T23:00:33Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","version":2},"reference_index":2002,"source":"pdf_text","source_observed_at":"2026-08-07T06:01:42.209057Z"},"links":{"cited_paper":"/paper/2407.16668","citing_paper":"/paper/2506.06947"},"observation_digest":"sha256:431892748ced154658a2bd54abe9c1c0f0fd7b0751c04689e8ddd1618ba9560f","observation_id":"9d0772f7-5bd0-41f3-8774-644739dd9981","resolution":{"observed_at":"2026-08-07T06:01:42.209057Z","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":"2026-08-07T06:01:42.732972Z","title":"Small random perturbations of Peano phenomena.Stochastics, 6(3- 4):279–292, 1981/82","venue":null,"work_id":"90ae3312-b1ff-4abc-baba-360ec584ca87","year":1981},"citing_paper":{"arxiv_id":"2506.06947","last_updated":"2025-06-23T07:50:22Z","snapshot_observed_at":"2026-08-10T00:22:56.770830Z","submitted_at":"2025-06-07T23:00:33Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","version":2},"reference_index":2004,"source":"pdf_text","source_observed_at":"2026-08-07T06:01:42.142806Z"},"links":{"citing_paper":"/paper/2506.06947"},"observation_digest":"sha256:1d95f9b3c17af59ee242a35a5c492f2f34c5a921b714435d6968ed443128366d","observation_id":"5e45ad77-4f1e-4d6e-8879-070bba69f907","resolution":{"observed_at":"2026-08-07T06:01:42.737652Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T06:01:42.635768Z","title":"On some recent results concerning non-uniqueness for the transport equation","venue":null,"work_id":"123d0c33-1183-4b75-90ec-2a55ff2a0648","year":2020},"citing_paper":{"arxiv_id":"2506.06947","last_updated":"2025-06-23T07:50:22Z","snapshot_observed_at":"2026-08-10T00:22:56.770830Z","submitted_at":"2025-06-07T23:00:33Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","version":2},"reference_index":2007,"source":"pdf_text","source_observed_at":"2026-08-07T06:01:42.224352Z"},"links":{"citing_paper":"/paper/2506.06947"},"observation_digest":"sha256:6f48beacf9894631faa3360f6db9553b21aaaf6e0621ec2615c43f93e822e460","observation_id":"2a18d278-d62d-419e-8edd-7916f25e1fbe","resolution":{"observed_at":"2026-08-07T06:01:42.640519Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2406.09267","last_updated":"2026-07-31T09:52:19Z","snapshot_observed_at":"2026-08-16T13:43:16.652736Z","submitted_at":"2024-06-13T16:06:42Z","title":"Global smooth solutions by transport noise of 3D Navier-Stokes equations with small hyperviscosity","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2406.09267","snapshot_observed_at":"2026-08-07T06:01:42.137718Z","title":"Global smooth solutions by transport noise of 3D Navier-Stokes equations with small hyperviscosity.arXiv preprint arXiv:2406.09267,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.06947","last_updated":"2025-06-23T07:50:22Z","snapshot_observed_at":"2026-08-10T00:22:56.770830Z","submitted_at":"2025-06-07T23:00:33Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","version":2},"reference_index":2009,"source":"pdf_text","source_observed_at":"2026-08-07T06:01:42.137718Z"},"links":{"cited_paper":"/paper/2406.09267","citing_paper":"/paper/2506.06947"},"observation_digest":"sha256:a2b9245b3a30e9aaeca580b9acbff9c4966c0c1b70aaaa92330d006ddcca50ec","observation_id":"ffc8eabd-b67f-4688-9bca-6ee10d2932f2","resolution":{"observed_at":"2026-08-07T06:01:42.137718Z","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":"2026-08-07T06:01:42.620800Z","title":"[Ver81] Alexander Ju Veretennikov","venue":null,"work_id":"688db1b1-f4c6-48b1-b0a8-601f71a47139","year":1983},"citing_paper":{"arxiv_id":"2506.06947","last_updated":"2025-06-23T07:50:22Z","snapshot_observed_at":"2026-08-10T00:22:56.770830Z","submitted_at":"2025-06-07T23:00:33Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","version":2},"reference_index":2010,"source":"pdf_text","source_observed_at":"2026-08-07T06:01:42.234598Z"},"links":{"citing_paper":"/paper/2506.06947"},"observation_digest":"sha256:88e8e4e74a0420555a5dbc9919b30456b53563df2364af543d4c932b6a4d3140","observation_id":"701558e8-471f-4fe7-af70-ac18dd51d730","resolution":{"observed_at":"2026-08-07T06:01:42.625706Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T06:01:42.650566Z","title":"[Saint-Flour Probability Summer School]","venue":null,"work_id":"fc455d61-a66c-4397-ba56-a6861532f1fc","year":2010},"citing_paper":{"arxiv_id":"2506.06947","last_updated":"2025-06-23T07:50:22Z","snapshot_observed_at":"2026-08-10T00:22:56.770830Z","submitted_at":"2025-06-07T23:00:33Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","version":2},"reference_index":2011,"source":"pdf_text","source_observed_at":"2026-08-07T06:01:42.199803Z"},"links":{"citing_paper":"/paper/2506.06947"},"observation_digest":"sha256:9341cc7363927fef9f5690ad0387164c643bf5574b1508dc7b3c2c07dc13553c","observation_id":"ebe181b8-ae1d-4145-8fd5-621c0914d165","resolution":{"observed_at":"2026-08-07T06:01:42.655017Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"nlin/0207058","last_updated":"2002-07-30T09:26:14Z","snapshot_observed_at":"2026-08-10T11:09:33.837718Z","submitted_at":"2002-07-30T09:26:14Z","title":"Soluble models of turbulent advection","version":1},"cited_work":{"arxiv_id":"nlin/0207058","doi":null,"metadata_source":"pith","pith_arxiv_id":"nlin/0207058","snapshot_observed_at":"2026-08-07T06:01:42.472852Z","title":"Soluble models of turbulent advection","venue":"nlin.CD","work_id":"895f9ce7-1923-4222-b431-b5a72e2973d5","year":2002},"citing_paper":{"arxiv_id":"2506.06947","last_updated":"2025-06-23T07:50:22Z","snapshot_observed_at":"2026-08-10T00:22:56.770830Z","submitted_at":"2025-06-07T23:00:33Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","version":2},"reference_index":2012,"source":"pdf_text","source_observed_at":"2026-08-07T06:01:42.204396Z"},"links":{"cited_paper":"/paper/nlin/0207058","citing_paper":"/paper/2506.06947"},"observation_digest":"sha256:47878ab0db18d60f215bf7954358e37e43df0164d58061b25fa2b8e2a73e792f","observation_id":"a20c0941-cbad-4d75-b082-c33e42b2bac3","resolution":{"observed_at":"2026-08-07T06:01:42.477682Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2504.03578","last_updated":"2025-04-04T16:30:24Z","snapshot_observed_at":"2026-08-16T12:43:54.305806Z","submitted_at":"2025-04-04T16:30:24Z","title":"A convex integration scheme for the continuity equation past the Sobolev embedding threshold","version":1},"cited_work":{"arxiv_id":"2504.03578","doi":null,"metadata_source":"pith","pith_arxiv_id":"2504.03578","snapshot_observed_at":"2026-08-07T06:01:42.533382Z","title":"A convex integration scheme for the continuity equation past the Sobolev embedding threshold","venue":"math.AP","work_id":"9c0478ce-69be-4a40-9b6f-3909b7d5a54f","year":2025},"citing_paper":{"arxiv_id":"2506.06947","last_updated":"2025-06-23T07:50:22Z","snapshot_observed_at":"2026-08-10T00:22:56.770830Z","submitted_at":"2025-06-07T23:00:33Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","version":2},"reference_index":2013,"source":"pdf_text","source_observed_at":"2026-08-07T06:01:42.169043Z"},"links":{"cited_paper":"/paper/2504.03578","citing_paper":"/paper/2506.06947"},"observation_digest":"sha256:f22de831391ceb28eab87c3c544da03958ee3cceab3567809e96f488ce9e06ac","observation_id":"256b6874-c9b3-4062-8b8e-f2584a4f73a5","resolution":{"observed_at":"2026-08-07T06:01:42.539036Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-07T06:01:42.717439Z","title":"Stochastic geometric wave equations with values in compact Riemannian homogeneous spaces.The Annals of Probability, 41(3B):1938–1977,","venue":null,"work_id":"cffaffc5-8059-43d1-9ec3-bc81a883d826","year":1938},"citing_paper":{"arxiv_id":"2506.06947","last_updated":"2025-06-23T07:50:22Z","snapshot_observed_at":"2026-08-10T00:22:56.770830Z","submitted_at":"2025-06-07T23:00:33Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","version":2},"reference_index":2014,"source":"pdf_text","source_observed_at":"2026-08-07T06:01:42.163380Z"},"links":{"citing_paper":"/paper/2506.06947"},"observation_digest":"sha256:0d4f7e8f7c61fffb6d21fec16926bfe95252ffcc609e3b62516d2a97cfdc704f","observation_id":"8bf32676-7c9f-4603-916c-0f0e5c7342be","resolution":{"observed_at":"2026-08-07T06:01:42.722706Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.12181","last_updated":"2025-03-27T11:50:42Z","snapshot_observed_at":"2026-08-16T13:51:14.627780Z","submitted_at":"2024-05-20T17:06:52Z","title":"Regularization by rough Kraichnan noise for the generalised SQG equations","version":3},"cited_work":{"arxiv_id":"2405.12181","doi":null,"metadata_source":"pith","pith_arxiv_id":"2405.12181","snapshot_observed_at":"2026-08-07T06:01:42.576391Z","title":"Regularization by rough Kraichnan noise for the generalised SQG equations","venue":"math.PR","work_id":"da0ae7c2-6fa5-429f-8a26-51c75e8fd953","year":2024},"citing_paper":{"arxiv_id":"2506.06947","last_updated":"2025-06-23T07:50:22Z","snapshot_observed_at":"2026-08-10T00:22:56.770830Z","submitted_at":"2025-06-07T23:00:33Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","version":2},"reference_index":2017,"source":"pdf_text","source_observed_at":"2026-08-07T06:01:42.153070Z"},"links":{"cited_paper":"/paper/2405.12181","citing_paper":"/paper/2506.06947"},"observation_digest":"sha256:3b4322bff95e572487c96b48386aeb8c817a18b7d25a7f4a63751859b9e076ea","observation_id":"01bb6ddd-a634-4f12-8748-965973814209","resolution":{"observed_at":"2026-08-07T06:01:42.581399Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1805.09440","last_updated":"2018-05-23T21:59:30Z","snapshot_observed_at":"2026-08-17T04:33:27.913796Z","submitted_at":"2018-05-23T21:59:30Z","title":"Instability and non-uniqueness in the Cauchy problem for the Euler equations of an ideal incompressible fluid. Part II","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1805.09440","snapshot_observed_at":"2026-08-07T06:01:42.245250Z","title":"Instability and non-uniqueness in the Cauchy problem for the Euler equations of an ideal incompressible fluid","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.06947","last_updated":"2025-06-23T07:50:22Z","snapshot_observed_at":"2026-08-10T00:22:56.770830Z","submitted_at":"2025-06-07T23:00:33Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","version":2},"reference_index":2018,"source":"pdf_text","source_observed_at":"2026-08-07T06:01:42.245250Z"},"links":{"cited_paper":"/paper/1805.09440","citing_paper":"/paper/2506.06947"},"observation_digest":"sha256:bae6c9fb9938e429d1f30633522e4aea8f06e60d6618249fb4b696cdd2d878a0","observation_id":"24276267-a22e-4080-8345-b026754269d2","resolution":{"observed_at":"2026-08-07T06:01:42.245250Z","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":"2026-08-07T06:01:42.747784Z","title":"[AF09] Stefano Attanasio and Franco Flandoli","venue":null,"work_id":"c1910ab8-9c81-4626-b185-2f2e1f97bdcd","year":2019},"citing_paper":{"arxiv_id":"2506.06947","last_updated":"2025-06-23T07:50:22Z","snapshot_observed_at":"2026-08-10T00:22:56.770830Z","submitted_at":"2025-06-07T23:00:33Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","version":2},"reference_index":2019,"source":"pdf_text","source_observed_at":"2026-08-07T06:01:42.132107Z"},"links":{"citing_paper":"/paper/2506.06947"},"observation_digest":"sha256:30fc872e9f312cfb3cf7b092a2e88d18cdb61282759e17a1f3243353ae5e89e2","observation_id":"9c2f7254-0ab3-4cda-980d-bf62fd5c4fb8","resolution":{"observed_at":"2026-08-07T06:01:42.753062Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.01670","last_updated":"2024-05-02T18:46:58Z","snapshot_observed_at":"2026-08-16T13:55:50.290748Z","submitted_at":"2024-05-02T18:46:58Z","title":"Sharp Nonuniqueness in the Transport Equation with Sobolev Velocity Field","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.01670","snapshot_observed_at":"2026-08-07T06:01:42.147950Z","title":"Sharp Nonuniqueness in the Transport Equation with Sobolev Velocity Field.arXiv preprint arXiv:2405.01670,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.06947","last_updated":"2025-06-23T07:50:22Z","snapshot_observed_at":"2026-08-10T00:22:56.770830Z","submitted_at":"2025-06-07T23:00:33Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","version":2},"reference_index":2021,"source":"pdf_text","source_observed_at":"2026-08-07T06:01:42.147950Z"},"links":{"cited_paper":"/paper/2405.01670","citing_paper":"/paper/2506.06947"},"observation_digest":"sha256:2131884400642e729b2a0ddd3db17e12cf85f2028fa5020ecef618bbc2fe3992","observation_id":"6a484338-dedf-45d6-877f-e3de492707c4","resolution":{"observed_at":"2026-08-07T06:01:42.147950Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2411.09482","last_updated":"2024-11-14T14:37:35Z","snapshot_observed_at":"2026-08-16T15:51:21.223658Z","submitted_at":"2024-11-14T14:37:35Z","title":"Anomalous Regularization in Kazantsev-Kraichnan Model","version":1},"cited_work":{"arxiv_id":"2411.09482","doi":null,"metadata_source":"pith","pith_arxiv_id":"2411.09482","snapshot_observed_at":"2026-08-07T06:01:42.555657Z","title":"Anomalous Regularization in Kazantsev-Kraichnan Model","venue":"math.PR","work_id":"d0c8fcc5-8ed3-49a3-a68e-23bedfca45bc","year":2024},"citing_paper":{"arxiv_id":"2506.06947","last_updated":"2025-06-23T07:50:22Z","snapshot_observed_at":"2026-08-10T00:22:56.770830Z","submitted_at":"2025-06-07T23:00:33Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions","version":2},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-07T06:01:42.158165Z"},"links":{"cited_paper":"/paper/2411.09482","citing_paper":"/paper/2506.06947"},"observation_digest":"sha256:0065aedd1a5f57ae4c2d71983364fc7e9aa05b4f6ed66335eae002cd7686874e","observation_id":"d55e0c2b-843a-473c-8bdf-21266c337104","resolution":{"observed_at":"2026-08-07T06:01:42.560699Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.06947","last_updated":"2025-06-23T07:50:22Z","latest_version":2,"primary_category":"math.PR","snapshot_observed_at":"2026-08-10T00:22:56.770830Z","submitted_at":"2025-06-07T23:00:33Z","title":"Zero-noise selection and Large Deviations in $L^\\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions"},"reference_resolution":{"displayed":23,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":8,"verified_exact":6,"verified_fuzzy":8},"total_outbound_references":23},"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":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 2 inbound Pith citation observations for arXiv:2506.06947."}