{"as_of":"2026-08-11T19:05:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fb0fa9f8264f33dd2d26fad0803fcb638d065727edf84252785b0a5e6163d6e7","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":4,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":4,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+00:00","state":"measured"},{"denominator":4,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":4,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T11:27:01.874678Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-21T06:59:45.657155Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2405.01670","last_updated":"2024-05-02T18:46:58Z","snapshot_observed_at":"2026-08-10T18:28:04.392639Z","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":"2026-08-07T11:27:01.874678Z","title":"Bru\\`e, M","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.02747","last_updated":"2025-06-03T11:11:01Z","snapshot_observed_at":"2026-08-10T11:07:40.318874Z","submitted_at":"2025-06-03T11:11:01Z","title":"A priori error estimates for the $\\theta$-method for the flow of nonsmooth velocity fields","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-07T11:27:01.874678Z"},"links":{"cited_paper":"/paper/2405.01670","citing_paper":"/paper/2506.02747"},"observation_digest":"sha256:22dad8cac5a3cba7387cca338ba48a608e1e9a1f596fca364c4afd7f8a33cbcf","observation_id":"c6ceca8e-f308-44a4-bb7a-aa03c997ef42","resolution":{"observed_at":"2026-08-07T11:27:01.874678Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.01670","last_updated":"2024-05-02T18:46:58Z","snapshot_observed_at":"2026-08-10T18:28:04.392639Z","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":"sha256:38dcf1b82fb808f14ab46f55b160e21abefada7a5def9eedced7fd7e069f1e51","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":"2405.01670","last_updated":"2024-05-02T18:46:58Z","snapshot_observed_at":"2026-08-10T18:28:04.392639Z","submitted_at":"2024-05-02T18:46:58Z","title":"Sharp Nonuniqueness in the Transport Equation with Sobolev Velocity Field","version":1},"cited_work":{"arxiv_id":"2405.01670","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2405.01670","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Bru´ e, M","venue":null,"work_id":"98c9c402-c853-4c6a-bb80-bd65c826b09d","year":2024},"citing_paper":{"arxiv_id":"2605.12883","last_updated":"2026-05-13T01:57:33Z","snapshot_observed_at":"2026-08-02T02:15:17.722307Z","submitted_at":"2026-05-13T01:57:33Z","title":"Mixing and Small-Scale Formation in a Passive Divergence-Free Vector Field","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-14T19:06:49.917564Z"},"links":{"cited_paper":"/paper/2405.01670","citing_paper":"/paper/2605.12883"},"observation_digest":"sha256:3051c97fc38175d585001cf15369f5452d45fafa1a85b406ae94dbac887376b3","observation_id":"10d09f9c-2b33-4c38-b689-4106fd459331","resolution":{"observed_at":"2026-05-14T19:07:50.882887Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.01670","last_updated":"2024-05-02T18:46:58Z","snapshot_observed_at":"2026-08-10T18:28:04.392639Z","submitted_at":"2024-05-02T18:46:58Z","title":"Sharp Nonuniqueness in the Transport Equation with Sobolev Velocity Field","version":1},"cited_work":{"arxiv_id":"2405.01670","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2405.01670","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Bru´ e, M","venue":null,"work_id":"98c9c402-c853-4c6a-bb80-bd65c826b09d","year":2024},"citing_paper":{"arxiv_id":"2605.20451","last_updated":"2026-05-19T20:04:18Z","snapshot_observed_at":"2026-08-05T19:15:35.638175Z","submitted_at":"2026-05-19T20:04:18Z","title":"Turbulent Dynamos on Bounded Domains and Their Generalization to the Geometric Transport Equation","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-05-21T06:55:38.591433Z"},"links":{"cited_paper":"/paper/2405.01670","citing_paper":"/paper/2605.20451"},"observation_digest":"sha256:77e6eb7bee6cd4e302e538d081685c4d6ebe173cba31f962df303a3aeb0f2402","observation_id":"1441179e-ac24-401d-b256-9768ee56518a","resolution":{"observed_at":"2026-05-21T06:59:45.659065Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2405.01670/citation-record","integrity":"/paper/2405.01670/integrity","json":"/paper/2405.01670/citation-record.json","paper":"/paper/2405.01670"},"outbound":[],"paper":{"arxiv_id":"2405.01670","last_updated":"2024-05-02T18:46:58Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-10T18:28:04.392639Z","submitted_at":"2024-05-02T18:46:58Z","title":"Sharp Nonuniqueness in the Transport Equation with Sobolev Velocity Field"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 4 inbound Pith citation observations for arXiv:2405.01670."}