{"as_of":"2026-08-17T03:47:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c96c84e24ee7838ce29420fdabe76e3fc18c2cd0d1e7bfd599c9213f215af941","coverage":[{"denominator":8,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":8,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T12:55:08.474191Z","state":"measured"},{"denominator":9,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":9,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+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":"2026-08-16T11:08:44.059319Z","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":"2026-08-16T11:08:46.229785Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2412.13828","last_updated":"2024-12-18T13:18:47Z","snapshot_observed_at":"2026-08-14T02:56:40.342414Z","submitted_at":"2024-12-18T13:18:47Z","title":"Regularity aspects of Leray-Hopf solutions to the 2D Inhomogeneous Navier-Stokes system and applications to weak-strong uniqueness","version":1},"cited_work":{"arxiv_id":"2412.13828","doi":null,"metadata_source":"pith","pith_arxiv_id":"2412.13828","snapshot_observed_at":"2026-08-16T11:08:46.229785Z","title":"Regularity aspects of Leray-Hopf solutions to the 2D Inhomogeneous Navier-Stokes system and applications to weak-strong uniqueness","venue":"math.AP","work_id":"c9e83762-2f09-468a-b4d7-4c6cd7461913","year":2024},"citing_paper":{"arxiv_id":"2504.16638","last_updated":"2026-07-25T21:29:39Z","snapshot_observed_at":"2026-08-16T10:56:31.269894Z","submitted_at":"2025-04-23T11:58:03Z","title":"Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-16T11:08:44.059319Z"},"links":{"cited_paper":"/paper/2412.13828","citing_paper":"/paper/2504.16638"},"observation_digest":"sha256:cd41e5be3b7da1fbb4b6f2a8311ee6dbca6f7e817013b4151a8155c5774fc626","observation_id":"73cf918a-487c-4f9c-9c1c-f9e311da5133","resolution":{"observed_at":"2026-08-16T11:08:46.233653Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2412.13828/citation-record","integrity":"/paper/2412.13828/integrity","json":"/paper/2412.13828/citation-record.json","paper":"/paper/2412.13828"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T12:55:08.618373Z","title":"Global well-posedness for the 2 -D inhomogeneous incompressible Navier-Stokes system with large initial data in critical sp aces","venue":null,"work_id":"30b9c57b-4957-44ac-aa0a-3b762d34b472","year":2021},"citing_paper":{"arxiv_id":"2412.13828","last_updated":"2024-12-18T13:18:47Z","snapshot_observed_at":"2026-08-14T02:56:40.342414Z","submitted_at":"2024-12-18T13:18:47Z","title":"Regularity aspects of Leray-Hopf solutions to the 2D Inhomogeneous Navier-Stokes system and applications to weak-strong uniqueness","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T12:55:08.439573Z"},"links":{"citing_paper":"/paper/2412.13828"},"observation_digest":"sha256:a20ae7a278d32f58951384bd94749a5485aeafa2151cb2c6581c1369e935fb20","observation_id":"93ee1d4c-7eed-4206-9d2c-c95eefacca3f","resolution":{"observed_at":"2026-08-11T12:55:08.623361Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-11T12:55:08.560332Z","title":"Global unique solv ability of inhomogeneous Navier- Stokes equations with bounded density","venue":null,"work_id":"bcb4ef81-184e-4b4b-a422-d0d4fcc9bb4a","year":2013},"citing_paper":{"arxiv_id":"2412.13828","last_updated":"2024-12-18T13:18:47Z","snapshot_observed_at":"2026-08-14T02:56:40.342414Z","submitted_at":"2024-12-18T13:18:47Z","title":"Regularity aspects of Leray-Hopf solutions to the 2D Inhomogeneous Navier-Stokes system and applications to weak-strong uniqueness","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T12:55:08.469216Z"},"links":{"citing_paper":"/paper/2412.13828"},"observation_digest":"sha256:9802654beeffa17378a37671616181bc1644749a38a97373a302c5b3ca06fc27","observation_id":"1d70a4ce-88da-4132-8726-690f4d47bc4f","resolution":{"observed_at":"2026-08-11T12:55:08.564998Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2406.19907","last_updated":"2024-06-28T13:23:12Z","snapshot_observed_at":"2026-08-16T13:38:44.641324Z","submitted_at":"2024-06-28T13:23:12Z","title":"Global well-posedness of inhomogeneous Navier-Stokes equations with bounded density","version":1},"cited_work":{"arxiv_id":"2406.19907","doi":null,"metadata_source":"pith","pith_arxiv_id":"2406.19907","snapshot_observed_at":"2026-08-11T12:55:08.510569Z","title":"Global well-posedness of inhomogeneous Navier-Stokes equations with bounded density","venue":"math.AP","work_id":"4af2452b-04d2-450c-b674-24c254c71be6","year":2024},"citing_paper":{"arxiv_id":"2412.13828","last_updated":"2024-12-18T13:18:47Z","snapshot_observed_at":"2026-08-14T02:56:40.342414Z","submitted_at":"2024-12-18T13:18:47Z","title":"Regularity aspects of Leray-Hopf solutions to the 2D Inhomogeneous Navier-Stokes system and applications to weak-strong uniqueness","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T12:55:08.463995Z"},"links":{"cited_paper":"/paper/2406.19907","citing_paper":"/paper/2412.13828"},"observation_digest":"sha256:54ce192b99b3c2b292e13432c5482ff18365910df0c6fe73df9f2276a9383f87","observation_id":"50d90f7b-53c9-42e5-a6fb-bed31552c9c1","resolution":{"observed_at":"2026-08-11T12:55:08.517690Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-11T12:55:08.548248Z","title":"Nonhomogeneous viscous incompressible fluids: existence of velocity, density, and pressure","venue":null,"work_id":"1f3d7f29-c3c5-4d7b-a509-138e06d0f996","year":1990},"citing_paper":{"arxiv_id":"2412.13828","last_updated":"2024-12-18T13:18:47Z","snapshot_observed_at":"2026-08-14T02:56:40.342414Z","submitted_at":"2024-12-18T13:18:47Z","title":"Regularity aspects of Leray-Hopf solutions to the 2D Inhomogeneous Navier-Stokes system and applications to weak-strong uniqueness","version":1},"reference_index":157,"source":"pdf_text","source_observed_at":"2026-08-11T12:55:08.474191Z"},"links":{"citing_paper":"/paper/2412.13828"},"observation_digest":"sha256:47527100c1f4cd3d1fbb6a66ff896b099eec6b2a106fb5e5e7774b9c98d4779f","observation_id":"c0becf41-e99f-4ee7-91ab-68e87e8e6ea5","resolution":{"observed_at":"2026-08-11T12:55:08.552439Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-11T12:55:08.587196Z","title":"Relati ve energy method for weak–strong uniqueness of the inhomogeneous Navier–Stokes equations f ar from vacuum","venue":null,"work_id":"22ac853c-c531-4446-a350-ff1f15613940","year":2025},"citing_paper":{"arxiv_id":"2412.13828","last_updated":"2024-12-18T13:18:47Z","snapshot_observed_at":"2026-08-14T02:56:40.342414Z","submitted_at":"2024-12-18T13:18:47Z","title":"Regularity aspects of Leray-Hopf solutions to the 2D Inhomogeneous Navier-Stokes system and applications to weak-strong uniqueness","version":1},"reference_index":225,"source":"pdf_text","source_observed_at":"2026-08-11T12:55:08.454312Z"},"links":{"citing_paper":"/paper/2412.13828"},"observation_digest":"sha256:36509caef015f4310c34241f343edf676dbdcbb3e7594e4b3894f749b6d1e83c","observation_id":"9ac5a0c7-c5c4-4a35-b995-d612a454c1e5","resolution":{"observed_at":"2026-08-11T12:55:08.591811Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-11T12:55:08.601856Z","title":"Springer, He idelberg, 2011, pp","venue":null,"work_id":"4d8e6418-f99a-4bd0-b658-457f568f9b1f","year":2011},"citing_paper":{"arxiv_id":"2412.13828","last_updated":"2024-12-18T13:18:47Z","snapshot_observed_at":"2026-08-14T02:56:40.342414Z","submitted_at":"2024-12-18T13:18:47Z","title":"Regularity aspects of Leray-Hopf solutions to the 2D Inhomogeneous Navier-Stokes system and applications to weak-strong uniqueness","version":1},"reference_index":343,"source":"pdf_text","source_observed_at":"2026-08-11T12:55:08.449713Z"},"links":{"citing_paper":"/paper/2412.13828"},"observation_digest":"sha256:0ffd3362e8554bd9dfcd879e00f46862852cdc2029a4adbab2d7f53ce3b2fec0","observation_id":"59d935da-d628-465b-a087-5761053ad45d","resolution":{"observed_at":"2026-08-11T12:55:08.608054Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-11T12:55:08.574541Z","title":"Density-dependent indecompressible viscous fluids in critical spaces","venue":null,"work_id":"4e98ea55-0ae2-42cf-a1b4-0a0e05415279","year":2003},"citing_paper":{"arxiv_id":"2412.13828","last_updated":"2024-12-18T13:18:47Z","snapshot_observed_at":"2026-08-14T02:56:40.342414Z","submitted_at":"2024-12-18T13:18:47Z","title":"Regularity aspects of Leray-Hopf solutions to the 2D Inhomogeneous Navier-Stokes system and applications to weak-strong uniqueness","version":1},"reference_index":2008,"source":"pdf_text","source_observed_at":"2026-08-11T12:55:08.459478Z"},"links":{"citing_paper":"/paper/2412.13828"},"observation_digest":"sha256:655460965802f783cc73768e138023e3d862095451bac62fe8584fc41d337734","observation_id":"68e62315-bd61-4c2b-afb0-1edd5d70a989","resolution":{"observed_at":"2026-08-11T12:55:08.578957Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.05438","last_updated":"2024-11-08T09:37:01Z","snapshot_observed_at":"2026-08-16T13:01:49.081776Z","submitted_at":"2024-11-08T09:37:01Z","title":"Inhomogenous Navier--Stokes equations with unbounded density","version":1},"cited_work":{"arxiv_id":"2411.05438","doi":null,"metadata_source":"pith","pith_arxiv_id":"2411.05438","snapshot_observed_at":"2026-08-11T12:55:08.533219Z","title":"Inhomogenous Navier--Stokes equations with unbounded density","venue":"math.AP","work_id":"29e81ab9-9261-48d8-9426-1ff64a0252d0","year":2024},"citing_paper":{"arxiv_id":"2412.13828","last_updated":"2024-12-18T13:18:47Z","snapshot_observed_at":"2026-08-14T02:56:40.342414Z","submitted_at":"2024-12-18T13:18:47Z","title":"Regularity aspects of Leray-Hopf solutions to the 2D Inhomogeneous Navier-Stokes system and applications to weak-strong uniqueness","version":1},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-11T12:55:08.445123Z"},"links":{"cited_paper":"/paper/2411.05438","citing_paper":"/paper/2412.13828"},"observation_digest":"sha256:88a22054fbb9ce2ed014ec5895d5538152230aca32f7be555eb16684d7677c3d","observation_id":"d70d7c0a-a3f9-43c1-812f-dc901d163303","resolution":{"observed_at":"2026-08-11T12:55:08.537689Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.13828","last_updated":"2024-12-18T13:18:47Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-14T02:56:40.342414Z","submitted_at":"2024-12-18T13:18:47Z","title":"Regularity aspects of Leray-Hopf solutions to the 2D Inhomogeneous Navier-Stokes system and applications to weak-strong uniqueness"},"reference_resolution":{"displayed":8,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":0,"verified_exact":1,"verified_fuzzy":6},"total_outbound_references":8},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 17 August 2026, this Paper Citation Record lists 8 of 8 outbound references and 1 inbound Pith citation observation for arXiv:2412.13828."}