{"as_of":"2026-08-11T19:49:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:571176c2e156c7bcdd49ae3ff674863cd03eca540c97339b6676035244da6b72","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":"2026-08-03T17:15:37.060377Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-06-30T13:24:40.796490Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2506.16917","last_updated":"2025-06-20T11:20:14Z","snapshot_observed_at":"2026-08-06T23:35:31.543220Z","submitted_at":"2025-06-20T11:20:14Z","title":"Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.16917","snapshot_observed_at":"2026-08-03T17:15:37.060377Z","title":"John, and Julia Novo","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.10473","last_updated":"2025-12-11T09:51:49Z","snapshot_observed_at":"2026-08-03T17:15:34.847052Z","submitted_at":"2025-12-11T09:51:49Z","title":"Second order reduced model via incremental projection for Navier Stokes","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-03T17:15:37.060377Z"},"links":{"cited_paper":"/paper/2506.16917","citing_paper":"/paper/2512.10473"},"observation_digest":"sha256:4fd61f38bcb174478c0234f649323d763cadc248f6583efdb8e6c6630da4c00c","observation_id":"f449b2f1-a0c0-46d8-a553-66cb337a9fe6","resolution":{"observed_at":"2026-08-03T17:15:37.060377Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.16917","last_updated":"2025-06-20T11:20:14Z","snapshot_observed_at":"2026-08-06T23:35:31.543220Z","submitted_at":"2025-06-20T11:20:14Z","title":"Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.16917","snapshot_observed_at":"2026-08-03T01:20:32.658327Z","title":"García-Archilla, V","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2602.10268","last_updated":"2026-07-04T01:03:25Z","snapshot_observed_at":"2026-08-07T01:07:38.360481Z","submitted_at":"2026-02-10T20:25:42Z","title":"Unconditionally Long-Time Stable Variable-Step Second-Order ETD Schemes for the 2D Periodic Incompressible NSE","version":3},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-03T01:20:32.658327Z"},"links":{"cited_paper":"/paper/2506.16917","citing_paper":"/paper/2602.10268"},"observation_digest":"sha256:5ade69700be077c6053f7c1b3034b6782c6ee7c14b0ee0810e9733d08f881434","observation_id":"040705e8-fe1c-4e39-bf89-c7414b09e11b","resolution":{"observed_at":"2026-08-03T01:20:32.658327Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.16917","last_updated":"2025-06-20T11:20:14Z","snapshot_observed_at":"2026-08-06T23:35:31.543220Z","submitted_at":"2025-06-20T11:20:14Z","title":"Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations","version":1},"cited_work":{"arxiv_id":"2506.16917","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2506.16917","snapshot_observed_at":"2026-06-30T13:24:40.796490Z","title":"Error analysis of","venue":null,"work_id":"ecfdf6c2-d215-4a16-aae9-a9b1cea8881d","year":null},"citing_paper":{"arxiv_id":"2606.28800","last_updated":"2026-06-27T08:11:47Z","snapshot_observed_at":"2026-08-08T06:44:36.880682Z","submitted_at":"2026-06-27T08:11:47Z","title":"Viscosity in error upper bound for a consistent splitting scheme of the Navier-Stokes equations","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-06-30T09:08:47.081963Z"},"links":{"cited_paper":"/paper/2506.16917","citing_paper":"/paper/2606.28800"},"observation_digest":"sha256:f3a454fd496faabbcbd9de49de82319f3e2fe82e688fd21ee8f20afab7edb05e","observation_id":"3b55c92b-2105-45df-b030-885329e61f86","resolution":{"observed_at":"2026-06-30T13:24:40.798110Z","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":"2506.16917","last_updated":"2025-06-20T11:20:14Z","snapshot_observed_at":"2026-08-06T23:35:31.543220Z","submitted_at":"2025-06-20T11:20:14Z","title":"Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.16917","snapshot_observed_at":"2026-07-30T14:55:19.298136Z","title":"Garc ´ ıa-Archilla, V","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.23720","last_updated":"2026-07-26T15:32:50Z","snapshot_observed_at":"2026-08-03T14:48:01.852675Z","submitted_at":"2026-07-26T15:32:50Z","title":"A spectral-vanishing-viscosity stabilization of a higher-order consistent splitting scheme for the Navier-Stokes equations","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-30T14:55:19.298136Z"},"links":{"cited_paper":"/paper/2506.16917","citing_paper":"/paper/2607.23720"},"observation_digest":"sha256:96e76ad14fc464d550bf12592f5b80846996543660c885ae56ddddbb2555b313","observation_id":"408500e2-1e91-45ca-909f-c49b93ce920c","resolution":{"observed_at":"2026-07-30T14:55:19.298136Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2506.16917/citation-record","integrity":"/paper/2506.16917/integrity","json":"/paper/2506.16917/citation-record.json","paper":"/paper/2506.16917"},"outbound":[],"paper":{"arxiv_id":"2506.16917","last_updated":"2025-06-20T11:20:14Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-06T23:35:31.543220Z","submitted_at":"2025-06-20T11:20:14Z","title":"Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations"},"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:2506.16917."}