{"as_of":"2026-08-20T10:57:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:a8b09f3762b9e92eb0cd6563ccb13ea57c4842566d668ce0f3def7d73ecaf19a","coverage":[{"denominator":5,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":5,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T12:26:02.628482Z","state":"measured"},{"denominator":5,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":5,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-20T06:33:59.587034+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2412.14316/citation-record","integrity":"/paper/2412.14316/integrity","json":"/paper/2412.14316/citation-record.json","paper":"/paper/2412.14316"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.camwa.2024.08.007","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T12:26:02.684808Z","title":"The Gradient Discretization Method for Slow and Fast Diffusion Porous Media Equations","venue":null,"work_id":"fc667329-ac64-48c6-864f-8a9a48c71daf","year":2017},"citing_paper":{"arxiv_id":"2412.14316","last_updated":"2024-12-18T20:35:02Z","snapshot_observed_at":"2026-08-15T14:46:39.436758Z","submitted_at":"2024-12-18T20:35:02Z","title":"Reaching the equilibrium: Long-term stable approximations for stochastic non-Newtonian Stokes equations with transport noise","version":1},"reference_index":140,"source":"pdf_text","source_observed_at":"2026-08-11T12:26:02.617182Z"},"links":{"citing_paper":"/paper/2412.14316"},"observation_digest":"sha256:dcb4d84dbb01521f74b69b297fd9425efff1465c1d76339b979d447d908cfb89","observation_id":"6157496b-defa-46e4-bac9-fd5a1f246fe5","resolution":{"observed_at":"2026-08-11T12:26:02.692703Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"an/2020012","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T12:26:02.809614Z","title":"Implicit Euler method for numerical solution of nonlinear stochastic partial differential equations with multiplicative trace class noise","venue":null,"work_id":"9b4f1456-fadc-4610-89f0-abb4520e0f85","year":2018},"citing_paper":{"arxiv_id":"2412.14316","last_updated":"2024-12-18T20:35:02Z","snapshot_observed_at":"2026-08-15T14:46:39.436758Z","submitted_at":"2024-12-18T20:35:02Z","title":"Reaching the equilibrium: Long-term stable approximations for stochastic non-Newtonian Stokes equations with transport noise","version":1},"reference_index":244,"source":"pdf_text","source_observed_at":"2026-08-11T12:26:02.628482Z"},"links":{"citing_paper":"/paper/2412.14316"},"observation_digest":"sha256:57f49c9f189fdc40eff3de8d6c5e5dc213be62a38f84fc041a031cbd027892cd","observation_id":"c1bbf021-b210-45dc-b941-9b8ced3b321d","resolution":{"observed_at":"2026-08-11T12:26:02.821146Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2305.10999","last_updated":"2024-10-18T08:06:04Z","snapshot_observed_at":"2026-08-16T15:31:59.639726Z","submitted_at":"2023-05-18T14:22:08Z","title":"Mean Square Temporal error estimates for the 2D stochastic Navier-Stokes equations with transport noise","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2305.10999","snapshot_observed_at":"2026-08-11T12:26:02.603992Z","title":"Gradient discretization of two-phase poro-mechanical models with discontinuouspressuresatmatrixfractureinterfaces","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2412.14316","last_updated":"2024-12-18T20:35:02Z","snapshot_observed_at":"2026-08-15T14:46:39.436758Z","submitted_at":"2024-12-18T20:35:02Z","title":"Reaching the equilibrium: Long-term stable approximations for stochastic non-Newtonian Stokes equations with transport noise","version":1},"reference_index":260,"source":"pdf_text","source_observed_at":"2026-08-11T12:26:02.603992Z"},"links":{"cited_paper":"/paper/2305.10999","citing_paper":"/paper/2412.14316"},"observation_digest":"sha256:d1fb36df1b50637d16c5f63e6281c7b28d18a834c8c560f7c64eeccd2a287df5","observation_id":"7402a3cc-9e99-4e6c-9173-301a1bf6672c","resolution":{"observed_at":"2026-08-11T12:26:02.603992Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T12:26:02.622877Z","title":"The Numerical Approximation of Stochastic Partial Differential Equations","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2412.14316","last_updated":"2024-12-18T20:35:02Z","snapshot_observed_at":"2026-08-15T14:46:39.436758Z","submitted_at":"2024-12-18T20:35:02Z","title":"Reaching the equilibrium: Long-term stable approximations for stochastic non-Newtonian Stokes equations with transport noise","version":1},"reference_index":1032,"source":"pdf_text","source_observed_at":"2026-08-11T12:26:02.622877Z"},"links":{"citing_paper":"/paper/2412.14316"},"observation_digest":"sha256:14c696befa2abc2420084ac1dfa086f93f93adf492f80d09429fae03562ed835","observation_id":"c81e5b69-fca5-486c-8818-e720a82fa5fc","resolution":{"observed_at":"2026-08-11T12:26:02.622877Z","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":"2022.11444","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T12:26:03.040189Z","title":"Numerical and convergence analysis of the stochastic Lagrangian averaged Navier–Stokes equations","venue":null,"work_id":"74fc39dd-7a2b-43ba-abd7-a8cdc6706211","year":2022},"citing_paper":{"arxiv_id":"2412.14316","last_updated":"2024-12-18T20:35:02Z","snapshot_observed_at":"2026-08-15T14:46:39.436758Z","submitted_at":"2024-12-18T20:35:02Z","title":"Reaching the equilibrium: Long-term stable approximations for stochastic non-Newtonian Stokes equations with transport noise","version":1},"reference_index":2607,"source":"pdf_text","source_observed_at":"2026-08-11T12:26:02.610752Z"},"links":{"citing_paper":"/paper/2412.14316"},"observation_digest":"sha256:e2f6da371466a1e374f46f08c02b30c88a76beb5d20d9930453a23aa21d5df98","observation_id":"90507408-5d84-4c80-ac29-bb4fbf531428","resolution":{"observed_at":"2026-08-11T12:26:03.052072Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.14316","last_updated":"2024-12-18T20:35:02Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-15T14:46:39.436758Z","submitted_at":"2024-12-18T20:35:02Z","title":"Reaching the equilibrium: Long-term stable approximations for stochastic non-Newtonian Stokes equations with transport noise"},"reference_resolution":{"displayed":5,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":2,"verified_exact":2,"verified_fuzzy":0},"total_outbound_references":5},"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":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"thesis":"As of 20 August 2026, this Paper Citation Record lists 5 of 5 outbound references and 0 inbound Pith citation observations for arXiv:2412.14316."}