{"as_of":"2026-08-14T10:29:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:6c0c56b32fb926d0cf3d500316961af11fb6babdbc19804f96ef756cd398ef0d","coverage":[{"denominator":4,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":4,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T11:26:07.843127Z","state":"measured"},{"denominator":10,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":10,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+00:00","state":"measured"},{"denominator":6,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":6,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T16:40:20.131830Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":1,"source":"arxiv_reference","source_observed_at":"2026-08-05T02:28:24.338817Z","state":"measured"}],"external_citation_measurements":[{"count":5,"observed_at":"2026-08-05T02:28:24.338817Z","source":"arxiv_reference"}],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2411.18240","last_updated":"2024-11-27T11:27:18Z","snapshot_observed_at":"2026-08-12T11:20:54.913584Z","submitted_at":"2024-11-27T11:27:18Z","title":"Physics Informed Neural Networks (PINNs) as intelligent computing technique for solving partial differential equations: Limitation and Future prospects","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.18240","snapshot_observed_at":"2026-08-06T16:40:20.131830Z","title":"Zhang, W","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.12941","last_updated":"2026-07-10T06:47:47Z","snapshot_observed_at":"2026-08-13T22:16:25.083418Z","submitted_at":"2025-07-17T09:29:22Z","title":"Adaptive feature capture method for solving partial differential equations with near singular solutions","version":4},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:20.131830Z"},"links":{"cited_paper":"/paper/2411.18240","citing_paper":"/paper/2507.12941"},"observation_digest":"sha256:b90634d0d8fb1a4e1fcbbe155f4ab5c583374b20fd1e543023203338fb609861","observation_id":"7dcf7f32-5ff4-4933-baf1-8e6227af0181","resolution":{"observed_at":"2026-08-06T16:40:20.131830Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2411.18240","last_updated":"2024-11-27T11:27:18Z","snapshot_observed_at":"2026-08-12T11:20:54.913584Z","submitted_at":"2024-11-27T11:27:18Z","title":"Physics Informed Neural Networks (PINNs) as intelligent computing technique for solving partial differential equations: Limitation and Future prospects","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.18240","snapshot_observed_at":"2026-08-06T05:15:42.081951Z","title":"Zhang , author W","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2508.02166","last_updated":"2025-08-04T08:06:37Z","snapshot_observed_at":"2026-08-14T10:17:02.279222Z","submitted_at":"2025-08-04T08:06:37Z","title":"Physics-informed Fourier Basis Neural Network for Fluid Mechanics","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-06T05:15:42.081951Z"},"links":{"cited_paper":"/paper/2411.18240","citing_paper":"/paper/2508.02166"},"observation_digest":"sha256:822e9a4068bd02161c0c2217629234d1ef5dea784b73b3d3b7f3b92bd4db2c1f","observation_id":"6811c49b-20d8-4846-98dc-dd1515517ea3","resolution":{"observed_at":"2026-08-06T05:15:42.081951Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2411.18240","last_updated":"2024-11-27T11:27:18Z","snapshot_observed_at":"2026-08-12T11:20:54.913584Z","submitted_at":"2024-11-27T11:27:18Z","title":"Physics Informed Neural Networks (PINNs) as intelligent computing technique for solving partial differential equations: Limitation and Future prospects","version":1},"cited_work":{"arxiv_id":"2411.18240","doi":"10.48550/arxiv.2411.18240","metadata_source":"arxiv_reference","pith_arxiv_id":"2411.18240","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Zhang, W","venue":"arXiv (Cornell University)","work_id":"63fc51e3-e6fe-42e0-82d7-56799f78cf1d","year":2024},"citing_paper":{"arxiv_id":"2604.28180","last_updated":"2026-04-30T17:57:22Z","snapshot_observed_at":"2026-08-11T14:27:25.693654Z","submitted_at":"2026-04-30T17:57:22Z","title":"An adaptive wavelet-based PINN for problems with localized high-magnitude source","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-07T07:14:05.096056Z"},"links":{"cited_paper":"/paper/2411.18240","citing_paper":"/paper/2604.28180"},"observation_digest":"sha256:7669bef0c70ef6b2d4f94ebd6a0863f3ac745d96ae45ccfd12f0129c227fda4e","observation_id":"f8e5a913-a718-4d66-8d02-a0099da47df4","resolution":{"observed_at":"2026-05-09T04:50:11.691731Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.18240","last_updated":"2024-11-27T11:27:18Z","snapshot_observed_at":"2026-08-12T11:20:54.913584Z","submitted_at":"2024-11-27T11:27:18Z","title":"Physics Informed Neural Networks (PINNs) as intelligent computing technique for solving partial differential equations: Limitation and Future prospects","version":1},"cited_work":{"arxiv_id":"2411.18240","doi":"10.48550/arxiv.2411.18240","metadata_source":"arxiv_reference","pith_arxiv_id":"2411.18240","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Zhang, W","venue":"arXiv (Cornell University)","work_id":"63fc51e3-e6fe-42e0-82d7-56799f78cf1d","year":2024},"citing_paper":{"arxiv_id":"2605.16078","last_updated":"2026-05-15T15:39:52Z","snapshot_observed_at":"2026-08-13T05:04:23.388906Z","submitted_at":"2026-05-15T15:39:52Z","title":"A numerical study into neural network surrogate model performance for uncertainty propagation","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-19T18:57:56.373765Z"},"links":{"cited_paper":"/paper/2411.18240","citing_paper":"/paper/2605.16078"},"observation_digest":"sha256:420489b01793c55553ff2224b3cdbfa32fc65a9f6fe89dce5bb44ab0e3bfeefe","observation_id":"bcfe0714-f427-4926-b130-9a67e33b6805","resolution":{"observed_at":"2026-05-19T19:02:43.611576Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.18240","last_updated":"2024-11-27T11:27:18Z","snapshot_observed_at":"2026-08-12T11:20:54.913584Z","submitted_at":"2024-11-27T11:27:18Z","title":"Physics Informed Neural Networks (PINNs) as intelligent computing technique for solving partial differential equations: Limitation and Future prospects","version":1},"cited_work":{"arxiv_id":"2411.18240","doi":"10.48550/arxiv.2411.18240","metadata_source":"arxiv_reference","pith_arxiv_id":"2411.18240","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Zhang, W","venue":"arXiv (Cornell University)","work_id":"63fc51e3-e6fe-42e0-82d7-56799f78cf1d","year":2024},"citing_paper":{"arxiv_id":"2606.23435","last_updated":"2026-06-22T14:55:38Z","snapshot_observed_at":"2026-08-13T17:36:52.059176Z","submitted_at":"2026-06-22T14:55:38Z","title":"Bayesian Analysis Using a Constrained Mixture of Normal-Inverse-Gamma Models","version":1},"reference_index":172,"source":"arxiv_source","source_observed_at":"2026-06-26T07:35:00.683580Z"},"links":{"cited_paper":"/paper/2411.18240","citing_paper":"/paper/2606.23435"},"observation_digest":"sha256:ef062847ecdc10bcfb0341d41b9b561ecc5530266353ec0d6c71b9f9d0944da6","observation_id":"b32b4643-0d7b-4ee2-8f82-82ac1e8b9b1a","resolution":{"observed_at":"2026-07-04T11:49:50.830567Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.18240","last_updated":"2024-11-27T11:27:18Z","snapshot_observed_at":"2026-08-12T11:20:54.913584Z","submitted_at":"2024-11-27T11:27:18Z","title":"Physics Informed Neural Networks (PINNs) as intelligent computing technique for solving partial differential equations: Limitation and Future prospects","version":1},"cited_work":{"arxiv_id":"2411.18240","doi":"10.48550/arxiv.2411.18240","metadata_source":"arxiv_reference","pith_arxiv_id":"2411.18240","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Zhang, W","venue":"arXiv (Cornell University)","work_id":"63fc51e3-e6fe-42e0-82d7-56799f78cf1d","year":2024},"citing_paper":{"arxiv_id":"2606.24696","last_updated":"2026-06-23T15:24:05Z","snapshot_observed_at":"2026-08-06T20:09:32.635453Z","submitted_at":"2026-06-23T15:24:05Z","title":"A Physics-Informed Fourier-Wavelet Transformer for Multiscale Computational Fluid Dynamics Surrogate Modeling","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-25T22:47:05.775339Z"},"links":{"cited_paper":"/paper/2411.18240","citing_paper":"/paper/2606.24696"},"observation_digest":"sha256:59bf24b0df0be61d38deacea7a2f50b4540af2112d1e32e39810cdced49fbcd0","observation_id":"71a04c13-e20d-47db-afba-feb90da11e49","resolution":{"observed_at":"2026-07-04T18:30:02.725426Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2411.18240/citation-record","integrity":"/paper/2411.18240/integrity","json":"/paper/2411.18240/citation-record.json","paper":"/paper/2411.18240"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T11:26:07.927843Z","title":"Physics-informed neural networks","venue":null,"work_id":"b3efa7a5-d018-45ff-94dd-191bbdebaa04","year":2019},"citing_paper":{"arxiv_id":"2411.18240","last_updated":"2024-11-27T11:27:18Z","snapshot_observed_at":"2026-08-12T11:20:54.913584Z","submitted_at":"2024-11-27T11:27:18Z","title":"Physics Informed Neural Networks (PINNs) as intelligent computing technique for solving partial differential equations: Limitation and Future prospects","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-12T11:26:07.826732Z"},"links":{"citing_paper":"/paper/2411.18240"},"observation_digest":"sha256:76d0ffa4fea117785f931bcef2560711258e59ef3d4d5e53b748794c8c865a78","observation_id":"95504072-8d30-4645-9255-5d7364a97ff0","resolution":{"observed_at":"2026-08-12T11:26:07.934983Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:26:07.910600Z","title":null,"venue":null,"work_id":"a9df1b83-6faf-4635-8af0-6200825f67cf","year":2000},"citing_paper":{"arxiv_id":"2411.18240","last_updated":"2024-11-27T11:27:18Z","snapshot_observed_at":"2026-08-12T11:20:54.913584Z","submitted_at":"2024-11-27T11:27:18Z","title":"Physics Informed Neural Networks (PINNs) as intelligent computing technique for solving partial differential equations: Limitation and Future prospects","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-12T11:26:07.832289Z"},"links":{"citing_paper":"/paper/2411.18240"},"observation_digest":"sha256:35df62cb7fc74135c14b5d57e3e115288e40e48ee6f6f719ebc5420509738111","observation_id":"9d53231d-dfd8-40a9-83a4-73d49be574f6","resolution":{"observed_at":"2026-08-12T11:26:07.916336Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:26:07.876149Z","title":"Compatibility conditions for time-dependent partial differential equations and the rate of convergence of chebyshev and fourier spectral methods","venue":null,"work_id":"07fe7684-d782-4b47-aaab-42dcdb39f1ab","year":2009},"citing_paper":{"arxiv_id":"2411.18240","last_updated":"2024-11-27T11:27:18Z","snapshot_observed_at":"2026-08-12T11:20:54.913584Z","submitted_at":"2024-11-27T11:27:18Z","title":"Physics Informed Neural Networks (PINNs) as intelligent computing technique for solving partial differential equations: Limitation and Future prospects","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T11:26:07.843127Z"},"links":{"citing_paper":"/paper/2411.18240"},"observation_digest":"sha256:6cdc1855f0bb60a364df433aede2d2cee96e64d35fbc2376126b96e851a7bc6a","observation_id":"14922860-956d-4354-804b-455aba1a0802","resolution":{"observed_at":"2026-08-12T11:26:07.882967Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:26:07.894548Z","title":"For instance, in high Reynolds number wall-bounded turbulence with multiscale phenomenon, anisotropic grids within the boundary layer are often indispensable","venue":null,"work_id":"84a4abd2-f45a-4c3a-a09b-62410c5b5f29","year":2021},"citing_paper":{"arxiv_id":"2411.18240","last_updated":"2024-11-27T11:27:18Z","snapshot_observed_at":"2026-08-12T11:20:54.913584Z","submitted_at":"2024-11-27T11:27:18Z","title":"Physics Informed Neural Networks (PINNs) as intelligent computing technique for solving partial differential equations: Limitation and Future prospects","version":1},"reference_index":5000,"source":"pdf_text","source_observed_at":"2026-08-12T11:26:07.838012Z"},"links":{"citing_paper":"/paper/2411.18240"},"observation_digest":"sha256:e21aa43cc36c7bd011356e7c09ab8339f70d8d79d4c2c26a6b71a663e12b394f","observation_id":"e28e9fc4-912c-4708-9fc8-4ef7a8ef8b46","resolution":{"observed_at":"2026-08-12T11:26:07.899750Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2411.18240","last_updated":"2024-11-27T11:27:18Z","latest_version":1,"primary_category":"physics.comp-ph","snapshot_observed_at":"2026-08-12T11:20:54.913584Z","submitted_at":"2024-11-27T11:27:18Z","title":"Physics Informed Neural Networks (PINNs) as intelligent computing technique for solving partial differential equations: Limitation and Future prospects"},"reference_resolution":{"displayed":4,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":1,"verified_exact":0,"verified_fuzzy":3},"total_outbound_references":4},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 4 of 4 outbound references and 6 inbound Pith citation observations for arXiv:2411.18240."}