{"as_of":"2026-08-09T02:35:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:63e56309ceccec3a54afb7a61fb376081a6745d9efc2d394612f6297ad0dd9c1","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":12,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":12,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":12,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":12,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-08T21:53:31.172306Z","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":4,"observed_at":"2026-08-05T02:28:24.338817Z","source":"arxiv_reference"}],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2403.02913","last_updated":"2024-09-12T07:54:18Z","snapshot_observed_at":"2026-08-04T00:23:31.008797Z","submitted_at":"2024-03-05T12:28:04Z","title":"Scientific machine learning for closure models in multiscale problems: a review","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.02913","snapshot_observed_at":"2026-08-08T21:53:31.172306Z","title":"Sanderse, P","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.04703","last_updated":"2025-02-07T07:14:41Z","snapshot_observed_at":"2026-08-08T21:46:41.680196Z","submitted_at":"2025-02-07T07:14:41Z","title":"Symbolic Regression of Data-Driven Reduced Order Model Closures for Under-Resolved, Convection-Dominated Flows","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-08T21:53:31.172306Z"},"links":{"cited_paper":"/paper/2403.02913","citing_paper":"/paper/2502.04703"},"observation_digest":"sha256:bc181f64ab47ed252513e70645c547a715ff8d5060a0e7e9cd5432fa227eed31","observation_id":"e2c02989-8b21-4fc8-9d8b-08b5d52a9d73","resolution":{"observed_at":"2026-08-08T21:53:31.172306Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.02913","last_updated":"2024-09-12T07:54:18Z","snapshot_observed_at":"2026-08-04T00:23:31.008797Z","submitted_at":"2024-03-05T12:28:04Z","title":"Scientific machine learning for closure models in multiscale problems: a review","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.02913","snapshot_observed_at":"2026-08-07T04:15:05.081651Z","title":"Sanderse, P","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.11398","last_updated":"2025-06-13T01:45:37Z","snapshot_observed_at":"2026-08-07T23:57:03.876980Z","submitted_at":"2025-06-13T01:45:37Z","title":"FIGNN: Feature-Specific Interpretability for Graph Neural Network Surrogate Models","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T04:15:05.081651Z"},"links":{"cited_paper":"/paper/2403.02913","citing_paper":"/paper/2506.11398"},"observation_digest":"sha256:b807acd768e6f2dfe13df5a711d399e07bd53d65b3260ea5b95948b8f091b249","observation_id":"8066e7e7-7d03-46a6-bd2d-4fae9661b5bb","resolution":{"observed_at":"2026-08-07T04:15:05.081651Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.02913","last_updated":"2024-09-12T07:54:18Z","snapshot_observed_at":"2026-08-04T00:23:31.008797Z","submitted_at":"2024-03-05T12:28:04Z","title":"Scientific machine learning for closure models in multiscale problems: a review","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.02913","snapshot_observed_at":"2026-08-06T18:17:56.638646Z","title":"Scientific ma- chine learning for closure models in multiscale problems: A review","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.08749","last_updated":"2025-07-11T16:59:27Z","snapshot_observed_at":"2026-08-06T18:07:26.000754Z","submitted_at":"2025-07-11T16:59:27Z","title":"Modeling Partially Observed Nonlinear Dynamical Systems and Efficient Data Assimilation via Discrete-Time Conditional Gaussian Koopman Network","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T18:17:56.638646Z"},"links":{"cited_paper":"/paper/2403.02913","citing_paper":"/paper/2507.08749"},"observation_digest":"sha256:e3a5f03526f5c4ca8014fac108ccd0804989425a053a323a9c8795fee61fc0bb","observation_id":"0b5cd7c7-5d64-4fb7-ab12-6ab290d82cde","resolution":{"observed_at":"2026-08-06T18:17:56.638646Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.02913","last_updated":"2024-09-12T07:54:18Z","snapshot_observed_at":"2026-08-04T00:23:31.008797Z","submitted_at":"2024-03-05T12:28:04Z","title":"Scientific machine learning for closure models in multiscale problems: a review","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.02913","snapshot_observed_at":"2026-08-06T13:15:43.370986Z","title":"Scientific machine learning for closure models in multiscale problems: A review.arXiv preprint arXiv:2403.02913,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.20975","last_updated":"2026-06-06T17:15:42Z","snapshot_observed_at":"2026-08-07T06:09:01.935216Z","submitted_at":"2025-07-28T16:37:56Z","title":"Locally Adaptive Conformal Inference for Operator Models","version":5},"reference_index":2019,"source":"pdf_text","source_observed_at":"2026-08-06T13:15:43.370986Z"},"links":{"cited_paper":"/paper/2403.02913","citing_paper":"/paper/2507.20975"},"observation_digest":"sha256:60342ff5d4fa2cf7441acf334e77fbb32e0e976929b53068090f5d67a7c4fc62","observation_id":"234fc238-48a8-4bd4-a610-b8f7d23f9e23","resolution":{"observed_at":"2026-08-06T13:15:43.370986Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.02913","last_updated":"2024-09-12T07:54:18Z","snapshot_observed_at":"2026-08-04T00:23:31.008797Z","submitted_at":"2024-03-05T12:28:04Z","title":"Scientific machine learning for closure models in multiscale problems: a review","version":2},"cited_work":{"arxiv_id":"2403.02913","doi":"10.48550/arxiv.2403.02913","metadata_source":"arxiv_reference","pith_arxiv_id":"2403.02913","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Scientific machine learning for closure models in multiscale problems: A review","venue":"arXiv (Cornell University)","work_id":"44bddcda-b3e0-4f60-a49f-93a9f1b56313","year":2024},"citing_paper":{"arxiv_id":"2604.05652","last_updated":"2026-04-07T09:54:50Z","snapshot_observed_at":"2026-07-06T22:54:21.571606Z","submitted_at":"2026-04-07T09:54:50Z","title":"Multiscale Physics-Informed Neural Network for Complex Fluid Flows with Long-Range Dependencies","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-10T19:13:18.894727Z"},"links":{"cited_paper":"/paper/2403.02913","citing_paper":"/paper/2604.05652"},"observation_digest":"sha256:0ec72f5d8973107fc6f89498fcbcdad906690ed236c66856db994420edb2557c","observation_id":"a3c7947c-358a-4d1a-a65d-84bef18f678b","resolution":{"observed_at":"2026-05-10T23:20:51.531523Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2403.02913","last_updated":"2024-09-12T07:54:18Z","snapshot_observed_at":"2026-08-04T00:23:31.008797Z","submitted_at":"2024-03-05T12:28:04Z","title":"Scientific machine learning for closure models in multiscale problems: a review","version":2},"cited_work":{"arxiv_id":"2403.02913","doi":"10.48550/arxiv.2403.02913","metadata_source":"arxiv_reference","pith_arxiv_id":"2403.02913","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Scientific machine learning for closure models in multiscale problems: A review","venue":"arXiv (Cornell University)","work_id":"44bddcda-b3e0-4f60-a49f-93a9f1b56313","year":2024},"citing_paper":{"arxiv_id":"2605.08436","last_updated":"2026-05-08T19:59:40Z","snapshot_observed_at":"2026-08-08T10:21:00.730080Z","submitted_at":"2026-05-08T19:59:40Z","title":"A meshfree exterior calculus for generalizable and data-efficient learning of physics from point clouds","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-05-12T02:09:01.875110Z"},"links":{"cited_paper":"/paper/2403.02913","citing_paper":"/paper/2605.08436"},"observation_digest":"sha256:5250288a00eedbabd71eff2b99d5ba10870117f989f97ea625b56ead1857eb39","observation_id":"4a84ca8d-ee1f-4b8d-ad9f-2c4a04cc0f34","resolution":{"observed_at":"2026-05-12T02:11:15.883780Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2403.02913","last_updated":"2024-09-12T07:54:18Z","snapshot_observed_at":"2026-08-04T00:23:31.008797Z","submitted_at":"2024-03-05T12:28:04Z","title":"Scientific machine learning for closure models in multiscale problems: a review","version":2},"cited_work":{"arxiv_id":"2403.02913","doi":"10.48550/arxiv.2403.02913","metadata_source":"arxiv_reference","pith_arxiv_id":"2403.02913","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Scientific machine learning for closure models in multiscale problems: A review","venue":"arXiv (Cornell University)","work_id":"44bddcda-b3e0-4f60-a49f-93a9f1b56313","year":2024},"citing_paper":{"arxiv_id":"2605.16573","last_updated":"2026-05-15T19:24:31Z","snapshot_observed_at":"2026-07-06T23:27:43.762904Z","submitted_at":"2026-05-15T19:24:31Z","title":"Wavelet Flow Matching for Multi-Scale Physics Emulation","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-05-20T19:31:31.583420Z"},"links":{"cited_paper":"/paper/2403.02913","citing_paper":"/paper/2605.16573"},"observation_digest":"sha256:0c7140289ed327dee7a17debf6d9d02c4f27c81d7b905c26a3199d301a570760","observation_id":"dab05810-78a7-40b4-9a02-d55ff448c0ac","resolution":{"observed_at":"2026-05-20T19:33:41.876401Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2403.02913","last_updated":"2024-09-12T07:54:18Z","snapshot_observed_at":"2026-08-04T00:23:31.008797Z","submitted_at":"2024-03-05T12:28:04Z","title":"Scientific machine learning for closure models in multiscale problems: a review","version":2},"cited_work":{"arxiv_id":"2403.02913","doi":"10.48550/arxiv.2403.02913","metadata_source":"arxiv_reference","pith_arxiv_id":"2403.02913","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Scientific machine learning for closure models in multiscale problems: A review","venue":"arXiv (Cornell University)","work_id":"44bddcda-b3e0-4f60-a49f-93a9f1b56313","year":2024},"citing_paper":{"arxiv_id":"2606.02145","last_updated":"2026-06-01T12:10:48Z","snapshot_observed_at":"2026-07-06T23:42:35.063977Z","submitted_at":"2026-06-01T12:10:48Z","title":"Hybrid Neural Ordinary Differential Equations for Data-Efficient Polymerization Modeling with Incomplete Kinetics","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-06-28T16:01:16.642276Z"},"links":{"cited_paper":"/paper/2403.02913","citing_paper":"/paper/2606.02145"},"observation_digest":"sha256:3747f78333a337abca4b5efaf7953284b4ab744ca705ac8a36f3948946cceeb7","observation_id":"7cfcbba1-f103-4113-83d4-74986150d573","resolution":{"observed_at":"2026-07-01T21:56:15.819741Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2403.02913","last_updated":"2024-09-12T07:54:18Z","snapshot_observed_at":"2026-08-04T00:23:31.008797Z","submitted_at":"2024-03-05T12:28:04Z","title":"Scientific machine learning for closure models in multiscale problems: a review","version":2},"cited_work":{"arxiv_id":"2403.02913","doi":"10.48550/arxiv.2403.02913","metadata_source":"arxiv_reference","pith_arxiv_id":"2403.02913","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Scientific machine learning for closure models in multiscale problems: A review","venue":"arXiv (Cornell University)","work_id":"44bddcda-b3e0-4f60-a49f-93a9f1b56313","year":2024},"citing_paper":{"arxiv_id":"2606.05141","last_updated":"2026-06-03T17:49:47Z","snapshot_observed_at":"2026-08-02T08:19:59.447909Z","submitted_at":"2026-06-03T17:49:47Z","title":"Generalized Forcing Method: Generation of Diverse Data for Training Linear Transport PDE Closure Models","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-28T03:49:50.921104Z"},"links":{"cited_paper":"/paper/2403.02913","citing_paper":"/paper/2606.05141"},"observation_digest":"sha256:353c1aa087738d15873629f82899878d25c6d2c48b977e5a8cff9d3ab164b1d2","observation_id":"5200b68a-9303-4503-8673-da1f70e03ed0","resolution":{"observed_at":"2026-07-02T11:26:54.542265Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2403.02913","last_updated":"2024-09-12T07:54:18Z","snapshot_observed_at":"2026-08-04T00:23:31.008797Z","submitted_at":"2024-03-05T12:28:04Z","title":"Scientific machine learning for closure models in multiscale problems: a review","version":2},"cited_work":{"arxiv_id":"2403.02913","doi":"10.48550/arxiv.2403.02913","metadata_source":"arxiv_reference","pith_arxiv_id":"2403.02913","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Scientific machine learning for closure models in multiscale problems: A review","venue":"arXiv (Cornell University)","work_id":"44bddcda-b3e0-4f60-a49f-93a9f1b56313","year":2024},"citing_paper":{"arxiv_id":"2606.09857","last_updated":"2026-05-27T18:35:05Z","snapshot_observed_at":"2026-08-02T10:05:30.388502Z","submitted_at":"2026-05-27T18:35:05Z","title":"Uncertainty-aware Multi-fidelity Closure via Conditional Normalizing Flows","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-29T13:39:13.750453Z"},"links":{"cited_paper":"/paper/2403.02913","citing_paper":"/paper/2606.09857"},"observation_digest":"sha256:240395f68ec416f6ed79abed9b1a5347ffb42ec9d23826409182aebd950c2f1c","observation_id":"0b4bd3a4-b462-4249-a458-3179e2faa287","resolution":{"observed_at":"2026-06-29T13:43:28.758195Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2403.02913","last_updated":"2024-09-12T07:54:18Z","snapshot_observed_at":"2026-08-04T00:23:31.008797Z","submitted_at":"2024-03-05T12:28:04Z","title":"Scientific machine learning for closure models in multiscale problems: a review","version":2},"cited_work":{"arxiv_id":"2403.02913","doi":"10.48550/arxiv.2403.02913","metadata_source":"arxiv_reference","pith_arxiv_id":"2403.02913","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Scientific machine learning for closure models in multiscale problems: A review","venue":"arXiv (Cornell University)","work_id":"44bddcda-b3e0-4f60-a49f-93a9f1b56313","year":2024},"citing_paper":{"arxiv_id":"2606.11657","last_updated":"2026-06-10T04:38:45Z","snapshot_observed_at":"2026-08-08T17:05:55.149087Z","submitted_at":"2026-06-10T04:38:45Z","title":"Sparse probes and murky physics: a case study of interpretability challenges in a foundation model for continuum dynamics","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-06-27T10:55:15.050341Z"},"links":{"cited_paper":"/paper/2403.02913","citing_paper":"/paper/2606.11657"},"observation_digest":"sha256:f171fd21d985c6f2840fac576563b0b32a77ea65121d46b088c952a98bf9982b","observation_id":"f2039aa4-71d7-431a-8a6d-5197b6e0476e","resolution":{"observed_at":"2026-06-27T11:00:50.703680Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2403.02913","last_updated":"2024-09-12T07:54:18Z","snapshot_observed_at":"2026-08-04T00:23:31.008797Z","submitted_at":"2024-03-05T12:28:04Z","title":"Scientific machine learning for closure models in multiscale problems: a review","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.02913","snapshot_observed_at":"2026-08-05T00:42:28.448125Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.00591","last_updated":"2026-08-01T11:07:24Z","snapshot_observed_at":"2026-08-08T18:26:12.855604Z","submitted_at":"2026-08-01T11:07:24Z","title":"Why Does the Future Branch? Identifiable Closure Tests for Stochastic Physical World Models","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-05T00:42:28.448125Z"},"links":{"cited_paper":"/paper/2403.02913","citing_paper":"/paper/2608.00591"},"observation_digest":"sha256:537d74ecd2ae3adf7ad0ba7db5fa38c3038239cd628331bdccdc0315a36e8826","observation_id":"0c471c75-4758-4b80-a588-7dca0b860104","resolution":{"observed_at":"2026-08-05T00:42:28.448125Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2403.02913/citation-record","integrity":"/paper/2403.02913/integrity","json":"/paper/2403.02913/citation-record.json","paper":"/paper/2403.02913"},"outbound":[],"paper":{"arxiv_id":"2403.02913","last_updated":"2024-09-12T07:54:18Z","latest_version":2,"primary_category":"math.NA","snapshot_observed_at":"2026-08-04T00:23:31.008797Z","submitted_at":"2024-03-05T12:28:04Z","title":"Scientific machine learning for closure models in multiscale problems: a review"},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 12 inbound Pith citation observations for arXiv:2403.02913."}