{"as_of":"2026-08-09T01:47:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5290f8414070c072cb1a3fc96fa609670cdfa727e2a1ecd68310d960cfd1b1c8","coverage":[{"denominator":33,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":33,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T13:53:38.626157Z","state":"measured"},{"denominator":39,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":39,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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":"2026-08-03T13:08:22.792062Z","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":"2026-06-29T22:24:00.563121Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"cited_work":{"arxiv_id":"2505.20721","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2505.20721","snapshot_observed_at":"2026-06-29T22:24:00.563121Z","title":"Ye, C.-S","venue":null,"work_id":"cb9d9844-7911-4f77-9381-8d089a4c4b9b","year":2025},"citing_paper":{"arxiv_id":"2510.00233","last_updated":"2026-05-01T14:44:54Z","snapshot_observed_at":"2026-08-07T10:52:53.033148Z","submitted_at":"2025-09-30T19:57:52Z","title":"Differentiable Autoencoding Neural Operator for Interpretable and Integrable Latent Space Modeling","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-05-18T11:26:06.622876Z"},"links":{"cited_paper":"/paper/2505.20721","citing_paper":"/paper/2510.00233"},"observation_digest":"sha256:3a0bcd396192c8702a5d58973e7f6a278014e6e494dc6d4c207441b5d9fa4bfe","observation_id":"cc18e0e8-d9b0-4e61-897d-3b52bc9f393b","resolution":{"observed_at":"2026-05-18T11:26:18.470086Z","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":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"cited_work":{"arxiv_id":"2505.20721","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2505.20721","snapshot_observed_at":"2026-06-29T22:24:00.563121Z","title":"Ye, C.-S","venue":null,"work_id":"cb9d9844-7911-4f77-9381-8d089a4c4b9b","year":2025},"citing_paper":{"arxiv_id":"2605.10154","last_updated":"2026-05-11T08:00:42Z","snapshot_observed_at":"2026-07-06T23:22:08.560919Z","submitted_at":"2026-05-11T08:00:42Z","title":"Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-12T03:23:42.788576Z"},"links":{"cited_paper":"/paper/2505.20721","citing_paper":"/paper/2605.10154"},"observation_digest":"sha256:3100b38694edee77c45913c95770cd0320b49092fd1e84bdb68059a7b612b780","observation_id":"14ee7b02-aca2-42ca-9180-4fccb7ad5210","resolution":{"observed_at":"2026-05-12T03:26:19.757874Z","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":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"cited_work":{"arxiv_id":"2505.20721","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2505.20721","snapshot_observed_at":"2026-06-29T22:24:00.563121Z","title":"Ye, C.-S","venue":null,"work_id":"cb9d9844-7911-4f77-9381-8d089a4c4b9b","year":2025},"citing_paper":{"arxiv_id":"2605.25413","last_updated":"2026-06-05T14:54:43Z","snapshot_observed_at":"2026-08-07T05:42:38.760223Z","submitted_at":"2026-05-25T04:28:41Z","title":"Autoregression-Free Neural Operators for Time-Dependent PDEs","version":3},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-06-29T22:18:06.388832Z"},"links":{"cited_paper":"/paper/2505.20721","citing_paper":"/paper/2605.25413"},"observation_digest":"sha256:bce978fe97c451e8c3cc22348909ce63f0a39befa0dd127768e9932dab9f2ddf","observation_id":"35af1503-2eaa-475c-9676-4639f113a48f","resolution":{"observed_at":"2026-06-29T22:24:00.564858Z","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":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.20721","snapshot_observed_at":"2026-08-02T09:07:17.976701Z","title":"Reza Zangeneh and Carl F","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.19387","last_updated":"2026-07-02T02:12:13Z","snapshot_observed_at":"2026-08-07T18:15:52.561075Z","submitted_at":"2026-07-02T02:12:13Z","title":"Scale-Aware Learning of Chaotic Dynamics on Unstructured Meshes via Binned Spectral Losses","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-02T09:07:17.976701Z"},"links":{"cited_paper":"/paper/2505.20721","citing_paper":"/paper/2607.19387"},"observation_digest":"sha256:b56bcccbf9b973453bdc43b2de30559667e009ffbccc3657cb85dc45b8565465","observation_id":"479298eb-f1ca-4ff5-99d6-47005a3bda1f","resolution":{"observed_at":"2026-08-02T09:07:17.976701Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.20721","snapshot_observed_at":"2026-07-30T16:23:26.545464Z","title":"Ye, C.-S","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.23667","last_updated":"2026-07-26T14:02:46Z","snapshot_observed_at":"2026-08-07T14:03:08.676589Z","submitted_at":"2026-07-26T14:02:46Z","title":"No Free Lunch in Flow Surrogates under Time-Varying Boundary Conditions: A Two-Regime Study","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-07-30T16:23:26.545464Z"},"links":{"cited_paper":"/paper/2505.20721","citing_paper":"/paper/2607.23667"},"observation_digest":"sha256:f628e21203c0c40af5e86a25700d0a3fddd263f6c278136bf456e80a39816bbf","observation_id":"3c6eed9b-2d1c-47d0-9f2f-5c504fa6a5ba","resolution":{"observed_at":"2026-07-30T16:23:26.545464Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.20721","snapshot_observed_at":"2026-08-03T13:08:22.792062Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.29135","last_updated":"2026-07-31T08:05:46Z","snapshot_observed_at":"2026-08-07T17:37:00.687823Z","submitted_at":"2026-07-31T08:05:46Z","title":"HERO: History-Enriched Rollout Training for Long-Horizon Autoregressive Neural Operators","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-03T13:08:22.792062Z"},"links":{"cited_paper":"/paper/2505.20721","citing_paper":"/paper/2607.29135"},"observation_digest":"sha256:9890e1fa8aa5063a048891fc1cfc611c2c9c2ac40a7cf7974e576d0c33d856d1","observation_id":"fe3f1fef-6347-466a-b4f0-bdbe9cbfd864","resolution":{"observed_at":"2026-08-03T13:08:22.792062Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2505.20721/citation-record","integrity":"/paper/2505.20721/integrity","json":"/paper/2505.20721/citation-record.json","paper":"/paper/2505.20721"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:47.110794Z","title":"LNO: Laplace Neural Operator for Solving Differential Equations.Nature Machine Intelligence, 6(6):631–640, June 2024","venue":null,"work_id":"306ae8e2-f5a6-44ef-9422-039291feb539","year":2024},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:34.191672Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:b1783f6fa81cd36dd94c4e39002e435a03eaa95c4ac52215e857d71bd2a737ea","observation_id":"1ac83e79-b77d-4644-990c-ba49cdb3a5ec","resolution":{"observed_at":"2026-08-07T13:53:47.197429Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:46.735324Z","title":null,"venue":null,"work_id":"6bd1e3e2-101e-46bb-be0c-d69bda258aac","year":2017},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:34.270618Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:71449dd7ed4c625d1a39d9e2f5ae6546ead6018fe9448a90614c9e4e73acc1a8","observation_id":"94eeab2a-bb0f-4159-8619-840bcf73ee9b","resolution":{"observed_at":"2026-08-07T13:53:46.963318Z","resolver_source":"raw_fallback","status":"unresolved"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:46.465533Z","title":"The Deep Ritz Method: A Deep Learning-Based Numerical Algorithm for Solving Variational Problems.Communications in Mathematics and Statistics, 6(1):1–12, February 2018","venue":null,"work_id":"fb164b14-c4a6-4b3a-a28b-725acfedec5c","year":2018},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:34.357585Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:e5e8c212b58cc31827ae86f9d090a970e12665ffc7d28cfa3ded4cb7f493cfab","observation_id":"a7947323-8fa2-4e56-ac16-6a30a23be19e","resolution":{"observed_at":"2026-08-07T13:53:46.564074Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:46.203021Z","title":"MgNO: Efficient Parameterization of Linear Operators via Multigrid","venue":null,"work_id":"e5d88240-6c88-4fca-8c49-7001405cb0a2","year":2024},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:34.444746Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:a8886ce63a643402c6d70b7917b5df0a7e7381e8f5b96a0d99b768c4c92a256b","observation_id":"c9fe57f8-6240-4110-8ab2-8b1456caf5a6","resolution":{"observed_at":"2026-08-07T13:53:46.333645Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"2409.03231","last_updated":"2025-01-27T07:22:28Z","snapshot_observed_at":"2026-08-04T02:01:48.138021Z","submitted_at":"2024-09-05T03:57:28Z","title":"State-space models are accurate and efficient neural operators for dynamical systems","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.03231","snapshot_observed_at":"2026-08-07T13:53:34.567646Z","title":"State-space models are accurate and efficient neural operators for dynamical systems","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:34.567646Z"},"links":{"cited_paper":"/paper/2409.03231","citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:fa7c1242010a8ff98d9eaddabcf26225a4010fdf03be3c7442d74dfa6cb77d05","observation_id":"ea85af77-d80a-4e4a-b720-8080bd806a69","resolution":{"observed_at":"2026-08-07T13:53:34.567646Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:45.936827Z","title":"Deep backward schemes for high-dimensional nonlinear PDEs.Mathematics of Computation, 89(324):1547–1579, January 2020","venue":null,"work_id":"9f371703-6379-48ab-bbb0-239a9cf2d197","year":2020},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:34.725539Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:38d4a4a3c937d3a099b39ca738319826ac02f873646ae28e1f1e691076830a31","observation_id":"5611f74f-5e4b-404c-9646-8b6d75597f77","resolution":{"observed_at":"2026-08-07T13:53:46.045023Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:45.577044Z","title":"DPM: A Novel Training Method for Physics-Informed Neural Networks in Extrapolation","venue":null,"work_id":"6b4fe43a-b73b-4508-bdd9-b813333342c9","year":2021},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:34.878175Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:6fcb525ff8d402e1feb4c6b088352081b060171a913997a5700d47b0d9f4811e","observation_id":"6d6f7d96-ebed-4faf-bbff-1b8ed3edff33","resolution":{"observed_at":"2026-08-07T13:53:45.732731Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:45.265618Z","title":"Approximating Numerical Fluxes Using Fourier Neural Operators for Hyperbolic Conservation Laws.Communications in Computational Physics, 37(2):420–456, January 2025","venue":null,"work_id":"4afceddf-489e-4aac-a30c-7716be076225","year":2025},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:35.114548Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:53788cc8f6b6418b5c09076f790874cb43ec873dc5e3e98487a03f9fc2991a9b","observation_id":"56e81580-b267-47d1-ab5b-b8ae8ab8622c","resolution":{"observed_at":"2026-08-07T13:53:45.401258Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:44.905231Z","title":"On Universal Approximation and Error Bounds for Fourier Neural Operators.Journal of Machine Learning Research, 22(290):1–76, January 2021","venue":null,"work_id":"d39da887-1905-49c4-b601-b5103a37d6c2","year":2021},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:35.340177Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:f341385d52ee74b121a43e62140eff5644e159e29866217fe3c777761c94cec2","observation_id":"e2700e91-69c7-470b-8e8f-b279712db830","resolution":{"observed_at":"2026-08-07T13:53:45.058524Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:44.553828Z","title":"Neural Operator: Learning Maps Between Function Spaces With Applica- tions to PDEs.Journal of Machine Learning Research, 24(89):1–97, January 2023","venue":null,"work_id":"1f1f6768-9828-466b-9859-77fae4f1b0b3","year":2023},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:35.547475Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:cf4da7d23fcb9deeb2457023f2cc7ae395e2370bfe5cff34e824bc18a9e3c210","observation_id":"b9ce907b-1892-4082-abe4-c2d871cb926e","resolution":{"observed_at":"2026-08-07T13:53:44.747823Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:44.299958Z","title":"Fourier Neural Operator with Learned Deformations for PDEs on General Geometries.The Journal of Machine Learning Research, 24(1):1532–4435, January 2023","venue":null,"work_id":"17eaf11c-7a6e-4a80-a1fe-36f933cc671a","year":2023},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:35.737250Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:f3d4606fa39ae4ab7cb8c69b398727b3a566ad7b58b0d8cd4fbe75c7a1311595","observation_id":"13190015-7f7b-4a50-a870-265edf390f08","resolution":{"observed_at":"2026-08-07T13:53:44.368692Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:43.980404Z","title":"Fourier Neural Operator for Parametric Partial Differential Equations","venue":null,"work_id":"5004fd7d-b2c9-4d48-98f7-134c6e922224","year":2021},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:35.842538Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:a4a7382e86158677d56d4998bd98dcc2791435b89cad1f98d25abf95dc417cf6","observation_id":"8d424cde-e803-4d20-983f-ee6f08b5e8f6","resolution":{"observed_at":"2026-08-07T13:53:44.128431Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:43.802182Z","title":"Geometry-Informed Neural Operator for Large-Scale 3D PDEs","venue":null,"work_id":"80ed84c4-7ab8-4dcb-80f5-f38a06c1b55c","year":2023},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:35.912723Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:1a5216d912717a418dd28a7d6bf7a36ce38a6ce95d0645f86895a76d2b5a5174","observation_id":"e9455b73-b951-43f7-bc34-ad6d88486970","resolution":{"observed_at":"2026-08-07T13:53:43.868492Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:43.621186Z","title":"Veeling, Paris Perdikaris, Richard E","venue":null,"work_id":"45a9e934-c61d-4ec3-a868-16d7f0b84743","year":2023},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:36.050604Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:64eebe24f966a171a4cd98a391a3ff5ae0a9eb0ce7e8e3f44d17c5fcda5c59c7","observation_id":"521c144d-1c5f-42f0-acee-5e16dd013680","resolution":{"observed_at":"2026-08-07T13:53:43.713402Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:43.198223Z","title":"Mitigating spectral bias for the multiscale operator learning.Journal of Computational Physics, 506:112944, June 2024","venue":null,"work_id":"cab1c56c-c1e8-4324-9f67-25752263c5de","year":2024},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:36.136477Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:13b90e3ad223ab5da73a65557ed4d6877544d31c8fecd0523f212aaa1f35a91d","observation_id":"ae7a3573-7b0d-4d3f-b539-512fc161f87e","resolution":{"observed_at":"2026-08-07T13:53:43.404374Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:42.953498Z","title":"A MgNO Method for Multiphase Flow in Porous Media","venue":null,"work_id":"872ea2cc-ae69-4b36-a00c-966d5ff3b64f","year":2025},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:36.227102Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:74ae187f9598eab3ebb7c5129027e3aa40a0a5342bc430a39b5d115b6b42ab23","observation_id":"eedc4ecb-a835-4394-96a2-fc9b92522eea","resolution":{"observed_at":"2026-08-07T13:53:43.037295Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:42.622982Z","title":"Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators","venue":null,"work_id":"0a90c1ab-0d6e-4fa4-ab35-3ac2aed17683","year":2021},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:36.336555Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:984d4b27807617c6b8122b3bfc5bb16b47a1c4c167736a61a7d9a2d319c45385","observation_id":"45c3e1c9-d965-4718-962f-8aa051e1c706","resolution":{"observed_at":"2026-08-07T13:53:42.823448Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:42.132892Z","title":"Towards Stability of Autoregressive Neural Operators.Transactions on machine learning research, October 2023","venue":null,"work_id":"ea731c61-c939-4853-978f-83784dfa68e6","year":2023},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:36.458736Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:5bea154de2449be8a7cba3818a11494e733a756011e417ce4c7e913c016635eb","observation_id":"26ca6241-b5b1-42c6-ac25-3b4f4530bd3f","resolution":{"observed_at":"2026-08-07T13:53:42.344758Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:41.855656Z","title":"Neural Operator Learning for Long-Time Integration in Dynamical Systems with Recurrent Neural Networks","venue":null,"work_id":"eb57cddc-890f-4722-b02a-e23d06e7dad0","year":2024},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:36.586604Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:62dc6f9c74110ec59fdd5f25c493c24384f6e008d9dd42c11975f4525c66c744","observation_id":"d69671b7-92fd-412e-b251-80229aee77c5","resolution":{"observed_at":"2026-08-07T13:53:41.985862Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:41.615860Z","title":"FourCastNet: A Global Data- driven High-resolution Weather Model using Adaptive Fourier Neural Operators","venue":null,"work_id":"bbebfcd6-f44c-497d-8e00-eb56b3394628","year":2023},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:36.766730Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:f65182369f233bbca1629c8862fc3552397e2ec92a8be7fdfd89626cda5c4304","observation_id":"85cbf4cc-824d-49f1-8517-d998b714a030","resolution":{"observed_at":"2026-08-07T13:53:41.725340Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:41.335320Z","title":"Forward–Backward Stochastic Neural Networks: Deep Learning of High- Dimensional Partial Differential Equations","venue":null,"work_id":"ee1d824e-c0bc-4a88-aea6-a3e339ad704d","year":2023},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:36.956839Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:7e5b4d80f6f7ef516ef024f03235dc40f579f1063c9b95f5ad4f047e291a3ac4","observation_id":"3c91a942-c6d2-4231-8a2e-e112d917fa72","resolution":{"observed_at":"2026-08-07T13:53:41.436522Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:41.071749Z","title":null,"venue":null,"work_id":"e2cf2cea-148f-4064-ae6d-a79d87434237","year":2019},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:37.097605Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:dedec1cc6da5ceffd862fa08e96a6e9d78bbe2b2f2fc57b5cf0f5a808dba30d6","observation_id":"2d3d53cc-9e26-4759-8913-e4480d3a3aec","resolution":{"observed_at":"2026-08-07T13:53:41.182124Z","resolver_source":"raw_fallback","status":"unresolved"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:37.217531Z","title":"Finite Operator Learning: Bridging Neural Operators and Numerical Methods for Efficient Parametric Solution and Optimization of PDEs","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:37.217531Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:84ee4a2b811fa79339ba3bc9c6cd72a9fb556929b71e197a230e7b3a2ce3dd6f","observation_id":"0499367d-969f-4fff-b384-435b894df9cc","resolution":{"observed_at":"2026-08-07T13:53:37.217531Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:40.831357Z","title":"DGM: A deep learning algorithm for solving partial differential equations.Journal of Computational Physics, 375:1339–1364, December 2018","venue":null,"work_id":"5a7ebd2b-da0e-4f76-b28a-1c60ad77ecae","year":2018},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:37.373662Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:d195579b0daa31873799fb5ee41933255ba4d767ce59e47c5ad9179ccc9e4447","observation_id":"9e2a60fd-eea1-470e-86b9-e810e9929f65","resolution":{"observed_at":"2026-08-07T13:53:40.912840Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:40.623251Z","title":"Factorized Fourier Neural Operators","venue":null,"work_id":"31330214-7668-4e32-abcd-19b41d769bd8","year":2023},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:37.483537Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:1087d72644dca807add7093ef824021055e0c356edf721785172f7f2aef5e786","observation_id":"ddf73d44-ddb4-436d-8b87-e28a5231c454","resolution":{"observed_at":"2026-08-07T13:53:40.729416Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:37.611152Z","title":"COAST: Intelligent Time-Adaptive Neural Operators","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:37.611152Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:653bce3b75b4fe434d15b0871e8444ce25aa8ea89c456edeb4b5ee6ae2bc315e","observation_id":"9bbb95ea-781e-49dc-816f-8c557dfc7618","resolution":{"observed_at":"2026-08-07T13:53:37.611152Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:40.424334Z","title":"Amortized Fourier Neural Operators","venue":null,"work_id":"b5038721-aa65-4df8-bc67-b8d2cef83c77","year":2024},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:37.771286Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:5e109e039529aee3701948fcfc2498dd69cce827080d4c64bf1cf15f0adf28ff","observation_id":"55108148-b9b0-4632-bdcd-f1f848fc215a","resolution":{"observed_at":"2026-08-07T13:53:40.540572Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:40.166067Z","title":"Transfer Learning Enhanced DeepONet for Long- Time Prediction of Evolution Equations","venue":null,"work_id":"b2d949e6-1eb7-43e9-b2f8-2b24f42ecc58","year":2023},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:37.919481Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:91cbad0a067c40b4a71781b803401c02e5bf6b08d25af025d62cb6d92339d142","observation_id":"9250f5aa-c834-467a-b6da-754e31b27bcb","resolution":{"observed_at":"2026-08-07T13:53:40.293111Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"2412.11010","last_updated":"2024-12-15T01:37:48Z","snapshot_observed_at":"2026-07-06T20:07:10.352535Z","submitted_at":"2024-12-15T01:37:48Z","title":"FBSJNN: A Theoretically Interpretable and Efficiently Deep Learning method for Solving Partial Integro-Differential Equations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.11010","snapshot_observed_at":"2026-08-07T13:53:38.043720Z","title":"FBSJNN: A Theoretically Interpretable and Efficiently Deep Learning method for Solving Partial Integro-Differential Equations","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:38.043720Z"},"links":{"cited_paper":"/paper/2412.11010","citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:f872b5d71eb44cce06c0432f77ea39f29dd4d088739f90676de7a980597d43b9","observation_id":"b4da9aa1-3887-4b2c-b749-acfad9b9e2bf","resolution":{"observed_at":"2026-08-07T13:53:38.043720Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:39.918296Z","title":"Reliable extrapolation of deep neural operators informed by physics or sparse observations.Computer Methods in Applied Mechanics and Engineering, 412:116064, July 2023","venue":null,"work_id":"25f34893-16c7-4428-b39b-7b307cd0e25c","year":2023},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:38.169774Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:e2b1be701fdd31836fa9922d7c33976b8a3b4d8775526066d4eb72396a05473e","observation_id":"38192298-6f44-4863-8976-397c0a970c50","resolution":{"observed_at":"2026-08-07T13:53:40.035255Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:39.557856Z","title":null,"venue":null,"work_id":"320e1d54-03de-48d8-9953-ac7b039b00c8","year":null},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:38.339526Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:b2008a98c0b8cce77032abc626f753c6bd7007c4abb76750f16e233bc8aa6d7b","observation_id":"b3810c2f-786c-499d-84fe-9d06d5478ccd","resolution":{"observed_at":"2026-08-07T13:53:39.734755Z","resolver_source":"raw_fallback","status":"unresolved"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:39.386667Z","title":null,"venue":null,"work_id":"88df4d38-2f70-4a50-88c8-94da20c8975a","year":null},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:38.455861Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:8991a6ef85d788340b5653ccdfd69a675f8e6187e80d38c69e67b0da3125d4db","observation_id":"4c2ad734-c1bf-42d3-a530-b78afdfef30c","resolution":{"observed_at":"2026-08-07T13:53:39.462624Z","resolver_source":"raw_fallback","status":"unresolved"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:53:39.136264Z","title":null,"venue":null,"work_id":"f085a8f9-2026-4ff9-a0ae-613b94e2eec7","year":null},"citing_paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T13:53:38.626157Z"},"links":{"citing_paper":"/paper/2505.20721"},"observation_digest":"sha256:e9b8f32eb55f49c9ffd817c866d9f609990099381a8f4f759b998bb5488080f2","observation_id":"877911d3-872d-486c-be32-3a6a6b081797","resolution":{"observed_at":"2026-08-07T13:53:39.247410Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"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"}}],"paper":{"arxiv_id":"2505.20721","last_updated":"2025-05-27T05:04:35Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-07T13:45:40.223493Z","submitted_at":"2025-05-27T05:04:35Z","title":"Recurrent Neural Operators: Stable Long-Term PDE Prediction"},"reference_resolution":{"displayed":33,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":8,"verified_exact":0,"verified_fuzzy":24},"total_outbound_references":33},"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 33 of 33 outbound references and 6 inbound Pith citation observations for arXiv:2505.20721."}