{"as_of":"2026-08-09T01:14:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:cf8d50b1ce583967be4606ccfc3affaa16e1afb044fa8393ace6269fad9ac391","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":41,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":41,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":41,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":41,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-08T05:46:28.133504Z","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":79,"observed_at":"2026-08-05T02:28:24.338817Z","source":"arxiv_reference"}],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2305.14703","last_updated":"2026-04-17T20:21:10Z","snapshot_observed_at":"2026-07-06T15:32:14.701994Z","submitted_at":"2023-05-24T04:15:34Z","title":"Generative diffusion learning for parametric partial differential equations","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-24T09:06:10.327568Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2305.14703"},"observation_digest":"sha256:19f448b70eb75210c0e9c2ab4ef2d81f189dc36044b98309527812da06dc0574","observation_id":"e72c7a0d-9d01-426e-a4f8-c48d40eaea2a","resolution":{"observed_at":"2026-05-24T09:09:15.695837Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2407.00809","last_updated":"2026-06-02T21:20:03Z","snapshot_observed_at":"2026-07-06T18:39:11.695278Z","submitted_at":"2024-06-30T19:28:12Z","title":"Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning","version":3},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-05-23T23:08:36.689122Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2407.00809"},"observation_digest":"sha256:abadb708837020425807aa93a89ea709a74aa15d42f68b10d348866d3bbfe8c9","observation_id":"0ae81296-4958-4e52-ab45-b4575f810be2","resolution":{"observed_at":"2026-05-23T23:13:37.081139Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-08T05:46:28.133504Z","title":"Neural operator: Learning maps between function spaces","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2502.08683","last_updated":"2025-02-12T11:16:15Z","snapshot_observed_at":"2026-08-08T05:34:45.071140Z","submitted_at":"2025-02-12T11:16:15Z","title":"A Deep Learning approach for parametrized and time dependent Partial Differential Equations using Dimensionality Reduction and Neural ODEs","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-08T05:46:28.133504Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2502.08683"},"observation_digest":"sha256:871479e9f919796f296717765cd4b2000e17611165ce3f91a405ee302c2e4058","observation_id":"7cab24c7-16be-49bc-9f95-99cf82168681","resolution":{"observed_at":"2026-08-08T05:46:28.133504Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-07T19:43:57.768053Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2502.10033","last_updated":"2025-02-14T09:23:13Z","snapshot_observed_at":"2026-08-08T07:21:52.321579Z","submitted_at":"2025-02-14T09:23:13Z","title":"Phi-FEM-FNO: a new approach to train a Neural Operator as a fast PDE solver for variable geometries","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T19:43:57.768053Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2502.10033"},"observation_digest":"sha256:0fd5f7baf121278a34c6e2c2e8f9841f377b4e6c4ccab06d6f1b9e90489778ba","observation_id":"dfbca8f4-6bc6-4071-9c2e-12703dbca6e0","resolution":{"observed_at":"2026-08-07T19:43:57.768053Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2503.14568","last_updated":"2025-03-18T11:19:08Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-03-18T11:19:08Z","title":"Teaching Artificial Intelligence to Perform Rapid, Resolution-Invariant Grain Growth Modeling via Fourier Neural Operator","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-05-22T23:51:39.466995Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2503.14568"},"observation_digest":"sha256:3736ba3a01d82971e36b125b9fe15b13bfabd953019f8818dfc805e8a0e50933","observation_id":"acbca17f-c801-41da-9363-28ec9c5468e0","resolution":{"observed_at":"2026-05-22T23:52:16.918861Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-07T14:58:38.018328Z","title":"Neural Operator : Learning Maps Between Function Spaces , May 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.16996","last_updated":"2025-05-22T17:56:38Z","snapshot_observed_at":"2026-08-08T23:33:30.137374Z","submitted_at":"2025-05-22T17:56:38Z","title":"A Unified Framework for Simultaneous Parameter and Function Discovery in Differential Equations","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-07T14:58:38.018328Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2505.16996"},"observation_digest":"sha256:51104411e5bf2f8128e28e880776b90eebd04555a63f58c5969ce7d5cebb0cbd","observation_id":"453965a8-81c8-44cf-be95-625fdf05be59","resolution":{"observed_at":"2026-08-07T14:58:38.018328Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-07T14:24:44.047914Z","title":"Neural operator: Learning maps between function spaces.arXiv preprint arXiv:2108.08481,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.19105","last_updated":"2025-05-28T07:11:21Z","snapshot_observed_at":"2026-08-07T14:18:02.854393Z","submitted_at":"2025-05-25T11:51:31Z","title":"Latent Mamba Operator for Partial Differential Equations","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T14:24:44.047914Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2505.19105"},"observation_digest":"sha256:fd822050943ab7e980390d8f68b778eff3a9a70d6b88ef15d9bc0406b0d62105","observation_id":"95b9b567-a5ad-49dd-82f2-e8c218a29413","resolution":{"observed_at":"2026-08-07T14:24:44.047914Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-07T06:01:41.912814Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2506.06623","last_updated":"2025-09-09T02:29:24Z","snapshot_observed_at":"2026-08-07T05:50:52.488153Z","submitted_at":"2025-06-07T01:57:08Z","title":"Neural Operators for Forward and Inverse Potential-Density Mappings in Classical Density Functional Theory","version":2},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-08-07T06:01:41.912814Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2506.06623"},"observation_digest":"sha256:6e28282376de799936fa3371110afa3fc424a8a51cdafa9a1b8c28097531f7c3","observation_id":"54e62085-dc27-4f66-acea-0011bc21ed95","resolution":{"observed_at":"2026-08-07T06:01:41.912814Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-07T05:23:49.111356Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2506.08226","last_updated":"2025-06-09T20:52:04Z","snapshot_observed_at":"2026-08-07T05:14:41.496836Z","submitted_at":"2025-06-09T20:52:04Z","title":"Mondrian: Transformer Operators via Domain Decomposition","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T05:23:49.111356Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2506.08226"},"observation_digest":"sha256:1b080bca01ecebc37288bccea1d184dbdda44e9b6122772cbdf42521e5db6b39","observation_id":"e5c31bbc-cb84-4d4c-bd11-e1cc523fddc2","resolution":{"observed_at":"2026-08-07T05:23:49.111356Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2506.14665","last_updated":"2026-04-21T17:59:57Z","snapshot_observed_at":"2026-08-07T17:23:00.353321Z","submitted_at":"2025-06-17T15:56:56Z","title":"Accurate and scalable exchange-correlation with deep learning","version":6},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-05-19T09:06:01.804744Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2506.14665"},"observation_digest":"sha256:a62ed746c4f550c1828add208bbe257abd86dc039d64dd024f17a02bc568642e","observation_id":"73678889-47ce-4b6e-8979-01cbe0406b2d","resolution":{"observed_at":"2026-05-19T09:07:13.947633Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-06T21:26:34.338031Z","title":"Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew M","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.00278","last_updated":"2025-06-30T21:35:52Z","snapshot_observed_at":"2026-08-06T21:17:52.730266Z","submitted_at":"2025-06-30T21:35:52Z","title":"Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-06T21:26:34.338031Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2507.00278"},"observation_digest":"sha256:ccb8a2c7b9013fcad1914b8b48bee1d426953e0facfdf5556c60afb355d6d4a1","observation_id":"1b4e4631-634c-431a-842d-0a1d3ee9410c","resolution":{"observed_at":"2026-08-06T21:26:34.338031Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-06T19:27:46.639151Z","title":"arXiv preprint arXiv:2108.08481 (2021)","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.05584","last_updated":"2025-07-08T01:43:33Z","snapshot_observed_at":"2026-08-06T19:20:21.506240Z","submitted_at":"2025-07-08T01:43:33Z","title":"The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T19:27:46.639151Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2507.05584"},"observation_digest":"sha256:b3ea5a688c7834ba3f30e5a52ae244129b38284942a721c74cf0a93e2a9217e1","observation_id":"ec2973c2-c63c-4f23-9b75-8f9b6b9383ce","resolution":{"observed_at":"2026-08-06T19:27:46.639151Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2507.15774","last_updated":"2026-05-14T16:58:20Z","snapshot_observed_at":"2026-07-06T22:00:28.955116Z","submitted_at":"2025-07-21T16:29:29Z","title":"Time Series Forecasting Through the Lens of Dynamics","version":3},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-05-19T03:31:48.513830Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2507.15774"},"observation_digest":"sha256:de6ce2535c526f02ffcbfd49de67cca301318c5e208cdaa7bc6ff404ca976ea2","observation_id":"f8f7839d-69f0-40d9-8b1c-623ea2dbd3a6","resolution":{"observed_at":"2026-05-19T03:32:01.331749Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-06T13:02:54.464045Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.21244","last_updated":"2025-07-28T18:02:57Z","snapshot_observed_at":"2026-08-06T13:02:50.048207Z","submitted_at":"2025-07-28T18:02:57Z","title":"Bubbleformer: Forecasting Boiling with Transformers","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T13:02:54.464045Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2507.21244"},"observation_digest":"sha256:8ad4cec3efa00142797d3982d279bc38c1bd153be0597a3334f6b45a8f45d69d","observation_id":"fb6952aa-d2cb-4603-aeb7-5aadff637db4","resolution":{"observed_at":"2026-08-06T13:02:54.464045Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-06T11:54:56.893686Z","title":"Neural operator: Learning maps between function spaces,","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.22301","last_updated":"2025-07-30T00:24:17Z","snapshot_observed_at":"2026-08-06T11:54:56.326385Z","submitted_at":"2025-07-30T00:24:17Z","title":"Toward Intelligent Electronic-Photonic Design Automation for Large-Scale Photonic Integrated Circuits: from Device Inverse Design to Physical Layout Generation","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T11:54:56.893686Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2507.22301"},"observation_digest":"sha256:07b1937d65461674df885015ef31452ce35b05c93aaeb593d72a935bdfcd93db","observation_id":"017054dd-9e09-4ec1-9fee-928057c78a5e","resolution":{"observed_at":"2026-08-06T11:54:56.893686Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T16:16:13.303354Z","title":"Kovachki, Z","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2508.18806","last_updated":"2025-08-26T08:40:42Z","snapshot_observed_at":"2026-08-05T16:16:08.363538Z","submitted_at":"2025-08-26T08:40:42Z","title":"Temperature-Aware Recurrent Neural Operator for Temperature-Dependent Anisotropic Plasticity in HCP Materials","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-05T16:16:13.303354Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2508.18806"},"observation_digest":"sha256:53343fd1cf099597643e593549be2385c12a7c33737c4c913a932bc0b216896f","observation_id":"d5771126-6644-43fc-86bd-7a27543f2f80","resolution":{"observed_at":"2026-08-05T16:16:13.303354Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-04T17:57:20.298639Z","title":"Neural Operator: Learning Maps Between Function Spaces, April 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.10378","last_updated":"2025-09-12T16:10:18Z","snapshot_observed_at":"2026-08-04T17:57:16.488443Z","submitted_at":"2025-09-12T16:10:18Z","title":"Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-04T17:57:20.298639Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2509.10378"},"observation_digest":"sha256:c256b61be95c6e6bbbc5836e71e7911fcb0bacb4eed8beebe8c014a51875e77d","observation_id":"70de1d89-488e-413b-9b55-ae4160e23cfc","resolution":{"observed_at":"2026-08-04T17:57:20.298639Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-04T18:00:37.393578Z","title":"B., Li, Z., Liu, B., Azizzadenesheli, K., Bhattacharya, K., Stuart, A","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.10384","last_updated":"2025-09-12T16:18:16Z","snapshot_observed_at":"2026-08-04T18:00:35.925309Z","submitted_at":"2025-09-12T16:18:16Z","title":"Flow Straight and Fast in Hilbert Space: Functional Rectified Flow","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-04T18:00:37.393578Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2509.10384"},"observation_digest":"sha256:e07c1d61c2aff16ec057f4476af886e72a41d505ddd4dba7a6a31b24ec7c70c9","observation_id":"d1e7a98a-a8c9-440d-a8da-dc8925ea71c5","resolution":{"observed_at":"2026-08-04T18:00:37.393578Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2511.22112","last_updated":"2025-11-27T05:05:29Z","snapshot_observed_at":"2026-07-06T22:37:08.086095Z","submitted_at":"2025-11-27T05:05:29Z","title":"Toward Data-Driven Surrogates of the Solar Wind with Spherical Fourier Neural Operator","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-05-17T04:28:07.806965Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2511.22112"},"observation_digest":"sha256:f0a9e856317c87567bc04c5a0bcf1a7730d460342ca9a3e121f2673b3d5a12d7","observation_id":"0bc7f050-cf83-4141-83c4-65c0cfcbbfce","resolution":{"observed_at":"2026-05-17T04:29:01.577905Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-03T10:03:08.114701Z","title":"Neural operator: Learning maps between function spaces.arXiv preprint arXiv:2108.08481,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2601.11428","last_updated":"2026-05-22T18:30:16Z","snapshot_observed_at":"2026-08-03T10:03:06.940199Z","submitted_at":"2026-01-16T16:47:44Z","title":"Diagnosing Failure Modes of Neural Operators Across Diverse PDE Families","version":7},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-03T10:03:08.114701Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2601.11428"},"observation_digest":"sha256:1ba1f8e9004eef2958ee9b7374c3ff5ccec174d8a9504e7327d173eff9632186","observation_id":"089473c7-acdf-48d8-8017-b2c163fc9a93","resolution":{"observed_at":"2026-08-03T10:03:08.114701Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-03T08:39:53.658327Z","title":"Kovachki, Z","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2601.17074","last_updated":"2026-07-27T14:35:04Z","snapshot_observed_at":"2026-08-03T08:39:52.356083Z","submitted_at":"2026-01-23T00:43:51Z","title":"Physics-Encoded Inverse Modeling for Arctic Snow Depth Estimation","version":5},"reference_index":2021,"source":"pdf_text","source_observed_at":"2026-08-03T08:39:53.658327Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2601.17074"},"observation_digest":"sha256:37305de10239e8a35137300455f0a5baad2a5a014994e3e9ba1613d9a16a752d","observation_id":"770e2f02-32e8-47e6-81c6-f30b2ed725a7","resolution":{"observed_at":"2026-08-03T08:39:53.658327Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-02T17:47:08.876587Z","title":"Nikola B","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2603.28791","last_updated":"2026-07-22T20:51:41Z","snapshot_observed_at":"2026-08-07T17:21:34.087930Z","submitted_at":"2026-03-21T23:14:13Z","title":"Learning 3D Hypersonic Flow with Physics-Enhanced Neural Fields: A Case Study on the Orion Reentry Capsule","version":2},"reference_index":2017,"source":"pdf_text","source_observed_at":"2026-08-02T17:47:08.876587Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2603.28791"},"observation_digest":"sha256:85bf1be128a2c50785ad6e899ea1b0b50d01c5a1c62996886e000e5b39c02248","observation_id":"6f14a7d7-4e29-43c5-a9a1-6025b4e9ea56","resolution":{"observed_at":"2026-08-02T17:47:08.876587Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2604.17922","last_updated":"2026-04-20T07:59:22Z","snapshot_observed_at":"2026-07-06T23:04:55.190916Z","submitted_at":"2026-04-20T07:59:22Z","title":"Optimal Linear Interpolation under Differential Information: application to the prediction of perfect flows","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-05-10T04:32:48.021389Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2604.17922"},"observation_digest":"sha256:f05ec6186f5e6286db15a5d25409cc6183bb43a13517504e720db0d4306b36fd","observation_id":"4bb34af7-2d61-4b35-a07d-30fbc1d9da79","resolution":{"observed_at":"2026-05-11T11:51:02.887767Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2604.25985","last_updated":"2026-04-28T17:08:25Z","snapshot_observed_at":"2026-08-02T14:31:27.993830Z","submitted_at":"2026-04-28T17:08:25Z","title":"Learning Neural Operator Surrogates for the Black Hole Accretion Code","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-07T15:28:38.494462Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2604.25985"},"observation_digest":"sha256:a8107cc0f9a5f383e3407fae888f62efbf31a8d6d5b381180631fbae7517640f","observation_id":"db4d474d-4d4a-4a05-a4ba-92c2bb20e277","resolution":{"observed_at":"2026-05-12T00:21:23.706098Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2604.26621","last_updated":"2026-04-29T12:46:00Z","snapshot_observed_at":"2026-08-07T00:19:55.648763Z","submitted_at":"2026-04-29T12:46:00Z","title":"Large-eddy simulation nets (LESnets) based on physics-informed neural operator for wall-bounded turbulence","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-05-07T10:58:07.460227Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2604.26621"},"observation_digest":"sha256:e7ad6c9f4da07d381b0f82128b3e80eb912f73be38038c8be9b48164dd084b3f","observation_id":"ab798e1b-4da5-49a8-a430-01c00b4238ff","resolution":{"observed_at":"2026-05-09T04:00:13.226916Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2604.27158","last_updated":"2026-04-29T20:04:20Z","snapshot_observed_at":"2026-08-02T10:11:32.769739Z","submitted_at":"2026-04-29T20:04:20Z","title":"Hybrid Fourier Neural Operator-Lattice Boltzmann Method","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-05-07T08:13:46.567661Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2604.27158"},"observation_digest":"sha256:63f976abf039dc99b2203f4e39fd818a4a9eb621164e5f5722db630dc19c6307","observation_id":"9a352f99-0b3f-43c7-a269-373f17867da5","resolution":{"observed_at":"2026-05-12T10:01:29.191030Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2605.07738","last_updated":"2026-05-08T13:46:28Z","snapshot_observed_at":"2026-07-06T23:20:06.574823Z","submitted_at":"2026-05-08T13:46:28Z","title":"Physics-Informed Reduced-Order Operator Learning for Hyperelasticity in Continuum Micromechanics","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-11T03:02:47.843748Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2605.07738"},"observation_digest":"sha256:9e810b19678b41b180059459678b2c37e7929e3f55f637213631890fabb98dd1","observation_id":"a7563a6a-68f8-4a24-8e23-9792fd5b8799","resolution":{"observed_at":"2026-05-11T03:05:52.639855Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2605.08170","last_updated":"2026-08-02T06:51:30Z","snapshot_observed_at":"2026-08-06T23:24:39.169338Z","submitted_at":"2026-05-04T22:15:21Z","title":"Quantitative Sobolev Approximation Bounds for Neural Operators with Empirical Validation on Burgers Equation","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-05-12T01:38:54.274354Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2605.08170"},"observation_digest":"sha256:11b98a3ea7f0e521d95f6d3ebd868e831fc53f393e3a4fb4c7e78554a73c9583","observation_id":"0577a301-314c-4ce4-a2e2-ed27a03db1d1","resolution":{"observed_at":"2026-05-12T01:46:14.665992Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-04T05:24:02.533981Z","title":"Neural operator: Learning maps between function spaces","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2605.08170","last_updated":"2026-08-02T06:51:30Z","snapshot_observed_at":"2026-08-06T23:24:39.169338Z","submitted_at":"2026-05-04T22:15:21Z","title":"Quantitative Sobolev Approximation Bounds for Neural Operators with Empirical Validation on Burgers Equation","version":2},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-04T05:24:02.533981Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2605.08170"},"observation_digest":"sha256:c4eb5c47e9ed6afaca415a7cd451de9fded0fcaf60755cc2e70909cdbc4cc1d7","observation_id":"b2825f0b-305f-4db1-ae0e-709b9d9f7a9b","resolution":{"observed_at":"2026-08-04T05:24:02.533981Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2605.28909","last_updated":"2026-05-27T17:18:39Z","snapshot_observed_at":"2026-08-07T21:49:17.996658Z","submitted_at":"2026-05-27T17:18:39Z","title":"Sequential Physics-Constrained Neural Operator Forward Modeling for the $\\textit{Norne}$ Reservoir System","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-06-29T14:37:05.393813Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2605.28909"},"observation_digest":"sha256:d83c4701ab0bfb6027c02bf333031e8d80b638d00549140f8cb2b6914b749361","observation_id":"8020b2c7-0eff-4682-828a-8711f7e8e7c7","resolution":{"observed_at":"2026-06-29T14:43:30.814908Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2606.08654","last_updated":"2026-06-07T14:49:37Z","snapshot_observed_at":"2026-08-08T20:05:37.837184Z","submitted_at":"2026-06-07T14:49:37Z","title":"Operator learning for the 2D incompressible Navier-Stokes equations: a conformal prediction approach in the data-scarce regime","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-06-27T18:39:56.578189Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2606.08654"},"observation_digest":"sha256:7d3789541e4a457b8cfa3f05a873a70e8feab7197980e046a8dc8d70f918e371","observation_id":"8a1d67db-173e-42a4-99b6-1a409fb035ed","resolution":{"observed_at":"2026-07-02T22:47:25.734752Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2606.09432","last_updated":"2026-06-08T12:42:10Z","snapshot_observed_at":"2026-07-06T23:48:48.962930Z","submitted_at":"2026-06-08T12:42:10Z","title":"Graph Mamba Operator: A Latent Simulator for Interacting Particle Systems","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-06-27T17:07:27.417845Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2606.09432"},"observation_digest":"sha256:417778ff7cd1872323d1520b5854bb1a944115775614d4f36edc57d3b6547cbb","observation_id":"7a68dcee-5982-4e44-9b3a-625f89151e7b","resolution":{"observed_at":"2026-07-03T00:37:29.962633Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2606.20771","last_updated":"2026-06-18T15:38:20Z","snapshot_observed_at":"2026-08-07T19:51:19.973545Z","submitted_at":"2026-06-18T15:38:20Z","title":"ELADO: Elliptic PDE Assessment Datasets for Operator Learning","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-26T18:20:00.248849Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2606.20771"},"observation_digest":"sha256:ce525b498328c1624c103f1a2981147b927907581199091bd401c475ea350a4a","observation_id":"83867a57-49bb-49a1-9e83-f420380419a3","resolution":{"observed_at":"2026-07-04T03:09:30.476831Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":"2108.08481","doi":"10.48550/arxiv.2108.08481","metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kovachki, Z","venue":"arXiv (Cornell University)","work_id":"78b4e0f6-bbe9-445b-886a-94d33230f448","year":2021},"citing_paper":{"arxiv_id":"2606.25259","last_updated":"2026-06-24T00:34:53Z","snapshot_observed_at":"2026-08-02T02:19:26.871201Z","submitted_at":"2026-06-24T00:34:53Z","title":"A Neural Surrogate Approach for Simulating Natural Convection Problems","version":1},"reference_index":98,"source":"pdf_text","source_observed_at":"2026-06-25T20:40:24.100365Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2606.25259"},"observation_digest":"sha256:5cd3aceb2efac17a6a17015e7a7c7e87f9be1682be4aded9a53718aee4cfbe5f","observation_id":"32be2990-fc75-4d23-8324-235d9fbcf085","resolution":{"observed_at":"2026-06-25T21:18:24.265402Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-08T07:38:14.145609+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-02T07:10:15.668361Z","title":"Journal of Machine Learning Research 24, 1–97","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13074","last_updated":"2026-07-12T20:04:39Z","snapshot_observed_at":"2026-08-08T05:31:26.457089Z","submitted_at":"2026-07-12T20:04:39Z","title":"When is the combined load identifiable from a stress-intensity profile? A coupled forward-inverse study on SIFBench finite-element data","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-02T07:10:15.668361Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2607.13074"},"observation_digest":"sha256:320fbbc6c4bf1888fa335e59c02768a98d0d2df1869e01b91c504c8d7cb36786","observation_id":"31970c1b-1e79-4d27-b105-ec6fecf51f0f","resolution":{"observed_at":"2026-08-02T07:10:15.668361Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-02T02:17:07.159977Z","title":"Neural operator: Learning maps between function spaces with applications to PDEs,","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.14394","last_updated":"2026-07-15T22:17:25Z","snapshot_observed_at":"2026-08-06T10:37:58.454127Z","submitted_at":"2026-07-15T22:17:25Z","title":"DRIFT: Direct Reduced Fourier Transforms for Distributed Spectral Neural Operators","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-02T02:17:07.159977Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2607.14394"},"observation_digest":"sha256:e0ada046997bc748d53d6fbe4094463e672c87129f8fae6280697b5ceee722e0","observation_id":"45037c94-c6cc-423f-978c-df46b14d5e62","resolution":{"observed_at":"2026-08-02T02:17:07.159977Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-01T06:09:01.761928Z","title":"Neural operator: Learning maps between function spaces.arXiv preprint arXiv:2108.08481,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.22004","last_updated":"2026-07-24T06:07:14Z","snapshot_observed_at":"2026-08-08T14:04:39.357267Z","submitted_at":"2026-07-24T06:07:14Z","title":"Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers","version":1},"reference_index":2001,"source":"pdf_text","source_observed_at":"2026-08-01T06:09:01.761928Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2607.22004"},"observation_digest":"sha256:d87686e99311c747ab2ef47bebd8d71414ad625655140fff839f4e80d42376cd","observation_id":"eeb4939a-a03e-4a91-aa8c-d7e2a6accdfa","resolution":{"observed_at":"2026-08-01T06:09:01.761928Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-07-31T01:28:50.733155Z","title":"Neural operator: Learning maps between function spaces.arXiv preprint arXiv:2108.08481,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25100","last_updated":"2026-07-27T21:58:13Z","snapshot_observed_at":"2026-08-07T08:20:14.884654Z","submitted_at":"2026-07-27T21:58:13Z","title":"Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-31T01:28:50.733155Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2607.25100"},"observation_digest":"sha256:c76eade733d25a22b94d6585ce539e9f770cc3aecc58093b4b48f3b83a68f354","observation_id":"54143cd1-341d-4100-b70c-ec769592ed0a","resolution":{"observed_at":"2026-07-31T01:28:50.733155Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-07-31T02:27:17.167700Z","title":"arXiv e-prints , keywords =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28604","last_updated":"2026-07-30T17:54:43Z","snapshot_observed_at":"2026-08-06T11:18:05.221988Z","submitted_at":"2026-07-30T17:54:43Z","title":"Cosmo-SPINN: Fuzzy Dark Matter Simulations with Physics-Informed Generative Networks","version":1},"reference_index":98,"source":"arxiv_source","source_observed_at":"2026-07-31T02:27:17.167700Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2607.28604"},"observation_digest":"sha256:a041e5c7c809c21dcace46a7ea164e3e7f03941d0aa880a8076388b5c0fa04b9","observation_id":"e069b584-2f4c-412b-9f3b-8ac1dfa9087a","resolution":{"observed_at":"2026-07-31T02:27:17.167700Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-04T19:54:15.550167Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.01839","last_updated":"2026-08-03T07:49:27Z","snapshot_observed_at":"2026-08-06T23:33:17.959732Z","submitted_at":"2026-08-03T07:49:27Z","title":"tFUSOperator: Operator Learning for Transcranial Focused Ultrasound Digital Twins","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-04T19:54:15.550167Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2608.01839"},"observation_digest":"sha256:43257c9c4935a1dbcd732d6ad67971707d436d0f03c0d025aed9e3a2cea5731e","observation_id":"9718d6a2-f21b-40e5-87f6-3695857158d9","resolution":{"observed_at":"2026-08-04T19:54:15.550167Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08481","snapshot_observed_at":"2026-08-06T18:32:35.100763Z","title":"Kovachki, Z","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.04708","last_updated":"2026-08-05T11:19:21Z","snapshot_observed_at":"2026-08-08T23:12:20.108480Z","submitted_at":"2026-08-05T11:19:21Z","title":"Benchmarking Multi-fidelity Neural Operators on Complex PDE Problems with Non-trivial Fidelity Differences","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T18:32:35.100763Z"},"links":{"cited_paper":"/paper/2108.08481","citing_paper":"/paper/2608.04708"},"observation_digest":"sha256:3ff3151b01fe15f6fcff77d5b8fbbb3f6167a86b1e0089c146e3b5ad7f744836","observation_id":"1f007116-23d8-4c08-a1a2-75621fd337ac","resolution":{"observed_at":"2026-08-06T18:32:35.100763Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2108.08481/citation-record","integrity":"/paper/2108.08481/integrity","json":"/paper/2108.08481/citation-record.json","paper":"/paper/2108.08481"},"outbound":[],"paper":{"arxiv_id":"2108.08481","last_updated":"2024-05-02T17:19:54Z","latest_version":6,"primary_category":"cs.LG","snapshot_observed_at":"2026-07-06T11:39:29.892520Z","submitted_at":"2021-08-19T03:56:49Z","title":"Neural Operator: Learning Maps Between Function Spaces"},"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 41 inbound Pith citation observations for arXiv:2108.08481."}