{"as_of":"2026-08-18T18:47:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fc16c96a9c5032e2cb8596052c25927cc32a3d6a5971b029d8642ae07fb01a9e","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":4,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":4,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+00:00","state":"measured"},{"denominator":4,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":4,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T23:41:59.534285Z","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":"2026-05-20T15:03:24.813382Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2107.07562","last_updated":"2021-07-15T18:49:20Z","snapshot_observed_at":"2026-08-16T18:09:42.974123Z","submitted_at":"2021-07-15T18:49:20Z","title":"On universal approximation and error bounds for Fourier Neural Operators","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2107.07562","snapshot_observed_at":"2026-08-06T23:41:59.534285Z","title":"On universal approximation and error bounds for Fourier Neural Operators, July 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2506.16918","last_updated":"2025-06-20T11:25:26Z","snapshot_observed_at":"2026-08-18T14:32:54.732234Z","submitted_at":"2025-06-20T11:25:26Z","title":"A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T23:41:59.534285Z"},"links":{"cited_paper":"/paper/2107.07562","citing_paper":"/paper/2506.16918"},"observation_digest":"sha256:58a3b8a6571bea17185e19ed1a4536ed7c8eb5b141c00aef676a955cba99bdea","observation_id":"77b1ff58-04c6-48ad-b43d-00420496923b","resolution":{"observed_at":"2026-08-06T23:41:59.534285Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2107.07562","last_updated":"2021-07-15T18:49:20Z","snapshot_observed_at":"2026-08-16T18:09:42.974123Z","submitted_at":"2021-07-15T18:49:20Z","title":"On universal approximation and error bounds for Fourier Neural Operators","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2107.07562","snapshot_observed_at":"2026-08-04T22:56:16.139524Z","title":"Kovachki, S","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.07084","last_updated":"2026-05-28T18:02:31Z","snapshot_observed_at":"2026-08-14T05:06:55.900841Z","submitted_at":"2025-09-08T18:00:03Z","title":"Fourier Neural Operators for Time-Periodic Quantum Systems: Learning Floquet Hamiltonians, Observable Dynamics, and Operator Growth","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-04T22:56:16.139524Z"},"links":{"cited_paper":"/paper/2107.07562","citing_paper":"/paper/2509.07084"},"observation_digest":"sha256:2fa4fda148a24c5efcb8263b64216b730c91cd67b606247a3b7c61db24ff2b98","observation_id":"ab186eeb-00c0-4d8e-a258-706cff291db8","resolution":{"observed_at":"2026-08-04T22:56:16.139524Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2107.07562","last_updated":"2021-07-15T18:49:20Z","snapshot_observed_at":"2026-08-16T18:09:42.974123Z","submitted_at":"2021-07-15T18:49:20Z","title":"On universal approximation and error bounds for Fourier Neural Operators","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2107.07562","snapshot_observed_at":"2026-08-03T15:14:42.079321Z","title":"Kovachki, Samuel Lanthaler, and Siddhartha Mishra","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2512.17884","last_updated":"2025-12-19T18:36:24Z","snapshot_observed_at":"2026-08-13T05:54:49.277118Z","submitted_at":"2025-12-19T18:36:24Z","title":"Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-03T15:14:42.079321Z"},"links":{"cited_paper":"/paper/2107.07562","citing_paper":"/paper/2512.17884"},"observation_digest":"sha256:eea8d8f7a8813d25d9f0a0c05ecee69d18e30eb8e9a42d8054d1ab9616f0097e","observation_id":"0423fb34-e6ff-4b20-b116-f6052df80bbd","resolution":{"observed_at":"2026-08-03T15:14:42.079321Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2107.07562","last_updated":"2021-07-15T18:49:20Z","snapshot_observed_at":"2026-08-16T18:09:42.974123Z","submitted_at":"2021-07-15T18:49:20Z","title":"On universal approximation and error bounds for Fourier Neural Operators","version":1},"cited_work":{"arxiv_id":"2107.07562","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2107.07562","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"On universal approximation and error bounds for fourier neural operators","venue":null,"work_id":"c7cfdb7d-96af-4c37-bcc3-bceba208a73a","year":2021},"citing_paper":{"arxiv_id":"2605.18905","last_updated":"2026-05-17T14:14:54Z","snapshot_observed_at":"2026-08-16T11:50:41.830369Z","submitted_at":"2026-05-17T14:14:54Z","title":"Stability and Discretization Error of State Space Model Neural Operators","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-05-20T14:58:34.478482Z"},"links":{"cited_paper":"/paper/2107.07562","citing_paper":"/paper/2605.18905"},"observation_digest":"sha256:9e95e3aab3656c0f5b3e2569d20e57fbb09c8a86f83dca756e0d70039d133593","observation_id":"0af1f9d8-a7b3-4ad8-856d-570ce05c1460","resolution":{"observed_at":"2026-05-20T15:03:24.815002Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2107.07562/citation-record","integrity":"/paper/2107.07562/integrity","json":"/paper/2107.07562/citation-record.json","paper":"/paper/2107.07562"},"outbound":[],"paper":{"arxiv_id":"2107.07562","last_updated":"2021-07-15T18:49:20Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-16T18:09:42.974123Z","submitted_at":"2021-07-15T18:49:20Z","title":"On universal approximation and error bounds for Fourier Neural Operators"},"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":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 4 inbound Pith citation observations for arXiv:2107.07562."}