{"as_of":"2026-08-11T19:44:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:65711fe2efbf4866a6ba5203d5436cc6cc7432382c509bd7fd42e92146448347","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":5,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":5,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+00:00","state":"measured"},{"denominator":5,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":5,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T00:09:09.766953Z","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":"2026-07-04T07:59:40.351899Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2006.15733","last_updated":"2020-12-10T20:43:11Z","snapshot_observed_at":"2026-08-11T12:27:07.354039Z","submitted_at":"2020-06-28T22:24:51Z","title":"Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2006.15733","snapshot_observed_at":"2026-08-11T00:09:09.766953Z","title":"Two-layer neural networks for partial differential equa- tions: Optimization and generalization theory,","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2501.04023","last_updated":"2025-01-14T13:40:35Z","snapshot_observed_at":"2026-08-11T16:07:50.585864Z","submitted_at":"2024-12-27T20:16:04Z","title":"Approximation Rates in Fr\\'echet Metrics: Barron Spaces, Paley-Wiener Spaces, and Fourier Multipliers","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-11T00:09:09.766953Z"},"links":{"cited_paper":"/paper/2006.15733","citing_paper":"/paper/2501.04023"},"observation_digest":"sha256:15f9da5c0186f1dca7228bbb41af5a2b9cb54fb5bd7a43400ec26bd65d125416","observation_id":"e95dbadf-660b-4661-9cc4-a173a9e92ae2","resolution":{"observed_at":"2026-08-11T00:09:09.766953Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2006.15733","last_updated":"2020-12-10T20:43:11Z","snapshot_observed_at":"2026-08-11T12:27:07.354039Z","submitted_at":"2020-06-28T22:24:51Z","title":"Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2006.15733","snapshot_observed_at":"2026-08-09T18:57:13.596940Z","title":"and Yang, H","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2502.00488","last_updated":"2025-05-29T08:37:00Z","snapshot_observed_at":"2026-08-10T04:18:07.859517Z","submitted_at":"2025-02-01T16:26:53Z","title":"Learn Singularly Perturbed Solutions via Homotopy Dynamics","version":3},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-09T18:57:13.596940Z"},"links":{"cited_paper":"/paper/2006.15733","citing_paper":"/paper/2502.00488"},"observation_digest":"sha256:82ebf0d70d774aaa5a605b56d40d753068c63a4a52503386966723307c01ab11","observation_id":"0806837c-fb6e-4d3b-b2a1-0fd3c9787acd","resolution":{"observed_at":"2026-08-09T18:57:13.596940Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2006.15733","last_updated":"2020-12-10T20:43:11Z","snapshot_observed_at":"2026-08-11T12:27:07.354039Z","submitted_at":"2020-06-28T22:24:51Z","title":"Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2006.15733","snapshot_observed_at":"2026-08-06T16:47:35.571344Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2507.12766","last_updated":"2025-07-17T03:43:18Z","snapshot_observed_at":"2026-08-06T16:36:40.822146Z","submitted_at":"2025-07-17T03:43:18Z","title":"Layer Separation Deep Learning Model with Auxiliary Variables for Partial Differential Equations","version":1},"reference_index":2020,"source":"pdf_text","source_observed_at":"2026-08-06T16:47:35.571344Z"},"links":{"cited_paper":"/paper/2006.15733","citing_paper":"/paper/2507.12766"},"observation_digest":"sha256:d9390b84f394eb5226916d05431bfa760d0d62a6383587ebb5ffc4029804ae05","observation_id":"762840bb-80ed-4dc9-96e6-867398ea3e0e","resolution":{"observed_at":"2026-08-06T16:47:35.571344Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2006.15733","last_updated":"2020-12-10T20:43:11Z","snapshot_observed_at":"2026-08-11T12:27:07.354039Z","submitted_at":"2020-06-28T22:24:51Z","title":"Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2006.15733","snapshot_observed_at":"2026-08-06T15:23:02.176801Z","title":"Luo and H","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2507.16380","last_updated":"2025-07-22T09:24:22Z","snapshot_observed_at":"2026-08-09T23:02:07.636272Z","submitted_at":"2025-07-22T09:24:22Z","title":"Optimization and generalization analysis for two-layer physics-informed neural networks without over-parametrization","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-06T15:23:02.176801Z"},"links":{"cited_paper":"/paper/2006.15733","citing_paper":"/paper/2507.16380"},"observation_digest":"sha256:be3246bf401c7901a3b73867062b94fbb41f7e0e7a3d38550e017a93b1449143","observation_id":"e4b0cace-70de-4d28-bd44-e4e04a2c0570","resolution":{"observed_at":"2026-08-06T15:23:02.176801Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2006.15733","last_updated":"2020-12-10T20:43:11Z","snapshot_observed_at":"2026-08-11T12:27:07.354039Z","submitted_at":"2020-06-28T22:24:51Z","title":"Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory","version":2},"cited_work":{"arxiv_id":"2006.15733","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2006.15733","snapshot_observed_at":"2026-07-04T07:59:40.351899Z","title":null,"venue":null,"work_id":"ce3c7490-8f21-4c34-b45d-6acb851b48d9","year":2006},"citing_paper":{"arxiv_id":"2606.22150","last_updated":"2026-06-20T17:02:30Z","snapshot_observed_at":"2026-07-06T23:57:04.096779Z","submitted_at":"2026-06-20T17:02:30Z","title":"Parameterized Representations via Implicit Stochastic Modulation for High-Dimensional and High-Order Neural PDE Solvers","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-06-26T12:20:25.523371Z"},"links":{"cited_paper":"/paper/2006.15733","citing_paper":"/paper/2606.22150"},"observation_digest":"sha256:b250132ac72245ddd141477f72a700065a579699934ad0e6503f6cf11b5e0771","observation_id":"74560603-7629-4a9a-9392-013970fc3ef2","resolution":{"observed_at":"2026-07-04T07:59:40.353092Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2006.15733/citation-record","integrity":"/paper/2006.15733/integrity","json":"/paper/2006.15733/citation-record.json","paper":"/paper/2006.15733"},"outbound":[],"paper":{"arxiv_id":"2006.15733","last_updated":"2020-12-10T20:43:11Z","latest_version":2,"primary_category":"math.NA","snapshot_observed_at":"2026-08-11T12:27:07.354039Z","submitted_at":"2020-06-28T22:24:51Z","title":"Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory"},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 5 inbound Pith citation observations for arXiv:2006.15733."}