{"as_of":"2026-08-12T08:34:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:6874c5ceb6d70834af702e3277ab47ab996b020d3adb475833a2834bef9613fa","coverage":[{"denominator":37,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":37,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T20:00:01.413267Z","state":"measured"},{"denominator":37,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":37,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2608.06843/citation-record","integrity":"/paper/2608.06843/integrity","json":"/paper/2608.06843/citation-record.json","paper":"/paper/2608.06843"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2411.04108","last_updated":"2024-11-06T18:36:21Z","snapshot_observed_at":"2026-08-09T22:43:57.281082Z","submitted_at":"2024-11-06T18:36:21Z","title":"Weighted Sobolev Approximation Rates for Neural Networks on Unbounded Domains","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.04108","snapshot_observed_at":"2026-08-10T20:00:01.160630Z","title":"Weighted Sobolev approximation rates for neural networks on unbounded domains.arXiv preprint arXiv:2411.04108, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.160630Z"},"links":{"cited_paper":"/paper/2411.04108","citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:ea8ed0c0e05f9e51a1321539282f90f9a364c913be9954083cce55cbd486e7c9","observation_id":"9f0d443f-ff5a-409f-8fa0-bcbce96b1ea0","resolution":{"observed_at":"2026-08-10T20:00:01.160630Z","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":"2026-08-10T20:00:02.209769Z","title":"Approximations with deep neural networks in Sobolev time-space.Anal","venue":null,"work_id":"d09c993a-f049-4411-a520-2a1181d4b257","year":2022},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.170039Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:e588fd200a237d1c0a259cee875da12816a4d1363551cc6ad791644c85d6df8e","observation_id":"8e5751f0-af9e-481f-b08f-2385bcfc677c","resolution":{"observed_at":"2026-08-10T20:00:02.216216Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:02.190723Z","title":"Breaking the curse of dimensionality with convex neutral networks.J","venue":null,"work_id":"1eb2a950-e23f-4e50-a7a3-f3f97d4e7861","year":2017},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.178448Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:d93927435c0c9a05f206e1d2b8db9113aa42cbfab6ca10a13fe5aaa85722312d","observation_id":"34ae0e28-8c32-4bcd-979f-f2ff30b1472d","resolution":{"observed_at":"2026-08-10T20:00:02.197100Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:02.171789Z","title":null,"venue":null,"work_id":"a03a6a72-e96b-40b8-af53-43e48d45e210","year":1993},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.187305Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:af0d7c08022772a795f71a9d134556f6224faaaafafad7136cdb2f190d4409e0","observation_id":"e8d27bb1-82d4-4491-80fa-e2a0de5f07c3","resolution":{"observed_at":"2026-08-10T20:00:02.178065Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:02.152726Z","title":"Analysis of Tikhonov regularization for function approximation by neural networks.Neural Networks, 16(1):79–90, 2003","venue":null,"work_id":"4a22f00e-2c40-47b2-9ab0-f4eb9ba04ac0","year":2003},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.193713Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:35e3cb8619aee8df10f3ecdaafdf4cb4f37aa39ab998516dac503cc48d08ed3d","observation_id":"20d30bd2-1550-4f64-b36b-b1f9d29a3184","resolution":{"observed_at":"2026-08-10T20:00:02.158298Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:02.133401Z","title":"A regularity theory for static Schrödinger equations onRd in spectral Barron spaces.SIAM J","venue":null,"work_id":"dc23818e-e670-43f1-85c2-fd7c832bf535","year":2023},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.201088Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:a84457ee0722ed164c837653c34fe18f19da6468b7b01ba4252aa77de62d93c5","observation_id":"e5cc8ce1-c38f-4d20-a03a-06012f39b931","resolution":{"observed_at":"2026-08-10T20:00:02.139870Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.06778","last_updated":"2026-05-16T00:05:58Z","snapshot_observed_at":"2026-08-07T07:05:26.657640Z","submitted_at":"2025-07-09T12:10:58Z","title":"Functional analysis and partial differential equations in spectral Barron spaces","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.06778","snapshot_observed_at":"2026-08-10T20:00:01.209020Z","title":"Functional analysis and partial differential equations in spectral Barron spaces.arXiv:2507.06778; to appear at SIAM J","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.209020Z"},"links":{"cited_paper":"/paper/2507.06778","citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:563255016bff8ef00995520dbb282c860ca9407884345dc71fd58f7283e202e6","observation_id":"514acb82-c015-4608-911f-502619594868","resolution":{"observed_at":"2026-08-10T20:00:01.209020Z","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":"2026-08-10T20:00:02.112472Z","title":"Cohn.Measure theory","venue":null,"work_id":"f56c5fc2-7624-4aee-8ddb-4a5d58ee99d6","year":2013},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.214932Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:93e4b81b54d4f86a5486c075c90cfa0a70a70c2957e5ec218a3c7dab13e4d660","observation_id":"67351a61-3bc9-4e8e-8e91-6be3a5588a48","resolution":{"observed_at":"2026-08-10T20:00:02.118598Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:02.092735Z","title":"Approximation by superpositions of a sigmoidal function.Math","venue":null,"work_id":"84cec764-b2de-4544-bf8a-1e72cbbdc0ff","year":1989},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.220313Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:c582c136f86ecffd49d42a7839dc020f57f06e5d9126ae5b2043ea8d5833ea0f","observation_id":"67a1f26c-f8f4-435a-bf3e-024d428f0234","resolution":{"observed_at":"2026-08-10T20:00:02.098936Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:02.071731Z","title":"Neural network approximation.Acta Numer., 30:327–444, 2021","venue":null,"work_id":"7054ab51-2f98-4191-92d6-5455aba60f0f","year":2021},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.227582Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:323c701704d85b0fa2ba095e8ea32242dadc376f02cfb4014b938503602261ce","observation_id":"a3436e75-a999-427f-900d-71c96540a037","resolution":{"observed_at":"2026-08-10T20:00:02.078114Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:02.053169Z","title":"The Barron space and the flow-induced function spaces for neural network models.Constr","venue":null,"work_id":"eaef3147-158b-4789-a5cb-ebdf3b1525fd","year":2022},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.237781Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:595f0e35e2eb73dae24a684150ea5617acbb6735debacd233bac51f223ffd717","observation_id":"d5664784-e7a1-40b7-8bc6-086be01493fb","resolution":{"observed_at":"2026-08-10T20:00:02.058699Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:02.035781Z","title":"Engl, Martin Hanke, and Andreas Neubauer.Regularization of inverse problems","venue":null,"work_id":"64cb987d-4255-4f8f-b878-ebd61474c126","year":1996},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.244556Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:a41ec78a206f6c76d915e3ee0676d178c3980d114774e937b47fde5816fe46a7","observation_id":"479580c3-d1f6-4710-bdb3-3a7fbbda8073","resolution":{"observed_at":"2026-08-10T20:00:02.040875Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:02.019233Z","title":"Approximation spaces of deep neural networks.Constr","venue":null,"work_id":"cbdf122c-1c3c-438e-acde-2a90e0c1a491","year":2022},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.253315Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:411ebfe6b42ef31b219a2d1c6d2e8be50367beb42683cbdb5e054753b39ad2d1","observation_id":"0a4639bd-f82b-451c-96ea-5521ad0676c9","resolution":{"observed_at":"2026-08-10T20:00:02.024930Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:02.002231Z","title":"Schwenninger, and Christoph Brune","venue":null,"work_id":"432050b5-1c07-4214-b5c5-9f7c1fc9ebd6","year":2024},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.260423Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:b97b624636a3d1080d23b65050a7c7691f0057b8a9bc113b2b174f2be974e945","observation_id":"3dc86fbd-1474-4c55-8927-b51c9f917ae3","resolution":{"observed_at":"2026-08-10T20:00:02.007954Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.267672Z","title":"Approximation capabilities of multilayer feedforward networks.Neural Networks, 4(2):251–257, 1991","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.267672Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:586aad5409c3b41e5171d9eb51a301e2c522689638fcf5f92fe2a7514444b511","observation_id":"4219ae39-0d7d-4ec4-a8ad-381f625a815a","resolution":{"observed_at":"2026-08-10T20:00:01.267672Z","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":"2026-08-10T20:00:01.972131Z","title":"Deep neural networks with ReLU-sine-exponential activations break curse of dimensionality in approximation on Hölder class.SIAM J","venue":null,"work_id":"eeb557aa-c462-46aa-a134-0662b49a1cc7","year":2023},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.273145Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:2592f1f711b332620595b0a841dc75a4f05661c204e779e260e0a80bc581e561","observation_id":"58ccef6d-1b43-486d-bcf8-6246de01097a","resolution":{"observed_at":"2026-08-10T20:00:01.977983Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.956132Z","title":"Klusowski and Andrew R","venue":null,"work_id":"9dd46742-f9fe-4a06-81d5-c3b96fe954c8","year":2018},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.282603Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:dd76935eaae05e4acbd6fc6d4c3e178a8fe7e6f580fb0a5c611dd8558f046d21","observation_id":"cf467cef-c16b-4b7f-87af-218b2d486d72","resolution":{"observed_at":"2026-08-10T20:00:01.961068Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.292305Z","title":"Deep learning.Nature, 521(7553):436–444, May 2015","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.292305Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:b891486108e8406e5d1d730f10e57433a74922ee2fd0ab15652d65647cee75d3","observation_id":"9d150868-6019-4213-83e0-e059ffadd54f","resolution":{"observed_at":"2026-08-10T20:00:01.292305Z","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":"2026-08-10T20:00:01.928062Z","title":"Pereverzev","venue":null,"work_id":"c79854d5-e4e1-4378-b5df-9129b3d408b7","year":2024},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.298607Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:71999ac74cb92c8f5f8d33f4b3f0805610816e7c9af3e772a0716c5bec527262","observation_id":"92e943c8-618b-4ae3-bd80-6aaea644507a","resolution":{"observed_at":"2026-08-10T20:00:01.933246Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.911614Z","title":"Spectral Barron space for deep neural network approximation","venue":null,"work_id":"678d81e4-5dc4-4424-a2bf-2236857494c0","year":2025},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.304300Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:81d61146ca70b01b50de7ae03802a71cfad5560baa3befd957ac65e5b14bc8b6","observation_id":"1c8680ec-4914-431a-b56e-30dcab36a47e","resolution":{"observed_at":"2026-08-10T20:00:01.916868Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.312423Z","title":"Interpolation and inverse problems in spectral Barron spaces","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.312423Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:89b3622b0517ceba24c55b44ebe4d8493d15a7f036bc7f64f8df701c982fd780","observation_id":"8170ec7e-c1ee-4aaa-a374-b8ef561bd1cc","resolution":{"observed_at":"2026-08-10T20:00:01.312423Z","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":"2026-08-10T20:00:01.895007Z","title":"Pereverzev.Regularization theory for ill-posed problems, volume 58","venue":null,"work_id":"87a91b72-850f-4ad6-8671-50ea03b88f18","year":2013},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.317983Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:0147924c19848b74391b0b2c26f67b57073d632829987b373ac26b7e93890c88","observation_id":"2beae09d-f5ea-4534-8e71-a43862fe5675","resolution":{"observed_at":"2026-08-10T20:00:01.900574Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.875831Z","title":"A logical calculus of the ideas immanent in nervous activity (1943)","venue":null,"work_id":"81583e9d-4434-483d-8644-6a757a88f794","year":1943},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.324669Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:82ca1b1e4876ba18242b72a8ff790ad9d5fb6eaef83b7b25e3a575ba4ffd5029","observation_id":"3faaf871-ca4a-4e94-a34e-4990a9d1fd9e","resolution":{"observed_at":"2026-08-10T20:00:01.880920Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.860456Z","title":"A new function space from Barron class and application to neural network approximation.Commun","venue":null,"work_id":"9d791e52-86a7-4199-a1e4-e9399b8da334","year":2022},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.331103Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:f63f8ad480a622525240a92b5dd1bfa56e07ca0aa5227164fe6ebffd5b064862","observation_id":"7c7aa1f8-f9b8-42d3-85a6-031966d44a03","resolution":{"observed_at":"2026-08-10T20:00:01.865661Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.843843Z","title":null,"venue":null,"work_id":"a8a97cf2-17e5-4bcf-907e-1e0b2da685b6","year":1996},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.337673Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:530118d81fb34bb5be064dac199bbf5696773dbcbad44c4e7c6f3fb79830c848","observation_id":"7f22574c-2a5b-4f17-a381-96575048ca62","resolution":{"observed_at":"2026-08-10T20:00:01.848768Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.826923Z","title":null,"venue":null,"work_id":"e4ef9ca0-2e8c-474b-b485-ad481792500b","year":2021},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.342847Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:8289d39740525540086a49e4b82ab3e7af8cf6ce5a00ea38e4152bb547b5b9f0","observation_id":"05c1584e-7f2f-4f64-906f-d70d467bf543","resolution":{"observed_at":"2026-08-10T20:00:01.831873Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.804386Z","title":"Longman Scientific & Technical, Harlow, 1993","venue":null,"work_id":"2046982e-ef38-45f1-a820-614148f177c5","year":1993},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.348198Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:673058a59d29a50d286de44cd549e57ae34a4d061375a3c8c5f1f800bed83aa8","observation_id":"4ad39eb6-084e-4146-ab47-0eb7278d28cc","resolution":{"observed_at":"2026-08-10T20:00:01.811896Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.785662Z","title":"The perceptron: a probabilistic model for information storage and orga- nization (1958)","venue":null,"work_id":"3096b70f-beae-4aa8-b4f1-4e00cc2df4c7","year":1958},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.353821Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:d2268afdc751cd4b61d39c53a15773dec52932dd70f81426381a3fb93b34a68f","observation_id":"53219cb2-5348-4446-bb8c-4b09c2ef666d","resolution":{"observed_at":"2026-08-10T20:00:01.791975Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.767004Z","title":"Siegel and Jinchao Xu","venue":null,"work_id":"d1c5f6db-8f2c-4a5e-a7f6-e2a2e1b1bea2","year":2020},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.359410Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:96a9cfc26091b9c8ec9ca2d6fc8c379e9c033f97700d40ff72ba1a990481d1f5","observation_id":"8f1f9d6e-c406-4a82-a9a2-44ff152598a7","resolution":{"observed_at":"2026-08-10T20:00:01.772217Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.748708Z","title":"Siegel and Jinchao Xu","venue":null,"work_id":"c8706e9a-28d7-4709-b37f-668ad9d6567f","year":2022},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.364298Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:31b39bec6e5c7dcae343717faee856ca507bd48a1b2505a2d442c43fd27d01fe","observation_id":"1569c073-242a-460c-8357-cd0efc995d9c","resolution":{"observed_at":"2026-08-10T20:00:01.754661Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.730170Z","title":"Siegel and Jinchao Xu","venue":null,"work_id":"df56cba2-3069-44aa-893a-3bdb88506571","year":2023},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.370285Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:ee2b832cba5f3405db5e430891033897952ec42b5318dda51b3af8b0f58183ea","observation_id":"71744ada-ef9e-498d-afbc-0c490f6c9b8a","resolution":{"observed_at":"2026-08-10T20:00:01.735833Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.711866Z","title":"Siegel and Jinchao Xu","venue":null,"work_id":"256ad381-1849-4a21-a6d7-a0653fc87c3f","year":2024},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.376245Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:7b4e3500c0bfaeb24e4942cc4e3c5a5b21b1d44c4e591b24227625caa1dc5d9e","observation_id":"51b12a8c-bae7-45e6-8355-458fa47b9a11","resolution":{"observed_at":"2026-08-10T20:00:01.717471Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.682769Z","title":"Implicit neural representations with periodic activation functions","venue":null,"work_id":"fc0b2c25-e3a1-4e81-aff3-fe1b6bc0681c","year":2020},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.383019Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:c8e7f84bbed13ca4d2b2e25ef7877948d97d3530ebe82c5cc5d553f23ac32306","observation_id":"cd5ecba6-e2e6-404d-a08d-e1bab533308a","resolution":{"observed_at":"2026-08-10T20:00:01.691050Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.661710Z","title":"Embedding inequalities for Barron-type spaces.J","venue":null,"work_id":"7ae88621-b046-4c60-999d-838daf1f3ffa","year":2023},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.389325Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:bb3368e16a37c1eecaa8b5a7246524b0c4fdb25e50d89a7d81ba4a42c7f42ba4","observation_id":"7ae1ae9f-13b9-4c93-96ed-41fbb2258786","resolution":{"observed_at":"2026-08-10T20:00:01.667198Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.640287Z","title":"Finite neuron method and convergence analysis.Commun","venue":null,"work_id":"b3b13309-2453-401f-a912-d7260cb6330f","year":2020},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.397956Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:120cc9d93ef4efe50872df5d70ebcbf2dd7b3fb471dda695a95718650263ad22","observation_id":"396f2e50-09fe-4658-88bb-2226429af796","resolution":{"observed_at":"2026-08-10T20:00:01.647085Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.404048Z","title":"Error bounds for approximations with deep ReLU networks.Neural Networks, 94:103–114, 2017","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.404048Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:e0f696347b7107decd992de8fda63bc0bc98d8f577c63d65df436a7dafabbe2d","observation_id":"edfd1d0d-71dc-4e53-a0eb-ee8bb91a3278","resolution":{"observed_at":"2026-08-10T20:00:01.404048Z","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":"2026-08-10T20:00:01.608271Z","title":"Universality of deep convolutional neural networks.Appl","venue":null,"work_id":"a51a06c4-cb9a-4815-b743-b3472b45df74","year":2020},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.413267Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:03a7711133fab0788539fd3c6a2dabceadd4f6d879c1452d8a979c1ac8af4edc","observation_id":"98703297-2cdf-499a-9fa1-6bbe89347188","resolution":{"observed_at":"2026-08-10T20:00:01.615855Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-12T08:10:44.084657Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks"},"reference_resolution":{"displayed":37,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":9,"verified_exact":0,"verified_fuzzy":28},"total_outbound_references":37},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2608.06843."}