{"as_of":"2026-08-10T14:54:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:d49ff1d1149d94810f86e6ea1f416719aa4c733743f15bdd0cc35b71c846070c","coverage":[{"denominator":24,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":24,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-30T23:28:29.166212Z","state":"measured"},{"denominator":24,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":24,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+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/2607.23397/citation-record","integrity":"/paper/2607.23397/integrity","json":"/paper/2607.23397/citation-record.json","paper":"/paper/2607.23397"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T23:28:29.094965Z","title":"Allen-Zhu and Y","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.23397","last_updated":"2026-07-26T00:11:54Z","snapshot_observed_at":"2026-08-09T09:04:19.129940Z","submitted_at":"2026-07-26T00:11:54Z","title":"A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-30T23:28:29.094965Z"},"links":{"citing_paper":"/paper/2607.23397"},"observation_digest":"sha256:749676dff6fa017d7501d5270f387001367c9556fb6b1cb64efa4ea168170519","observation_id":"20d2af5b-5e77-4d31-a6a9-4e351ba6708f","resolution":{"observed_at":"2026-07-30T23:28:29.094965Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T23:28:29.098900Z","title":"Amari, N","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2607.23397","last_updated":"2026-07-26T00:11:54Z","snapshot_observed_at":"2026-08-09T09:04:19.129940Z","submitted_at":"2026-07-26T00:11:54Z","title":"A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-30T23:28:29.098900Z"},"links":{"citing_paper":"/paper/2607.23397"},"observation_digest":"sha256:9e05a7a97006e599dddc4a768f65637ece722848253cb626fbe134bdddcbb8ad","observation_id":"9208b43c-0793-426e-8768-eeb159a3fac5","resolution":{"observed_at":"2026-07-30T23:28:29.098900Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T23:28:29.102113Z","title":"Amari and N","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2607.23397","last_updated":"2026-07-26T00:11:54Z","snapshot_observed_at":"2026-08-09T09:04:19.129940Z","submitted_at":"2026-07-26T00:11:54Z","title":"A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-30T23:28:29.102113Z"},"links":{"citing_paper":"/paper/2607.23397"},"observation_digest":"sha256:a43f0ee8b2f82bcdedc2caebc547b23fcfa0917507db33084197455bbf070005","observation_id":"ce2decbc-14af-406b-909c-fc6e6fb8649f","resolution":{"observed_at":"2026-07-30T23:28:29.102113Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T23:28:29.105274Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.23397","last_updated":"2026-07-26T00:11:54Z","snapshot_observed_at":"2026-08-09T09:04:19.129940Z","submitted_at":"2026-07-26T00:11:54Z","title":"A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-30T23:28:29.105274Z"},"links":{"citing_paper":"/paper/2607.23397"},"observation_digest":"sha256:1199d99a6148580056849bfbe5fd49a3ffd5f831b6aead04616220cabb9e5193","observation_id":"3fec1bc2-4f19-458d-af4c-3436a3d68454","resolution":{"observed_at":"2026-07-30T23:28:29.105274Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T23:28:29.108856Z","title":"Aoyagi and K","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2607.23397","last_updated":"2026-07-26T00:11:54Z","snapshot_observed_at":"2026-08-09T09:04:19.129940Z","submitted_at":"2026-07-26T00:11:54Z","title":"A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-30T23:28:29.108856Z"},"links":{"citing_paper":"/paper/2607.23397"},"observation_digest":"sha256:3f6c6355967b68c8c56a57a8c62136023ccd3811c6296279ad9dd1b4a66218fe","observation_id":"3da90594-dfdf-4fec-8d11-ed5c423bbe17","resolution":{"observed_at":"2026-07-30T23:28:29.108856Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T23:28:29.112012Z","title":"Aoyagi and S","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2607.23397","last_updated":"2026-07-26T00:11:54Z","snapshot_observed_at":"2026-08-09T09:04:19.129940Z","submitted_at":"2026-07-26T00:11:54Z","title":"A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-30T23:28:29.112012Z"},"links":{"citing_paper":"/paper/2607.23397"},"observation_digest":"sha256:34816fca2ff2ebf00bff2964e37bc487c1ac41be16698cfb1dbbcbf32e3994d6","observation_id":"8447de5d-fde9-4a2d-b9fd-08115ecf2b19","resolution":{"observed_at":"2026-07-30T23:28:29.112012Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T23:28:29.115426Z","title":null,"venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2607.23397","last_updated":"2026-07-26T00:11:54Z","snapshot_observed_at":"2026-08-09T09:04:19.129940Z","submitted_at":"2026-07-26T00:11:54Z","title":"A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-30T23:28:29.115426Z"},"links":{"citing_paper":"/paper/2607.23397"},"observation_digest":"sha256:fe8c7ea102abe3c6d044207acf2bebb8fec73e203de0d8540023e7c2254633ec","observation_id":"256a33de-31a2-4c93-bced-6c91ad607f63","resolution":{"observed_at":"2026-07-30T23:28:29.115426Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T23:28:29.118401Z","title":"Chizat, E","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.23397","last_updated":"2026-07-26T00:11:54Z","snapshot_observed_at":"2026-08-09T09:04:19.129940Z","submitted_at":"2026-07-26T00:11:54Z","title":"A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-30T23:28:29.118401Z"},"links":{"citing_paper":"/paper/2607.23397"},"observation_digest":"sha256:a9bf63eb5a199c87b095b852c6aeceb7e08a99fc28a1c66d55fc9b9df520ce3d","observation_id":"9d5c572a-fda7-498f-a203-d4ac22f18d23","resolution":{"observed_at":"2026-07-30T23:28:29.118401Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2511.15419","last_updated":"2026-06-25T13:46:11Z","snapshot_observed_at":"2026-08-09T12:20:47.873275Z","submitted_at":"2025-11-19T13:18:29Z","title":"Singular Learning Theory for Factor Analysis","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2511.15419","snapshot_observed_at":"2026-07-30T23:28:29.121548Z","title":"Drton, E.Gross, , D","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.23397","last_updated":"2026-07-26T00:11:54Z","snapshot_observed_at":"2026-08-09T09:04:19.129940Z","submitted_at":"2026-07-26T00:11:54Z","title":"A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-30T23:28:29.121548Z"},"links":{"cited_paper":"/paper/2511.15419","citing_paper":"/paper/2607.23397"},"observation_digest":"sha256:ab359a9ed9cabc82ff8a14b5d8856dc400aa35e708fb0f52ffc372e06b6e3e87","observation_id":"c6f5acad-eda2-46e8-8b11-a1b927161df2","resolution":{"observed_at":"2026-07-30T23:28:29.121548Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T23:28:29.124794Z","title":"Ghorbani, S","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.23397","last_updated":"2026-07-26T00:11:54Z","snapshot_observed_at":"2026-08-09T09:04:19.129940Z","submitted_at":"2026-07-26T00:11:54Z","title":"A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-30T23:28:29.124794Z"},"links":{"citing_paper":"/paper/2607.23397"},"observation_digest":"sha256:54afc0304736f8cbfdfa31ecea172e3b18a34532ff9a904e8274474d83f68aca","observation_id":"98f64693-eca6-4ad3-b1d5-308a57d50659","resolution":{"observed_at":"2026-07-30T23:28:29.124794Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T23:28:29.127777Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.23397","last_updated":"2026-07-26T00:11:54Z","snapshot_observed_at":"2026-08-09T09:04:19.129940Z","submitted_at":"2026-07-26T00:11:54Z","title":"A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-30T23:28:29.127777Z"},"links":{"citing_paper":"/paper/2607.23397"},"observation_digest":"sha256:1aa3c9402c5a28b0e375e4b1d2f1c04ef4764b515746b6755d475ca7b255c4ed","observation_id":"47caa038-1953-4891-a802-c1cb2c177663","resolution":{"observed_at":"2026-07-30T23:28:29.127777Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.02364","last_updated":"2025-08-01T09:20:40Z","snapshot_observed_at":"2026-08-10T06:47:42.759048Z","submitted_at":"2024-02-04T06:23:05Z","title":"Loss Landscape Degeneracy and Stagewise Development in Transformers","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.02364","snapshot_observed_at":"2026-07-30T23:28:29.130740Z","title":"Hoogland, G","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.23397","last_updated":"2026-07-26T00:11:54Z","snapshot_observed_at":"2026-08-09T09:04:19.129940Z","submitted_at":"2026-07-26T00:11:54Z","title":"A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-30T23:28:29.130740Z"},"links":{"cited_paper":"/paper/2402.02364","citing_paper":"/paper/2607.23397"},"observation_digest":"sha256:97f3418835dee7122f6bccc75a11dfcaa43fd4f9936f4b4379429fee3c9d129c","observation_id":"8b167b22-37a8-411c-98b9-83b147e8fe58","resolution":{"observed_at":"2026-07-30T23:28:29.130740Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T23:28:29.133926Z","title":"Jacot, F","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.23397","last_updated":"2026-07-26T00:11:54Z","snapshot_observed_at":"2026-08-09T09:04:19.129940Z","submitted_at":"2026-07-26T00:11:54Z","title":"A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-30T23:28:29.133926Z"},"links":{"citing_paper":"/paper/2607.23397"},"observation_digest":"sha256:be146a6726e0feb5be40c74c34cc9f0da175c79fc7842d8212bebe21e692b781","observation_id":"60dcb9fc-25c7-4b61-98c2-148cac1a2206","resolution":{"observed_at":"2026-07-30T23:28:29.133926Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T23:28:29.136922Z","title":"Kurumadani","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.23397","last_updated":"2026-07-26T00:11:54Z","snapshot_observed_at":"2026-08-09T09:04:19.129940Z","submitted_at":"2026-07-26T00:11:54Z","title":"A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-30T23:28:29.136922Z"},"links":{"citing_paper":"/paper/2607.23397"},"observation_digest":"sha256:85b8206ed8104f2588a49ba86979707385b29b65923191eb1de5587ca87a572a","observation_id":"2197c168-a14b-4c11-a7e9-c05d5f1e81cb","resolution":{"observed_at":"2026-07-30T23:28:29.136922Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1711.00165","last_updated":"2018-03-03T00:45:00Z","snapshot_observed_at":"2026-08-04T10:06:19.819372Z","submitted_at":"2017-11-01T02:13:25Z","title":"Deep Neural Networks as Gaussian Processes","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1711.00165","snapshot_observed_at":"2026-07-30T23:28:29.139978Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.23397","last_updated":"2026-07-26T00:11:54Z","snapshot_observed_at":"2026-08-09T09:04:19.129940Z","submitted_at":"2026-07-26T00:11:54Z","title":"A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-30T23:28:29.139978Z"},"links":{"cited_paper":"/paper/1711.00165","citing_paper":"/paper/2607.23397"},"observation_digest":"sha256:560fc43945205e2128293a70f9e84a5d7531d8b76bb6498d0fc1285211d493c6","observation_id":"283d6811-5312-4ff4-9a28-ce004cf22bc5","resolution":{"observed_at":"2026-07-30T23:28:29.139978Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T23:28:29.143174Z","title":"Murata, S","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2607.23397","last_updated":"2026-07-26T00:11:54Z","snapshot_observed_at":"2026-08-09T09:04:19.129940Z","submitted_at":"2026-07-26T00:11:54Z","title":"A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-30T23:28:29.143174Z"},"links":{"citing_paper":"/paper/2607.23397"},"observation_digest":"sha256:59999d31a03ebab57fca3fd895990981bf756c6b1af80ef35259c86577065329","observation_id":"97ab2d2b-0013-41df-a321-3782cd7adc90","resolution":{"observed_at":"2026-07-30T23:28:29.143174Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T23:28:29.146005Z","title":"Neal.Bayesian learning for neural networks, volume 118","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2607.23397","last_updated":"2026-07-26T00:11:54Z","snapshot_observed_at":"2026-08-09T09:04:19.129940Z","submitted_at":"2026-07-26T00:11:54Z","title":"A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-07-30T23:28:29.146005Z"},"links":{"citing_paper":"/paper/2607.23397"},"observation_digest":"sha256:4e4960a422c82ba1e0a5d8556a76b73b473e03a1fec5204dfc5186f588184166","observation_id":"4be50055-3cbd-4508-b793-fe36c8fcd5ba","resolution":{"observed_at":"2026-07-30T23:28:29.146005Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T23:28:29.148668Z","title":"Watanabe","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2607.23397","last_updated":"2026-07-26T00:11:54Z","snapshot_observed_at":"2026-08-09T09:04:19.129940Z","submitted_at":"2026-07-26T00:11:54Z","title":"A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-07-30T23:28:29.148668Z"},"links":{"citing_paper":"/paper/2607.23397"},"observation_digest":"sha256:a43968843a5fcd6b0e6a009ccbf38e4b399bd5029c0b47845b0778f6f81fb3c6","observation_id":"3eccfa69-6fa4-4432-a44d-f40db4384fdd","resolution":{"observed_at":"2026-07-30T23:28:29.148668Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T23:28:29.151559Z","title":"Watanabe","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2607.23397","last_updated":"2026-07-26T00:11:54Z","snapshot_observed_at":"2026-08-09T09:04:19.129940Z","submitted_at":"2026-07-26T00:11:54Z","title":"A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-07-30T23:28:29.151559Z"},"links":{"citing_paper":"/paper/2607.23397"},"observation_digest":"sha256:cf67a334d7956aff8967747e859d44a37dfa817cbcb93e8bdcecef2a0ffcabbb","observation_id":"aeceb777-abe9-464d-90ad-adb6cfa1f211","resolution":{"observed_at":"2026-07-30T23:28:29.151559Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T23:28:29.154277Z","title":"Watanabe.Algebraic geometry and statistical learning theory","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.23397","last_updated":"2026-07-26T00:11:54Z","snapshot_observed_at":"2026-08-09T09:04:19.129940Z","submitted_at":"2026-07-26T00:11:54Z","title":"A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-07-30T23:28:29.154277Z"},"links":{"citing_paper":"/paper/2607.23397"},"observation_digest":"sha256:33ff32518ca640699f4fad881edcacc889c71ce695ec2beae1c5fdae60486541","observation_id":"3d0b1160-49c8-4853-bebf-094b686ec40d","resolution":{"observed_at":"2026-07-30T23:28:29.154277Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T23:28:29.157470Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.23397","last_updated":"2026-07-26T00:11:54Z","snapshot_observed_at":"2026-08-09T09:04:19.129940Z","submitted_at":"2026-07-26T00:11:54Z","title":"A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-07-30T23:28:29.157470Z"},"links":{"citing_paper":"/paper/2607.23397"},"observation_digest":"sha256:1c93d686ca303279f0bbcf4d94e0eb58f03cc3490c891b809a87476af239c6a5","observation_id":"b4278622-d035-492b-827a-b0302b02dcef","resolution":{"observed_at":"2026-07-30T23:28:29.157470Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T23:28:29.160446Z","title":"Yamazaki and S","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.23397","last_updated":"2026-07-26T00:11:54Z","snapshot_observed_at":"2026-08-09T09:04:19.129940Z","submitted_at":"2026-07-26T00:11:54Z","title":"A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-07-30T23:28:29.160446Z"},"links":{"citing_paper":"/paper/2607.23397"},"observation_digest":"sha256:9308d83db929d5996492d68d255e206daa266a7bf2e0a52bd86551a7a4232676","observation_id":"ba616a74-2637-4cd1-9cf7-581a241cb721","resolution":{"observed_at":"2026-07-30T23:28:29.160446Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T23:28:29.163504Z","title":"Yamazaki and S","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2607.23397","last_updated":"2026-07-26T00:11:54Z","snapshot_observed_at":"2026-08-09T09:04:19.129940Z","submitted_at":"2026-07-26T00:11:54Z","title":"A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-07-30T23:28:29.163504Z"},"links":{"citing_paper":"/paper/2607.23397"},"observation_digest":"sha256:2ca42b09180058a59f978d9681a1496646f980410e8a675da106b55e7f7a67aa","observation_id":"9820a4cd-f01f-4f08-9c51-130f373cd056","resolution":{"observed_at":"2026-07-30T23:28:29.163504Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T23:28:29.166212Z","title":"Yamazaki and S","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2607.23397","last_updated":"2026-07-26T00:11:54Z","snapshot_observed_at":"2026-08-09T09:04:19.129940Z","submitted_at":"2026-07-26T00:11:54Z","title":"A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-07-30T23:28:29.166212Z"},"links":{"citing_paper":"/paper/2607.23397"},"observation_digest":"sha256:3eaaf7ee22f841723090c63c43a87e0f18b6a8c8256f3ad22ee08ea706ce2164","observation_id":"86d529d8-3cce-4eb0-a94f-1355de2bac50","resolution":{"observed_at":"2026-07-30T23:28:29.166212Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.23397","last_updated":"2026-07-26T00:11:54Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-09T09:04:19.129940Z","submitted_at":"2026-07-26T00:11:54Z","title":"A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks"},"reference_resolution":{"displayed":24,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":24,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":24},"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":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 0 inbound Pith citation observations for arXiv:2607.23397."}