{"as_of":"2026-08-07T19:46:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:b6ef4c6071cd2e2009fab05da16099ff6c1b07585ccc7b576920867bf398d651","coverage":[{"denominator":35,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":35,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T03:14:40.031214Z","state":"measured"},{"denominator":35,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":35,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+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/2607.25200/citation-record","integrity":"/paper/2607.25200/integrity","json":"/paper/2607.25200/citation-record.json","paper":"/paper/2607.25200"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2310.17813","last_updated":"2024-05-14T00:10:33Z","snapshot_observed_at":"2026-07-06T16:39:16.652626Z","submitted_at":"2023-10-26T23:17:39Z","title":"A Spectral Condition for Feature Learning","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2310.17813","snapshot_observed_at":"2026-08-01T03:14:39.925495Z","title":"and Bernstein, Jeremy , month = may, year =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:39.925495Z"},"links":{"cited_paper":"/paper/2310.17813","citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:0c351bdd4b8b61c1bd6412fb814677862d8890eeb18a4b8de5d7eb722b06aa95","observation_id":"2c8999f1-332a-4ab8-812f-62fb0759ebc4","resolution":{"observed_at":"2026-08-01T03:14:39.925495Z","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":"2026-08-01T03:14:39.929490Z","title":", month = jul, year =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:39.929490Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:d1f2b07258230cf34ff724a0d2dbfef6b725838a7ce0d49c64726e89d16d736a","observation_id":"2f05a4e0-72a1-4ace-a27d-f5ce17d3b243","resolution":{"observed_at":"2026-08-01T03:14:39.929490Z","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":"2026-08-01T03:14:39.934048Z","title":"Proceedings of the IEEE International Conference on Computer Vision (ICCV) , month =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:39.934048Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:ac9a89418988d7660cb26d5c74a5ade41cdba2582bf2ed11b3141ad322f03fe5","observation_id":"36718faa-49bd-46ca-982b-51f3f1e8b3d7","resolution":{"observed_at":"2026-08-01T03:14:39.934048Z","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":"2026-08-01T03:14:39.937135Z","title":"2026 , eprint=","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:39.937135Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:3feabe85a3e7a2b11d8e2d50bbf19e9e95e45f6f8b0d968ac07065eec7ff72ce","observation_id":"0bde6a8f-3dba-48fa-a79a-92bb68cbd797","resolution":{"observed_at":"2026-08-01T03:14:39.937135Z","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":"2026-08-01T03:14:39.940192Z","title":"Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics , pages =","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:39.940192Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:9078fa54e9579ebf589299d3f7572dea327eb38a9b80fece3eb8539d4c97f3eb","observation_id":"044cc3e0-2c00-4b3f-a88b-aa147a3e12b2","resolution":{"observed_at":"2026-08-01T03:14:39.940192Z","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":"2026-08-01T03:14:39.943517Z","title":"Journal of the ACM (JACM) , author =","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:39.943517Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:636dc455fd4e08b78055c664ea8be065e6701e6d0a13a263f3f74399cc4cae4e","observation_id":"debd3ef2-ef8c-443d-868c-d01450cf784b","resolution":{"observed_at":"2026-08-01T03:14:39.943517Z","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":"2026-08-01T03:14:39.946656Z","title":"Failures of","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:39.946656Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:ce073094f2028b87670d2b07b555b00bb511ceaf07b8368bdbef1b7f00fdc52f","observation_id":"42853685-dbf3-48e2-a1cf-85c640374437","resolution":{"observed_at":"2026-08-01T03:14:39.946656Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2607.03347","last_updated":"2026-07-03T14:02:42Z","snapshot_observed_at":"2026-08-04T04:21:48.715795Z","submitted_at":"2026-07-03T14:02:42Z","title":"The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning","version":1},"cited_work":{"arxiv_id":"2607.03347","doi":"10.48550/arxiv.2607.03347","metadata_source":"pith","pith_arxiv_id":"2607.03347","snapshot_observed_at":"2026-08-01T06:16:24.888925Z","title":"The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning","venue":"cs.LG","work_id":"9b7ec80b-d261-4351-8137-dc467840761e","year":2026},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:39.949582Z"},"links":{"cited_paper":"/paper/2607.03347","citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:0011f73d1578fd48702e770e5fd3d2233fb28702f72e1617d9ef3b1034d55107","observation_id":"1b1e3e37-0966-4b0d-a65c-e758d6955df8","resolution":{"observed_at":"2026-08-01T03:19:17.644733Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-01T03:14:39.952843Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:39.952843Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:9a7c48c3450142c0f9e3665e8544190a1849c5dcb22c1426160ac189bffdf5ef","observation_id":"344be888-409d-417c-972c-6e0a6a185bf5","resolution":{"observed_at":"2026-08-01T03:14:39.952843Z","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":"2026-08-01T03:14:39.955941Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:39.955941Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:f31ab61fae9f4cd310a38d642f97aa6533b12c0a51151c3cf50373d71d36ccec","observation_id":"f7fa04bf-0244-41ad-bca1-efbaf514f164","resolution":{"observed_at":"2026-08-01T03:14:39.955941Z","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":"2026-08-01T03:14:39.959367Z","title":"and Favero, Alessandro and Wyart, Matthieu , month = jul, year =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:39.959367Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:88120a21c4156c7bfa29282c4a77b51eebeb6501771ec7fb8e7ad99f97524dd2","observation_id":"d9ac52cf-1702-4ce6-aa51-6197955b5d30","resolution":{"observed_at":"2026-08-01T03:14:39.959367Z","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":"2601.00455","doi":"10.48550/arxiv.2601.00455","metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"arXiv (Cornell University)","work_id":"180e6f0e-09a6-4641-8178-2556f6cb8e3c","year":null},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:39.962699Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:10247dfb02ac709fbe2b6f2ef6a2f5019b7acd32db0ef626ec15421624cbb060","observation_id":"6db83150-6de6-4c47-a8ee-ed2ade99d7e3","resolution":{"observed_at":"2026-08-01T03:19:17.575477Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-01T03:14:39.965736Z","title":"What can","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:39.965736Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:95fa6501bfabda3354a4e0e51ba571167d54ce69e626a05540125e3201fc63e5","observation_id":"56336011-ffbb-4dd8-80d8-a004b88963cf","resolution":{"observed_at":"2026-08-01T03:14:39.965736Z","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":"2026-08-01T03:14:39.968482Z","title":"Backward","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:39.968482Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:017b099cbc454c06c6b1ef0490bb29e8cd1f721869d22efc8a1611f737ae0ba7","observation_id":"7c7d107d-f67b-4dd8-87a2-d6ec63c9f3b3","resolution":{"observed_at":"2026-08-01T03:14:39.968482Z","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":"2026-08-01T03:14:39.971256Z","title":", month = oct, year =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:39.971256Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:32a7093d4dcdfdc64119397f194022aff3585f548eb6477adbb2d0561179020c","observation_id":"2c28ab14-5f02-4905-bbc3-b3b56951d99c","resolution":{"observed_at":"2026-08-01T03:14:39.971256Z","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":"2026-08-01T03:14:39.974436Z","title":"International Conference on Representation Learning , author =","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:39.974436Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:1de5cddf70f671047383942e367b58675cc3ce791cadea003c244daf322cc974","observation_id":"3f0dbac9-8fdb-491f-bb42-2a4074628006","resolution":{"observed_at":"2026-08-01T03:14:39.974436Z","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":"2026-08-01T03:14:39.977392Z","title":"The merged-staircase property: a necessary and nearly sufficient condition for","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:39.977392Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:660d62ebb4c91385c02d8694716497e4c399dc342f6387d085563622c42b7898","observation_id":"4432163e-ba38-4c3f-8126-90e40333c1f3","resolution":{"observed_at":"2026-08-01T03:14:39.977392Z","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":"2026-08-01T03:14:39.980193Z","title":"The staircase property:","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:39.980193Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:e3b181d2916323e42458e0eeedef1f847318f85cfccee7407c4a693093a88feb","observation_id":"8d6f5ba3-64f7-4899-9a8c-c6fa797c25cc","resolution":{"observed_at":"2026-08-01T03:14:39.980193Z","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":"2026-08-01T03:14:39.983152Z","title":"2024 , eprint=","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:39.983152Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:099c005b9a4cec38d54300f640b1936ef5f883cf5de9352edc49a271df2682ab","observation_id":"57bd9f5d-f352-4fdc-9b2a-a3b5f24c9a6c","resolution":{"observed_at":"2026-08-01T03:14:39.983152Z","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":"2026-08-01T03:14:39.986185Z","title":"Proceedings of","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:39.986185Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:68e257acb5543ce371cba4968583eeaf5f0389adfc6c01597037bbdcf8eecda8","observation_id":"71184ade-1965-4948-82bf-0c0ce22eb199","resolution":{"observed_at":"2026-08-01T03:14:39.986185Z","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":"2026-08-01T03:14:39.989334Z","title":", editor =","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:39.989334Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:a2e318eb29c55bcaa586cc8bf6dea6603d575a3556f720fb7169fa1f6a42c119","observation_id":"6500dea9-5215-446c-848d-677c5f977298","resolution":{"observed_at":"2026-08-01T03:14:39.989334Z","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":"2026-08-01T03:14:39.992099Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:39.992099Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:994a21c5b1f1932b7aada4411c37910e538e897065d35a407fe0fe8924315bb6","observation_id":"844dfde8-5dd7-42c2-8f1a-b70d6a858889","resolution":{"observed_at":"2026-08-01T03:14:39.992099Z","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":"2026-08-01T03:14:39.994962Z","title":"Optimization-","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:39.994962Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:378cd240321c8965f971321233940aebf0c5d7d0cdf162dfbf6b11c817308110","observation_id":"7cee90bf-3dc3-4061-87b1-e733e9ea1104","resolution":{"observed_at":"2026-08-01T03:14:39.994962Z","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":"2026-08-01T03:14:39.997847Z","title":"Provable","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:39.997847Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:9251f4ca5df5dc2e34cc454371e53319034f5a59e1ba97202acee6d7ac804e94","observation_id":"c9e27c70-7663-4d52-befe-f492442282a5","resolution":{"observed_at":"2026-08-01T03:14:39.997847Z","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":"2026-08-01T03:14:40.001111Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:40.001111Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:4d0958b8fa49f8c71b3416822b6946a3bdc20ddd9d342fd0fb9a95b5ef1bf492","observation_id":"551ae528-be24-4892-84db-a923d8f14ec9","resolution":{"observed_at":"2026-08-01T03:14:40.001111Z","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":"2026-08-01T03:14:40.004344Z","title":"Journal of Machine Learning Research , author =","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:40.004344Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:d8c4f92c4bdd2610932144a7c4ea07f451ca92e3266b46a9d165a06242951956","observation_id":"a3bf6034-6711-44cb-87cd-b19957a20be0","resolution":{"observed_at":"2026-08-01T03:14:40.004344Z","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":"2026-08-01T03:14:40.007385Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:40.007385Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:6c35f9e2579265c2a219bc15775e225b55cb47faa9affcd5adf2da8bc1fb1711","observation_id":"9bfd6638-3f9b-4daa-9e16-0f91ee76e557","resolution":{"observed_at":"2026-08-01T03:14:40.007385Z","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":"2026-08-01T03:14:40.010302Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:40.010302Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:6ca186c47eab040f0b0fcc59180d88e1637cffec431dde1660461191534865c9","observation_id":"2b07e3af-6402-47b9-87a0-9f01ba1f855f","resolution":{"observed_at":"2026-08-01T03:14:40.010302Z","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":"2026-08-01T03:14:40.013119Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:40.013119Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:cdd01cf5db7cc732c8f1723855477b6782b1c7ba7a59f55c24d321d7e7fdfd43","observation_id":"96d0d7b5-cfa3-49b1-8a29-842f65518265","resolution":{"observed_at":"2026-08-01T03:14:40.013119Z","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":"2026-08-01T03:14:40.015977Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:40.015977Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:f631a25cf16be97db4c08fb0ab62e7196196c50a16bb03bdeba57ee96ed4b241","observation_id":"1c271235-2791-4120-8cd7-649eaa3fed67","resolution":{"observed_at":"2026-08-01T03:14:40.015977Z","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":"2026-08-01T03:14:40.019238Z","title":"benefits of depth in neural networks , volume =","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:40.019238Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:5cdbf2740e70cfac46fe05f40b1d97755f5a8a50efa8c35dfb9f1ec78198dfa3","observation_id":"a7a496f2-6d6b-4d4d-ab91-4d03cb68ba5b","resolution":{"observed_at":"2026-08-01T03:14:40.019238Z","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":"2026-08-01T03:14:40.022027Z","title":", year =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:40.022027Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:f06199fad68c21acf06daef01299b8ce29ff7611955aa2590666c2be5fa00c24","observation_id":"3288a254-eae1-40df-a106-5853b7b05e26","resolution":{"observed_at":"2026-08-01T03:14:40.022027Z","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":"2026-08-01T03:14:40.025011Z","title":", year =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:40.025011Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:13362f54e515e00e9f5f77ab39afaa501c11511140c228ab572ae8f2d30d3f37","observation_id":"ff8756fd-2eea-4e94-9e2b-69daf28b49f6","resolution":{"observed_at":"2026-08-01T03:14:40.025011Z","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":"2026-08-01T03:14:40.028139Z","title":"Concentration inequalities: a nonasymptotic theory of independence , isbn =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:40.028139Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:97a35c2fdfbbfc359ade81215747cee38e6b33dce6524e9a976d70aa957c5427","observation_id":"20a91c80-9127-45ff-987d-6956c97674de","resolution":{"observed_at":"2026-08-01T03:14:40.028139Z","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":"2026-08-01T03:14:40.031214Z","title":"Analysis of","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-01T03:14:40.031214Z"},"links":{"citing_paper":"/paper/2607.25200"},"observation_digest":"sha256:67495df24e31c3ace7ae31c81e0bf40d269289b1b848bba9c99ff2788393ed50","observation_id":"971f4860-6998-497a-89e4-78d998f24f8d","resolution":{"observed_at":"2026-08-01T03:14:40.031214Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.25200","last_updated":"2026-07-28T02:13:30Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-07T02:47:07.655693Z","submitted_at":"2026-07-28T02:13:30Z","title":"Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks"},"reference_resolution":{"displayed":35,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":33,"verified_exact":2,"verified_fuzzy":0},"total_outbound_references":35},"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":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 7 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 0 inbound Pith citation observations for arXiv:2607.25200."}