{"as_of":"2026-07-11T15:34:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:e6e4924584c662069811fa04db78045e4ee0645804ecd49690986f004caba1b7","coverage":[{"denominator":7,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":7,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-08T04:02:37.785615Z","state":"measured"},{"denominator":8,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":8,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-07-11T06:31:22.384518+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-27T05:08:00.711576Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-07-03T16:38:40.639612Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2604.24878","last_updated":"2026-04-27T18:04:11Z","snapshot_observed_at":"2026-07-06T23:10:47.277692Z","submitted_at":"2026-04-27T18:04:11Z","title":"Transformer Approximations from ReLUs","version":1},"cited_work":{"arxiv_id":"2604.24878","doi":null,"metadata_source":"pith","pith_arxiv_id":"2604.24878","snapshot_observed_at":"2026-07-03T16:38:40.639612Z","title":"Transformer Approximations from ReLUs","venue":"cs.LG","work_id":"fd8714cc-6597-4295-9495-34bdc62b970e","year":2026},"citing_paper":{"arxiv_id":"2606.13280","last_updated":"2026-06-11T12:34:47Z","snapshot_observed_at":"2026-07-06T23:52:04.574604Z","submitted_at":"2026-06-11T12:34:47Z","title":"Generalization Bounds for Transformer-Based Next-Token Prediction in a Language Model","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-27T05:08:00.711576Z"},"links":{"cited_paper":"/paper/2604.24878","citing_paper":"/paper/2606.13280"},"observation_digest":"sha256:9c79447e4b58cc958a2accfe18650fc70de05b93a99b2e31f2a96ea87124d913","observation_id":"f1d4879a-a851-498b-a8aa-0c87d41b0441","resolution":{"observed_at":"2026-07-03T16:38:40.640997Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"html":"/paper/2604.24878/citation-record","json":"/paper/2604.24878/citation-record.json","paper":"/paper/2604.24878"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2403.11968","last_updated":"2024-03-18T17:08:24Z","snapshot_observed_at":"2026-07-06T17:46:25.142387Z","submitted_at":"2024-03-18T17:08:24Z","title":"Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory","version":1},"cited_work":{"arxiv_id":"2403.11968","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2403.11968","snapshot_observed_at":"2026-07-02T11:46:56.006595Z","title":"arXiv preprint arXiv:2403.11968 , year=","venue":null,"work_id":"54254db0-3be1-41e3-8709-a443fd7126be","year":2024},"citing_paper":{"arxiv_id":"2604.24878","last_updated":"2026-04-27T18:04:11Z","snapshot_observed_at":"2026-07-06T23:10:47.277692Z","submitted_at":"2026-04-27T18:04:11Z","title":"Transformer Approximations from ReLUs","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-08T04:02:37.785615Z"},"links":{"cited_paper":"/paper/2403.11968","citing_paper":"/paper/2604.24878"},"observation_digest":"sha256:7cede3e066723f022061fa3ff5a571fbd6f350bd1f7656521c530b5e51a87bb2","observation_id":"d8c6bf73-e385-4d90-be7a-74d1243e8b43","resolution":{"observed_at":"2026-05-11T21:51:30.247996Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.16525","last_updated":"2025-06-05T23:04:39Z","snapshot_observed_at":"2026-07-06T19:56:39.115630Z","submitted_at":"2024-11-25T16:12:17Z","title":"Fundamental Limits of Prompt Tuning Transformers: Universality, Capacity and Efficiency","version":2},"cited_work":{"arxiv_id":"2411.16525","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2411.16525","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Fun- damental limits of prompt tuning transformers: Universality, capacity and efficiency.arXiv preprint arXiv:2411.16525, 2024a","venue":null,"work_id":"8cb49205-2575-41d0-b75d-d0e82e462049","year":null},"citing_paper":{"arxiv_id":"2604.24878","last_updated":"2026-04-27T18:04:11Z","snapshot_observed_at":"2026-07-06T23:10:47.277692Z","submitted_at":"2026-04-27T18:04:11Z","title":"Transformer Approximations from ReLUs","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-08T04:02:37.785615Z"},"links":{"cited_paper":"/paper/2411.16525","citing_paper":"/paper/2604.24878"},"observation_digest":"sha256:bb58acaf342b262690b0da15aa3039a2cab6e8910bad30d248db6be8c1bc3ae8","observation_id":"40da8e62-187c-4710-9db4-8d29428e96b5","resolution":{"observed_at":"2026-05-11T21:51:30.210788Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2307.14023","last_updated":"2024-01-29T10:16:41Z","snapshot_observed_at":"2026-07-06T15:58:39.339004Z","submitted_at":"2023-07-26T08:07:37Z","title":"Are Transformers with One Layer Self-Attention Using Low-Rank Weight Matrices Universal Approximators?","version":3},"cited_work":{"arxiv_id":"2307.14023","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2307.14023","snapshot_observed_at":"2026-07-04T10:29:44.325402Z","title":"Are transformers with one layer self-attention using low-rank weight matrices universal approximators?arXiv preprint arXiv:2307.14023","venue":null,"work_id":"cc82db84-d987-4e40-92f8-7f2b13b7d260","year":null},"citing_paper":{"arxiv_id":"2604.24878","last_updated":"2026-04-27T18:04:11Z","snapshot_observed_at":"2026-07-06T23:10:47.277692Z","submitted_at":"2026-04-27T18:04:11Z","title":"Transformer Approximations from ReLUs","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-08T04:02:37.785615Z"},"links":{"cited_paper":"/paper/2307.14023","citing_paper":"/paper/2604.24878"},"observation_digest":"sha256:eeffaca01400d90839e9846d28ece5274447a4b0ffb04f631e287582e5366b87","observation_id":"9522d1fd-1b49-4d0b-860c-5c4098e0af94","resolution":{"observed_at":"2026-05-11T21:51:30.221196Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.09268","last_updated":"2024-02-14T15:54:55Z","snapshot_observed_at":"2026-07-06T17:30:03.953345Z","submitted_at":"2024-02-14T15:54:55Z","title":"Transformers, parallel computation, and logarithmic depth","version":1},"cited_work":{"arxiv_id":"2402.09268","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2402.09268","snapshot_observed_at":"2026-07-03T11:18:03.211693Z","title":"arXiv preprint arXiv:2402.09268 , year=","venue":null,"work_id":"8dcbe092-d753-4f4f-a4c1-4348615bf637","year":2024},"citing_paper":{"arxiv_id":"2604.24878","last_updated":"2026-04-27T18:04:11Z","snapshot_observed_at":"2026-07-06T23:10:47.277692Z","submitted_at":"2026-04-27T18:04:11Z","title":"Transformer Approximations from ReLUs","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-08T04:02:37.785615Z"},"links":{"cited_paper":"/paper/2402.09268","citing_paper":"/paper/2604.24878"},"observation_digest":"sha256:0ce6d50e342102710ddd59d3d0a0409572cf287d040a97f0e207f195e19b8a97","observation_id":"e1af48db-cec8-4cc4-81c1-a229ba5be22f","resolution":{"observed_at":"2026-05-11T21:51:30.235337Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1214/19-aos1875","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T23:25:06.618964Z","title":"The Annals of Statistics 48(4):1875--1897, ://dx.doi.org/10.1214/19-AOS1875","venue":"The Annals of Statistics","work_id":"5a21e60a-e024-482d-9a1b-7ca5533cc9d6","year":2020},"citing_paper":{"arxiv_id":"2604.24878","last_updated":"2026-04-27T18:04:11Z","snapshot_observed_at":"2026-07-06T23:10:47.277692Z","submitted_at":"2026-04-27T18:04:11Z","title":"Transformer Approximations from ReLUs","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-08T04:02:37.785615Z"},"links":{"citing_paper":"/paper/2604.24878"},"observation_digest":"sha256:61a60f2a5b6f54e25dda85f67084c147e17d42bd1597485b90ee069e1a40933e","observation_id":"c9df388c-3704-4b9e-9efa-a3650ce10794","resolution":{"observed_at":"2026-05-09T00:14:27.762690Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1810.08033","last_updated":"2018-10-18T13:17:20Z","snapshot_observed_at":"2026-07-06T07:09:07.505216Z","submitted_at":"2018-10-18T13:17:20Z","title":"Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionality","version":1},"cited_work":{"arxiv_id":"1810.08033","doi":null,"metadata_source":"pith","pith_arxiv_id":"1810.08033","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionality","venue":"stat.ML","work_id":"f00dc1b5-bd38-42bf-808e-a4e54f55b4c1","year":2018},"citing_paper":{"arxiv_id":"2604.24878","last_updated":"2026-04-27T18:04:11Z","snapshot_observed_at":"2026-07-06T23:10:47.277692Z","submitted_at":"2026-04-27T18:04:11Z","title":"Transformer Approximations from ReLUs","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-08T04:02:37.785615Z"},"links":{"cited_paper":"/paper/1810.08033","citing_paper":"/paper/2604.24878"},"observation_digest":"sha256:1279f4b2683e22049f23a75055dbdf87387f9a750247d5943820d5df58e8059e","observation_id":"9d46cfc0-234d-4293-8493-10aa6e9478d4","resolution":{"observed_at":"2026-05-11T21:51:30.252208Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2510.00368","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"The transformer cookbook.arXiv preprint arXiv:2510.00368","venue":null,"work_id":"f5267241-4254-4070-a54f-63982a331e2c","year":null},"citing_paper":{"arxiv_id":"2604.24878","last_updated":"2026-04-27T18:04:11Z","snapshot_observed_at":"2026-07-06T23:10:47.277692Z","submitted_at":"2026-04-27T18:04:11Z","title":"Transformer Approximations from ReLUs","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-08T04:02:37.785615Z"},"links":{"citing_paper":"/paper/2604.24878"},"observation_digest":"sha256:6384295ee581521dd436f0055e190b7a0594e016539261f20f7ebe2d47640436","observation_id":"0236d33b-d54c-485f-a33f-afd040ea0e27","resolution":{"observed_at":"2026-05-11T21:51:30.199583Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2604.24878","last_updated":"2026-04-27T18:04:11Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-07-06T23:10:47.277692Z","submitted_at":"2026-04-27T18:04:11Z","title":"Transformer Approximations from ReLUs"},"reference_resolution":{"displayed":7,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":7,"verified_fuzzy":0},"total_outbound_references":7},"schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}]}