{"as_of":"2026-08-08T02:30:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:e888719ce18db6795288fbbb405dda2246f9180e886fcbf537799657e3785d99","coverage":[{"denominator":23,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":23,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T14:40:56.463055Z","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":"2026-08-07T06:34:17.273281+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":"2026-05-08T14:59:19.883399Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-11T18:36:08.612584Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.18346","last_updated":"2025-05-23T20:09:09Z","snapshot_observed_at":"2026-08-07T14:30:33.768874Z","submitted_at":"2025-05-23T20:09:09Z","title":"On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective","version":1},"cited_work":{"arxiv_id":"2505.18346","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2505.18346","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"arXiv preprint arXiv:2505.18346 , year=","venue":null,"work_id":"26acf6f0-be75-4417-9b61-8d2eabf65780","year":null},"citing_paper":{"arxiv_id":"2605.05710","last_updated":"2026-05-07T05:55:10Z","snapshot_observed_at":"2026-07-06T23:18:17.333660Z","submitted_at":"2026-05-07T05:55:10Z","title":"On the Blessing of Pre-training in Weak-to-Strong Generalization","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-05-08T14:59:19.883399Z"},"links":{"cited_paper":"/paper/2505.18346","citing_paper":"/paper/2605.05710"},"observation_digest":"sha256:c9485b448fac3dc7ffca72556460319306569c35f07f7d3ef533a001d4e823e1","observation_id":"7413a1d5-e0fb-41a4-8b18-78d66d577252","resolution":{"observed_at":"2026-05-11T18:36:08.614558Z","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"}}],"links":{"evidence":"/evidence","html":"/paper/2505.18346/citation-record","integrity":"/paper/2505.18346/integrity","json":"/paper/2505.18346/citation-record.json","paper":"/paper/2505.18346"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:40:57.725244Z","title":"The solutions are given by ( λ− s , λ+ s ) from (12)","venue":null,"work_id":"7a2f68a3-7626-47ee-93a2-3cae2d759125","year":2019},"citing_paper":{"arxiv_id":"2505.18346","last_updated":"2025-05-23T20:09:09Z","snapshot_observed_at":"2026-08-07T14:30:33.768874Z","submitted_at":"2025-05-23T20:09:09Z","title":"On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T14:40:56.132667Z"},"links":{"citing_paper":"/paper/2505.18346"},"observation_digest":"sha256:313c28d4555f85ff61df4f57836760c39a4155a99b7bc9c1dd5912ef145b0caa","observation_id":"333690de-6f45-4442-ba0b-3dd0a1646d8b","resolution":{"observed_at":"2026-08-07T14:40:57.796379Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:40:57.854369Z","title":"Similarly, for the remaining terms, we have d−1 X Tr h ˆR ˜R i →P mt,1ms,1 d−1 X Tr h ˆR ˜R2 i →P mt,1ms,2, and d−1 X Tr h ˆR2 ˜R i →P mt,2ms,1","venue":null,"work_id":"5f4ce684-3d34-4533-bb83-9b5297530f57","year":1991},"citing_paper":{"arxiv_id":"2505.18346","last_updated":"2025-05-23T20:09:09Z","snapshot_observed_at":"2026-08-07T14:30:33.768874Z","submitted_at":"2025-05-23T20:09:09Z","title":"On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T14:40:56.064795Z"},"links":{"citing_paper":"/paper/2505.18346"},"observation_digest":"sha256:1fdb494852430f3442dab4c25710967985afb72e60bf49415aac2ee592a6cb39","observation_id":"e9d5db6d-9baf-4abe-9553-ce2d25254eb1","resolution":{"observed_at":"2026-08-07T14:40:57.931921Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":{"arxiv_id":"2305.18270","last_updated":"2025-06-03T19:12:56Z","snapshot_observed_at":"2026-07-06T15:34:51.593721Z","submitted_at":"2023-05-29T17:43:44Z","title":"How Two-Layer Neural Networks Learn, One (Giant) Step at a Time","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2305.18270","snapshot_observed_at":"2026-08-07T14:40:54.621375Z","title":"Learning two-layer neural networks, one (giant) step at a time","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.18346","last_updated":"2025-05-23T20:09:09Z","snapshot_observed_at":"2026-08-07T14:30:33.768874Z","submitted_at":"2025-05-23T20:09:09Z","title":"On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T14:40:54.621375Z"},"links":{"cited_paper":"/paper/2305.18270","citing_paper":"/paper/2505.18346"},"observation_digest":"sha256:7ad3973c5560e641740972a9166d311d41b84583e68ae04c4919cf5b7044cd38","observation_id":"538f54cd-b6d1-4db0-a809-544ffa8652d4","resolution":{"observed_at":"2026-08-07T14:40:54.621375Z","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":"2409.20250","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:40:56.989628Z","title":"Random features outperform linear models: Effect of strong input-label correlation in spiked covariance data","venue":null,"work_id":"8f982e6d-a05f-4614-97d2-f87508824a8a","year":null},"citing_paper":{"arxiv_id":"2505.18346","last_updated":"2025-05-23T20:09:09Z","snapshot_observed_at":"2026-08-07T14:30:33.768874Z","submitted_at":"2025-05-23T20:09:09Z","title":"On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T14:40:54.738784Z"},"links":{"citing_paper":"/paper/2505.18346"},"observation_digest":"sha256:852b52203388dad61becb75d2773d1e6da371532564197689fae1bedf796a30b","observation_id":"08c48c37-5b88-4c8d-98a7-16321ab2282e","resolution":{"observed_at":"2026-08-07T14:40:57.032442Z","resolver_source":"raw_fallback","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":{"arxiv_id":"2402.03749","last_updated":"2024-02-06T06:30:34Z","snapshot_observed_at":"2026-07-06T17:26:02.434883Z","submitted_at":"2024-02-06T06:30:34Z","title":"Vision Superalignment: Weak-to-Strong Generalization for Vision Foundation Models","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.03749","snapshot_observed_at":"2026-08-07T14:40:54.963411Z","title":"Vision super- alignment: Weak-to-strong generalization for vision foundation models","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.18346","last_updated":"2025-05-23T20:09:09Z","snapshot_observed_at":"2026-08-07T14:30:33.768874Z","submitted_at":"2025-05-23T20:09:09Z","title":"On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T14:40:54.963411Z"},"links":{"cited_paper":"/paper/2402.03749","citing_paper":"/paper/2505.18346"},"observation_digest":"sha256:08bf8f7f79fd1d53b9e3e22e7b95606bb38305d58a132fe162c6b98ef3a1034f","observation_id":"4a313f6c-b36f-4958-b9ec-ef366c2f2e42","resolution":{"observed_at":"2026-08-07T14:40:54.963411Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.13991","last_updated":"2024-10-17T19:46:51Z","snapshot_observed_at":"2026-07-06T19:35:39.803671Z","submitted_at":"2024-10-17T19:46:51Z","title":"Generalization for Least Squares Regression With Simple Spiked Covariances","version":1},"cited_work":{"arxiv_id":"2410.13991","doi":null,"metadata_source":"pith","pith_arxiv_id":"2410.13991","snapshot_observed_at":"2026-08-07T14:40:56.760945Z","title":"Generalization for Least Squares Regression With Simple Spiked Covariances","venue":"math.ST","work_id":"173a7c24-541f-458f-8fe2-7bec990130a5","year":2024},"citing_paper":{"arxiv_id":"2505.18346","last_updated":"2025-05-23T20:09:09Z","snapshot_observed_at":"2026-08-07T14:30:33.768874Z","submitted_at":"2025-05-23T20:09:09Z","title":"On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T14:40:55.068699Z"},"links":{"cited_paper":"/paper/2410.13991","citing_paper":"/paper/2505.18346"},"observation_digest":"sha256:e9800d4b6cffe4123bcf3abfff557b2450006ebd30e19bd62145fede6a6e46a4","observation_id":"a2a703d3-f5a5-40e9-b767-b0ff9f9811ea","resolution":{"observed_at":"2026-08-07T14:40:56.816879Z","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":{"arxiv_id":"2402.15505","last_updated":"2024-02-23T18:56:11Z","snapshot_observed_at":"2026-08-04T17:35:29.079244Z","submitted_at":"2024-02-23T18:56:11Z","title":"Co-Supervised Learning: Improving Weak-to-Strong Generalization with Hierarchical Mixture of Experts","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.15505","snapshot_observed_at":"2026-08-07T14:40:55.168928Z","title":"Co-supervised learning: Improving weak-to-strong generalization with hierarchical mixture of experts","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.18346","last_updated":"2025-05-23T20:09:09Z","snapshot_observed_at":"2026-08-07T14:30:33.768874Z","submitted_at":"2025-05-23T20:09:09Z","title":"On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T14:40:55.168928Z"},"links":{"cited_paper":"/paper/2402.15505","citing_paper":"/paper/2505.18346"},"observation_digest":"sha256:c2afe6a1275d38be30f51e284c5068a26008484c471f876d355cfc40f83d79f8","observation_id":"0cc8084a-71fb-417b-b5c3-3d9b6df60b16","resolution":{"observed_at":"2026-08-07T14:40:55.168928Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.18274","last_updated":"2024-05-28T15:24:35Z","snapshot_observed_at":"2026-07-06T18:21:22.569625Z","submitted_at":"2024-05-28T15:24:35Z","title":"Signal-Plus-Noise Decomposition of Nonlinear Spiked Random Matrix Models","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.18274","snapshot_observed_at":"2026-08-07T14:40:55.339442Z","title":"Signal-plus-noise decomposition of nonlinear spiked random matrix models","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.18346","last_updated":"2025-05-23T20:09:09Z","snapshot_observed_at":"2026-08-07T14:30:33.768874Z","submitted_at":"2025-05-23T20:09:09Z","title":"On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T14:40:55.339442Z"},"links":{"cited_paper":"/paper/2405.18274","citing_paper":"/paper/2505.18346"},"observation_digest":"sha256:d4e4be1ad53fb91adcd24e8cbff6b7b92a1014210a87a5a13b0a2ee3f69876ca","observation_id":"10681d7c-7428-487c-8ee3-b45b04344f85","resolution":{"observed_at":"2026-08-07T14:40:55.339442Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.19105","last_updated":"2025-02-03T20:44:05Z","snapshot_observed_at":"2026-08-05T22:16:25.859359Z","submitted_at":"2025-01-31T12:57:58Z","title":"Relating Misfit to Gain in Weak-to-Strong Generalization Beyond the Squared Loss","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.19105","snapshot_observed_at":"2026-08-07T14:40:55.435466Z","title":"Relating misfit to gain in weak-to-strong generalization beyond the squared loss","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.18346","last_updated":"2025-05-23T20:09:09Z","snapshot_observed_at":"2026-08-07T14:30:33.768874Z","submitted_at":"2025-05-23T20:09:09Z","title":"On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T14:40:55.435466Z"},"links":{"cited_paper":"/paper/2501.19105","citing_paper":"/paper/2505.18346"},"observation_digest":"sha256:f2540e040a3f2d7aa134e5725348a4efe65b2ec24296180872df419b34c0ad33","observation_id":"037fabfc-e9d2-45b8-95ff-5c80e8c68bb4","resolution":{"observed_at":"2026-08-07T14:40:55.435466Z","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":"2026-08-07T14:40:58.330011Z","title":"Weak-to-strong reasoning","venue":null,"work_id":"a90f1548-e22f-4d0a-ba71-18a178b840e9","year":2024},"citing_paper":{"arxiv_id":"2505.18346","last_updated":"2025-05-23T20:09:09Z","snapshot_observed_at":"2026-08-07T14:30:33.768874Z","submitted_at":"2025-05-23T20:09:09Z","title":"On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T14:40:55.803095Z"},"links":{"citing_paper":"/paper/2505.18346"},"observation_digest":"sha256:2f91efb448c86cf00a94528fd6aa6db9b2a6bddd10795094f218105c862c544d","observation_id":"e2aadcf7-71f6-415d-9c1a-26983c8a8cc6","resolution":{"observed_at":"2026-08-07T14:40:58.409609Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:40:58.032501Z","title":"Note that using [Abramowitz and Stegun, 1968, Equation 22.8.8] we have d dx Hk(x) = kHk−1(x)","venue":null,"work_id":"16b5bb4c-10f6-4a41-8f29-b0cc45aaf86a","year":1968},"citing_paper":{"arxiv_id":"2505.18346","last_updated":"2025-05-23T20:09:09Z","snapshot_observed_at":"2026-08-07T14:30:33.768874Z","submitted_at":"2025-05-23T20:09:09Z","title":"On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T14:40:55.985179Z"},"links":{"citing_paper":"/paper/2505.18346"},"observation_digest":"sha256:b71cbef9d653cbd2f059f0416073d43e68a0125b924d226ea45e884974925044","observation_id":"495ea2c1-ada0-471c-8ad2-ef2134e56a6e","resolution":{"observed_at":"2026-08-07T14:40:58.101769Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:40:57.591780Z","title":"Figure 7: The test error of the student model Ls as a function of γt for σε = 1, γs = 0.1, λt → 0 (ridgeless), and different values of λs","venue":null,"work_id":"51392c77-0b13-42e1-b612-d483f9b72ade","year":2021},"citing_paper":{"arxiv_id":"2505.18346","last_updated":"2025-05-23T20:09:09Z","snapshot_observed_at":"2026-08-07T14:30:33.768874Z","submitted_at":"2025-05-23T20:09:09Z","title":"On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T14:40:56.225364Z"},"links":{"citing_paper":"/paper/2505.18346"},"observation_digest":"sha256:c14363c0b9d06a4cc01c4963d1448bb5d70c887de3f18ebb136889765426500c","observation_id":"422a0fff-1a7a-406b-9ca9-e43c251b90f8","resolution":{"observed_at":"2026-08-07T14:40:57.646621Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:40:57.472986Z","title":"From the definition of ms,1 and ms,2 and using the Marchenko-Pastur theorem, we have ˆβ⊤ ˜R2 ˆβ →P ms,2, and also ˆβ⊤ ˜R ˆβ →P ms,1","venue":null,"work_id":"012bddcf-d09a-4aba-8f64-59b0cbd38380","year":1991},"citing_paper":{"arxiv_id":"2505.18346","last_updated":"2025-05-23T20:09:09Z","snapshot_observed_at":"2026-08-07T14:30:33.768874Z","submitted_at":"2025-05-23T20:09:09Z","title":"On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T14:40:56.328979Z"},"links":{"citing_paper":"/paper/2505.18346"},"observation_digest":"sha256:8d13fb16bde2d95c2bcc9488f91334116a3a4778e6cf59959470e25562ce0eed","observation_id":"03b09c06-50e3-404d-a5cb-cecd02530c0c","resolution":{"observed_at":"2026-08-07T14:40:57.532658Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:40:57.315328Z","title":"Thus, using [Vershynin, 2012, Theorem 5.44], we have ∥σ′ ⊥(Wt,0X⊤)∥op = O(√nt)","venue":null,"work_id":"2c04cd58-01fc-46b5-8845-42c40cdb2b02","year":2012},"citing_paper":{"arxiv_id":"2505.18346","last_updated":"2025-05-23T20:09:09Z","snapshot_observed_at":"2026-08-07T14:30:33.768874Z","submitted_at":"2025-05-23T20:09:09Z","title":"On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T14:40:56.403324Z"},"links":{"citing_paper":"/paper/2505.18346"},"observation_digest":"sha256:0595d2e5ebcafa272aebff6c7386e2447db1e6dbc3cdeb594c77cf5da18f9e61","observation_id":"660177bc-2ddb-40e7-a743-32220a1ac507","resolution":{"observed_at":"2026-08-07T14:40:57.396618Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:40:57.161588Z","title":"as ˜y⊤ ⊙","venue":null,"work_id":"0e00bbea-30e7-4052-a1a1-3d7006fda96f","year":2024},"citing_paper":{"arxiv_id":"2505.18346","last_updated":"2025-05-23T20:09:09Z","snapshot_observed_at":"2026-08-07T14:30:33.768874Z","submitted_at":"2025-05-23T20:09:09Z","title":"On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T14:40:56.463055Z"},"links":{"citing_paper":"/paper/2505.18346"},"observation_digest":"sha256:66371ec46c48e40e61bf39756d02bac07d3380d7068255cab0e3c36faaeaf5e1","observation_id":"e3a675ae-fcc1-4f1a-a1e8-d9aac4719271","resolution":{"observed_at":"2026-08-07T14:40:57.219194Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"2026-08-07T14:40:55.271241Z","title":"Weak-to-strong generalization even in random feature networks, provably","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.18346","last_updated":"2025-05-23T20:09:09Z","snapshot_observed_at":"2026-08-07T14:30:33.768874Z","submitted_at":"2025-05-23T20:09:09Z","title":"On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective","version":1},"reference_index":1967,"source":"pdf_text","source_observed_at":"2026-08-07T14:40:55.271241Z"},"links":{"citing_paper":"/paper/2505.18346"},"observation_digest":"sha256:d1605ba283e124fac7c6405cae689141b6733d92485e70a11fa26fd5a85e1bbb","observation_id":"182e48f3-90e5-40f8-a817-1c56a5bfda8b","resolution":{"observed_at":"2026-08-07T14:40:55.271241Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2211.06506","last_updated":"2023-11-08T04:50:55Z","snapshot_observed_at":"2026-08-04T16:45:41.426786Z","submitted_at":"2022-11-11T23:00:30Z","title":"Spectral Evolution and Invariance in Linear-width Neural Networks","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2211.06506","snapshot_observed_at":"2026-08-07T14:40:55.616708Z","title":"Spectral evolution and invariance in linear-width neural networks","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.18346","last_updated":"2025-05-23T20:09:09Z","snapshot_observed_at":"2026-08-07T14:30:33.768874Z","submitted_at":"2025-05-23T20:09:09Z","title":"On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective","version":1},"reference_index":1991,"source":"pdf_text","source_observed_at":"2026-08-07T14:40:55.616708Z"},"links":{"cited_paper":"/paper/2211.06506","citing_paper":"/paper/2505.18346"},"observation_digest":"sha256:e149a00af3ee469f15104be9bb53408a6adb8686c74d8d9a8027d02c71d66999","observation_id":"d3fbe4de-8e87-4987-a2c3-032f43e07d2f","resolution":{"observed_at":"2026-08-07T14:40:55.616708Z","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":"2026-08-07T14:40:58.189934Z","title":"Theorem 13 (Hanson-Wright Inequality [Hanson and Wright, 1971])","venue":null,"work_id":"dc8fad42-7b27-4a4a-9c7b-7a441755fb13","year":1971},"citing_paper":{"arxiv_id":"2505.18346","last_updated":"2025-05-23T20:09:09Z","snapshot_observed_at":"2026-08-07T14:30:33.768874Z","submitted_at":"2025-05-23T20:09:09Z","title":"On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective","version":1},"reference_index":2013,"source":"pdf_text","source_observed_at":"2026-08-07T14:40:55.896893Z"},"links":{"citing_paper":"/paper/2505.18346"},"observation_digest":"sha256:0997b88cca9c83515ece1f999cfa69aca5350949870bdcdb7faf41fef3e235c0","observation_id":"a63defbb-cd75-47a1-86c7-04e70527475e","resolution":{"observed_at":"2026-08-07T14:40:58.259134Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":{"arxiv_id":"2409.08813","last_updated":"2025-04-25T05:34:47Z","snapshot_observed_at":"2026-08-05T21:33:42.721843Z","submitted_at":"2024-09-13T13:24:52Z","title":"Your Weak LLM is Secretly a Strong Teacher for Alignment","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.08813","snapshot_observed_at":"2026-08-07T14:40:55.530030Z","title":"Your weak LLM is secretly a strong teacher for alignment","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.18346","last_updated":"2025-05-23T20:09:09Z","snapshot_observed_at":"2026-08-07T14:30:33.768874Z","submitted_at":"2025-05-23T20:09:09Z","title":"On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective","version":1},"reference_index":2021,"source":"pdf_text","source_observed_at":"2026-08-07T14:40:55.530030Z"},"links":{"cited_paper":"/paper/2409.08813","citing_paper":"/paper/2505.18346"},"observation_digest":"sha256:e9e540ba33269fff72a52d82ae00a0e7f2019b6d0ea7418db9c4a10bd4302a82","observation_id":"e5138138-272d-42a8-9ee3-d38fda765cf0","resolution":{"observed_at":"2026-08-07T14:40:55.530030Z","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":"2026-08-07T14:40:58.473179Z","title":"Provable weak-to-strong generalization via benign overfitting","venue":null,"work_id":"e9907ae5-6bd2-4776-9e68-d32146ccb97e","year":2024},"citing_paper":{"arxiv_id":"2505.18346","last_updated":"2025-05-23T20:09:09Z","snapshot_observed_at":"2026-08-07T14:30:33.768874Z","submitted_at":"2025-05-23T20:09:09Z","title":"On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective","version":1},"reference_index":2022,"source":"pdf_text","source_observed_at":"2026-08-07T14:40:55.700634Z"},"links":{"citing_paper":"/paper/2505.18346"},"observation_digest":"sha256:bc6d4797c76acbecea05cdf6f9e8d3594194c3dda6aedb1c504c47c52d2867e8","observation_id":"4e9c488e-7aa2-42bc-8296-4e2c79d88e9b","resolution":{"observed_at":"2026-08-07T14:40:58.531816Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":{"arxiv_id":"2405.15459","last_updated":"2025-02-10T09:33:48Z","snapshot_observed_at":"2026-08-05T15:27:10.774229Z","submitted_at":"2024-05-24T11:34:31Z","title":"Repetita Iuvant: Data Repetition Allows SGD to Learn High-Dimensional Multi-Index Functions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.15459","snapshot_observed_at":"2026-08-07T14:40:54.390971Z","title":"Repetita iuvant: Data repetition allows SGD to learn high-dimensional multi-index functions","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.18346","last_updated":"2025-05-23T20:09:09Z","snapshot_observed_at":"2026-08-07T14:30:33.768874Z","submitted_at":"2025-05-23T20:09:09Z","title":"On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective","version":1},"reference_index":2023,"source":"pdf_text","source_observed_at":"2026-08-07T14:40:54.390971Z"},"links":{"cited_paper":"/paper/2405.15459","citing_paper":"/paper/2505.18346"},"observation_digest":"sha256:506483f8120f783e3913054fe7543e97c71251a490299d0084f03d0f5921f65f","observation_id":"77158d68-8908-4806-9133-922debe71e6c","resolution":{"observed_at":"2026-08-07T14:40:54.390971Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2408.04607","last_updated":"2026-06-02T21:27:54Z","snapshot_observed_at":"2026-07-06T18:58:30.942582Z","submitted_at":"2024-08-08T17:27:29Z","title":"Risk and cross validation in ridge regression with correlated samples","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2408.04607","snapshot_observed_at":"2026-08-07T14:40:54.491180Z","title":"Risk and cross validation in ridge regression with correlated samples","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.18346","last_updated":"2025-05-23T20:09:09Z","snapshot_observed_at":"2026-08-07T14:30:33.768874Z","submitted_at":"2025-05-23T20:09:09Z","title":"On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective","version":1},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-07T14:40:54.491180Z"},"links":{"cited_paper":"/paper/2408.04607","citing_paper":"/paper/2505.18346"},"observation_digest":"sha256:8f886b3d1df193848a9c8ad5f85234be9607ffa24e00f589e3cce0a1f5d11ed3","observation_id":"6d8fb6e3-3200-4866-9368-9579d5bde8f9","resolution":{"observed_at":"2026-08-07T14:40:54.491180Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2310.14055","last_updated":"2023-10-21T16:23:59Z","snapshot_observed_at":"2026-07-06T16:36:35.423639Z","submitted_at":"2023-10-21T16:23:59Z","title":"Spectral Phase Transitions in Non-Linear Wigner Spiked Models","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2310.14055","snapshot_observed_at":"2026-08-07T14:40:54.844353Z","title":"Spectral phase transitions in non-linear wigner spiked models","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.18346","last_updated":"2025-05-23T20:09:09Z","snapshot_observed_at":"2026-08-07T14:30:33.768874Z","submitted_at":"2025-05-23T20:09:09Z","title":"On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective","version":1},"reference_index":2025,"source":"pdf_text","source_observed_at":"2026-08-07T14:40:54.844353Z"},"links":{"cited_paper":"/paper/2310.14055","citing_paper":"/paper/2505.18346"},"observation_digest":"sha256:3744389911c5f1d75c8eb7a8d9526f6eaf5bf7b088db0ab342f193b1a8bfd2ff","observation_id":"7916e744-e64b-422a-8ac5-db39bfb1ee7e","resolution":{"observed_at":"2026-08-07T14:40:54.844353Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2505.18346","last_updated":"2025-05-23T20:09:09Z","latest_version":1,"primary_category":"stat.ML","snapshot_observed_at":"2026-08-07T14:30:33.768874Z","submitted_at":"2025-05-23T20:09:09Z","title":"On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective"},"reference_resolution":{"displayed":23,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":11,"verified_exact":2,"verified_fuzzy":10},"total_outbound_references":23},"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 8 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 1 inbound Pith citation observation for arXiv:2505.18346."}