{"as_of":"2026-08-11T14:32:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:532375c22e435fc7e9d059aa7242160ef1c35121857d39f28a81a517fb2da5dd","coverage":[{"denominator":10,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":10,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T15:24:03.887368Z","state":"measured"},{"denominator":10,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":10,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+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/2508.20036/citation-record","integrity":"/paper/2508.20036/integrity","json":"/paper/2508.20036/citation-record.json","paper":"/paper/2508.20036"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2201.04753","last_updated":"2022-01-13T00:48:20Z","snapshot_observed_at":"2026-08-09T19:43:51.075319Z","submitted_at":"2022-01-13T00:48:20Z","title":"Largest Eigenvalues of the Conjugate Kernel of Single-Layered Neural Networks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2201.04753","snapshot_observed_at":"2026-08-05T15:24:02.928881Z","title":"Abou Assaly and L","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2508.20036","last_updated":"2025-08-27T16:41:01Z","snapshot_observed_at":"2026-08-10T19:38:52.985029Z","submitted_at":"2025-08-27T16:41:01Z","title":"Eigenvalue distribution of the Neural Tangent Kernel in the quadratic scaling","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-05T15:24:02.928881Z"},"links":{"cited_paper":"/paper/2201.04753","citing_paper":"/paper/2508.20036"},"observation_digest":"sha256:9f1b5dcdee4428fe42843aa3d51cb9c2d52083ced6476af3c157d95f2c95e79b","observation_id":"52e0a3b4-bd70-43fd-89f8-77c649f9fd62","resolution":{"observed_at":"2026-08-05T15:24:02.928881Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.17515","last_updated":"2024-10-23T02:42:13Z","snapshot_observed_at":"2026-08-10T19:39:21.895934Z","submitted_at":"2024-10-23T02:42:13Z","title":"Extremal Eigenvalues of Random Kernel Matrices with Polynomial Scaling","version":1},"cited_work":{"arxiv_id":"2410.17515","doi":null,"metadata_source":"pith","pith_arxiv_id":"2410.17515","snapshot_observed_at":"2026-08-05T15:24:04.241293Z","title":"Extremal Eigenvalues of Random Kernel Matrices with Polynomial Scaling","venue":"math.PR","work_id":"01e328c7-47d3-4beb-88b6-e884a09aee23","year":2024},"citing_paper":{"arxiv_id":"2508.20036","last_updated":"2025-08-27T16:41:01Z","snapshot_observed_at":"2026-08-10T19:38:52.985029Z","submitted_at":"2025-08-27T16:41:01Z","title":"Eigenvalue distribution of the Neural Tangent Kernel in the quadratic scaling","version":1},"reference_index":949,"source":"pdf_text","source_observed_at":"2026-08-05T15:24:03.540616Z"},"links":{"cited_paper":"/paper/2410.17515","citing_paper":"/paper/2508.20036"},"observation_digest":"sha256:3f3e3a02f6f3c0ede07a823750f3176ca0add1ff9601ab7fe5dd5fd141848718","observation_id":"1068a912-4dba-4392-bc4b-2e4650729cc9","resolution":{"observed_at":"2026-08-05T15:24:04.351852Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T15:24:05.152954Z","title":"Probab.26 (1998), no","venue":null,"work_id":"5a17913a-4466-4807-ac53-d39ef4f0b986","year":1998},"citing_paper":{"arxiv_id":"2508.20036","last_updated":"2025-08-27T16:41:01Z","snapshot_observed_at":"2026-08-10T19:38:52.985029Z","submitted_at":"2025-08-27T16:41:01Z","title":"Eigenvalue distribution of the Neural Tangent Kernel in the quadratic scaling","version":1},"reference_index":2010,"source":"pdf_text","source_observed_at":"2026-08-05T15:24:03.035850Z"},"links":{"citing_paper":"/paper/2508.20036"},"observation_digest":"sha256:cf9bd3f426eda20b2e6823775bb3a1c17886714315da37feae2d0754b315cbd5","observation_id":"17dc0697-73cf-4688-91de-192c6ffeb4a4","resolution":{"observed_at":"2026-08-05T15:24:05.261225Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T15:24:03.639638Z","title":"Louart, Z","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2508.20036","last_updated":"2025-08-27T16:41:01Z","snapshot_observed_at":"2026-08-10T19:38:52.985029Z","submitted_at":"2025-08-27T16:41:01Z","title":"Eigenvalue distribution of the Neural Tangent Kernel in the quadratic scaling","version":1},"reference_index":2012,"source":"pdf_text","source_observed_at":"2026-08-05T15:24:03.639638Z"},"links":{"citing_paper":"/paper/2508.20036"},"observation_digest":"sha256:6fe32a4b5a780b54f3e72fe05f946e939aec7ba2569b3a24fd91db1e7062f48a","observation_id":"34617538-1231-4568-8df7-9a069b1cc723","resolution":{"observed_at":"2026-08-05T15:24:03.639638Z","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":"2026-08-05T15:24:04.955163Z","title":"Montanari and Y","venue":null,"work_id":"d0bc66aa-3ae9-48d4-b7aa-31b95990409b","year":2022},"citing_paper":{"arxiv_id":"2508.20036","last_updated":"2025-08-27T16:41:01Z","snapshot_observed_at":"2026-08-10T19:38:52.985029Z","submitted_at":"2025-08-27T16:41:01Z","title":"Eigenvalue distribution of the Neural Tangent Kernel in the quadratic scaling","version":1},"reference_index":2017,"source":"pdf_text","source_observed_at":"2026-08-05T15:24:03.754464Z"},"links":{"citing_paper":"/paper/2508.20036"},"observation_digest":"sha256:ca7b553c22a9a5c3bfab7da7b68524b16b1180f4d8bef753a6ffb36665967cf2","observation_id":"044fef2d-310e-4158-907a-a205d4e99277","resolution":{"observed_at":"2026-08-05T15:24:05.033953Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2406.00961","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T15:24:04.528977Z","title":null,"venue":null,"work_id":"f8e09ac4-b371-4ffb-8f35-36c90f87c185","year":2025},"citing_paper":{"arxiv_id":"2508.20036","last_updated":"2025-08-27T16:41:01Z","snapshot_observed_at":"2026-08-10T19:38:52.985029Z","submitted_at":"2025-08-27T16:41:01Z","title":"Eigenvalue distribution of the Neural Tangent Kernel in the quadratic scaling","version":1},"reference_index":2019,"source":"pdf_text","source_observed_at":"2026-08-05T15:24:03.327667Z"},"links":{"citing_paper":"/paper/2508.20036"},"observation_digest":"sha256:4b3fe64289615ba8195b2fa5ee313b270fbb43af9d81a97ed84d3902148ae94f","observation_id":"90ad5a46-bac8-4f73-8291-f06f1970d177","resolution":{"observed_at":"2026-08-05T15:24:04.625964Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2403.08160","last_updated":"2024-03-13T00:59:25Z","snapshot_observed_at":"2026-08-10T19:37:19.331145Z","submitted_at":"2024-03-13T00:59:25Z","title":"Asymptotics of Random Feature Regression Beyond the Linear Scaling Regime","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.08160","snapshot_observed_at":"2026-08-05T15:24:03.434596Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2508.20036","last_updated":"2025-08-27T16:41:01Z","snapshot_observed_at":"2026-08-10T19:38:52.985029Z","submitted_at":"2025-08-27T16:41:01Z","title":"Eigenvalue distribution of the Neural Tangent Kernel in the quadratic scaling","version":1},"reference_index":2020,"source":"pdf_text","source_observed_at":"2026-08-05T15:24:03.434596Z"},"links":{"cited_paper":"/paper/2403.08160","citing_paper":"/paper/2508.20036"},"observation_digest":"sha256:936b8e7e58cae9b3ce4b3c1897a69ff9f0f231153f1b541ae5583692561292b2","observation_id":"453991ba-1fa5-4b33-8a95-d959168e0e4d","resolution":{"observed_at":"2026-08-05T15:24:03.434596Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2310.18280","last_updated":"2023-10-27T17:15:55Z","snapshot_observed_at":"2026-08-10T09:34:33.670394Z","submitted_at":"2023-10-27T17:15:55Z","title":"Universality for the global spectrum of random inner-product kernel matrices in the polynomial regime","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2310.18280","snapshot_observed_at":"2026-08-05T15:24:03.227978Z","title":"Chizat, E","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2508.20036","last_updated":"2025-08-27T16:41:01Z","snapshot_observed_at":"2026-08-10T19:38:52.985029Z","submitted_at":"2025-08-27T16:41:01Z","title":"Eigenvalue distribution of the Neural Tangent Kernel in the quadratic scaling","version":1},"reference_index":2022,"source":"pdf_text","source_observed_at":"2026-08-05T15:24:03.227978Z"},"links":{"cited_paper":"/paper/2310.18280","citing_paper":"/paper/2508.20036"},"observation_digest":"sha256:7874ae212baf1b9263af220705ac72fb6c4eecda8913bb2355223e11e79e18e5","observation_id":"4af7e092-ea37-4168-bd3e-662b9bcd59c9","resolution":{"observed_at":"2026-08-05T15:24:03.227978Z","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":"2026-08-05T15:24:03.887368Z","title":"Piccolo and D","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2508.20036","last_updated":"2025-08-27T16:41:01Z","snapshot_observed_at":"2026-08-10T19:38:52.985029Z","submitted_at":"2025-08-27T16:41:01Z","title":"Eigenvalue distribution of the Neural Tangent Kernel in the quadratic scaling","version":1},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-05T15:24:03.887368Z"},"links":{"citing_paper":"/paper/2508.20036"},"observation_digest":"sha256:f94acc0fcb18170ba1a6c5bb72b19f5f95464da8ec6deab9fca962fd3fcfff8f","observation_id":"84802c3e-7112-4e0c-a322-f1e6fca2f446","resolution":{"observed_at":"2026-08-05T15:24:03.887368Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2306.05850","last_updated":"2023-06-09T12:31:59Z","snapshot_observed_at":"2026-07-06T15:40:43.125224Z","submitted_at":"2023-06-09T12:31:59Z","title":"Deterministic equivalent of the Conjugate Kernel matrix associated to Artificial Neural Networks","version":1},"cited_work":{"arxiv_id":"2306.05850","doi":null,"metadata_source":"pith","pith_arxiv_id":"2306.05850","snapshot_observed_at":"2026-08-05T15:24:04.761799Z","title":"Deterministic equivalent of the Conjugate Kernel matrix associated to Artificial Neural Networks","venue":"math.PR","work_id":"749ad23c-f53a-4863-ad62-5ec001ebf104","year":2023},"citing_paper":{"arxiv_id":"2508.20036","last_updated":"2025-08-27T16:41:01Z","snapshot_observed_at":"2026-08-10T19:38:52.985029Z","submitted_at":"2025-08-27T16:41:01Z","title":"Eigenvalue distribution of the Neural Tangent Kernel in the quadratic scaling","version":1},"reference_index":2914,"source":"pdf_text","source_observed_at":"2026-08-05T15:24:03.136818Z"},"links":{"cited_paper":"/paper/2306.05850","citing_paper":"/paper/2508.20036"},"observation_digest":"sha256:26eb38fd522ab43461a7ad41894006d4acef3d36ecdd63f3f8a58ebd101b65d9","observation_id":"dfda3534-48e8-4122-8571-87ff9ac41f9a","resolution":{"observed_at":"2026-08-05T15:24:04.837864Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2508.20036","last_updated":"2025-08-27T16:41:01Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-10T19:38:52.985029Z","submitted_at":"2025-08-27T16:41:01Z","title":"Eigenvalue distribution of the Neural Tangent Kernel in the quadratic scaling"},"reference_resolution":{"displayed":10,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":3,"verified_fuzzy":2},"total_outbound_references":10},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 10 of 10 outbound references and 0 inbound Pith citation observations for arXiv:2508.20036."}