{"as_of":"2026-08-09T14:33:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:a1844f0da253e0d32345bd7a2931d2c5896fae5fa356000cc1b0a228c585fdc4","coverage":[{"denominator":16,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":16,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-08T04:56:54.620345Z","state":"measured"},{"denominator":17,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":17,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+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":"2026-06-28T13:17:11.219557Z","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":"2026-07-02T00:46:24.654519Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2502.08532","last_updated":"2025-06-16T23:04:01Z","snapshot_observed_at":"2026-08-08T04:40:53.045522Z","submitted_at":"2025-02-12T16:12:17Z","title":"Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness","version":2},"cited_work":{"arxiv_id":"2502.08532","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2502.08532","snapshot_observed_at":"2026-07-02T00:46:24.654519Z","title":"Non- linearly preconditioned gradient methods under generalized smoothness.arXiv preprint arXiv:2502.08532, 2025","venue":null,"work_id":"e4564115-1731-4b3f-b6a6-40314dd63dfe","year":2025},"citing_paper":{"arxiv_id":"2606.02787","last_updated":"2026-06-01T18:51:26Z","snapshot_observed_at":"2026-07-06T23:43:07.940839Z","submitted_at":"2026-06-01T18:51:26Z","title":"Adaptive Accelerated Mirror Descent in Primal and Dual Spaces","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-06-28T13:17:11.219557Z"},"links":{"cited_paper":"/paper/2502.08532","citing_paper":"/paper/2606.02787"},"observation_digest":"sha256:ac8ed2fa2611f43c3f26568c1a9301724c311d6360f176eb5bbf37fbab30d018","observation_id":"3041039d-a36c-49b7-b4ac-6db03c40086a","resolution":{"observed_at":"2026-07-02T00:46:24.656614Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2502.08532/citation-record","integrity":"/paper/2502.08532/integrity","json":"/paper/2502.08532/citation-record.json","paper":"/paper/2502.08532"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:56:54.907881Z","title":"Thus we can further bound (30): AK ξ(xK)−ξ(x ⋆) ≤ D0 K−1X k=0 a2 k+1 Ak+1","venue":null,"work_id":"8fe9b249-ee65-4523-97ce-0e96885f3001","year":2020},"citing_paper":{"arxiv_id":"2502.08532","last_updated":"2025-06-16T23:04:01Z","snapshot_observed_at":"2026-08-08T04:40:53.045522Z","submitted_at":"2025-02-12T16:12:17Z","title":"Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-08T04:56:54.609417Z"},"links":{"citing_paper":"/paper/2502.08532"},"observation_digest":"sha256:87e14d0018ea47a19b4083efc32a70748063722b3733437482b8b25226141f5e","observation_id":"60591c33-283e-4153-8350-f54728fc65e5","resolution":{"observed_at":"2026-08-08T04:56:54.912770Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T04:56:54.874335Z","title":"Note that in this case as well,H∇2f(x)is a symmetric matrix and it follows from Theorem D.2 that the operatorTδL−1, ¯L−1 is injective for anyδ <1","venue":null,"work_id":"a7770377-1e77-4a76-972f-ab4213cd9de2","year":2019},"citing_paper":{"arxiv_id":"2502.08532","last_updated":"2025-06-16T23:04:01Z","snapshot_observed_at":"2026-08-08T04:40:53.045522Z","submitted_at":"2025-02-12T16:12:17Z","title":"Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-08T04:56:54.620345Z"},"links":{"citing_paper":"/paper/2502.08532"},"observation_digest":"sha256:3cc1066a73800bd4b7f2ba246efc2a0e427e933baceb64280f0f168c67f38311","observation_id":"8ce1e9f8-61c5-4985-8d3f-5b499cb281e6","resolution":{"observed_at":"2026-08-08T04:56:54.879441Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.19449","last_updated":"2024-07-12T05:10:32Z","snapshot_observed_at":"2026-07-06T17:37:39.610989Z","submitted_at":"2024-02-29T18:47:52Z","title":"Heavy-Tailed Class Imbalance and Why Adam Outperforms Gradient Descent on Language Models","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.19449","snapshot_observed_at":"2026-08-08T04:56:54.561543Z","title":"Heavy-tailed class imbalance and why Adam outperforms gradient descent on language models.arXiv preprint arXiv:2402.19449,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2502.08532","last_updated":"2025-06-16T23:04:01Z","snapshot_observed_at":"2026-08-08T04:40:53.045522Z","submitted_at":"2025-02-12T16:12:17Z","title":"Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-08T04:56:54.561543Z"},"links":{"cited_paper":"/paper/2402.19449","citing_paper":"/paper/2502.08532"},"observation_digest":"sha256:40e73ef6a36f588a59e694c7f9d54c6bef0c1a5117f76be2a61a74052a81291a","observation_id":"b0d0ba62-37af-4f0e-bcbd-11c0dd21b4e3","resolution":{"observed_at":"2026-08-08T04:56:54.561543Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2305.04917","last_updated":"2023-06-12T15:29:49Z","snapshot_observed_at":"2026-07-06T15:24:42.200476Z","submitted_at":"2023-05-08T17:53:13Z","title":"Gradient descent with a general cost","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2305.04917","snapshot_observed_at":"2026-08-08T04:56:54.572784Z","title":"and Aubin-Frankowski, P.-C","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2502.08532","last_updated":"2025-06-16T23:04:01Z","snapshot_observed_at":"2026-08-08T04:40:53.045522Z","submitted_at":"2025-02-12T16:12:17Z","title":"Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-08T04:56:54.572784Z"},"links":{"cited_paper":"/paper/2305.04917","citing_paper":"/paper/2502.08532"},"observation_digest":"sha256:62aac230491976fab51d5b5a18120a8ae1e8bed12db86fcaf99fb17bdc28df5b","observation_id":"0637655f-160b-499d-bff0-38b94638158a","resolution":{"observed_at":"2026-08-08T04:56:54.572784Z","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":"2026-08-08T04:56:54.990142Z","title":"Improved anal- ysis of clipping algorithms for non-convex optimization","venue":null,"work_id":"5503e701-28ec-4d7a-8218-9cccef07736f","year":1998},"citing_paper":{"arxiv_id":"2502.08532","last_updated":"2025-06-16T23:04:01Z","snapshot_observed_at":"2026-08-08T04:40:53.045522Z","submitted_at":"2025-02-12T16:12:17Z","title":"Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-08T04:56:54.583051Z"},"links":{"citing_paper":"/paper/2502.08532"},"observation_digest":"sha256:ded90694ac6d3fc6ac7b0e840a377bd237d4a41c8c4648679a370a2bf3e9bc69","observation_id":"987dc433-f523-4cc0-ac49-7ea355f10d2c","resolution":{"observed_at":"2026-08-08T04:56:54.995457Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T04:56:54.973638Z","title":"Therefore, through (Bauschke et al., 2017b, Proposition 11.7) we get thath ∗ is increasing onR +","venue":null,"work_id":"57626ec1-4c0f-405f-899d-5e1d8b920f85","year":1977},"citing_paper":{"arxiv_id":"2502.08532","last_updated":"2025-06-16T23:04:01Z","snapshot_observed_at":"2026-08-08T04:40:53.045522Z","submitted_at":"2025-02-12T16:12:17Z","title":"Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-08T04:56:54.588258Z"},"links":{"citing_paper":"/paper/2502.08532"},"observation_digest":"sha256:9eae2cd8bc2d44eb25a340f0c188cc16b41eac211495b8e92b5666cbca58a79d","observation_id":"fc79ba83-3f5c-499f-b16a-f2578e1c4f49","resolution":{"observed_at":"2026-08-08T04:56:54.978845Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T04:56:54.940132Z","title":"Using Theorem 1.3 we thus obtain ∇ϕ∗(y) = min(1,∥y∥) sgn(y)and the algorithm becomes: xk+1 =x k −γmin(1/∥∇f(x k)∥, λ)∇f(xk), by pulling the norm inside themin","venue":null,"work_id":"90127d70-8c76-4199-9e66-cc71e1370341","year":1998},"citing_paper":{"arxiv_id":"2502.08532","last_updated":"2025-06-16T23:04:01Z","snapshot_observed_at":"2026-08-08T04:40:53.045522Z","submitted_at":"2025-02-12T16:12:17Z","title":"Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-08T04:56:54.598676Z"},"links":{"citing_paper":"/paper/2502.08532"},"observation_digest":"sha256:803dc3d6a7cbfe4a9f60bd2beffc8e0ec5d3aad7b2db4d15bfe81d604b83c656","observation_id":"128affbc-c83a-4ee3-8f62-825c2a71e36b","resolution":{"observed_at":"2026-08-08T04:56:54.946319Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T04:56:54.923939Z","title":null,"venue":null,"work_id":"476871e4-45e1-488a-a8bf-a742684fb5dc","year":2021},"citing_paper":{"arxiv_id":"2502.08532","last_updated":"2025-06-16T23:04:01Z","snapshot_observed_at":"2026-08-08T04:40:53.045522Z","submitted_at":"2025-02-12T16:12:17Z","title":"Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-08T04:56:54.604205Z"},"links":{"citing_paper":"/paper/2502.08532"},"observation_digest":"sha256:1d9bfff9801780604b2f58f47ce543fb8de2d72766df3a33fd89ea2305ab474d","observation_id":"4f6524ae-f603-433c-bfa5-4c24c9f63a1e","resolution":{"observed_at":"2026-08-08T04:56:54.928946Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T04:56:54.890609Z","title":null,"venue":null,"work_id":"854e05e9-5a24-428b-9a90-e242cc9175ee","year":2003},"citing_paper":{"arxiv_id":"2502.08532","last_updated":"2025-06-16T23:04:01Z","snapshot_observed_at":"2026-08-08T04:40:53.045522Z","submitted_at":"2025-02-12T16:12:17Z","title":"Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-08T04:56:54.615269Z"},"links":{"citing_paper":"/paper/2502.08532"},"observation_digest":"sha256:8b168637c09b99f4cebb5877175daa1517a56d9528624be77b2def717a24967c","observation_id":"7d051e34-ddda-4d27-9ded-a736b35add37","resolution":{"observed_at":"2026-08-08T04:56:54.895716Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T04:56:54.958214Z","title":null,"venue":null,"work_id":"b278025b-7813-46cb-a1e6-1a0dd4918e73","year":2000},"citing_paper":{"arxiv_id":"2502.08532","last_updated":"2025-06-16T23:04:01Z","snapshot_observed_at":"2026-08-08T04:40:53.045522Z","submitted_at":"2025-02-12T16:12:17Z","title":"Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-08T04:56:54.593485Z"},"links":{"citing_paper":"/paper/2502.08532"},"observation_digest":"sha256:a978a7713c7d00ae2eb1880641d1d8ee5fe2fa47fab493745833a1b58f72b77b","observation_id":"bc4b7d1b-54d7-443f-8f47-08e60b06c2b6","resolution":{"observed_at":"2026-08-08T04:56:54.962869Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2311.17296","last_updated":"2024-05-15T05:16:24Z","snapshot_observed_at":"2026-08-04T08:53:23.652013Z","submitted_at":"2023-11-29T00:48:18Z","title":"Mirror Duality in Convex Optimization","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.17296","snapshot_observed_at":"2026-08-08T04:56:54.550547Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2502.08532","last_updated":"2025-06-16T23:04:01Z","snapshot_observed_at":"2026-08-08T04:40:53.045522Z","submitted_at":"2025-02-12T16:12:17Z","title":"Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness","version":2},"reference_index":2012,"source":"pdf_text","source_observed_at":"2026-08-08T04:56:54.550547Z"},"links":{"cited_paper":"/paper/2311.17296","citing_paper":"/paper/2502.08532"},"observation_digest":"sha256:f628c81f5f3a0917a6169b36fd7bffca9e30457b362c61ba10f5841bf5eed435","observation_id":"fd8a9e62-d6aa-47de-bd40-78ee1264af13","resolution":{"observed_at":"2026-08-08T04:56:54.550547Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2406.08938","last_updated":"2024-11-18T20:56:37Z","snapshot_observed_at":"2026-07-06T18:30:10.950834Z","submitted_at":"2024-06-13T09:07:22Z","title":"Mirror and Preconditioned Gradient Descent in Wasserstein Space","version":2},"cited_work":{"arxiv_id":"2406.08938","doi":null,"metadata_source":"pith","pith_arxiv_id":"2406.08938","snapshot_observed_at":"2026-08-08T04:56:54.855379Z","title":"Mirror and Preconditioned Gradient Descent in Wasserstein Space","venue":"math.OC","work_id":"db7abc72-2e91-4818-b806-9293d9e7af4b","year":2024},"citing_paper":{"arxiv_id":"2502.08532","last_updated":"2025-06-16T23:04:01Z","snapshot_observed_at":"2026-08-08T04:40:53.045522Z","submitted_at":"2025-02-12T16:12:17Z","title":"Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness","version":2},"reference_index":2018,"source":"pdf_text","source_observed_at":"2026-08-08T04:56:54.539277Z"},"links":{"cited_paper":"/paper/2406.08938","citing_paper":"/paper/2502.08532"},"observation_digest":"sha256:816987e1768ccf272ca9c5c809a43a220b35a21e2c3ea7ce02054a2921f25e4a","observation_id":"d9a7425b-0cb6-4533-97d6-ad8458bf34f0","resolution":{"observed_at":"2026-08-08T04:56:54.862894Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2410.10800","last_updated":"2025-03-07T20:23:27Z","snapshot_observed_at":"2026-07-06T19:33:16.949210Z","submitted_at":"2024-10-14T17:57:33Z","title":"Optimizing $(L_0, L_1)$-Smooth Functions by Gradient Methods","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.10800","snapshot_observed_at":"2026-08-08T04:56:54.578227Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2502.08532","last_updated":"2025-06-16T23:04:01Z","snapshot_observed_at":"2026-08-08T04:40:53.045522Z","submitted_at":"2025-02-12T16:12:17Z","title":"Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness","version":2},"reference_index":2019,"source":"pdf_text","source_observed_at":"2026-08-08T04:56:54.578227Z"},"links":{"cited_paper":"/paper/2410.10800","citing_paper":"/paper/2502.08532"},"observation_digest":"sha256:7e5f63b668c6572bf3f47e1815035a393d4c171efd2035ee0a8001295db135c4","observation_id":"8c9e6964-da6a-406d-b9b1-4b6315c04c33","resolution":{"observed_at":"2026-08-08T04:56:54.578227Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2409.14989","last_updated":"2024-12-25T15:02:32Z","snapshot_observed_at":"2026-08-01T19:23:09.616554Z","submitted_at":"2024-09-23T13:11:37Z","title":"Methods for Convex $(L_0,L_1)$-Smooth Optimization: Clipping, Acceleration, and Adaptivity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.14989","snapshot_observed_at":"2026-08-08T04:56:54.545328Z","title":"Meth- ods for convex(L 0, L1)-smooth optimization: Clip- ping, acceleration, and adaptivity.arXiv preprint arXiv:2409.14989,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2502.08532","last_updated":"2025-06-16T23:04:01Z","snapshot_observed_at":"2026-08-08T04:40:53.045522Z","submitted_at":"2025-02-12T16:12:17Z","title":"Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness","version":2},"reference_index":2020,"source":"pdf_text","source_observed_at":"2026-08-08T04:56:54.545328Z"},"links":{"cited_paper":"/paper/2409.14989","citing_paper":"/paper/2502.08532"},"observation_digest":"sha256:f9b469aa5ae19aa60c38fb97b8f9068224862a7f7d4ffa08a648485a34c12c7b","observation_id":"68ffc6e6-f75d-41be-948d-d456195b48e9","resolution":{"observed_at":"2026-08-08T04:56:54.545328Z","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":"2026-08-08T04:56:54.566990Z","title":"and Patrinos, P","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2502.08532","last_updated":"2025-06-16T23:04:01Z","snapshot_observed_at":"2026-08-08T04:40:53.045522Z","submitted_at":"2025-02-12T16:12:17Z","title":"Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness","version":2},"reference_index":2021,"source":"pdf_text","source_observed_at":"2026-08-08T04:56:54.566990Z"},"links":{"citing_paper":"/paper/2502.08532"},"observation_digest":"sha256:85b5ffae04c217ac7240446be4cd1ed8658bdacdaa81bb4d01796d9efca15cf6","observation_id":"53871856-5521-4ca3-bda1-151d711e62f5","resolution":{"observed_at":"2026-08-08T04:56:54.566990Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1412.6980","last_updated":"2017-01-30T01:27:54Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2014-12-22T13:54:29Z","title":"Adam: A Method for Stochastic Optimization","version":9},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1412.6980","snapshot_observed_at":"2026-08-08T04:56:54.555901Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2502.08532","last_updated":"2025-06-16T23:04:01Z","snapshot_observed_at":"2026-08-08T04:40:53.045522Z","submitted_at":"2025-02-12T16:12:17Z","title":"Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness","version":2},"reference_index":2023,"source":"pdf_text","source_observed_at":"2026-08-08T04:56:54.555901Z"},"links":{"cited_paper":"/paper/1412.6980","citing_paper":"/paper/2502.08532"},"observation_digest":"sha256:83d31c79f5a221413a721306d01a6c1d14c81764de28c5f055fed985e76f0b8b","observation_id":"9536f7ba-5991-4d40-b0e3-f2e3f142869b","resolution":{"observed_at":"2026-08-08T04:56:54.555901Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2502.08532","last_updated":"2025-06-16T23:04:01Z","latest_version":2,"primary_category":"math.OC","snapshot_observed_at":"2026-08-08T04:40:53.045522Z","submitted_at":"2025-02-12T16:12:17Z","title":"Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness"},"reference_resolution":{"displayed":16,"state_counts":{"malformed_identifier":2,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":9,"verified_exact":1,"verified_fuzzy":4},"total_outbound_references":16},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 1 inbound Pith citation observation for arXiv:2502.08532."}