{"as_of":"2026-08-09T18:57:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:abf487b2d7027d32865a6458c4e7c9d23c5d8a346dbd147ff6edd325326ee854","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":4,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":4,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":4,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":4,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-08T11:35:29.572008Z","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":"2026-05-22T15:51:45.785757Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2410.15637","last_updated":"2025-03-22T03:59:25Z","snapshot_observed_at":"2026-07-06T19:36:49.949466Z","submitted_at":"2024-10-21T04:50:57Z","title":"Large Deviation Upper Bounds and Improved MSE Rates of Nonlinear SGD: Heavy-tailed Noise and Power of Symmetry","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.15637","snapshot_observed_at":"2026-08-08T11:35:29.572008Z","title":"Large deviations and improved mean-squared error rates of nonlinear sgd: Heavy-tailed noise and power of symmetry","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.572008Z"},"links":{"cited_paper":"/paper/2410.15637","citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:f4518f0b182b129b1374c64c736e49b1bdfe353cd59080c36f54c1700ff5e9f5","observation_id":"572cd5c0-e405-444e-b68b-2cfb0a13ded0","resolution":{"observed_at":"2026-08-08T11:35:29.572008Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.15637","last_updated":"2025-03-22T03:59:25Z","snapshot_observed_at":"2026-07-06T19:36:49.949466Z","submitted_at":"2024-10-21T04:50:57Z","title":"Large Deviation Upper Bounds and Improved MSE Rates of Nonlinear SGD: Heavy-tailed Noise and Power of Symmetry","version":2},"cited_work":{"arxiv_id":"2410.15637","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2410.15637","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Large deviations and improved mean-squared error rates of nonlinear sgd: Heavy-tailed noise and power of symmetry","venue":null,"work_id":"da1f8188-852c-4db5-9948-2e6f1c3e2fab","year":2024},"citing_paper":{"arxiv_id":"2505.03736","last_updated":"2026-04-16T07:40:20Z","snapshot_observed_at":"2026-07-06T21:19:53.873736Z","submitted_at":"2025-05-06T17:59:36Z","title":"Decentralized Nonconvex Optimization under Heavy-Tailed Noise: Normalization and Optimal Convergence","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-05-22T15:49:07.709952Z"},"links":{"cited_paper":"/paper/2410.15637","citing_paper":"/paper/2505.03736"},"observation_digest":"sha256:0d2e68e9eff78b4abbde8115c9228841096e6abc3a34202eb8f215006e6dfe44","observation_id":"dd122282-7da8-4691-a97f-36fd858e45ff","resolution":{"observed_at":"2026-05-22T15:51:45.788922Z","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"}},{"citation":{"cited_paper":{"arxiv_id":"2410.15637","last_updated":"2025-03-22T03:59:25Z","snapshot_observed_at":"2026-07-06T19:36:49.949466Z","submitted_at":"2024-10-21T04:50:57Z","title":"Large Deviation Upper Bounds and Improved MSE Rates of Nonlinear SGD: Heavy-tailed Noise and Power of Symmetry","version":2},"cited_work":{"arxiv_id":"2410.15637","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2410.15637","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Large deviations and improved mean-squared error rates of nonlinear sgd: Heavy-tailed noise and power of symmetry","venue":null,"work_id":"da1f8188-852c-4db5-9948-2e6f1c3e2fab","year":2024},"citing_paper":{"arxiv_id":"2510.06141","last_updated":"2026-05-21T09:57:40Z","snapshot_observed_at":"2026-07-06T22:31:58.848080Z","submitted_at":"2025-10-07T17:15:08Z","title":"High-Probability Convergence Guarantees of Decentralized SGD","version":5},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-05-18T08:45:22.688243Z"},"links":{"cited_paper":"/paper/2410.15637","citing_paper":"/paper/2510.06141"},"observation_digest":"sha256:9ca47a7c988235fa71cd6b44e34e58c96b59c093ad9c64d23596cd86d6061bee","observation_id":"3bd73bcd-cc1a-46ab-954e-9181071adee4","resolution":{"observed_at":"2026-05-18T08:46:07.870578Z","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"}},{"citation":{"cited_paper":{"arxiv_id":"2410.15637","last_updated":"2025-03-22T03:59:25Z","snapshot_observed_at":"2026-07-06T19:36:49.949466Z","submitted_at":"2024-10-21T04:50:57Z","title":"Large Deviation Upper Bounds and Improved MSE Rates of Nonlinear SGD: Heavy-tailed Noise and Power of Symmetry","version":2},"cited_work":{"arxiv_id":"2410.15637","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2410.15637","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Large deviations and improved mean-squared error rates of nonlinear sgd: Heavy-tailed noise and power of symmetry","venue":null,"work_id":"da1f8188-852c-4db5-9948-2e6f1c3e2fab","year":2024},"citing_paper":{"arxiv_id":"2510.06141","last_updated":"2026-05-21T09:57:40Z","snapshot_observed_at":"2026-07-06T22:31:58.848080Z","submitted_at":"2025-10-07T17:15:08Z","title":"High-Probability Convergence Guarantees of Decentralized SGD","version":6},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-05-22T13:14:57.263058Z"},"links":{"cited_paper":"/paper/2410.15637","citing_paper":"/paper/2510.06141"},"observation_digest":"sha256:1707631fbb53148b71dc2b85f41dcb6a91ca4a85a1ed9745de49633e8a77a489","observation_id":"a99a18b2-0e92-4f22-87ef-770675cf4dab","resolution":{"observed_at":"2026-05-22T13:16:35.017539Z","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/2410.15637/citation-record","integrity":"/paper/2410.15637/integrity","json":"/paper/2410.15637/citation-record.json","paper":"/paper/2410.15637"},"outbound":[],"paper":{"arxiv_id":"2410.15637","last_updated":"2025-03-22T03:59:25Z","latest_version":2,"primary_category":"cs.LG","snapshot_observed_at":"2026-07-06T19:36:49.949466Z","submitted_at":"2024-10-21T04:50:57Z","title":"Large Deviation Upper Bounds and Improved MSE Rates of Nonlinear SGD: Heavy-tailed Noise and Power of Symmetry"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"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 0 of 0 outbound references and 4 inbound Pith citation observations for arXiv:2410.15637."}