{"as_of":"2026-08-07T06:54:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:7cc98e546f57d25666cc444a8469f95bb74362d04ae3f5af5c70f156daff6935","coverage":[{"denominator":25,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":25,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T22:42:10.459058Z","state":"measured"},{"denominator":26,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":26,"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":"2026-05-17T23:17:34.914457Z","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":"2026-05-17T23:20:27.667990Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization","version":1},"cited_work":{"arxiv_id":"2508.06743","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2508.06743","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Analysis of schedule-free nonconvex optimization.arXiv preprint arXiv:2508.06743","venue":null,"work_id":"4b7d6dae-75b1-4b63-ab73-bb1fef8d6149","year":null},"citing_paper":{"arxiv_id":"2511.07767","last_updated":"2026-05-12T15:05:44Z","snapshot_observed_at":"2026-08-02T18:37:31.673813Z","submitted_at":"2025-11-11T02:33:24Z","title":"Taking the Road Less Scheduled with Adaptive Polyak Steps","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-17T23:17:34.914457Z"},"links":{"cited_paper":"/paper/2508.06743","citing_paper":"/paper/2511.07767"},"observation_digest":"sha256:bbf4ecdc273e55d42f3c2b7ceb5616ec0923dc517e965a13440e8088959e6d3b","observation_id":"0cb2a3a8-a1f6-4130-a392-df937fbdb7af","resolution":{"observed_at":"2026-05-17T23:20:27.670616Z","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/2508.06743/citation-record","integrity":"/paper/2508.06743/integrity","json":"/paper/2508.06743/citation-record.json","paper":"/paper/2508.06743"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2405.15682","last_updated":"2024-10-29T22:40:23Z","snapshot_observed_at":"2026-07-06T18:19:25.869339Z","submitted_at":"2024-05-24T16:20:46Z","title":"The Road Less Scheduled","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.15682","snapshot_observed_at":"2026-08-05T22:42:10.351490Z","title":"The Road Less Scheduled","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-05T22:42:10.351490Z"},"links":{"cited_paper":"/paper/2405.15682","citing_paper":"/paper/2508.06743"},"observation_digest":"sha256:1436117973dac311ce4bf5cb3f9e52708676a61e830d305d1413c8fbc89dd00d","observation_id":"4c174d28-5204-429b-8e06-55475cc841e2","resolution":{"observed_at":"2026-08-05T22:42:10.351490Z","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":"2026-08-05T22:42:10.864939Z","title":"Performance of First-Order Methods for Convex Optimization","venue":null,"work_id":"26d0e9da-d562-4090-b25e-116505244ac4","year":2014},"citing_paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-05T22:42:10.356576Z"},"links":{"citing_paper":"/paper/2508.06743"},"observation_digest":"sha256:d48bc0f373c2fe6a0b4a36789f6ee00389104fd04cb152052eb0884fb4b2ce63","observation_id":"204e771a-3955-4182-8db3-301375f53f8c","resolution":{"observed_at":"2026-08-05T22:42:10.869449Z","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":"2026-08-05T22:42:10.851219Z","title":"Robust stochastic approximation approach to stochastic program- ming","venue":null,"work_id":"a3ddd2cb-ba7b-4c16-a5a9-943248cca892","year":2009},"citing_paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-05T22:42:10.361114Z"},"links":{"citing_paper":"/paper/2508.06743"},"observation_digest":"sha256:0e42c7699f03c2c963045e440372383a1fe987e71e6b07fb049ec67c5f1f5c19","observation_id":"bf168f9e-13c9-43fb-b419-c652be9c1e35","resolution":{"observed_at":"2026-08-05T22:42:10.855544Z","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":"2026-08-05T22:42:10.837488Z","title":"Stochastic first- and zeroth-order methods for nonconvex stochastic programming","venue":null,"work_id":"254fd41e-aa9e-404f-958f-3f16aad41a21","year":2013},"citing_paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-05T22:42:10.365526Z"},"links":{"citing_paper":"/paper/2508.06743"},"observation_digest":"sha256:3e3fae0bd41d395aea8c8cd03b322c7f727ee625465496637ff00097e337732a","observation_id":"906d3922-b179-46f5-b835-4ad870015411","resolution":{"observed_at":"2026-08-05T22:42:10.841807Z","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":"2026-08-05T22:42:10.823049Z","title":"Stochastic gradient descent for nonconvex learning without variance reduction","venue":null,"work_id":"a92d0d9f-d3d9-46e7-b060-70f125fdb600","year":2019},"citing_paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-05T22:42:10.369999Z"},"links":{"citing_paper":"/paper/2508.06743"},"observation_digest":"sha256:7b1acc275fa30d8e5bbf0be2a7a9f7dcf323f4593b008794317a20cd2d198b68","observation_id":"eddac4b6-1d4d-4824-9c8c-b109e1b7f98d","resolution":{"observed_at":"2026-08-05T22:42:10.827870Z","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":"2026-08-05T22:42:10.809014Z","title":"New Stochastic Approximation Type Procedures","venue":null,"work_id":"37a1cf72-719b-4a83-b7e0-eec2ad6a995f","year":1990},"citing_paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-05T22:42:10.374449Z"},"links":{"citing_paper":"/paper/2508.06743"},"observation_digest":"sha256:4108633f37e437c949a78b5dbdc61644b95b5f9969fe2e8116211dbc17132fb8","observation_id":"0bf5a05c-34dc-41ab-964b-56e3edb7e14a","resolution":{"observed_at":"2026-08-05T22:42:10.813532Z","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":"2026-08-05T22:42:10.794323Z","title":"Acceleration of Stochastic Approximation by Averaging","venue":null,"work_id":"00e158c1-5840-416b-bdf2-448c2373f3fc","year":1992},"citing_paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-05T22:42:10.379526Z"},"links":{"citing_paper":"/paper/2508.06743"},"observation_digest":"sha256:144d4a7387e7372ac0ba97d03bea1d0900e9e8f501d300984d59b28080e7beeb","observation_id":"9e340d0e-8a6a-4226-b2c3-2477de25c85b","resolution":{"observed_at":"2026-08-05T22:42:10.798575Z","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":"2026-08-05T22:42:10.780375Z","title":"Efficient Estimations from a Slowly Convergent Robbins-Monro Process","venue":null,"work_id":"24c3815d-0eae-4e8b-967b-d85f9549b848","year":1988},"citing_paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-05T22:42:10.383968Z"},"links":{"citing_paper":"/paper/2508.06743"},"observation_digest":"sha256:2b859160d2b2cd66cc72a344d9a7cf7e9b798e06ccc6d6413d68580a7263f7e0","observation_id":"26b5e73a-756f-438c-b407-8cd4ba3499c0","resolution":{"observed_at":"2026-08-05T22:42:10.784777Z","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":"2411.07061","last_updated":"2024-11-11T15:25:48Z","snapshot_observed_at":"2026-08-06T06:15:19.216332Z","submitted_at":"2024-11-11T15:25:48Z","title":"General framework for online-to-nonconvex conversion: Schedule-free SGD is also effective for nonconvex optimization","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.07061","snapshot_observed_at":"2026-08-05T22:42:10.388011Z","title":"General framework for online-to- nonconvex conversion: Schedule-free SGD is also effective for nonconvex optimization","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-05T22:42:10.388011Z"},"links":{"cited_paper":"/paper/2411.07061","citing_paper":"/paper/2508.06743"},"observation_digest":"sha256:82af66baac70b478afad6a30080ba5f57645eb8a83d050644641c9688d1e6b30","observation_id":"3319ad9c-3986-4ebd-a358-a586468ca060","resolution":{"observed_at":"2026-08-05T22:42:10.388011Z","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":"2026-08-05T22:42:10.766297Z","title":"Non-Asymptotic Analysis of Stochastic Approximation Algorithms for Machine Learning","venue":null,"work_id":"77f7e8c0-cab0-4b8a-bace-fe9d2f7c0f0a","year":2011},"citing_paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-05T22:42:10.392696Z"},"links":{"citing_paper":"/paper/2508.06743"},"observation_digest":"sha256:7f56b81f568a1059ccd1b14c5a9e1fedd30492c875d4baf7cf13fc1565db852d","observation_id":"fc9799cb-bcf8-4c22-a8fe-20fe0a3f376b","resolution":{"observed_at":"2026-08-05T22:42:10.770956Z","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":"2026-08-05T22:42:10.751972Z","title":"Making gradient descent optimal for strongly convex stochastic optimization","venue":null,"work_id":"60080293-a74a-40fe-bf0b-a5fdd3aa1a03","year":2012},"citing_paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-05T22:42:10.396887Z"},"links":{"citing_paper":"/paper/2508.06743"},"observation_digest":"sha256:385e5dc4a4ca3b523a53d30dbd26531ef31af1b0e5c51bcdefc7cd4b29b1e436","observation_id":"77b9272e-d2fc-45c4-affb-f6e6e601227c","resolution":{"observed_at":"2026-08-05T22:42:10.756585Z","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":"2026-08-05T22:42:10.736296Z","title":"Optimal Non-Asymptotic Bound of the Ruppert–Polyak Averaging without Strong Convexity","venue":null,"work_id":"29478e22-8f77-41ef-855b-e6b54593ca6e","year":2017},"citing_paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-05T22:42:10.401090Z"},"links":{"citing_paper":"/paper/2508.06743"},"observation_digest":"sha256:1a7a4bb2de6bfefe1cf99cb78e99116d589fe28e66421a80ddd288fcf0c236c8","observation_id":"79b7dd9b-f4a5-4457-a2c6-fbaf7ed5a75c","resolution":{"observed_at":"2026-08-05T22:42:10.741461Z","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":"2010.00406","last_updated":"2021-06-01T17:53:38Z","snapshot_observed_at":"2026-08-05T12:04:05.058060Z","submitted_at":"2020-10-01T13:46:32Z","title":"Momentum via Primal Averaging: Theoretical Insights and Learning Rate Schedules for Non-Convex Optimization","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2010.00406","snapshot_observed_at":"2026-08-05T22:42:10.405053Z","title":"Momentum via Primal Averaging: Theoretical Insights and Learning Rate Schedules for Non-Convex Optimization","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-05T22:42:10.405053Z"},"links":{"cited_paper":"/paper/2010.00406","citing_paper":"/paper/2508.06743"},"observation_digest":"sha256:83cfcf09d4589864cee456eacb18b2d05a48f2e661955c7d52062ef9e06b3cc6","observation_id":"02e29999-abb2-4e8a-9ab1-67737833cc57","resolution":{"observed_at":"2026-08-05T22:42:10.405053Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2007.07989","last_updated":"2020-08-18T03:55:26Z","snapshot_observed_at":"2026-08-05T11:18:58.735828Z","submitted_at":"2020-07-15T20:49:35Z","title":"An Improved Analysis of Stochastic Gradient Descent with Momentum","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2007.07989","snapshot_observed_at":"2026-08-05T22:42:10.411689Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-05T22:42:10.411689Z"},"links":{"cited_paper":"/paper/2007.07989","citing_paper":"/paper/2508.06743"},"observation_digest":"sha256:97e8a928cb627c11e4e06a39bf1d43c37121356c5cf4503e56d276c394523e8a","observation_id":"722c7471-74f2-4ab3-9df0-45fd7e08450f","resolution":{"observed_at":"2026-08-05T22:42:10.411689Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1412.7457","last_updated":"2014-12-23T18:01:17Z","snapshot_observed_at":"2026-07-06T04:04:34.630458Z","submitted_at":"2014-12-23T18:01:17Z","title":"Global convergence of the Heavy-ball method for convex optimization","version":1},"cited_work":{"arxiv_id":"1412.7457","doi":null,"metadata_source":"pith","pith_arxiv_id":"1412.7457","snapshot_observed_at":"2026-08-05T22:42:10.513632Z","title":"Global convergence of the Heavy-ball method for convex optimization","venue":"math.OC","work_id":"97f45cb8-c75b-4e61-a421-c296826cd6f1","year":2014},"citing_paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-05T22:42:10.416447Z"},"links":{"cited_paper":"/paper/1412.7457","citing_paper":"/paper/2508.06743"},"observation_digest":"sha256:a2ad0e5f8f72820e8a951e35bcbbe36bfdde2e0fcdf727c4f5a58d2bc1852c4b","observation_id":"aaef8263-9842-4fa4-ad36-f3674659166c","resolution":{"observed_at":"2026-08-05T22:42:10.520468Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T22:42:10.720484Z","title":"Exact Worst-Case Performance of First-Order Methods for Composite Convex Optimization","venue":null,"work_id":"b65567d8-abb7-43fe-904f-8dd5f0c58504","year":2017},"citing_paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-05T22:42:10.420872Z"},"links":{"citing_paper":"/paper/2508.06743"},"observation_digest":"sha256:1b417029d8a2572e5571678abf05627b6a41ae17a2db8909def0e3e0736f2353","observation_id":"d61405bf-8308-4047-af51-fc95021bc370","resolution":{"observed_at":"2026-08-05T22:42:10.725917Z","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":"2026-08-05T22:42:10.705270Z","title":"Exact Worst-case Performance of First-Order Methods for Smooth Convex Optimization","venue":null,"work_id":"9d75e465-13b9-4c7b-be13-489fe108e135","year":2016},"citing_paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-05T22:42:10.425055Z"},"links":{"citing_paper":"/paper/2508.06743"},"observation_digest":"sha256:5d38c1ce4ff7fc8975fb3d84215095aa37539b3a2a897cbdcdbbba9f47f43acc","observation_id":"5be2d11e-2a6f-4adc-9a55-ecd5895c6ebc","resolution":{"observed_at":"2026-08-05T22:42:10.710081Z","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":"2026-08-05T22:42:10.689810Z","title":"Introductory Lectures on Convex Optimization: A Basic Course","venue":null,"work_id":"c8e085e9-c236-4d81-b6f9-621d3ff508c2","year":2013},"citing_paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-05T22:42:10.429203Z"},"links":{"citing_paper":"/paper/2508.06743"},"observation_digest":"sha256:d743d18d5ea43e312095aa20a5807b9e36cf7d982a053181eb1b18d4e4adf4fb","observation_id":"d3931d19-0e5a-495e-a158-f65bc455e346","resolution":{"observed_at":"2026-08-05T22:42:10.694530Z","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":"2026-08-05T22:42:10.673860Z","title":"Smooth Strongly Convex Interpolation and Exact Worst-case Perfor- mance of First-order Methods","venue":null,"work_id":"bfc3763d-60f6-40fe-9918-e5e077dd8ac8","year":2019},"citing_paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-05T22:42:10.433266Z"},"links":{"citing_paper":"/paper/2508.06743"},"observation_digest":"sha256:401d60c0f5626b84ec2b8ed0cac31d970d3e584331d8eeb735dbc46b00ab227a","observation_id":"91604a6f-a82d-4428-9dad-7a19b3b2e96c","resolution":{"observed_at":"2026-08-05T22:42:10.678461Z","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":"2026-08-05T22:42:10.656825Z","title":"Stochastic Performance Esti- mation Problem: Tight Convergence Guarantees for Stochastic Gradient Methods","venue":null,"work_id":"88e0f5c7-6e41-4f0b-b9a6-f873aee2406e","year":2021},"citing_paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-05T22:42:10.437363Z"},"links":{"citing_paper":"/paper/2508.06743"},"observation_digest":"sha256:0e04b8baa387fa2a06076e506d5418ee21822db9aca4d5f582108b5b8ef83d2a","observation_id":"9d689c9a-4c32-4724-8b0d-ddde1350bdfe","resolution":{"observed_at":"2026-08-05T22:42:10.661525Z","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":"2026-08-05T22:42:10.641446Z","title":"On worst-case analyses for first-order optimization methods","venue":null,"work_id":"79fa8769-301e-4c1c-8d3a-349fa4ebfecc","year":2024},"citing_paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-05T22:42:10.442077Z"},"links":{"citing_paper":"/paper/2508.06743"},"observation_digest":"sha256:2db8d4844d84b28c3d880627f408688ab97aa7970341202fdeaf2ed35880222c","observation_id":"0cebab8b-24e0-42b3-befc-7f23fe1342a1","resolution":{"observed_at":"2026-08-05T22:42:10.646197Z","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":"2405.18392","last_updated":"2024-10-17T12:01:15Z","snapshot_observed_at":"2026-07-06T18:21:26.195207Z","submitted_at":"2024-05-28T17:33:54Z","title":"Scaling Laws and Compute-Optimal Training Beyond Fixed Training Durations","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.18392","snapshot_observed_at":"2026-08-05T22:42:10.446190Z","title":"Scaling Laws and Compute-Optimal Training Beyond Fixed Training Durations","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-05T22:42:10.446190Z"},"links":{"cited_paper":"/paper/2405.18392","citing_paper":"/paper/2508.06743"},"observation_digest":"sha256:e3b7c0aa7affdd4a139fb9ab3dc8703dcef9de660a702106a5d0e42488fc74ef","observation_id":"25ab7824-863b-428a-92a9-768cb60b62eb","resolution":{"observed_at":"2026-08-05T22:42:10.446190Z","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":"2026-08-05T22:42:10.626721Z","title":null,"venue":null,"work_id":"20da7b81-4b6c-43fd-8cac-3ad25e73a1ca","year":null},"citing_paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-05T22:42:10.450722Z"},"links":{"citing_paper":"/paper/2508.06743"},"observation_digest":"sha256:463fe684fccf2cfe695e9968cf40e042a45b207391ef30c89e61b82e6bb1494d","observation_id":"51daeb0a-fad2-4d14-8c9d-e88444d878a7","resolution":{"observed_at":"2026-08-05T22:42:10.631185Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2026-08-05T22:42:10.611365Z","title":null,"venue":null,"work_id":"ae133b21-051a-430e-be20-c561a79dc9f6","year":null},"citing_paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-05T22:42:10.454853Z"},"links":{"citing_paper":"/paper/2508.06743"},"observation_digest":"sha256:3f06588dd0670f600651ab7a9faa05621d92efdc3228c1b77e53cf7089980e8e","observation_id":"eb397e76-cf2f-4253-8034-6157e7e91859","resolution":{"observed_at":"2026-08-05T22:42:10.616121Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2026-08-05T22:42:10.594973Z","title":"O M P _ N U M _ T H R E A D S","venue":null,"work_id":"51d5acb7-ed7a-4839-ae49-847c942032c0","year":null},"citing_paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-05T22:42:10.459058Z"},"links":{"citing_paper":"/paper/2508.06743"},"observation_digest":"sha256:80803feac364425ef635df90d047efe6b776f6e8ccbf80eae37fba85a884ab75","observation_id":"1d4dcff6-d1ad-4f01-bde6-b5aa4bff6e9e","resolution":{"observed_at":"2026-08-05T22:42:10.599414Z","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"}}],"paper":{"arxiv_id":"2508.06743","last_updated":"2025-08-08T22:54:35Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-06T15:57:28.533084Z","submitted_at":"2025-08-08T22:54:35Z","title":"Analysis of Schedule-Free Nonconvex Optimization"},"reference_resolution":{"displayed":25,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":7,"verified_exact":1,"verified_fuzzy":17},"total_outbound_references":25},"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 7 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 1 inbound Pith citation observation for arXiv:2508.06743."}