{"as_of":"2026-08-07T19:13:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5b4d6035c12c77ec798470734a7f601ee77866f2f0e22963b5f7a0b77af01b7f","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":"2026-08-07T06:34:17.273281+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":"2026-08-05T22:42:10.405053Z","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":"2026-07-02T01:56:27.784307Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"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":"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":"2010.00406","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2010.00406","snapshot_observed_at":"2026-07-02T01:56:27.784307Z","title":null,"venue":null,"work_id":"e6edd4d0-9a0c-4c39-a887-7698a8f264d0","year":2010},"citing_paper":{"arxiv_id":"2510.04988","last_updated":"2026-05-10T14:57:23Z","snapshot_observed_at":"2026-08-04T04:12:48.359316Z","submitted_at":"2025-10-06T16:24:57Z","title":"Adaptive Memory Momentum via a Model-Based Framework for Deep Learning Optimization","version":3},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-18T09:44:53.004293Z"},"links":{"cited_paper":"/paper/2010.00406","citing_paper":"/paper/2510.04988"},"observation_digest":"sha256:77ec665fdf231b5b6a26ed1ebdaf83f21d79cdb3e6920a05902e8730e9750932","observation_id":"85cf2d24-84f0-46fe-9cca-60b84f8a9143","resolution":{"observed_at":"2026-05-18T09:46:12.499461Z","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"}},{"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":"2010.00406","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2010.00406","snapshot_observed_at":"2026-07-02T01:56:27.784307Z","title":null,"venue":null,"work_id":"e6edd4d0-9a0c-4c39-a887-7698a8f264d0","year":2010},"citing_paper":{"arxiv_id":"2606.03899","last_updated":"2026-06-03T02:06:07Z","snapshot_observed_at":"2026-08-01T15:38:47.150046Z","submitted_at":"2026-06-02T16:54:38Z","title":"Denoise First, Orthogonalize Later: Understanding Momentum in Muon via Spectral Filtering","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-28T11:24:38.292078Z"},"links":{"cited_paper":"/paper/2010.00406","citing_paper":"/paper/2606.03899"},"observation_digest":"sha256:7732c32b3047b572fdd728e97900a8840b1d47d7f2a901126da0bc17cf67ecc9","observation_id":"d64c9c43-ff53-41a0-b828-2d2c34f1ff4a","resolution":{"observed_at":"2026-07-02T01:56:27.786559Z","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"}},{"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":"2026-07-13T04:58:09.207999Z","title":"Momentum via primal averaging: Theoretical insights and learning rate schedules for non-convex optimization.arXiv preprint arXiv:2010.00406, 2020","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.09167","last_updated":"2026-07-10T07:52:01Z","snapshot_observed_at":"2026-08-07T12:16:39.890395Z","submitted_at":"2026-07-10T07:52:01Z","title":"Understanding Schedule-Free Methods in Nonconvex Optimization: Rate Guarantees and Escaping Saddles","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-13T04:58:09.207999Z"},"links":{"cited_paper":"/paper/2010.00406","citing_paper":"/paper/2607.09167"},"observation_digest":"sha256:cc1ba74771178858a012d430d2948148f8621092a506a4f5ecfb479ed2ffacda","observation_id":"0f0c96b3-181e-48ca-b41a-c414d3cbe6b2","resolution":{"observed_at":"2026-07-13T04:58:09.207999Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2010.00406/citation-record","integrity":"/paper/2010.00406/integrity","json":"/paper/2010.00406/citation-record.json","paper":"/paper/2010.00406"},"outbound":[],"paper":{"arxiv_id":"2010.00406","last_updated":"2021-06-01T17:53:38Z","latest_version":4,"primary_category":"cs.LG","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"},"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":"2026-08-07T06:34:17.273281+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 0 of 0 outbound references and 4 inbound Pith citation observations for arXiv:2010.00406."}