{"as_of":"2026-08-06T11:27:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:75dbb504e9789a232dbaa17e35723ba48eb98d936e548412c53c238115e8e5be","coverage":[{"denominator":30,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":30,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-23T05:26:37.263966Z","state":"measured"},{"denominator":31,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":31,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-06T06:34:29.942622+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":"2026-08-02T05:23:28.760890Z","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":[{"citation":{"cited_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.10806","snapshot_observed_at":"2026-08-02T05:23:28.760890Z","title":"Non-expansive mappings in two-time-scale stochastic approximation: Finite-time analysis","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.13414","last_updated":"2026-07-15T03:33:03Z","snapshot_observed_at":"2026-08-02T05:23:25.761648Z","submitted_at":"2026-07-15T03:33:03Z","title":"Non-Expansive Two-Time-Scale Stochastic Approximation: A Fixed-Schedule One-Quarter Barrier and Bias-Corrected Acceleration","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-02T05:23:28.760890Z"},"links":{"cited_paper":"/paper/2501.10806","citing_paper":"/paper/2607.13414"},"observation_digest":"sha256:783c35738ca821e54cce334fe32ef3edeca54701230a9a307b2b97fd9dabf92f","observation_id":"63c369d2-6897-4e6a-96a8-3e3a196fccf4","resolution":{"observed_at":"2026-08-02T05:23:28.760890Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2501.10806/citation-record","integrity":"/paper/2501.10806/integrity","json":"/paper/2501.10806/citation-record.json","paper":"/paper/2501.10806"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"8ea44c2d-a580-453c-bf50-12b265f16114","year":2011},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:4fd74743143310660a89c6f035bd7940758bf6e3dff9c10e72d0c831694f5e89","observation_id":"67ab41f5-51a0-49e2-ad27-6e42480cad87","resolution":{"observed_at":"2026-05-23T05:27:36.376070Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Borkar , Stochastic Approximation: A Dynamical Systems Viewpoint: Second Edition , Texts and Readings in Mathematics, Hindustan Book Agency","venue":null,"work_id":"ca405e9e-60c4-48e5-809b-1d48a51b9191","year":2022},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:a64936b310afd3faa78e00dbbf230231eb41a115ca22e4d7ccea793f20f03979","observation_id":"ce044a14-f0aa-43e6-a2a2-456553be58a8","resolution":{"observed_at":"2026-05-23T05:27:36.384771Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Bravo and R","venue":null,"work_id":"a5eff64b-4086-4b54-8e6a-7c9368c30592","year":2024},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:e85dc826ec787cb6f0f8e408aba57ee7f90d24ef78fd47f704e09bfc85c1693b","observation_id":"8fad1c5d-59cb-4bc5-b154-a2461835e955","resolution":{"observed_at":"2026-05-23T05:27:36.332122Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Bravo, R","venue":null,"work_id":"6343eaeb-6aa4-4834-8361-baf14fb7c418","year":2019},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:96a97928b6064c6be5279dee6abe793fc6a8c87e722ae1298176e5e96d9f1b17","observation_id":"e1e14bf0-2a02-49ac-8c69-9adc6ea5c139","resolution":{"observed_at":"2026-05-23T05:27:36.334758Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2504.19375","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Chandak, o(1/k) finite-time bound for non-linear two-time-scale stochastic approximation , 2025, https://arxiv.org/abs/2504.19375","venue":null,"work_id":"334aa458-9ed9-4308-b9e1-62eca3f116bd","year":2025},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:b07e04a98227fd00a2d35855e382bd0f96ccf7da28407166ee4be2849069c006","observation_id":"a119243c-e505-44f5-bb24-841de7d902b7","resolution":{"observed_at":"2026-05-23T05:27:36.025949Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2407.00575","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Chandak, I","venue":null,"work_id":"b1b697f7-256d-4b69-9231-31718b1ecf2a","year":2024},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:c1df6e2c61b8ce1e1ec85840f4b98f6dd013e005ca900bd72a7a70ed0cedede4","observation_id":"58378cdf-9044-4fc4-a621-a734d110c701","resolution":{"observed_at":"2026-05-23T05:27:36.035978Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Chandak, V","venue":null,"work_id":"a4787304-4cca-4cef-a40e-e602378aa6c0","year":2022},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:0bdf362600aadbde0a37d7d61236349a2f24d86bddded98b7ba1e4e358725716","observation_id":"0f22443d-17e0-4a5f-a230-a668c1d77134","resolution":{"observed_at":"2026-05-23T05:27:36.329162Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2503.18391","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Chandak, S","venue":null,"work_id":"657cbf85-26f3-43c9-9be9-9e0d6ac96895","year":2025},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:0eba34d5f70542172f1b1bacd4f31ce0b2469cea10c2a75b3b1c43054b2676c8","observation_id":"a04c7e4f-70e5-4e0f-b469-281e7e359355","resolution":{"observed_at":"2026-05-23T05:27:36.020311Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"e04f47b1-6be5-4fe7-a7e2-d10c0eaa4664","year":2020},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:0c53fecde7b53f3db0df199a3b90e4791880353f3f48d711185f45f0551a04d8","observation_id":"94b73246-f973-40fb-b1cf-5e944e368865","resolution":{"observed_at":"2026-05-23T05:27:36.378902Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2303.15740","last_updated":"2024-09-17T01:23:33Z","snapshot_observed_at":"2026-07-06T15:08:49.727355Z","submitted_at":"2023-03-28T05:32:30Z","title":"Concentration of Contractive Stochastic Approximation: Additive and Multiplicative Noise","version":2},"cited_work":{"arxiv_id":"2303.15740","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2303.15740","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"6a11e275-0da2-4788-a363-9740a9a32b6c","year":2024},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"cited_paper":"/paper/2303.15740","citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:b6ea16180d07e172c8c61381d28bbf3900429abf8f2bc3e3bb8b90ef4c7f05cc","observation_id":"2b9dbc19-93b1-4844-9873-4b80866931d3","resolution":{"observed_at":"2026-05-23T05:27:36.040325Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Davis and W","venue":null,"work_id":"a6e9a608-3427-428d-ad00-69d2f766ff82","year":2016},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:22a0e5606e08a6a200240a0d24e5cbe2cf0c145d48d8492035335f98be66d487","observation_id":"07f72026-e0c4-4c11-8dba-589747ee88d6","resolution":{"observed_at":"2026-05-23T05:27:36.323505Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"c9b92079-e3ab-4a6f-9d0a-2d0b043be022","year":2023},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:dfa34646fc13ecbc04561a791f0076944944ea7fa458983f0e087e15c7c80d27","observation_id":"a6388ff5-b8a5-4059-ba26-f1b4d33108df","resolution":{"observed_at":"2026-05-23T05:27:36.306027Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"ee1706f0-4931-4e16-bf46-96a7b7545d29","year":2022},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:fcf05c46b1104e2bbdb7cbb6b23190a3b18e0a9b39c7466fe72b0ab492083ec2","observation_id":"a0d6563a-9313-48c0-9d41-e68444fea051","resolution":{"observed_at":"2026-05-23T05:27:36.320781Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Facchinei and C","venue":null,"work_id":"9adcd0fb-96a4-4e35-b2ed-8f9c249af5b0","year":2010},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:d901579a50e18513a9a3fa3a2c1e946ad9bf4467d2853056b04671aa23588aa9","observation_id":"e8797504-50e4-4023-863c-cadcbb8942f6","resolution":{"observed_at":"2026-05-23T05:27:36.302883Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Facchinei and J.-S","venue":null,"work_id":"db5655f7-614a-4335-84d2-fa603a0b8c5c","year":2007},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:3c25c52f48dbd4b4d4e537bb8de4b73fb4d1126166c5a49da245dc96c418d392","observation_id":"e0883880-2b1f-46ae-ae60-7304063a6c6d","resolution":{"observed_at":"2026-05-23T05:27:36.309183Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2401.00364","last_updated":"2025-05-11T19:55:30Z","snapshot_observed_at":"2026-07-06T17:10:16.873073Z","submitted_at":"2023-12-31T01:30:14Z","title":"Tight Finite Time Bounds of Two-Time-Scale Linear Stochastic Approximation with Markovian Noise","version":2},"cited_work":{"arxiv_id":"2401.00364","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2401.00364","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"U., Khodadadian, S., and Maguluri, S","venue":null,"work_id":"fd491c76-bfc6-42b4-abf4-2c721ea80d2d","year":2023},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"cited_paper":"/paper/2401.00364","citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:ca4b324f1fc9b71280a459b8efc6d53bf5f77978133971f1c4c5e9963006504e","observation_id":"aef51157-2292-4b1a-b4c1-7e6fc6bfe2f8","resolution":{"observed_at":"2026-05-23T05:27:36.031054Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Kaledin, E","venue":null,"work_id":"2f312150-ba14-4238-bb72-7305a5db12f0","year":2020},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:093a4fbb4f9079795936740bd707871c49c91527688c224bac450b1b925cd9c3","observation_id":"42e0ac0c-4852-41c0-b698-a394eba2a742","resolution":{"observed_at":"2026-05-23T05:27:36.373170Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"4e591130-f06c-4e05-8308-038754135b08","year":2004},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:536519eebd42bf5c0141b99f6a7cd053a27bb7b762fc902cc725a9a9c6d58c33","observation_id":"bdcb5bd8-647a-412a-9e94-cfaacd293f9b","resolution":{"observed_at":"2026-05-23T05:27:36.363392Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Liang, J","venue":null,"work_id":"889eaf58-78c2-4e39-9f37-edb15a9ce855","year":2016},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:30f3a3606059319248a6e973001b6c5d064a81c5fd5d6b2f95c27018655f264f","observation_id":"c6e41987-27ee-4ee3-a5d6-c6566daacb44","resolution":{"observed_at":"2026-05-23T05:27:36.366463Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2408.11974","last_updated":"2025-01-27T18:37:18Z","snapshot_observed_at":"2026-07-06T19:04:18.161175Z","submitted_at":"2024-08-21T20:14:54Z","title":"Two-Timescale Gradient Descent Ascent Algorithms for Nonconvex Minimax Optimization","version":3},"cited_work":{"arxiv_id":"2408.11974","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2408.11974","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"c7686ccc-75a3-4524-b650-d57b99527777","year":2024},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"cited_paper":"/paper/2408.11974","citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:67815a5ebe09a9fd299ce3a63b57ae1044ff830373886e4dcca6a175ed3d56ec","observation_id":"c04e86ab-1520-468d-8aa0-b7caae2b88d5","resolution":{"observed_at":"2026-05-23T05:27:36.044145Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"d410b91a-cc82-40aa-87b4-60d62b190f76","year":2024},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:58693672fd7d74b8373f80bda71d65aa80989be2269c3c4fdabddcb47f5fe4dd","observation_id":"e0c64d9e-f3ba-4f53-8e2f-4d6d58397b25","resolution":{"observed_at":"2026-05-23T05:27:36.357575Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Nagurney and D","venue":null,"work_id":"e2369fb3-d01d-4348-8561-2e4f3342719c","year":2012},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:fa8efbc05a6f4a35daeaf73de6dab0cd951703764e4f46991258d08edcee000c","observation_id":"2abf81bd-10d8-44c4-9a04-194c83d1a6c7","resolution":{"observed_at":"2026-05-23T05:27:36.318089Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Nesterov et al., Lectures on convex optimization, vol","venue":null,"work_id":"c9d94fdf-fe61-4ae6-9c7c-09c5de992839","year":2018},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:4417546f537f1694762cb81ca940396d48f30340975cd0c2239df0e4a39f644a","observation_id":"e4c1b16f-7d0e-4f24-95f4-763441348b5c","resolution":{"observed_at":"2026-05-23T05:27:36.312082Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Platt and A","venue":null,"work_id":"39bc1d67-2a67-49bb-a101-e091038fdff3","year":1987},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:c6c4c01f5096093cea13c2316a25bdef62646677387bd6459513cc342af11cfe","observation_id":"2894df19-824a-4dd2-9e04-678abc41c30c","resolution":{"observed_at":"2026-05-23T05:27:36.315230Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Robbins and S","venue":null,"work_id":"c65a846a-1052-4f22-b600-743366d11794","year":1951},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:1c7d10284854249fd9bbce339f3d31b0b0870c1dddd20ee37c0767b2476da7fc","observation_id":"274f6a6f-afbe-4c19-91b4-15426f9c0153","resolution":{"observed_at":"2026-05-23T05:27:36.300336Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":"Srikant and L","venue":null,"work_id":"5e2f9982-8240-43d1-9090-8319d890d642","year":2019},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:db53fc8cb0280edd9a4785f8fcf3092e4f817d5ed1a8a88589e2c9c4a832c56d","observation_id":"d5e61cc2-a868-46f6-9b81-0ae751d36463","resolution":{"observed_at":"2026-05-23T05:27:36.326341Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"e7338f22-1390-45c4-90d2-c8d7780c187c","year":2018},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:3f785257eda693415860cfb70e0fc524761a7fbf336fae56cd582cf362de4c1c","observation_id":"93b0309b-5fdc-4dc2-89bf-90f26d58ee1d","resolution":{"observed_at":"2026-05-23T05:27:36.354529Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"1ff87ef5-63c5-4d77-98ec-de9387f0a0f0","year":2009},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:50fe22d7ec264bd01063482f8c0e173e84c2e03f3a366e7a19cff3f059f39c01","observation_id":"ec0b8c77-8484-4355-8de5-a197b99a2194","resolution":{"observed_at":"2026-05-23T05:27:36.360440Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"96b52458-41ef-42dc-9ec3-e2182208dd36","year":2020},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:e65db59903effec3eaa5518d4012894f8c62247342b91b561637c78361dc74f4","observation_id":"0addf60b-3e1e-468b-a073-168c9ad6022b","resolution":{"observed_at":"2026-05-23T05:27:36.369664Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"bc7a4ca9-5a50-4130-a2be-da5b165403d5","year":2024},"citing_paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis","version":4},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-05-23T05:26:37.263966Z"},"links":{"citing_paper":"/paper/2501.10806"},"observation_digest":"sha256:cfe1a2418dd7e76c2eb7e8b7dc82b21d5bf86c4df754ec26b29e6297c424d6d5","observation_id":"cf71cf5b-2cf3-4d9f-8658-53b23e270242","resolution":{"observed_at":"2026-05-23T05:27:36.381813Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2501.10806","last_updated":"2026-04-07T21:37:47Z","latest_version":4,"primary_category":"math.OC","snapshot_observed_at":"2026-08-05T12:05:21.111274Z","submitted_at":"2025-01-18T16:00:14Z","title":"Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis"},"reference_resolution":{"displayed":30,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":10,"verified_exact":6,"verified_fuzzy":14},"total_outbound_references":30},"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":"2026-08-06T06:34:29.942622+00:00","source":"crossref"},{"observed_at":"2026-08-06T06:34:23.284952+00:00","source":"retraction_watch"}],"thesis":"As of 6 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 1 inbound Pith citation observation for arXiv:2501.10806."}