{"as_of":"2026-08-10T19:55:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:925484c83d7ca70ee29497950d51d1b9811c9761c9e72c49b9f972558413fece","coverage":[{"denominator":35,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":35,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T12:00:38.314620Z","state":"measured"},{"denominator":35,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":35,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"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":[],"links":{"evidence":"/evidence","html":"/paper/2608.07248/citation-record","integrity":"/paper/2608.07248/integrity","json":"/paper/2608.07248/citation-record.json","paper":"/paper/2608.07248"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T12:00:49.090460Z","title":"Hessian Riemannian gradient flows in convex programming","venue":null,"work_id":"3028ae71-6d2b-4417-96ca-614f4402ef66","year":2004},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.095383Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:ca670c3a5c55eef5b6c257510740c12fb4fe7bb086468e7e39c9e69ca3117bf5","observation_id":"2395d21b-b057-4718-9a3e-f4c89487c3c1","resolution":{"observed_at":"2026-08-10T12:00:49.100717Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-10T12:00:49.069769Z","title":"Singular Riemannian barrier methods and gradient-projection dynamical systems for constrained optimization.Optimization, 53(5–6):435–454, 2004","venue":null,"work_id":"a16d518e-0e4d-456b-9f23-56d13117ff2a","year":2004},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.103444Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:446d23ac630d0d1a1911a491687d2d193a9c4b40a0c7f55e54f2e9317e455930","observation_id":"fc605745-f60d-474f-a1fa-9778fe004b99","resolution":{"observed_at":"2026-08-10T12:00:49.076375Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-10T12:00:49.045389Z","title":null,"venue":null,"work_id":"691fe637-e29f-4cc8-8053-79706f1a1f46","year":2013},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.109579Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:ca61b17a1d5a288dfbbccbe9dea9c89a71614f4ee9dbd2bc2ca1802b3def9957","observation_id":"5ec4009b-b824-4855-933a-cc31e520f065","resolution":{"observed_at":"2026-08-10T12:00:49.052031Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-10T12:00:49.022383Z","title":"Bauschke, J´ erˆ ome Bolte, and Marc Teboulle","venue":null,"work_id":"367c9995-2472-44fc-ac12-d9972afae81e","year":2017},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.115953Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:84af3314beb36ca60c20e94ab1a4fe207252ae03659fa0d30b0278dc2cefb45f","observation_id":"fc19c3ed-575f-4a8a-8760-be0e9dfdc816","resolution":{"observed_at":"2026-08-10T12:00:49.028854Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-10T12:00:49.003409Z","title":null,"venue":null,"work_id":"caaa36d9-9abd-4163-b886-89132adf93ab","year":2007},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.123029Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:bb3ab55c15f8d0f2dd1046ced57f8b67381528dd4b5cf51b7002423f89ea2e76","observation_id":"1340cf75-28b7-435a-b904-1c1a8ab7b4a3","resolution":{"observed_at":"2026-08-10T12:00:49.009436Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-10T12:00:48.985859Z","title":"Lewis, and Masahiro Shiota","venue":null,"work_id":"520ec87f-4e86-4c54-a67a-ab3fc5351fc3","year":2007},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.130125Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:b215b810910095d63aae286771362e9c26fe2f7250ac43a18532f95302c7c602","observation_id":"b9e54e9c-c870-43fe-9685-f5602855f4d2","resolution":{"observed_at":"2026-08-10T12:00:48.991747Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-10T12:00:48.968451Z","title":"Curiosities and counterexamples in smooth convex optimization.Mathematical Programming, 195(1–2):553–603, 2022","venue":null,"work_id":"578a3f45-f5a4-47e7-9ac1-63a1365a6dbd","year":2022},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.136861Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:8cbd9dcc4a436cab117dff60e9776b676d2bbcb680c3d400f0a7eadeb13b7a0a","observation_id":"caed55d7-cc94-4193-8ffd-9bf3a9f2c79c","resolution":{"observed_at":"2026-08-10T12:00:48.974172Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T12:00:38.143148Z","title":"First order methods beyond convexity and Lipschitz gradient continuity with applications to quadratic inverse problems.SIAM Journal on Optimization, 28(3):2131–2151, 2018","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.143148Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:f5e3889c557f5f884007e4342f10e64b33901eba24b1cfa18bb47a8893bb4295","observation_id":"8380ba9e-b238-4211-996d-de70a9279bae","resolution":{"observed_at":"2026-08-10T12:00:38.143148Z","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":"2026-08-10T12:00:48.932504Z","title":"Bomze, Panayotis Mertikopoulos, Werner Schachinger, and Mathias Staudigl","venue":null,"work_id":"6af56b0e-b0ff-4c24-b10d-530c137984ff","year":2019},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.148851Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:e64a949966bb32fee066784da3d36fdf825640b6f7abffe6769d9bd711d53a8c","observation_id":"9be3e07c-4fbc-47b9-8d2a-4a187d8a07c0","resolution":{"observed_at":"2026-08-10T12:00:48.939233Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2404.08073","last_updated":"2026-05-25T08:13:38Z","snapshot_observed_at":"2026-07-06T17:59:04.250437Z","submitted_at":"2024-04-11T18:28:01Z","title":"Spurious Stationarity and Hardness Results for Bregman Proximal-Type Algorithms","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.08073","snapshot_observed_at":"2026-08-10T12:00:38.154467Z","title":"Spurious stationarity and hardness results for Bregman proximal- type algorithms.arXiv preprint arXiv:2404.08073, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.154467Z"},"links":{"cited_paper":"/paper/2404.08073","citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:1f63ae590bab75de6fd4b998dcf92d4719ba519999e64c75f1fbe92915aa1150","observation_id":"6e28424d-f28a-4d9d-a5ee-3af5a621518f","resolution":{"observed_at":"2026-08-10T12:00:38.154467Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2608.05035","last_updated":"2026-08-05T16:41:18Z","snapshot_observed_at":"2026-08-08T23:13:49.258606Z","submitted_at":"2026-08-05T16:41:18Z","title":"On the Iterate Convergence of Bregman Projected Gradient Method","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2608.05035","snapshot_observed_at":"2026-08-10T12:00:38.160589Z","title":"On the iterate convergence of Bregman projected gradient method.arXiv preprint arXiv:2608.05035, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.160589Z"},"links":{"cited_paper":"/paper/2608.05035","citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:f0b400e1837e4b4107fe6e20922607b3f66947ee6dc4ee69e2111065177a7270","observation_id":"e231797e-e820-4884-91fc-9a36679ca328","resolution":{"observed_at":"2026-08-10T12:00:38.160589Z","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":"2026-08-10T12:00:48.911828Z","title":"Sinkhorn distances: Lightspeed computation of optimal transport","venue":null,"work_id":"ca2e8a1e-c846-4e2f-ae8e-106eff28d084","year":2013},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.166707Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:3b6446ee7dcfe761dfe2667eea6b4c415a6b95bb01177344359cfc1abddf0ee7","observation_id":"86845fd0-677b-439b-bf46-f5b9f73d66ee","resolution":{"observed_at":"2026-08-10T12:00:48.917692Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-10T12:00:48.891836Z","title":"Dang and Guanghui Lan","venue":null,"work_id":"7d017490-b553-487c-9ae7-215663f77623","year":2015},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.175336Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:c3c4a7894c5edc35922779f7e3bb66cb98113276bf26d3b16ca99486472faf09","observation_id":"00a7e46a-c67a-4f50-aca0-5922e2f95960","resolution":{"observed_at":"2026-08-10T12:00:48.898550Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-10T12:00:48.872309Z","title":"Nonconvex stochastic Bregman proximal gradient method with application to deep learning.Journal of Machine Learning Research, 26(39):1–44, 2025","venue":null,"work_id":"e30c5593-6c3f-424f-b3d6-404d6dfa7908","year":2025},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.180559Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:27cb6a9696c05fc8b00a081bfc317a143e87fe3993eb2617882656c819bb4dd0","observation_id":"55f8c75b-f11d-4d06-8cee-f9268a6f3f7b","resolution":{"observed_at":"2026-08-10T12:00:48.878460Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.15264","last_updated":"2025-07-25T05:02:24Z","snapshot_observed_at":"2026-08-09T13:13:51.158159Z","submitted_at":"2025-07-21T05:58:52Z","title":"On exploration of an interior mirror descent flow for stochastic nonconvex constrained problem","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.15264","snapshot_observed_at":"2026-08-10T12:00:38.185645Z","title":"On exploration of an interior mirror descent flow for stochastic nonconvex constrained problem.arXiv preprint arXiv:2507.15264v3, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.185645Z"},"links":{"cited_paper":"/paper/2507.15264","citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:db0489f90f7114bc3aa1c99758c690e423349ca8eb09d523f8ff2546d4fb017a","observation_id":"2f460f4b-7463-4563-800e-aa4fb773ddf0","resolution":{"observed_at":"2026-08-10T12:00:38.185645Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2608.01658","last_updated":"2026-08-03T03:47:30Z","snapshot_observed_at":"2026-08-06T23:32:53.800828Z","submitted_at":"2026-08-03T03:47:30Z","title":"Non-KKT Accumulation in Entropic Mirror Descent","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2608.01658","snapshot_observed_at":"2026-08-10T12:00:38.191837Z","title":"Non-KKT accumulation in entropic mirror descent, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.191837Z"},"links":{"cited_paper":"/paper/2608.01658","citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:8f6ec3f3925545415fbbe4a8bf11e4b812b59e0a4b47440c66f52e1824960e8c","observation_id":"952e0195-e9d1-49be-b42e-6fdb15f4b32c","resolution":{"observed_at":"2026-08-10T12:00:38.191837Z","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":"2026-08-10T12:00:48.851110Z","title":"Doan, Subhonmesh Bose, D","venue":null,"work_id":"c9bf4166-ba6f-4e88-bc29-51019ac2e60e","year":2019},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.197723Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:ea1cd129a78fa163aed1422a464372fc66a7618bc284d9fa1e2d0b44b614007d","observation_id":"5e8a6288-8be7-4a1c-9b4f-e55b1852209e","resolution":{"observed_at":"2026-08-10T12:00:48.858451Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T12:00:38.204852Z","title":"A bregman ADMM for Bethe variational problem.arXiv preprint arXiv:2502.04613, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.204852Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:eeb147085ebb42c4528fbd7c5ff5eab9685796bbb9e86af94d361b46e86e94d5","observation_id":"0eda8218-ef94-4ede-8339-456737b8dce3","resolution":{"observed_at":"2026-08-10T12:00:38.204852Z","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":"2026-08-10T12:00:48.828786Z","title":"On gradients of functions definable in O-minimal structures.Annales de l’Institut Fourier, 48(3):769–783, 1998","venue":null,"work_id":"2210d68a-8613-4b9d-bcfa-1e31e96c3627","year":1998},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.212288Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:34a265e98fd5f1b5d4f2aa7546ec51f696f6b6813d965d5223ea8c668feb71e1","observation_id":"99e70ec5-11de-447f-9360-4674b09f0d22","resolution":{"observed_at":"2026-08-10T12:00:48.836113Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-10T12:00:48.808123Z","title":"A convergent single-loop algorithm for relaxation of Gromov–Wasserstein in graph data","venue":null,"work_id":"12c9b496-6a72-44d9-a94a-f2059cad2510","year":2023},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.219070Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:292e1d01d9f2249dfbe23744d608715468665dde3712bd76ff116e352a6c689e","observation_id":"b27ca811-c157-4165-b77f-c98dd98db449","resolution":{"observed_at":"2026-08-10T12:00:48.815786Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-10T12:00:48.789166Z","title":"Convergence of the exponentiated gradient method with Armijo line search","venue":null,"work_id":"d4b2bc09-28a1-45f2-bd8c-0b505eeac4d0","year":2019},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.225326Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:85612e1d2a7b6b89546d16c638a4f56235559d0582469082465850aef2d04a5c","observation_id":"97a3806d-1bba-40b0-b9a1-20919fc8da89","resolution":{"observed_at":"2026-08-10T12:00:48.795434Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-10T12:00:48.772049Z","title":"Lee, and Sanjeev Arora","venue":null,"work_id":"738964c9-02ed-450d-bbc3-745eb32e2d86","year":2022},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.231158Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:5493cb85967f0389074a37e6f4fdda6a596ae3b19329fa9b080081bcd820505b","observation_id":"8d679168-af54-4cd9-bdfb-43c4333cd8e9","resolution":{"observed_at":"2026-08-10T12:00:48.777457Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-10T12:00:48.754348Z","title":"Gromov–Wasserstein distances and the metric approach to object matching.Foundations of Computational Mathematics, 11(4):417–487, 2011","venue":null,"work_id":"29599270-77d8-46d8-99b3-9865e737091e","year":2011},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.236543Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:0374a0a68bae8ddf0ff2511f6ef524e0210a3d4fd709a6a71196c94d1a82c962","observation_id":"6adfe90f-57f3-4c68-95f2-f2c2b7981967","resolution":{"observed_at":"2026-08-10T12:00:48.759812Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-10T12:00:48.732763Z","title":"Global convergence of model function based Bregman proximal minimization algorithms.Journal of Global Optimization, 83(4):753–781, 2022","venue":null,"work_id":"f7f6ff33-8c80-4809-baac-d862e5ef514c","year":2022},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.242955Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:e1b2cf44fcaf44ebf795862a7924e1a4ad5298dc960357a484a4da8712039319","observation_id":"0d9cfe2b-b959-4421-b4e7-598d14293201","resolution":{"observed_at":"2026-08-10T12:00:48.739864Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-10T12:00:48.710903Z","title":"Elementary vectors and conformal sums in polyhedral geometry and their relevance for metabolic pathway analysis.Frontiers in Genetics, 7:90, 2016","venue":null,"work_id":"a0abfc83-f441-4dc6-9315-77d32af95b9c","year":2016},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.248317Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:a3bef9a0036ca3e4cd55ef00b87215fc88e44b0815be8bacf3e7fcf60ee3edf4","observation_id":"5d0aa69d-d2e0-4c12-b3f8-42bdcf18f7fa","resolution":{"observed_at":"2026-08-10T12:00:48.716950Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-10T12:00:48.693191Z","title":"Computational optimal transport.Foundations and Trends in Machine Learning, 11(5–6):355–607, 2019","venue":null,"work_id":"38bd31fa-a4bf-48bd-a4e5-0b4a954da54a","year":2019},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.253161Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:6a4096f5569d908f50fb1d74fbb4505cae4cb7a2543b3ca95ddc770debca4994","observation_id":"50ec6348-8016-4844-942a-56b9cd503a05","resolution":{"observed_at":"2026-08-10T12:00:48.699063Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-10T12:00:48.675552Z","title":"Gromov–Wasserstein averaging of kernel and distance matrices","venue":null,"work_id":"f3f5cd5d-e134-4260-bb63-41daa45b9736","year":2016},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.258388Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:bec8e5d616bc44eab218eeca0d9738a75509ec4f67ba73a9d4518cd0245b45f7","observation_id":"a49db340-8942-45fe-bd18-62ee9ba414f6","resolution":{"observed_at":"2026-08-10T12:00:48.681098Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2603.16042","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T12:00:42.945642Z","title":"Shuffling the stochastic mirror descent via dual lipschitz continuity and kernel conditioning.arXiv preprint arXiv:2603.16042, 2026","venue":null,"work_id":"35292154-9217-4a6d-bde4-56de95abf127","year":2026},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.265315Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:93854bf36ebacefc86ec444cd1e91de7151e80cddd30722edf1db616c54bd602","observation_id":"25192ee9-5391-4892-8684-8a66ac4ca225","resolution":{"observed_at":"2026-08-10T12:00:42.957242Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-10T12:00:48.659033Z","title":"Entropic Gromov–Wasserstein distances: Stability and algorithms","venue":null,"work_id":"8c21ea73-969f-4419-9004-5b867900a0f3","year":2024},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.274403Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:788c817f2f8d2a86f0bca2a4dd7efe2db2781688b748f5381d94ca2b4a5d085c","observation_id":"515849f7-4eb6-476e-8480-c3e7309a2ca2","resolution":{"observed_at":"2026-08-10T12:00:48.664178Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-10T12:00:48.641738Z","title":"Tyrrell Rockafellar","venue":null,"work_id":"e1517d41-d5fd-4f0f-b72e-3d4ee5b7c7a2","year":1969},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.281403Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:675a04035d717c7246da67549d56ee087dbe271011ed1dc823564da6c61857b6","observation_id":"56f0a5fb-a9f9-49c0-9c61-b104f2f7a599","resolution":{"observed_at":"2026-08-10T12:00:48.647170Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T12:00:38.287702Z","title":"Tyrrell Rockafellar.Convex Analysis, volume 28 ofPrinceton Mathematical Series","venue":null,"work_id":null,"year":1970},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.287702Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:02c1dfeb2c18cf9d18e49cfe61aa345f5966cdddcea1ba5a1ab59a07b8338e95","observation_id":"291f4f49-baf5-496a-adfc-5928ed655869","resolution":{"observed_at":"2026-08-10T12:00:38.287702Z","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":"2026-08-10T12:00:48.612032Z","title":"Tyrrell Rockafellar and Roger J.-B","venue":null,"work_id":"97d62d98-a2c1-47cf-aa18-3780e95aa59d","year":1998},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.294625Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:11c14c528c7749bfebc757b835b2b9e0a4869853b2cb9ce501d6837418baf877","observation_id":"294ab114-23fb-4dfa-9723-e060f427f54e","resolution":{"observed_at":"2026-08-10T12:00:48.617651Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-10T12:00:48.594858Z","title":"Linear-time Gromov–Wasserstein distances using low-rank couplings and costs","venue":null,"work_id":"a5e4ca98-19ce-4143-a96f-17b13629fe26","year":2022},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.303128Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:4f432b132e2ec4482647b117361071c4d48f058024142a36422dd268c925854f","observation_id":"52e41fa3-6bac-42c1-bcef-e17b74030c79","resolution":{"observed_at":"2026-08-10T12:00:48.600574Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1806.04781","last_updated":"2018-06-12T21:56:48Z","snapshot_observed_at":"2026-08-05T08:10:37.595665Z","submitted_at":"2018-06-12T21:56:48Z","title":"On the Convergence Rate of Stochastic Mirror Descent for Nonsmooth Nonconvex Optimization","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1806.04781","snapshot_observed_at":"2026-08-10T12:00:38.308592Z","title":"On the convergence rate of stochastic mirror descent for nonsmooth nonconvex optimization","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.308592Z"},"links":{"cited_paper":"/paper/1806.04781","citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:29975f83ad648cefc2159211163a78eb209d5fe4fadd64a9942cae415a370a65","observation_id":"98c4e22b-6c1f-4103-9073-981cfa5d0f6c","resolution":{"observed_at":"2026-08-10T12:00:38.308592Z","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":"2026-08-10T12:00:48.577024Z","title":"Boyd, and Peter W","venue":null,"work_id":"f36e388a-35ac-429e-a7e1-adea1a266911","year":2020},"citing_paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-10T12:00:38.314620Z"},"links":{"citing_paper":"/paper/2608.07248"},"observation_digest":"sha256:e145bee32f3a361d236485a86ddfb9a8d583523d5f56ab2728abe58910ac5d6f","observation_id":"4e443594-e486-40ce-8b21-b4e8bae3433a","resolution":{"observed_at":"2026-08-10T12:00:48.582337Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2608.07248","last_updated":"2026-08-07T14:06:54Z","latest_version":1,"primary_category":"math.OC","snapshot_observed_at":"2026-08-10T19:11:30.744091Z","submitted_at":"2026-08-07T14:06:54Z","title":"Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization"},"reference_resolution":{"displayed":35,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":10,"verified_exact":1,"verified_fuzzy":24},"total_outbound_references":35},"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":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 0 inbound Pith citation observations for arXiv:2608.07248."}