{"as_of":"2026-08-20T04:13:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fddced5e7638f1aabb67b18786e39d9119b991c8a54c648317840c15b2197389","coverage":[{"denominator":50,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":50,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T20:21:06.895943Z","state":"measured"},{"denominator":50,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":50,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-19T06:32:44.657259+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/2505.13632/citation-record","integrity":"/paper/2505.13632/integrity","json":"/paper/2505.13632/citation-record.json","paper":"/paper/2505.13632"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2502.00582","last_updated":"2025-02-01T22:38:10Z","snapshot_observed_at":"2026-08-17T13:13:52.242854Z","submitted_at":"2025-02-01T22:38:10Z","title":"Uniform-in-time weak propagation of chaos for consensus-based optimization","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.00582","snapshot_observed_at":"2026-08-15T20:21:06.696708Z","title":"Uniform-in-time weak propagation of chaos for consensus-based optimization","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.696708Z"},"links":{"cited_paper":"/paper/2502.00582","citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:063ef98496ff68659d2cabc02bdc4986a92de20bba0488f4d195020c7cd4dfed","observation_id":"b75bcb66-c72a-4f37-b736-5b7a185ac2d7","resolution":{"observed_at":"2026-08-15T20:21:06.696708Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T20:21:06.701880Z","title":"Constrained consensus-based optimization and numerical heuristics for the few particle regime","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.701880Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:adf17781c87c89681e0d088014d0b56e6aa8389082edc4d59b3dd960e53a6d68","observation_id":"18927446-7012-4d30-93ee-c046cc5e8b7d","resolution":{"observed_at":"2026-08-15T20:21:06.701880Z","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":"2026-08-15T20:21:07.761001Z","title":"Brown’s original fictitious play","venue":null,"work_id":"a2e2db37-b988-4cdb-9bed-56c4d4ef17e2","year":2007},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.706453Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:8e603b20ec05f33eb3b4bf558c5d1990bcc90856a1626d4d7175c34085b985f3","observation_id":"73685c98-e48c-4c35-a7cb-ae7c6848cd05","resolution":{"observed_at":"2026-08-15T20:21:07.765091Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.746832Z","title":"Stochastic differential equations: an introduction with applications","venue":null,"work_id":"e0a903a6-c1ac-43ca-8f25-6f388269e4c0","year":2003},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.710921Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:4ac68927f0910112985e63dfa74a7157b8b988a9bf86b601714c039f1f7b97a8","observation_id":"9932cb72-8b91-405d-a132-8e9edd063070","resolution":{"observed_at":"2026-08-15T20:21:07.752466Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.734295Z","title":"An Adaptive Consensus Based Method for Multi-objective Optimization with Uniform Pareto Front Approximation","venue":null,"work_id":"f12dd924-1b4a-4a19-85d6-3f0a98d16b2b","year":2023},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.714967Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:0dc60881cff94bb82ce1d5010f04170cfa739d3bc5ff9472dac7f36b5224a579","observation_id":"1a8f78c8-d033-485d-a0f7-bf72f29a0eb4","resolution":{"observed_at":"2026-08-15T20:21:07.738451Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.17373","last_updated":"2024-07-24T15:51:46Z","snapshot_observed_at":"2026-08-16T13:31:22.925122Z","submitted_at":"2024-07-24T15:51:46Z","title":"A particle consensus approach to solving nonconvex-nonconcave min-max problems","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.17373","snapshot_observed_at":"2026-08-15T20:21:06.719301Z","title":"A particle consensus approach to solving nonconvex-nonconcave min-max problems","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.719301Z"},"links":{"cited_paper":"/paper/2407.17373","citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:7be17c6331e9810ca8a03fbe7c8f9acde2002b345bbe50dbfed6a1fa3588810c","observation_id":"719e9c2c-ac95-44b3-a11c-35799b61962d","resolution":{"observed_at":"2026-08-15T20:21:06.719301Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.12189","last_updated":"2025-07-16T17:04:43Z","snapshot_observed_at":"2026-08-14T05:03:10.752419Z","submitted_at":"2025-01-21T14:50:19Z","title":"MirrorCBO: A consensus-based optimization method in the spirit of mirror descent","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.12189","snapshot_observed_at":"2026-08-15T20:21:06.724331Z","title":"Mirrorcbo: A consensus- based optimization method in the spirit of mirror descent","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.724331Z"},"links":{"cited_paper":"/paper/2501.12189","citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:fac7b3494e09413e499d25af20cb83f560c3ebd376689b62412f5c1b8fb4b2e0","observation_id":"f19ba123-9350-48dc-a0b4-09cd92b29a96","resolution":{"observed_at":"2026-08-15T20:21:06.724331Z","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":"2026-08-15T20:21:07.721719Z","title":"Polarized consensus-based dynamics for optimization and sampling, 2022","venue":null,"work_id":"cfaba448-35eb-4ae5-863c-46068d7d07ec","year":2022},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.728659Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:e68e1888bcfa782cf1bcf921b2410ff581428822b274a92acfb57f2f601d8a0a","observation_id":"c8c952fc-26d9-4a7f-994e-19a716b451b2","resolution":{"observed_at":"2026-08-15T20:21:07.725872Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.707519Z","title":"Carrillo, Young-Pil Choi, Claudia Totzeck, and Oliver Tse","venue":null,"work_id":"92c0c726-a1d8-4245-8992-6561ea2be519","year":2018},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.732625Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:8f81619435e9beccbc3c53757ff3212239a7e8f3f399923fcf82d7b5ab315bda","observation_id":"2cd3d305-0c86-412b-9a5e-723c55739456","resolution":{"observed_at":"2026-08-15T20:21:07.711743Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.694389Z","title":"Carrillo, Shi Jin, Lei Li, and Yuhua Zhu","venue":null,"work_id":"0dba8f96-e993-44ee-8ced-17d896a3e194","year":2021},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.736618Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:c85bfc13bda872a38b9bb46dbe5ca821d58509706d9f49a5df0b168bf0b7fced","observation_id":"fa02676c-99f5-462b-9a79-d631064e838f","resolution":{"observed_at":"2026-08-15T20:21:07.699345Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.681194Z","title":"Propagation of chaos: A review of models, methods and applications","venue":null,"work_id":"9524e971-89f0-4a99-994e-2d6eff514de3","year":2022},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.741182Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:37734dac68a90f7f8f96fcac3efbc15c97cac78a7362e2ad006d7542d00d322c","observation_id":"86ca74a0-c82b-4ec3-8856-efdabe87a3c4","resolution":{"observed_at":"2026-08-15T20:21:07.685764Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.668172Z","title":"A consensus-based algorithm for non-convex multiplayer games","venue":null,"work_id":"ea5b924e-a102-440b-8ba8-3b19864d33e4","year":2025},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.745200Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:79617213df54f23f6d49511ff693198fdd3af0a8dc0c2191eb20024591bac523","observation_id":"3e2971f1-7518-400f-a88c-06af174cd957","resolution":{"observed_at":"2026-08-15T20:21:07.672416Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.654206Z","title":"Springer Texts in Statistics","venue":null,"work_id":"30078f3f-1deb-481a-9713-b6580e8bec5f","year":1997},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.749184Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:4231fa07d41d7fe408e3d6e60928edfef6f3756e3f88d8b624a14f98bb384cb6","observation_id":"27b4a59b-a1a1-47b1-acaf-e40ad1251a41","resolution":{"observed_at":"2026-08-15T20:21:07.659376Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.640703Z","title":"SBEED: Convergent reinforcement learning with nonlinear function approximation","venue":null,"work_id":"3baeb80a-2f65-4f77-801d-a297912eb1bd","year":2018},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.753098Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:7504eeb08906b5ec87421752a65be2af9f9e8ca916390447f61c217f035e83f5","observation_id":"37452709-5b0e-43b6-9916-91714a154c79","resolution":{"observed_at":"2026-08-15T20:21:07.645457Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.628022Z","title":"Local Stochastic Gradient Descent Ascent: Convergence Analysis and Communication Efficiency","venue":null,"work_id":"fec146ec-6b25-4c5d-ad01-d80bd3318635","year":2021},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.757093Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:ef1cde3b162a5c48dc802f5257b8096409644e68518a306401eed36a3c000dc9","observation_id":"8eb4b24f-08f1-429c-af12-66177cc283e7","resolution":{"observed_at":"2026-08-15T20:21:07.632248Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.615361Z","title":"Evaluation for moments of a ratio with application to regression estimation","venue":null,"work_id":"4b835695-3eed-4efe-abb9-7bff25668181","year":2009},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.761056Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:6be82629985968b6e2c836340d640b96eeaa3ad0c8b7c13e47ba1a7596ee1f5a","observation_id":"66555045-d8ff-480d-87d7-081dc5fd0c46","resolution":{"observed_at":"2026-08-15T20:21:07.619516Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.601961Z","title":"Fault-Tolerant Federated Reinforcement Learning with Theoretical Guarantee","venue":null,"work_id":"eb5495ea-8876-43d4-b4c2-dcfd32b6ba3f","year":2021},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.764925Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:de4c660c4efd9fcfa3aa35216efa2405bb7fdff45dff4398fb3dc192d19624c9","observation_id":"6ee00085-5320-479f-95a5-2c8592c91100","resolution":{"observed_at":"2026-08-15T20:21:07.606350Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.588862Z","title":"Consensus-based optimization on hypersurfaces: Well-posedness and mean-field limit","venue":null,"work_id":"5a58d011-873d-4b1c-938e-21d416cd9970","year":2020},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.768771Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:61bef7f1ce9bc9c61eaef910d3b26bd5efb8e6d08821933405a013221625c05d","observation_id":"0279fcc1-5c7d-4af4-a8cd-f9596c1c1d9f","resolution":{"observed_at":"2026-08-15T20:21:07.593517Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.575836Z","title":"Consensus-based optimization on the sphere: Convergence to global minimizers and machine learning","venue":null,"work_id":"fd0ab666-dfed-40b9-8f9f-887e08c3c04d","year":2021},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.772717Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:a1733b0ffa7326f4f06ac95a6cbf487759b1607c19b676425476d35b6068c68a","observation_id":"4ef9610b-dfae-4308-beef-0c07aabf2114","resolution":{"observed_at":"2026-08-15T20:21:07.580149Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2103.15130","last_updated":"2024-08-02T11:10:06Z","snapshot_observed_at":"2026-08-16T18:35:47.771645Z","submitted_at":"2021-03-28T13:42:07Z","title":"Consensus-Based Optimization Methods Converge Globally","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2103.15130","snapshot_observed_at":"2026-08-15T20:21:06.776586Z","title":"Consensus-Based Optimization Meth- ods Converge Globally","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.776586Z"},"links":{"cited_paper":"/paper/2103.15130","citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:6a543ff2877bf3b6e779097a798fa08c6b59c9d09bea4148c39bac81b2df30f1","observation_id":"28e7e29d-1eb6-480d-8bf2-db3335358991","resolution":{"observed_at":"2026-08-15T20:21:06.776586Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T20:21:06.780707Z","title":"Uniform-in-time propa- gation of chaos for consensus-based optimization","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.780707Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:b497499c8aafb1e325b810df3295e10baa857649191e609a01ac202ec4f5042b","observation_id":"9d9ca337-9293-4d54-864c-9bf01cf9d703","resolution":{"observed_at":"2026-08-15T20:21:06.780707Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T20:21:06.784585Z","title":"Mean-field limits for Consensus- Based Optimization and Sampling","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.784585Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:4d341a4704fa90faec7c0690ddf43571e360554638608fdbfb7a19216e486f19","observation_id":"66398a9d-9461-4035-bdab-e1f7b4cf6f51","resolution":{"observed_at":"2026-08-15T20:21:06.784585Z","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":"2026-08-15T20:21:07.562509Z","title":"Trudinger","venue":null,"work_id":"7f0059b9-ba63-4f40-9355-c143e611e8ce","year":1998},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.788680Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:5012dd7b51c2fa4330e724f1ce262960b703d298fb6147a4614b132c5558877b","observation_id":"4222af24-d0f1-410b-a0fa-39f7ce9424ae","resolution":{"observed_at":"2026-08-15T20:21:07.566699Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1404.1421","last_updated":"2014-04-05T02:41:16Z","snapshot_observed_at":"2026-08-14T23:38:34.985214Z","submitted_at":"2014-04-05T02:41:16Z","title":"Evolutionary Multiplayer Games","version":1},"cited_work":{"arxiv_id":"1404.1421","doi":null,"metadata_source":"pith","pith_arxiv_id":"1404.1421","snapshot_observed_at":"2026-08-15T20:21:06.989651Z","title":"Evolutionary Multiplayer Games","venue":"q-bio.PE","work_id":"6e4d76f6-6f0d-49be-8db7-9acb1fd0ebd1","year":2014},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.792628Z"},"links":{"cited_paper":"/paper/1404.1421","citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:60f9ed8922aa3c49570328d24b3ac08b6f100a653eba7c174a04b239f058d628","observation_id":"b1caa581-0d45-419a-b56f-65d094400b2c","resolution":{"observed_at":"2026-08-15T20:21:06.994329Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.548849Z","title":"Stochastic consensus dynamics for nonconvex optimization on the Stiefel manifold: Mean-field limit and convergence","venue":null,"work_id":"bf124ea5-71b4-43b5-9fa2-76c133b18937","year":2022},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.796707Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:6d1416e700da4d0090e27f50c08dc9bdd60bf9ff63b3f18c357e3a1dbb1add10","observation_id":"67c94230-2841-4b20-9b2d-8e17e15a23b9","resolution":{"observed_at":"2026-08-15T20:21:07.553508Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.534729Z","title":"Adaptive Gradient Multiobjective Particle Swarm Optimization","venue":null,"work_id":"810ddf2f-50ac-44a5-85d6-1f87faab4bc8","year":2018},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.800488Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:8b0888e4a2fc5d64797c206a132e40bca9229f4c093e5ef3ceb85128c053b28d","observation_id":"3c57baad-f675-4927-aac7-1a9f085c8bff","resolution":{"observed_at":"2026-08-15T20:21:07.540232Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.521161Z","title":"A Simple Adaptive Procedure Leading to Correlated Equilibrium","venue":null,"work_id":"57d4bda2-5db5-49cc-9dd2-2f4f2bd5924f","year":2000},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.804963Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:d534e74fe28d3b3270793e8d8af39d7376021828dc5ac2b37751c75ec5c3ee60","observation_id":"7e1fd582-2370-4ae4-bbdc-996b6f4d3ab2","resolution":{"observed_at":"2026-08-15T20:21:07.525466Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.03986","last_updated":"2025-06-30T09:18:28Z","snapshot_observed_at":"2026-08-16T13:02:24.123502Z","submitted_at":"2024-11-06T15:25:42Z","title":"Uniform-in-time mean-field limit estimate for the Consensus-Based Optimization","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.03986","snapshot_observed_at":"2026-08-15T20:21:06.808860Z","title":"Uniform-in-time mean-field limit estimate for the consensus-based optimization","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.808860Z"},"links":{"cited_paper":"/paper/2411.03986","citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:7e6875b4f99809403174104a5aa8179201c7b0b65e67908b3853fa83bb07068a","observation_id":"ba2c624a-4118-49d5-a430-039bf9882471","resolution":{"observed_at":"2026-08-15T20:21:06.808860Z","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":"2026-08-15T20:21:07.507171Z","title":"Self-interacting cbo: Existence, uniqueness, and long-time convergence","venue":null,"work_id":"625a09c5-5f63-4b74-9d54-01da24e0ced2","year":2025},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.813342Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:2c7e6ce3376b60aa25a3ca75f1dbc1200cdb272244fbf7fda78fe583c9579428","observation_id":"657edf67-48dd-4630-bdd1-c984e13c400b","resolution":{"observed_at":"2026-08-15T20:21:07.511587Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2105.12919","last_updated":"2021-05-27T02:43:44Z","snapshot_observed_at":"2026-08-16T18:21:54.953971Z","submitted_at":"2021-05-27T02:43:44Z","title":"On the mean-field limit for the consensus-based optimization","version":1},"cited_work":{"arxiv_id":"2105.12919","doi":null,"metadata_source":"pith","pith_arxiv_id":"2105.12919","snapshot_observed_at":"2026-08-15T20:21:06.956182Z","title":"On the mean-field limit for the consensus-based optimization","venue":"math.OC","work_id":"24bcf2a5-9f8f-4942-9086-fdfd2035a601","year":2021},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.817026Z"},"links":{"cited_paper":"/paper/2105.12919","citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:dfd4f6d8560afef8bfd2042857b04d692e97fef8c7b4ef69bcbf7c04d05a7a6b","observation_id":"124e83f4-82a9-4f87-ab59-bb4cc4083832","resolution":{"observed_at":"2026-08-15T20:21:06.962318Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.494182Z","title":"On the global convergence of particle swarm optimization methods","venue":null,"work_id":"1b1a0d22-ea2c-4c63-869c-0d300f8b8925","year":2023},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.821116Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:77bcd888c7dd423dbbb2468ffd1b08a150cbb6e8e86588ea39ad16da4c8ff0ea","observation_id":"1c92521c-2c41-4c84-a3e9-06aa365dfec9","resolution":{"observed_at":"2026-08-15T20:21:07.498550Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.481143Z","title":"Consensus-based optimization for saddle point problems","venue":null,"work_id":"866b2f4e-a502-44d9-97bd-80d1294ce80a","year":2024},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.824975Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:3921569df018acc6405be0f1448d50f21a672e3ecdae2a11d2ee873ccd3df69f","observation_id":"a685324a-36e1-41ce-beb9-c41a55ac8e0c","resolution":{"observed_at":"2026-08-15T20:21:07.485528Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.468160Z","title":"A Consensus-Based Global Optimization Method with Adaptive Momentum Estimation","venue":null,"work_id":"a3797ecd-4667-4925-bf81-b641a26d4250","year":2022},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.828868Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:3aed9e8e70b173e0e16975394c65ebbfc429686ff5b2a61ecbdb2734935ac6d2","observation_id":"a9522bfd-bc15-4854-ac86-f6b9b7a4a5ef","resolution":{"observed_at":"2026-08-15T20:21:07.472936Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.455886Z","title":"Tretyakov","venue":null,"work_id":"6ac5c9e0-1ac7-48af-8355-267cf2ff02e2","year":2023},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.832762Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:bd74d63d8a3c745f13d0fdf3b94b796d483d61dbee0b42d25398054f5fd03980","observation_id":"e1bad332-bb23-4a4c-88bf-da2f9c3bfb94","resolution":{"observed_at":"2026-08-15T20:21:07.459738Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.442992Z","title":"Stochastic Stability of Differential Equations , volume 66 of Stochastic Modelling and Applied Probability","venue":null,"work_id":"a67edbb3-1b2f-4419-ab3e-5f79f4f3f52b","year":2012},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.836942Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:871445fdde799d4810d0b57f564ffb2e14f9cddeb9b3ff9bcd2239cc0996f4af","observation_id":"2ed49749-bfe4-457c-8eb7-d25495542123","resolution":{"observed_at":"2026-08-15T20:21:07.447398Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.430093Z","title":null,"venue":null,"work_id":"ff2d0a27-f193-40e0-903f-dff6e5c96081","year":2012},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.841015Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:784d5372bb9879f478a11a2349d727e0d02c1f3b7e317a99bd7c2426279f2fbf","observation_id":"cf54d75f-17b3-49c0-aac8-a82b7b7d0316","resolution":{"observed_at":"2026-08-15T20:21:07.434413Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.417190Z","title":"A unified game-theoretic approach to multiagent reinforcement learning","venue":null,"work_id":"d82eb4d6-7590-4051-b34d-4b3460a5cb7c","year":2017},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.844964Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:5b21961e2ab1d7a35e2cde7e69fd172bf42cc5d2b7227794e84bb80d86aa70ae","observation_id":"67ea39bf-5b1d-4719-93bb-4ea0859cd895","resolution":{"observed_at":"2026-08-15T20:21:07.421514Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.404369Z","title":"Triple Generative Adversarial Nets","venue":null,"work_id":"afcf18a8-a880-441e-9391-2f68e0d4e12c","year":2017},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.848892Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:8f313cce9ee34cefc735180e412374e4b196a4c534970c4cf6f1c33a926f5f75","observation_id":"a718b64b-c8d2-44bd-929b-1de17e5639ec","resolution":{"observed_at":"2026-08-15T20:21:07.408723Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.391078Z","title":"Budget Allocation Problem with Multiple Advertisers: A Game Theoretic View","venue":null,"work_id":"e18dd0d9-da03-4075-b74f-5ae5ccc82c45","year":2015},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.852699Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:7e82edf3e4b5081ed721985cd5ba328514d891ac42603f770d7c91e7e4d708cc","observation_id":"25781fa4-6f5e-4271-990c-48472c9a27f6","resolution":{"observed_at":"2026-08-15T20:21:07.395499Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.378074Z","title":"Stochastic differential equations and applications","venue":null,"work_id":"2540462c-e652-4a3e-b55c-a83f3ddb15e4","year":2011},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.856530Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:62ff0e0e3654aebd522de23c5301604057abdb836c29b831c06b5c186787d4cd","observation_id":"3f66eb83-0b27-4ead-8076-19dd56919a32","resolution":{"observed_at":"2026-08-15T20:21:07.382375Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.364580Z","title":"Game Theory and Mechanism Design , volume 4 of IISc Lecture Notes Series","venue":null,"work_id":"604cf32d-1285-477e-8e96-d5084eb09ef5","year":2014},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.860421Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:8360680ac881aa8a09981ff3c947d7d2ef10e19eb8d5d2a789adb3ed4668fc6f","observation_id":"d93a16b6-5399-4bff-b412-7c4c2dafea80","resolution":{"observed_at":"2026-08-15T20:21:07.369075Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.351146Z","title":null,"venue":null,"work_id":"5ec3e244-02d0-49fb-894b-bf55ee586995","year":1950},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.864544Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:32cba7a0b9892f76e052b75a904c7c28abb8df04be86303e8d238ecbde833002","observation_id":"b28f1828-28dc-4fe8-8fde-efe3734b02a1","resolution":{"observed_at":"2026-08-15T20:21:07.355444Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.336116Z","title":"Solving a Class of Non-Convex Min-Max Games Using Iterative First Order Methods","venue":null,"work_id":"683056a8-8f60-4215-9ce7-c1be4ac90177","year":2019},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.868771Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:03bd35d645003d253db37ab337c8a48bdf8ff395a2909e13dd4926ca8aa73b54","observation_id":"4f43b73e-d6f9-4958-8230-320054f03a6f","resolution":{"observed_at":"2026-08-15T20:21:07.341005Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.321940Z","title":"A consensus-based model for global optimization and its mean-field limit","venue":null,"work_id":"dd61d3b4-4653-4f1a-82dd-14c8f0d23517","year":2017},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.872668Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:0cb7392ab3c2da4c0a9ca186bf243b9548953ccb5878867d2ed91cb8aea9a96b","observation_id":"9e27c0b3-14a6-49ef-8d93-0a21ee7025c2","resolution":{"observed_at":"2026-08-15T20:21:07.326310Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.308797Z","title":"El-Gokhy, and Elsayed Sallam","venue":null,"work_id":"5de4e55a-e349-4cf4-9807-22649179fc4d","year":2018},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.876462Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:5045f2ca22d2e07134aefdf6f4ee400bc7b0caf98ebdd6ec8392c5e23f5aa85d","observation_id":"214f1882-08ba-4d85-99f6-c9e5bc971552","resolution":{"observed_at":"2026-08-15T20:21:07.313093Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.295342Z","title":"Multi-Agent Generative Adversarial Imitation Learning","venue":null,"work_id":"289ea7c5-7073-4038-994c-579fdd274b58","year":2018},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.880268Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:ab3bcc1e4de6ea3ff465231977e439ed718605c692c3bced26af174fd1aa2a57","observation_id":"8a10543c-9a11-4dec-9797-ca8d6e1f0b03","resolution":{"observed_at":"2026-08-15T20:21:07.299890Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:21:07.280477Z","title":"Trends in consensus-based optimization","venue":null,"work_id":"5590f99f-9c85-4f62-984b-b70ad0ca4543","year":2021},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.884095Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:35278e9a13562810cb3448c360cf948febb887e0cdf7b2316b6f2b9d0dd7bb47","observation_id":"39aedf7a-014b-4835-a3a7-c9b2a200bb78","resolution":{"observed_at":"2026-08-15T20:21:07.285166Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.13394","last_updated":"2025-05-10T20:40:37Z","snapshot_observed_at":"2026-08-20T00:46:52.697312Z","submitted_at":"2024-11-20T15:29:53Z","title":"CB$^2$O: Consensus-Based Bi-Level Optimization","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.13394","snapshot_observed_at":"2026-08-15T20:21:06.887895Z","title":"CB2O: Consensus-based bi-level optimization","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.887895Z"},"links":{"cited_paper":"/paper/2411.13394","citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:1805cc579d18a75c2d0404966d529d65a55fcc533782f9dec05a9ac7b2acdac5","observation_id":"c2ca8acc-0384-43bb-b27a-bb919ace1cc9","resolution":{"observed_at":"2026-08-15T20:21:06.887895Z","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":"2026-08-15T20:21:07.266487Z","title":"Particle swarm optimization algorithm: an overview","venue":null,"work_id":"4ebb90fc-b668-47c4-914c-3725ae83cc0a","year":2018},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.892057Z"},"links":{"citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:fe72466779205f5ff99cc389d7fec129338e99beee086e7fd93642b9ba2d6224","observation_id":"4f75ac86-1f14-4544-8efb-12d6e5980050","resolution":{"observed_at":"2026-08-15T20:21:07.271392Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2504.10990","last_updated":"2025-04-15T09:02:36Z","snapshot_observed_at":"2026-08-16T12:40:59.985094Z","submitted_at":"2025-04-15T09:02:36Z","title":"Mathematical Analysis of the PDE Model for the Consensus-based Optimization","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2504.10990","snapshot_observed_at":"2026-08-15T20:21:06.895943Z","title":"Mathematical analysis of the pde model for the consensus-based optimization","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-15T20:21:06.895943Z"},"links":{"cited_paper":"/paper/2504.10990","citing_paper":"/paper/2505.13632"},"observation_digest":"sha256:dbe4403d7126c2f58f50b64a611a9cade4617dec8056c094023ee801a099a482","observation_id":"ae2d8ccd-e5a7-4e5b-aeda-8fc936134927","resolution":{"observed_at":"2026-08-15T20:21:06.895943Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2505.13632","last_updated":"2025-05-19T18:09:10Z","latest_version":1,"primary_category":"math.OC","snapshot_observed_at":"2026-08-19T19:18:40.959732Z","submitted_at":"2025-05-19T18:09:10Z","title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games"},"reference_resolution":{"displayed":50,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":12,"verified_exact":1,"verified_fuzzy":36},"total_outbound_references":50},"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":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 20 August 2026, this Paper Citation Record lists 50 of 50 outbound references and 0 inbound Pith citation observations for arXiv:2505.13632."}