{"as_of":"2026-08-21T05:00:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:bfe189607fdff1dfd00637c1662d3fee7715de5921b158b433e7cb592424c9c2","coverage":[{"denominator":41,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":41,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T11:21:28.439314Z","state":"measured"},{"denominator":41,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":41,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-20T06:33:59.587034+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/2504.15898/citation-record","integrity":"/paper/2504.15898/integrity","json":"/paper/2504.15898/citation-record.json","paper":"/paper/2504.15898"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:21:29.230736Z","title":"and Ding, X.: On invariant measures of nonlin ear Markov processes, J","venue":null,"work_id":"c4b79e93-5e33-4037-9e91-b4a401d33451","year":1993},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.266741Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:97907d475bbf8700ba9a9669beea8c2be311591efafcd2a71fa7f10fd8528e1c","observation_id":"7da1f979-f183-40a5-a0ce-b2a77515fab8","resolution":{"observed_at":"2026-08-16T11:21:29.235091Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.01070","last_updated":"2024-12-02T03:09:45Z","snapshot_observed_at":"2026-08-17T23:19:44.230614Z","submitted_at":"2024-12-02T03:09:45Z","title":"A note on L\\'evy-driven McKean-Vlasov SDEs under monotonicity","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.01070","snapshot_observed_at":"2026-08-16T11:21:28.271848Z","title":"and Wang, J.: A note on Lévy-driven McKean -Vlasov SDEs under monotonicity, arXiv:2412.01070","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.271848Z"},"links":{"cited_paper":"/paper/2412.01070","citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:df4c081ddaef1a11354d4adc08bdace6c5d65c92173834d730df43eebe59cf4c","observation_id":"64f04e0b-ecd3-4f42-af0e-848f1279e747","resolution":{"observed_at":"2026-08-16T11:21:28.271848Z","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":"2026-08-16T11:21:29.216382Z","title":"and Xie, Y.: Quantitative estim ates for Lévy driven SDEs with diﬀerent drifts and applications, J","venue":null,"work_id":"ce3cfb6c-f269-408f-a011-aa32d863fad7","year":2024},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.276736Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:67690b6c37f9dd0e293a37a3ce203b853da14c64b46d04b5a05bfba9e8c9ec79","observation_id":"bde3f046-21bd-4e3e-816b-5dd948373b16","resolution":{"observed_at":"2026-08-16T11:21:29.220819Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:29.202614Z","title":"and Shaposhnikov, S.V.: Con vergence in variation of solutions of nonlinear Fokker-Planck-Kolmogorov equations to stationary measur es, J","venue":null,"work_id":"285cf134-7e04-4e92-b2a7-56e8cf8b0b23","year":2019},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.281395Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:413b208e0d3c9d0394dbba71336a61d153e05f3f6c4fb85d46a327ecd23d7c18","observation_id":"e31f6f2e-c6e2-4ed1-a820-89aeae7f83b8","resolution":{"observed_at":"2026-08-16T11:21:29.207334Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:29.188898Z","title":null,"venue":null,"work_id":"1a02088c-c483-49df-87f6-6d653ca36de2","year":2014},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.285844Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:d7885d4edf6f0c8ba477cf08f97706761f8a01c994c143144b9a8dd79344587c","observation_id":"f485e7b6-915c-4613-b2a7-6b4d0c7157b1","resolution":{"observed_at":"2026-08-16T11:21:29.193166Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:29.175487Z","title":"World Scientiﬁc, Singapore, 2004","venue":null,"work_id":"8aff4b9a-7939-44e5-b1a4-b7d8693b37da","year":2004},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.290137Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:c75d634f7c6ac3c2db98c13f16c6106e26fbdd8c23aa541bbf94deb103387088","observation_id":"c3be61f8-c568-43c5-a71e-e867ad848844","resolution":{"observed_at":"2026-08-16T11:21:29.179811Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2201.11612","last_updated":"2024-04-30T15:32:39Z","snapshot_observed_at":"2026-08-20T15:42:14.045283Z","submitted_at":"2022-01-27T16:13:33Z","title":"On the stability of the invariant probability measures of McKean-Vlasov equations","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2201.11612","snapshot_observed_at":"2026-08-16T11:21:28.294451Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.294451Z"},"links":{"cited_paper":"/paper/2201.11612","citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:f3cb3b792cb6dce2cf42b27ba3f89b703bf4f71e9f4e1efc1ae0433a7be06d76","observation_id":"bcfb339c-a558-4128-8878-777e5990033e","resolution":{"observed_at":"2026-08-16T11:21:28.294451Z","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":"2026-08-16T11:21:29.161507Z","title":"and Zabczyk, J.: Ergodicity for Inﬁnite Dimensional Systems , Cambridge university press, 1996","venue":null,"work_id":"d6df3568-3dc6-4b1d-98b9-a81fb4fd428f","year":1996},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.299120Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:6344f82a5a46157d2e47a4961aaae74168d786123d0e3dcba6419ef0df27d41b","observation_id":"473e6156-2951-43fd-9f36-59d330fa6382","resolution":{"observed_at":"2026-08-16T11:21:29.165939Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:29.147792Z","title":null,"venue":null,"work_id":"258e82f9-8a3a-4059-81c6-a1df8ac21164","year":1983},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.303764Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:d93cf7b94fddd421cddb760d2121c8dbdbf37536f554c6c58327773fbd6309fc","observation_id":"f8e0d5c6-59bd-44d0-ab12-0faab9d52c8f","resolution":{"observed_at":"2026-08-16T11:21:29.152391Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:29.134341Z","title":null,"venue":null,"work_id":"27ecbbfe-6ae7-412c-a16a-334e2eecfe2b","year":1985},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.307928Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:ff6aee807ecd18986c81cf8c3557c4e8d028281de0f0eb21ab75aa346941d31c","observation_id":"992d7214-0032-43c8-8de1-2207659765ba","resolution":{"observed_at":"2026-08-16T11:21:29.138712Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:29.120853Z","title":"and Guillin, A.: Subgeometric rates o f convergence of f -ergodic strong Markov processes, Stochastic Process","venue":null,"work_id":"22319f8d-7c3e-4ba9-afdb-6e1c6d692821","year":2009},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.312069Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:ccca34db530ad165c439912748309794bf96ea61449c961e715e8f5f8fcc5b66","observation_id":"8bbd33fc-6864-4474-9f68-b3218c54acd7","resolution":{"observed_at":"2026-08-16T11:21:29.125235Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:29.107359Z","title":null,"venue":null,"work_id":"8ba43d12-1f67-4535-8edb-f462419e1fb9","year":2003},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.316431Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:98d0836b41cbb9844aba61ab0f4de95ee473b6279f9d7db4b11eba724a361b30","observation_id":"b27057b3-1b5f-476b-8673-b5c1e15210cf","resolution":{"observed_at":"2026-08-16T11:21:29.111706Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:29.093273Z","title":"Theory Related Fields , 166 (2016), 851–886","venue":null,"work_id":"668dadc9-fb0f-4bce-9e14-00a10678ce6d","year":2016},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.320499Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:e9b5db951edece423e5270b2b862c96126d210f6a0034d93604553b51446ba18","observation_id":"ae513c28-6a3c-48fd-ac1a-6d1edeaeda3b","resolution":{"observed_at":"2026-08-16T11:21:29.098219Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:29.079464Z","title":"and Zimmer, R.: Quantitative Ha rris-type theorems for diﬀusions and McKean-Vlasov processes, Trans","venue":null,"work_id":"0683ff0d-2619-4be0-8a6e-37436e8ba86b","year":2019},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.324626Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:21f213572ea3d8b5bc0245bdb88b3d781a66bbdfdd857ad65825b662fa6224cc","observation_id":"4bb0e423-ccc1-43cd-9406-08ba4648eb4f","resolution":{"observed_at":"2026-08-16T11:21:29.083966Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:29.065441Z","title":"and Mattingly, J","venue":null,"work_id":"32703804-8568-490d-a7b7-8e4211412754","year":2011},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.328808Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:7433e0b793dfda47f2345632b2a299220c95beb337dc312d0db9489c09ce3ac5","observation_id":"36bed53b-579f-4581-8ecb-e6b1c190e1d3","resolution":{"observed_at":"2026-08-16T11:21:29.069689Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:29.051518Z","title":"and Scheutzow, M.: Asympto tic coupling and a general form of Harris’ theorem with applications to stochastic delay equations, Probab","venue":null,"work_id":"b2a52b4d-fd75-406a-91b0-8b42b70e06f9","year":2011},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.332848Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:62d46c62bed9681f2ef214a9da8cb16fd9350eed2ca8ae83e855e85e0db0f342","observation_id":"b202fb3d-14e9-4593-a939-75acdcfce908","resolution":{"observed_at":"2026-08-16T11:21:29.055915Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:29.037941Z","title":null,"venue":null,"work_id":"2baa29fd-ddf8-43c6-8ac7-44ce9b647b1b","year":null},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.336969Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:1ecbfb51c7e2e65c9377ad3de6ecdcca1647f87e3ee5898970d664d2d6c1511e","observation_id":"db4fe60f-644c-464d-b142-16f670253741","resolution":{"observed_at":"2026-08-16T11:21:29.042195Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:29.023165Z","title":"and Wang, J.: Approxima tion of heavy-tailed distributions via stable-driven SDEs, Bernoulli, 27 (2021), 2040–2068","venue":null,"work_id":"2335e39c-e008-48ea-9df3-bf69606fc51a","year":2021},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.341058Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:15dbb8f5a24fc4d699fa30febeca65af05b0148d359989a69be080e0f6badd55","observation_id":"969a6a88-b681-4803-94a2-5764a91c2925","resolution":{"observed_at":"2026-08-16T11:21:29.028054Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:29.007573Z","title":"and Sandrić, N.: On sub-geometric ergodicity of diﬀusion processes, Bernoulli, 27 (2021), 348–380","venue":null,"work_id":"9ccfc079-7963-48f2-b572-ab19de76008c","year":2021},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.345199Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:69b82d76b500fce1da66b4956eef0f17b2beaace69aeabcbbb7701d14697aa90","observation_id":"833e9ada-1700-437a-965d-ede07ad91996","resolution":{"observed_at":"2026-08-16T11:21:29.011831Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:28.993972Z","title":"and Wang, J.: Exponential e rgodicity for SDEs and McKean-Vlasov processes with Lévy noise, Ann","venue":null,"work_id":"84d3e235-a1ba-4d56-8296-61fb275a3136","year":2021},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.349273Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:4495c618b0b90a6cd343042236a4f7a01bfffb8238e1c4ef25e8a4b9910147b4","observation_id":"7eff8d29-4a66-47ea-a632-cc639ba093ad","resolution":{"observed_at":"2026-08-16T11:21:28.998250Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:28.979497Z","title":"and Zhang, C.: Long-time behaviors of mea n-ﬁeld interacting particle systems related to McKean-Vlasov equations, Comm","venue":null,"work_id":"28eb93bc-00ee-4188-b010-918812c0b177","year":2021},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.353250Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:3581ad7ef020187649a5ba0d3b8136279782da663cc0504edde8974fa85ffbcb","observation_id":"f29f5ac0-875b-4473-ba12-5bff7b1c5dc9","resolution":{"observed_at":"2026-08-16T11:21:28.984301Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:28.965506Z","title":"and Zhang, M.: Phase transitions for a cl ass of time-inhomogeneous diﬀusion processes, J","venue":null,"work_id":"6f1c508b-1d48-467f-b36c-f76dfcf47be9","year":2023},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.357934Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:1ba73310bb26bfb4b9aff63074e3c9d912da0ebd27fbfa7712da1d57150f2c81","observation_id":"0eca46a8-f361-48a6-bb1f-cdfa506618a3","resolution":{"observed_at":"2026-08-16T11:21:28.970054Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:28.951467Z","title":"and Wang, J.: Exponential convergence in Lp-Wasserstein distance for diﬀusion processes without uniformly dissipative drift, Math","venue":null,"work_id":"282b05d3-6a85-4b62-a924-cd08e6f3750a","year":2016},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.361941Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:66153d20f3cd5ce487e17c4e4c1542a02e628ce9c06cd50f4d12fa3c07d8f1ec","observation_id":"3adfeb56-0fb3-440e-adad-0ea948730d02","resolution":{"observed_at":"2026-08-16T11:21:28.956040Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:28.365963Z","title":"and Wang, J.: Reﬁned basic couplings and Wassers tein-type distances for SDEs with Lévy noises, Stochastic Process","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.365963Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:01ed3809bbf189b0c7a5124fb0db500f9017a7bd42a431411839a30de362dff6","observation_id":"fe2c3f77-4eb6-4b83-9e0b-47a2a51f5781","resolution":{"observed_at":"2026-08-16T11:21:28.365963Z","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":"2026-08-16T11:21:28.928471Z","title":"and Tweedie, R.L.: Stability of Markovian pr ocesses","venue":null,"work_id":"b9d2e071-2d0a-4658-a1c3-eb2f8e410945","year":1993},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.371232Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:27d6032223c432ab0b15bb61c3afc5e14ef14b6379922b3f7cfc11d6002ccc63","observation_id":"4967f1c9-d96d-4214-a1b8-7628c2cfaa58","resolution":{"observed_at":"2026-08-16T11:21:28.932625Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:28.914584Z","title":"and Reygner, J.: Local convergence rates for Wasserstein gradient ﬂows and McKean-Vlasov equations with multiple stationary solutions, arXiv:2404 .15725","venue":null,"work_id":"24502495-e55d-4297-924f-78f5a2150f1e","year":null},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.375365Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:0c32c58c92f301c197cba224523d3bdbf9c86b25fa06e4e3d9060f4a2591fecf","observation_id":"e8413f24-984a-41e4-a5bb-d0c9b937f4ff","resolution":{"observed_at":"2026-08-16T11:21:28.919219Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:28.900477Z","title":"and Röckner, M.: A Concise Course on Stochastic Partial Diﬀerential Equations , Lecture Notes in Mathematics, vol","venue":null,"work_id":"ba14e19c-73da-4140-800e-9a0a5d8c923a","year":1905},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.379611Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:0941769c7a16154011e983de5f3d957137efc4290b078f35255c6f6594f3a892","observation_id":"25b99e42-86ef-43d0-850c-607a451be23e","resolution":{"observed_at":"2026-08-16T11:21:28.905018Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2411.01364","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:21:28.681691Z","title":"and Zhi, Y.: Global dynamics of McKean-Vl asov SDEs via stochastic order, arXiv: 2411.01364","venue":null,"work_id":"3221529c-0b88-4604-a75e-e225ab70d5c7","year":null},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.384062Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:92fac62ab81fb14a458619886e99f61d3c4730986bcbde6455087e8afaa47f42","observation_id":"4ffa0a4e-6741-4199-922d-63757af5c7e9","resolution":{"observed_at":"2026-08-16T11:21:28.690173Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:28.887507Z","title":"Appl., XXIX (1985), 647–676","venue":null,"work_id":"ac22e9b4-959a-4a67-bd81-75d6f39bacf1","year":1985},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.388336Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:42c335e1fd16c5fa008d784cb45a02a9e1464b9c597538397e6e88b5e855d071","observation_id":"e10b98d1-2c6f-4ac6-bd06-034605d9c511","resolution":{"observed_at":"2026-08-16T11:21:28.891759Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:28.874089Z","title":"Probab., 41 (2010), 1427–1460","venue":null,"work_id":"523b6030-3b41-4e63-81a4-95101b1b00fa","year":2010},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.392475Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:eebc640089bee16e43cd1d62a9f8469a1a383065f31072a1882470cf71d53475","observation_id":"7801fa4e-b7ef-411e-b0bf-9d2d3814bd37","resolution":{"observed_at":"2026-08-16T11:21:28.878540Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:28.860214Z","title":null,"venue":null,"work_id":"bb5dc598-57ff-43d0-a07e-56fbb58e57c0","year":2014},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.396515Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:fa102473f5938fd3c4bfb5464445a4f91129b5d067432d718e8c00d1f5cc0a68","observation_id":"eeacaac6-23f5-4494-a91d-bf8b3f7e7227","resolution":{"observed_at":"2026-08-16T11:21:28.864570Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:28.846857Z","title":null,"venue":null,"work_id":"e783c378-473b-4391-9787-4ef4367535f2","year":2018},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.400759Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:fe61696640ae4177f6b2d91cb977b5589dbb4618de776988d09c5e04ca785bec","observation_id":"a66e30b8-08be-4e51-b0be-807075c7b3ec","resolution":{"observed_at":"2026-08-16T11:21:28.850953Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:28.832553Z","title":"Appl., 128 (2018), 595–621","venue":null,"work_id":"8e9e798f-56af-4630-a724-7d13b04cb753","year":2018},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.404873Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:32cd502d5986e6182dc3a74e21f7f1a7652054c50825f6c749f9f5bd0021723a","observation_id":"3c02a2cf-6fc5-40e5-a850-c25811961ecb","resolution":{"observed_at":"2026-08-16T11:21:28.836842Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:28.818722Z","title":null,"venue":null,"work_id":"abfce8e5-5714-419f-8e2e-8950ebe41262","year":2023},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.408946Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:2a49e23ec8ab203c9c16cc56c5e75307020f192aa58969a787e41dc17904128d","observation_id":"56946bbf-dbc9-48c3-99f5-681570d89b67","resolution":{"observed_at":"2026-08-16T11:21:28.823203Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:28.804027Z","title":"and Wang, J.: Harnack inequalities for stoc hastic equations driven by Lévy noise, J","venue":null,"work_id":"f21897bc-0211-4887-9bd9-f9d91aac3bf3","year":2014},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.413191Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:170eaf5589a705fdef9a2736032e980e4f7a6f690ebc957263c9cd23504a3135","observation_id":"20a8fb77-4641-487c-9a14-dbd7ae322aae","resolution":{"observed_at":"2026-08-16T11:21:28.808819Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:28.789026Z","title":"Appl., 120 (2010), 1680–1700","venue":null,"work_id":"2af5449d-b02d-434d-bee6-75c15b2bb72a","year":2010},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.417748Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:b67a3270c574e0df04c6b4b14444a9332f7a0e73048796dd1b02e90bdf599d89","observation_id":"634d7500-8f1f-422d-b960-d153e9826bd8","resolution":{"observed_at":"2026-08-16T11:21:28.793460Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:28.774867Z","title":"and Zhang, X.: Ergodicity of stochastic diﬀeren tial equations with jumps and singular coeﬃcients, Ann","venue":null,"work_id":"cfcf39bc-1ff2-495a-b9f7-9b7a1a95627b","year":2020},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.421854Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:c36ad0b609c5868dc1f8298d5ed83b4a03ae620e0a70635973a81a23922cc8ad","observation_id":"96cf2229-0e2c-4c9c-9a1c-93b0d4d14384","resolution":{"observed_at":"2026-08-16T11:21:28.779169Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:28.760166Z","title":"1321, Springer, 1988, 89–91","venue":null,"work_id":"982665d4-e296-4c32-9e02-d1165a7eccf4","year":1988},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.426025Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:104dff3434d6bb24c488543d699e115ea1a749eb0f9eec48fa1db88644950a14","observation_id":"4d87a97f-d36d-4abc-9e21-fb2f40219d04","resolution":{"observed_at":"2026-08-16T11:21:28.764910Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:28.745694Z","title":null,"venue":null,"work_id":"33601403-ccae-4748-9452-12a467b2d796","year":2023},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.430318Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:f25e1b1b410fc962061a55e8b7af5fbde3d00af5c6e8fdcf19ad4de928bd7ec6","observation_id":"df2fecbc-7276-4720-a608-df7a766b21a9","resolution":{"observed_at":"2026-08-16T11:21:28.750146Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T11:21:28.434466Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.434466Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:3a2d5fb39e106b3cdef53599a1e533978f272559071dbd57ab65fae1684cbcd3","observation_id":"a5975c9d-4039-446a-809c-b2748074f18d","resolution":{"observed_at":"2026-08-16T11:21:28.434466Z","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":"2026-08-16T11:21:28.731604Z","title":"Appl., 123 (2013), 1213–1228","venue":null,"work_id":"17bb17a1-beb0-4ce8-95be-552496b36d38","year":2013},"citing_paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-16T11:21:28.439314Z"},"links":{"citing_paper":"/paper/2504.15898"},"observation_digest":"sha256:0d55e34c9c97d1df05d8f04d4b099ecee1c859e4d7dc175753ab439e4dde5709","observation_id":"884c74a2-e88f-4e53-b021-d64907a126df","resolution":{"observed_at":"2026-08-16T11:21:28.736105Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2504.15898","last_updated":"2025-04-22T13:40:19Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-20T08:51:54.174208Z","submitted_at":"2025-04-22T13:40:19Z","title":"Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity"},"reference_resolution":{"displayed":41,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":13,"verified_exact":1,"verified_fuzzy":27},"total_outbound_references":41},"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":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"thesis":"As of 21 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 0 inbound Pith citation observations for arXiv:2504.15898."}