{"as_of":"2026-08-13T01:55:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:71d437d272fa91864485379e254f67fde880fe187877bec796fc039ca454d63a","coverage":[{"denominator":39,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":39,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T20:20:36.450938Z","state":"measured"},{"denominator":40,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":40,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T14:29:08.492281Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-10T14:29:08.545185Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"cited_work":{"arxiv_id":"2501.09176","doi":null,"metadata_source":"pith","pith_arxiv_id":"2501.09176","snapshot_observed_at":"2026-08-10T14:29:08.545185Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","venue":"math.PR","work_id":"3d56d79b-b660-436e-99f9-6ec8c581a234","year":2025},"citing_paper":{"arxiv_id":"2501.15416","last_updated":"2025-01-26T06:38:24Z","snapshot_observed_at":"2026-08-12T13:04:05.009815Z","submitted_at":"2025-01-26T06:38:24Z","title":"Periodic solutions for McKean-Vlasov SDEs under periodic distribution-dependent Lyapunov conditions","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-10T14:29:08.492281Z"},"links":{"cited_paper":"/paper/2501.09176","citing_paper":"/paper/2501.15416"},"observation_digest":"sha256:5807954bbafc369f062a814df9f986d1a96b423d7c867e575c88f357f1880f0a","observation_id":"4206f664-f66c-47a2-af39-dae1cc3851b5","resolution":{"observed_at":"2026-08-10T14:29:08.552286Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2501.09176/citation-record","integrity":"/paper/2501.09176/integrity","json":"/paper/2501.09176/citation-record.json","paper":"/paper/2501.09176"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:20:37.016545Z","title":null,"venue":null,"work_id":"9b200d79-b8fc-4da3-bf45-e32bc3916baa","year":1993},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.288505Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:d8bea3955c3be8dcf5ff39bdd8d6deb253cf87b10090aa1cf9403914af0a5e2e","observation_id":"94445698-8792-46c0-9d0c-c2ee34189205","resolution":{"observed_at":"2026-08-10T20:20:37.021096Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2408.17242","last_updated":"2024-12-04T08:42:20Z","snapshot_observed_at":"2026-08-12T22:54:28.064477Z","submitted_at":"2024-08-30T12:35:40Z","title":"The random periodic solutions for McKean-Vlasov stochastic differential equations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2408.17242","snapshot_observed_at":"2026-08-10T20:20:36.293440Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.293440Z"},"links":{"cited_paper":"/paper/2408.17242","citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:04adedb913c5f767e0f0059d5fcab7200f31b30721a841e6d9dc809fa91f0c94","observation_id":"24f82a46-ba44-4489-9dc7-5c1620138e18","resolution":{"observed_at":"2026-08-10T20:20:36.293440Z","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":"2026-08-10T20:20:36.998079Z","title":null,"venue":null,"work_id":"0f382515-535d-49b9-86a1-83dfade93958","year":2022},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.298500Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:34a548445875bf896bea1912249fea63f14304fa02dc64394fe08579054b4204","observation_id":"10450687-48ba-45e6-a4b4-b9568e1cfd23","resolution":{"observed_at":"2026-08-10T20:20:37.003291Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.981744Z","title":null,"venue":null,"work_id":"91f9d2df-9298-40d7-b6da-ad539d166c85","year":2019},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.303093Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:d5c11f7a657b393216891e389ebaa73d96f8ac625e3fc3565af3afbdd1e3a1f0","observation_id":"4208ba85-2752-4e31-8e01-a76f75cf54eb","resolution":{"observed_at":"2026-08-10T20:20:36.987172Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.967855Z","title":null,"venue":null,"work_id":"b61c8ed4-1b7d-4c31-b6ec-436cbf4da554","year":2014},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.308676Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:669dbe447611b5de7a87bf759683b4b6325b8e19b30504be19c60999056cce8b","observation_id":"ffa7d455-3c1d-462d-ada6-804ebc74d267","resolution":{"observed_at":"2026-08-10T20:20:36.971472Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.954565Z","title":"Carmona and F","venue":null,"work_id":"59c083fb-cf1c-49ff-ad14-b8683ef337c6","year":2018},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.314338Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:d6fef74e1c1b27850b3571849107704dfbcb8b5c1b7409ff9148aeaff2a91bf3","observation_id":"c2891e44-1178-42fa-b82e-d77415ca9adc","resolution":{"observed_at":"2026-08-10T20:20:36.959596Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.941173Z","title":null,"venue":null,"work_id":"42eb1ec2-e9bd-4551-b437-da393d20c492","year":2017},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.319151Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:c06bf163e1cc4a6c7a12e5ae033127e824eab2896ecab2c096c06c03b1439a1b","observation_id":"78c21946-eb44-4538-9a7b-c67ad193712b","resolution":{"observed_at":"2026-08-10T20:20:36.945288Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.926977Z","title":null,"venue":null,"work_id":"cfe3fc24-cfa1-4098-a3dc-65f202350bc7","year":1983},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.323174Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:a063ccf2740939a026f4630c89e2807b840c1b0ef2d7b564a8bc4b3cec91e99d","observation_id":"cbbd7864-d482-42c3-977b-980a7f7ad1c0","resolution":{"observed_at":"2026-08-10T20:20:36.931143Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.911965Z","title":null,"venue":null,"work_id":"0618c6e7-aefb-4775-8dbf-c30f1bbdce32","year":2023},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.327469Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:3994c05f230d9f04ce918ca41a104c7d2382c15b01f024520cd1c89858af75a9","observation_id":"4202f401-18b5-411b-b3dc-e54160b7108e","resolution":{"observed_at":"2026-08-10T20:20:36.916157Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.892060Z","title":null,"venue":null,"work_id":"1df6b6ee-1258-4bd7-b4e7-0e7f36e6afcd","year":2016},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.332193Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:57c8f5539afedd2b588afbf10dbdb517d19b0bcafbf98d5f727cdd98f8b5feec","observation_id":"a7ef4794-3d49-4347-a7fd-c0ffda30601d","resolution":{"observed_at":"2026-08-10T20:20:36.900496Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.878962Z","title":null,"venue":null,"work_id":"87897e69-1ad4-4d33-9afd-ba70117b1578","year":2009},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.336919Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:e29c5d095f42359900f031c62d82f7d1361e7bd86341fc562d15d38bc41d9aa5","observation_id":"3b38c517-c443-4b9c-a930-f9f8951ea61f","resolution":{"observed_at":"2026-08-10T20:20:36.883325Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.865172Z","title":"G¨ artner, On the McKean-Vlasov limit for interacting diffusions , Mathematische Nachrichten 137 (1988), 197–248","venue":null,"work_id":"4d015e09-5bc2-48f3-9a2d-160c6a143e1e","year":1988},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.340857Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:e8d34709d44a9e83dfdbb4b0b3b63e8d8608885617067ad1b1bab00eeb0165f9","observation_id":"f2a4b564-72f4-42f6-b5fe-da5e4952afaf","resolution":{"observed_at":"2026-08-10T20:20:36.869960Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.853016Z","title":"Guo and W","venue":null,"work_id":"8ef52e16-86de-499e-8372-fbcaa4aa21b0","year":2019},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.344731Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:605a842c20fe7dee98ab01192f9031536dc146f09422cb39ef175ffb645c8aaa","observation_id":"c3c069f9-b1f0-4acb-90f2-84af3819c622","resolution":{"observed_at":"2026-08-10T20:20:36.857487Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.840938Z","title":"Guo and W","venue":null,"work_id":"cf0c39d9-6692-43b6-a006-b36843182d31","year":2021},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.348615Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:a0108f3ce4630f38a7f9620cb6fa9c9de5d23f9d106ab1ed7d991ad61d59808e","observation_id":"795d324a-ccdc-4e92-ac94-1465ababc5a7","resolution":{"observed_at":"2026-08-10T20:20:36.845030Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.827382Z","title":"Hu and L","venue":null,"work_id":"e933307a-d476-46b6-a6a2-61845c2ec9d6","year":2018},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.352424Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:6066e01d27802923ae8c0db07f233c06b14e22b1aa4450290d831947637af82e","observation_id":"84540a35-4495-448b-90be-7710f329086e","resolution":{"observed_at":"2026-08-10T20:20:36.831245Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.813758Z","title":"Huang, R","venue":null,"work_id":"bd59c94c-3168-46a1-8a80-4fc749a87c86","year":2006},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.356465Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:e4f318d75f20a88d8b07e835843e29501236fde97a35ed67dc7e5ee855bc4b85","observation_id":"3a6bbc94-753c-4d0d-b680-15af6ddd6835","resolution":{"observed_at":"2026-08-10T20:20:36.818001Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.796219Z","title":"Huang, R","venue":null,"work_id":"03b9a97e-1828-4a14-8dd8-4d9cffc56306","year":2007},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.360120Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:2da7543fe0ee121919713aa951aaaa649ce87fd0a36ad529fab6355bbdfc8cd9","observation_id":"daefbb0b-70e8-4cc6-8689-9ef888594b67","resolution":{"observed_at":"2026-08-10T20:20:36.801685Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.783403Z","title":"Kac, Foundations of kinetic theory , Proceedings of the 3rd Berkeley Symposium on Mathematical Statistics and Probability 3 (1956), 171–197","venue":null,"work_id":"5a52dd49-3e3b-4d79-b5bd-14dd5dab0962","year":1956},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.363877Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:5c77975038c6b11226a214daa6ceac4caf5d8e68e95d5a6b413e746b2b17b178","observation_id":"c0d57240-a272-4db7-b92c-1036d416582a","resolution":{"observed_at":"2026-08-10T20:20:36.787873Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.770382Z","title":"Khasminskii, Stochastic Stability of Differential Equations , Springer, 2011","venue":null,"work_id":"d3b7d070-c44c-45b9-b206-f5a6a3f0f29e","year":2011},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.367636Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:8ea7c15996073d724501fcf3c3a4cf7448acef7d47d58cec19ae9e642589efec","observation_id":"577239fd-a083-462b-8022-76f936ead722","resolution":{"observed_at":"2026-08-10T20:20:36.774992Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.758393Z","title":null,"venue":null,"work_id":"455e9841-cfec-4a4f-89f1-a75201692191","year":2006},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.371359Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:8e37f8ed67ab3ba5d708672cc1c927b7214bac4602f343109f42329fa865e2ea","observation_id":"691470c6-195c-4e2d-933f-cf4ab11ccc3f","resolution":{"observed_at":"2026-08-10T20:20:36.762252Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.745206Z","title":null,"venue":null,"work_id":"41228e74-e916-4f96-b9eb-35707b0d5a1c","year":2006},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.375159Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:2ad1649670bd315675b8d212ebe000113e620c1758cac33883b378e65c40939f","observation_id":"3bb24883-c9b6-45b4-8ef5-41b071883018","resolution":{"observed_at":"2026-08-10T20:20:36.749280Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.731311Z","title":null,"venue":null,"work_id":"d5a42982-6998-4346-abcd-5dc47768bd71","year":2007},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.378842Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:add8e741d3e9c3729c63d828d0ddb6cf66d315791c6508631b66139314c3b0e6","observation_id":"c18ec8d0-ce6c-4b5a-8d39-5864befe4451","resolution":{"observed_at":"2026-08-10T20:20:36.736847Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.717321Z","title":"Liu and J","venue":null,"work_id":"3d60b592-ac64-4eb8-adb4-484d4678f5aa","year":2022},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.382624Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:498a65e290074047c46f576abd3e97444d14cdd70c4bb671f7f882c5e6fcf933","observation_id":"b30f5ccb-6652-45b7-a994-76a5942ddfe5","resolution":{"observed_at":"2026-08-10T20:20:36.723062Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2309.05411","last_updated":"2023-09-11T12:23:47Z","snapshot_observed_at":"2026-07-06T16:16:53.136732Z","submitted_at":"2023-09-11T12:23:47Z","title":"Existence, uniqueness and ergodicity for McKean-Vlasov SDEs under distribution-dependent Lyapunov conditions","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2309.05411","snapshot_observed_at":"2026-08-10T20:20:36.386524Z","title":"Liu and J","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.386524Z"},"links":{"cited_paper":"/paper/2309.05411","citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:be1705a9d3c4fef17c7d1b0516ec0b08c7bbd49c0280150f2c9549bdaa85f0aa","observation_id":"9571593f-d99e-47d3-b7d1-fc240a25adf6","resolution":{"observed_at":"2026-08-10T20:20:36.386524Z","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":"2026-08-10T20:20:36.703022Z","title":null,"venue":null,"work_id":"2d66e74c-00ba-4b7e-a35f-d2f1c870f17e","year":1966},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.391238Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:5970e6ed12167eb1b80a768e0fd8f918f96234d20527e258b130ed23fd65035a","observation_id":"64bb0619-901f-47cc-baef-09bd5a58913d","resolution":{"observed_at":"2026-08-10T20:20:36.707658Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.688220Z","title":"Poincar´ e,M´ emoire sur les courbes d´ efinies par une ´ equation diff´ erentielle I , Journal de Math´ ematiques Pures et Appliqu´ ees7 (1881), 375–422","venue":null,"work_id":"68338139-c34d-4c09-b904-ba991c503a84","year":null},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.395892Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:fad8cfc3bd482a1d2b55a34d18f5469ebc5b417354448771a7ced1f28729ebbc","observation_id":"8a116b9b-e62e-41f3-810f-2974c3acd19f","resolution":{"observed_at":"2026-08-10T20:20:36.692752Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.675217Z","title":"Poincar´ e, M´ emoire sur les courbes d´ efinies par une ´ equation diff´ erentielle II , Journal de Math´ ematiques Pures et Appliqu´ ees8 (1882), 251–296","venue":null,"work_id":"b4244a4b-ab76-4654-aa6a-5247e097033a","year":null},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.400571Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:c5c8f2ac260286c8666c64378c3ed773d51bca352b6eae3c459cdd6dbb41764d","observation_id":"274fcb3d-1478-41f5-a363-e106d45ca522","resolution":{"observed_at":"2026-08-10T20:20:36.679888Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.661613Z","title":"Poincar´ e,M´ emoire sur les courbes d´ efinies par une ´ equation diff´ erentielle III , Journal de Math´ ematiques Pures et Appliqu´ ees1 (1885), 167–244","venue":null,"work_id":"c49b70fb-df32-4a36-958a-15e63d216e05","year":null},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.404973Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:cb0d784f2f0df0b9a5f068b63e93f91fac6b8f10901ed11200a69dd755551bea","observation_id":"75b3936f-8dd4-45b4-870f-803c30458629","resolution":{"observed_at":"2026-08-10T20:20:36.666153Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.641750Z","title":"Poincar´ e,M´ emoire sur les courbes d´ efinies par une ´ equation diff´ erentielle IV , Journal de Math´ ematiques Pures et Appliqu´ ees2 (1886), 151–218","venue":null,"work_id":"bb11d3d4-853c-4183-933c-181f5854f9c0","year":null},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.409813Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:74b846c745baa93d02beaee35938f62eac2452862b7d308e0cfc1c0adaaa966c","observation_id":"28bcab04-98d9-4ae5-844d-e765f9008cc3","resolution":{"observed_at":"2026-08-10T20:20:36.652102Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.627999Z","title":null,"venue":null,"work_id":"3cd5b0c8-a3ca-4897-b3af-8ca6806cc425","year":2022},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.413970Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:27c273d43c0a0b5ff6ea0d333381a00e9dfef0c202990eeadc1ef7435297f090","observation_id":"83b1a28a-0a7d-4c16-842f-ffcc19e4335e","resolution":{"observed_at":"2026-08-10T20:20:36.632558Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.615309Z","title":null,"venue":null,"work_id":"03f662aa-9061-4818-9adf-f72f624c6ea3","year":2018},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.417936Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:b92b99bf3bc38c3978dc98534e03acb4d66f75663436766d29a7f6aaf6cdc7a9","observation_id":"9268662a-11bc-407b-afcd-ddb85fb0d347","resolution":{"observed_at":"2026-08-10T20:20:36.619491Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.603278Z","title":null,"venue":null,"work_id":"500b55fc-1180-4a6d-8f9d-87f4b04c32a6","year":1991},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.421960Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:ffcfc976e40f01fdad866b84bc9c676c13f2ece94b2f5c0ab6937fc123c392be","observation_id":"f71a8d3d-f875-4171-a371-b32725868632","resolution":{"observed_at":"2026-08-10T20:20:36.607187Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.590804Z","title":"Tugaut, Phase transitions of McKean-Vlasov processes in double-we lls landscape , Stochastics 86 (2014), 257–284","venue":null,"work_id":"9eb07a0b-757d-4516-b5dc-bb9f952cda3a","year":2014},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.425873Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:94c955b869ea518c483c5fe10e390c11794975e45b946e1413676980afa1ca39","observation_id":"e3d91346-c7e7-43a9-a7e0-f290ec92b229","resolution":{"observed_at":"2026-08-10T20:20:36.595294Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.577710Z","title":null,"venue":null,"work_id":"d0c7a418-982d-4fce-b797-2d479eacb76a","year":2006},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.429932Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:bb3d4e75e153db04699155624fc167ad73b002eb4b04dd97ddd290fd57013b09","observation_id":"adebbf87-0035-4d05-a756-235bdf51c7ce","resolution":{"observed_at":"2026-08-10T20:20:36.581979Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.562484Z","title":"Villani, Optimal Transport: Old and New , Springer, 2016","venue":null,"work_id":"d37ec928-0cd5-43c9-a152-2c8ca508b3b0","year":2016},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.433630Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:025988ffbcc75837641f318385245d14ec91c5e565600b3c91ad7f1aefc91eab","observation_id":"f2e40a7d-d318-42af-9e47-d33f45b2280b","resolution":{"observed_at":"2026-08-10T20:20:36.567303Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.547618Z","title":null,"venue":null,"work_id":"2b09315a-ede4-4ca5-a713-37821b17f626","year":2018},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.437967Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:c86b8fc34dda24a4257515d4e764bd656ab76b2b179636b1c532e4b770f915aa","observation_id":"58ae6243-d7aa-48f9-a732-d4c723b08a34","resolution":{"observed_at":"2026-08-10T20:20:36.552315Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.533961Z","title":null,"venue":null,"work_id":"a61191c8-caf6-468c-aadb-f41ac0321aa8","year":2009},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.442450Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:5382269bd35936736aeeca3db3eecdc2a9f365f1240f5ae07d421970c4eef9bc","observation_id":"b023c830-a4da-45bc-a2ec-7eb5a80c2611","resolution":{"observed_at":"2026-08-10T20:20:36.538286Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.521115Z","title":null,"venue":null,"work_id":"654e1510-dc01-4034-be61-df337f692624","year":2023},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.446493Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:726521dc48262747a1a138ea7f1417896715096e3f86327c7006f598fce761e6","observation_id":"0a59f3c4-bd1f-4961-81eb-baee6fa25ff2","resolution":{"observed_at":"2026-08-10T20:20:36.525665Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:20:36.506117Z","title":"Zhang, K","venue":null,"work_id":"3ead98cd-b689-4e2a-8097-d383b86fa8ee","year":2015},"citing_paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-10T20:20:36.450938Z"},"links":{"citing_paper":"/paper/2501.09176"},"observation_digest":"sha256:ca8f516ba47d6ad56914c375174945e8a78481b7d59fef2519d5225aab89c46e","observation_id":"4607e89c-5478-4569-b840-c89b84a27fdb","resolution":{"observed_at":"2026-08-10T20:20:36.511948Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2501.09176","last_updated":"2025-01-15T21:54:33Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-10T20:07:59.099529Z","submitted_at":"2025-01-15T21:54:33Z","title":"Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs"},"reference_resolution":{"displayed":39,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":22,"verified_exact":0,"verified_fuzzy":17},"total_outbound_references":39},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 39 of 39 outbound references and 1 inbound Pith citation observation for arXiv:2501.09176."}