{"as_of":"2026-08-16T22:36:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c94bcccac012130d8030f3914d8fee2e49ccc23077b25f497cb916c593afdc7f","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":"2026-08-14T14:28:22.518919Z","state":"measured"},{"denominator":39,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":39,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+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/1908.03397/citation-record","integrity":"/paper/1908.03397/integrity","json":"/paper/1908.03397/citation-record.json","paper":"/paper/1908.03397"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:28:22.943003Z","title":"Diffusions hypercontractives","venue":null,"work_id":"70a1bc85-1988-4915-b328-49ca2d5f7824","year":1983},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.389478Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:dabb287ebaf5b646ffa1f48fd5a799a8d730d30ef8d1374f2bab81bf18ce5d22","observation_id":"7143f3ef-46fd-4600-bf48-aed2c625a497","resolution":{"observed_at":"2026-08-14T14:28:22.946228Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.932762Z","title":"A kinetic equation for granular media","venue":null,"work_id":"5ff6d18c-0fdb-48cb-809c-ae2b5b1e90d0","year":1997},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.393853Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:7ae7219f7eea7b2b9663be8ff4abf37ddf0972d2dae0575f6e2158613dec0621","observation_id":"5fca1313-f9f4-40bb-bc27-94e67d16d600","resolution":{"observed_at":"2026-08-14T14:28:22.936587Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.921347Z","title":"Unif orm convergence to equilibrium for granular media","venue":null,"work_id":"89628c9d-aab2-4b21-b29d-f89d1d491ff6","year":2013},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.397550Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:c943ca2933b45352509ddb2a17e616186bb961635e4bd1a5d3250fcb4105972c","observation_id":"c2b4347b-2ee5-4e6e-ab24-eb6993689c7c","resolution":{"observed_at":"2026-08-14T14:28:22.925777Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.910901Z","title":"Limits of relative entropies associated with weakly interacting particle systems","venue":null,"work_id":"af2d04ee-fc93-43a6-a115-e0db6d2b7474","year":2015},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.401561Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:3052f5cf1312f16def08cd5bbde053077d977d8ea7579ca82a6ebe7519ffbaf1","observation_id":"7a9bd8f1-e2c0-448e-b7fa-fa2fccb014c4","resolution":{"observed_at":"2026-08-14T14:28:22.914655Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.900435Z","title":"Local stability of Kol- mogorov forward equations for finite state nonlinear Markov processes","venue":null,"work_id":"e4436479-342f-45bd-8985-c0f1c24c10f1","year":2015},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.405003Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:03ae77aa120cf91336bf454a8cddc779af24957d8bbb9e6436a27abb79bbdf11","observation_id":"d3d6194d-023a-403b-9bf4-1b546381b7cb","resolution":{"observed_at":"2026-08-14T14:28:22.903908Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.890360Z","title":"Convex e ntropy decay via the Bochner-Bakry- Emery approach","venue":null,"work_id":"dc0c69b8-ad89-43ff-a4cb-e9b5c0000a70","year":2009},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.408755Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:5c42c0737bc799c109f176226dc485a7d28dc67be661f25c05a772ef9915087f","observation_id":"50f8749b-1ee1-4dd6-88e5-a0dbf2099bc2","resolution":{"observed_at":"2026-08-14T14:28:22.894385Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.880928Z","title":"Entropy dissipation es timates in a zero-range dynamics","venue":null,"work_id":"28ab3bd9-b37c-4b28-9a54-afe9182825e6","year":2007},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.412561Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:bd4b7dc4f1770d8aa85975e958b0449d7b7ad0baf05e7c4ee75f224a21fadc9d","observation_id":"501b6f73-5787-4517-9e1c-486d55050db0","resolution":{"observed_at":"2026-08-14T14:28:22.884338Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.871224Z","title":null,"venue":null,"work_id":"ead962ca-c0ed-4408-a0b6-062c8632a877","year":2019},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.415929Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:aa08d50307786814770e360b7348dac36267d80bf29395ed051ded6d48cfb00f","observation_id":"b4a410ee-d40a-446c-97e7-5cec0edafcd9","resolution":{"observed_at":"2026-08-14T14:28:22.874622Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.861444Z","title":"Carrillo, Robert J","venue":null,"work_id":"426ce40c-b30c-46db-ace9-2b54c0fea25d","year":2003},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.419174Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:95d87fbd016101de347e5c4f79359c40993a053c145cfbf29562333fc345a875","observation_id":"7d52c4e2-c020-4108-bb5a-688b1d84fdf0","resolution":{"observed_at":"2026-08-14T14:28:22.864794Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.851330Z","title":"Carrillo, Robert J","venue":null,"work_id":"5e430498-8b61-41d7-b877-17630c39971b","year":2006},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.422425Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:1ba2cef22c94a67a43b32379355112625e651bf730cdd3d5552a525f77268597","observation_id":"2e18eb43-5152-47b8-8d12-e26fd090dd08","resolution":{"observed_at":"2026-08-14T14:28:22.855389Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.841188Z","title":"Stochastic Cucker–Smale models: Old and new","venue":null,"work_id":"338c73f0-1342-4d69-930c-a17264c590a8","year":2018},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.425760Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:f880105d170d73beff46e1cda6bec13a61bcbd30242792d059fdfe348ce8fe4b","observation_id":"72a2d066-8027-4807-a5fd-3b84312bbad3","resolution":{"observed_at":"2026-08-14T14:28:22.844865Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.830779Z","title":"Probabilistic approach for granular media equations in the non-uniformly convex case","venue":null,"work_id":"ef3e9574-8045-4685-95bc-ed2f393939dc","year":2008},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.429373Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:046d8c9140529301b0e155109774d518c5e26232d120fb19620ad70a11d40f1d","observation_id":"4f8bfd22-02fe-46f4-90a7-f9ccb7746425","resolution":{"observed_at":"2026-08-14T14:28:22.834532Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.819254Z","title":"Fokke r-Planck equations for a free energy functional or Markov process on a graph","venue":null,"work_id":"39fadd63-b6bd-4d44-9bdc-ae62c733c28a","year":2012},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.432754Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:a71f1fc7d6d74bdb85f33064c85048aa00699b9fff1fd14819b534c0e3e93ef1","observation_id":"0f1561ef-ac4b-4867-82f7-83f3ceffd105","resolution":{"observed_at":"2026-08-14T14:28:22.823060Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.809479Z","title":"Processus des misanthro pes","venue":null,"work_id":"75d4b84a-01f5-445d-8391-70409cb897e8","year":1985},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.435969Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:f4ee7be0e4727400b8e44d9e4c1637a9e35df6bda6c88b4da7418d0254974185","observation_id":"a8f49578-f727-4e46-ac28-089d77f9a46a","resolution":{"observed_at":"2026-08-14T14:28:22.812884Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.799426Z","title":"Eulerian calculus fo r the displacement convexity in the Wasser- stein distance","venue":null,"work_id":"e39b2554-9332-433c-9791-37da120619f0","year":2008},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.439438Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:2471ecc366b1e3245aa1862fea952545045526c70e373c4c63fd665969450767","observation_id":"216ef81f-edb8-42df-bad3-7ad5be70aea0","resolution":{"observed_at":"2026-08-14T14:28:22.802851Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.789888Z","title":"Macroscopic models of collective motion and self-organization","venue":null,"work_id":"77a015cc-8046-4256-8422-a5d0622be3cb","year":2012},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.442776Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:7ab6372b42b30ecfb36860b7923009acdfb55d309471c2aaf1fbdde062d7f3c7","observation_id":"ced57fd2-e4a9-4f31-a146-e7b40d797dc2","resolution":{"observed_at":"2026-08-14T14:28:22.793304Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.780362Z","title":"Reflection couplings and contraction r ates for diffusions","venue":null,"work_id":"f86f6aa0-4583-4aad-96ce-8229a3db3e1f","year":2016},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.446295Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:be5bb0344c9bc508db2e9187e2522b37128b08a7cea3bccbb2fbf2d1a84eefb0","observation_id":"62545959-5f8f-4313-a25e-a24d7bb77fae","resolution":{"observed_at":"2026-08-14T14:28:22.783859Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.770414Z","title":"Qu antitative Harris type theorems for dif- fusions and McKean-Vlasov processes","venue":null,"work_id":"26661675-48bf-476a-a0df-46ff17e65eca","year":2016},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.449465Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:03f886d7651831abbb69b6638e59e121a708a0df1590977d1c8441176c954403","observation_id":"cf06f7f3-d44b-4d6e-a454-a18c29c41a18","resolution":{"observed_at":"2026-08-14T14:28:22.774278Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.760807Z","title":"Gradient flow structure for McKean-Vlasov equations on discrete spaces","venue":null,"work_id":"4882af8a-671c-4fa8-9f7f-dfdc0d6b3c6d","year":2016},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.452652Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:dc7447704cd0a3604fdb8751a9eff03a2009d10975b3309e23496e1f5f2e12f5","observation_id":"5247a472-3c51-493a-9a6e-3dec2057cc9d","resolution":{"observed_at":"2026-08-14T14:28:22.764416Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.750483Z","title":"Ricci curvature bounds for weakly interacting Markov chains","venue":null,"work_id":"835dbe99-f5c6-4db5-963c-bc55854f1ab8","year":2017},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.455629Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:2c4bec80676d2c3f3d7f818d2a436528ec8313a3adcc3c363f6fff81162900fe","observation_id":"9f4adbca-d024-40d3-859e-6f38dbf9f428","resolution":{"observed_at":"2026-08-14T14:28:22.754297Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.740313Z","title":"Ricci Curvature of Finite M arkov Chains via Convexity of the Entropy","venue":null,"work_id":"31b61a21-7c69-4d37-9885-15ede918c590","year":2012},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.458756Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:9687e0ed9d045954240e3df9725754c208136def82e0801b08b3f0e176216573","observation_id":"c468fed5-23cc-4f97-b1b6-b16053dcb067","resolution":{"observed_at":"2026-08-14T14:28:22.743882Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.730434Z","title":"Entropic Ricci curvature bounds for discrete interacting systems","venue":null,"work_id":"a81016d6-7efe-400b-838a-d548a58a9dfc","year":2016},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.461822Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:33cc364737a08a54df032e95016879ca1fbdeae5d26840bd92f6aebc4b4a3921","observation_id":"76d675a8-038c-44e6-ad45-cbe291901432","resolution":{"observed_at":"2026-08-14T14:28:22.734113Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.720620Z","title":"Derivation of mean-field equations for sto- chastic particle systems","venue":null,"work_id":"e5cafb37-d5be-44a2-b7d9-1a1c7dc2e82e","year":2019},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.465001Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:1addb999fc6fef80c1dae2bff6bf25b3752661216f708cdae2c48f89b7e29df4","observation_id":"a93b9782-3af0-4298-abaf-681b127f2911","resolution":{"observed_at":"2026-08-14T14:28:22.724175Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.710500Z","title":"Cutoff for the mean-fie ld zero-range process with bounded monotone rates","venue":null,"work_id":"39b76bea-34e3-4161-a2eb-b2a5b828a414","year":2018},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.468537Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:da90a457c838e4296787e191ab02e9aa716f12c7cc993da68a26ee982e626c1b","observation_id":"6350d862-e8a9-4a94-a964-93a8406781e6","resolution":{"observed_at":"2026-08-14T14:28:22.714073Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.700108Z","title":"Entropy dissipation estimates for inhomogeneous zero-range processes","venue":null,"work_id":"eaf6c6a7-61b5-42fc-816c-1de6e22a4091","year":2019},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.471822Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:3868a198aa008ce7e235df04b39a2bb1a60212a20dcfeba08fd3134f028e3b17","observation_id":"486df541-221b-44b0-8520-0add65917e85","resolution":{"observed_at":"2026-08-14T14:28:22.703746Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1609.09637","last_updated":"2016-09-30T08:54:09Z","snapshot_observed_at":"2026-08-14T21:37:25.616317Z","submitted_at":"2016-09-30T08:54:09Z","title":"A large deviation perspective on exponential decay of entropy and lower bounds on the Ricci-curvature","version":1},"cited_work":{"arxiv_id":"1609.09637","doi":null,"metadata_source":"pith","pith_arxiv_id":"1609.09637","snapshot_observed_at":"2026-08-14T14:28:22.578681Z","title":"A large deviation perspective on exponential decay of entropy and lower bounds on the Ricci-curvature","venue":"math.PR","work_id":"42ca3b03-0dce-4f00-9d20-6df58015ca3b","year":2016},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.475022Z"},"links":{"cited_paper":"/paper/1609.09637","citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:ed8edc4473718995c19bbb5087cb0326752d764b96df1837d6156af2733cdebb","observation_id":"a54355b5-cb03-4612-8d4a-11b77314de44","resolution":{"observed_at":"2026-08-14T14:28:22.582599Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.690492Z","title":null,"venue":null,"work_id":"5c3b1934-257f-4149-aad1-58c1a12f26f8","year":2004},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.478675Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:ad61cfa25a7668f7e048d3c49e986580bf64f020a08de5ef3334f6ed166d1f21","observation_id":"151c5865-4d46-45e0-b426-14b1b5c88ada","resolution":{"observed_at":"2026-08-14T14:28:22.694009Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.680729Z","title":"Ricci curvature for metr ic-measure spaces via optimal transport","venue":null,"work_id":"0ccd97e7-31cb-4877-a2ac-5774e65cb340","year":2009},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.481961Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:97bc345e93d4dd7129e28111874e0306be6071cecfe28b605c0fe504e52f25dc","observation_id":"67d8a9b9-7fec-42c2-88b3-2156399c010d","resolution":{"observed_at":"2026-08-14T14:28:22.684318Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.671192Z","title":"Gradient flows of the entropy for finite Markov c hains","venue":null,"work_id":"6b271b1f-6202-4e65-bac7-5cbd355fe4af","year":2011},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.485141Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:6bc5385a447c705779d8012bcb2a08e8dd8128f9e798c614ea3d9f70d8d0eb43","observation_id":"f0626c46-a592-4b1c-ad52-e328442edb8d","resolution":{"observed_at":"2026-08-14T14:28:22.674509Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.661265Z","title":"Logarithmic sobolev inequalities in d iscrete product spaces: a proof by a trans- portation cost distance","venue":null,"work_id":"5bf42256-8b47-491d-8a21-86203cda24c9","year":2015},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.488271Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:53c6986a373fd59c9504e8f9d8109ee60aa97412574d5eac5ec47db41ead0758","observation_id":"4cb6098f-6d47-4c84-9dde-c4486084335e","resolution":{"observed_at":"2026-08-14T14:28:22.664667Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.651719Z","title":"Geodesic convexity of the relative e ntropy in reversible Markov chains","venue":null,"work_id":"2ee45cf6-c95d-44d1-98f5-94c80f978bf0","year":2013},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.491424Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:57341fd9149bf61addaeec774a95eb10542bb2f32e4cab61155fcd129f4d7ee6","observation_id":"054a4fa3-4e6e-4372-beb4-7b473a67705d","resolution":{"observed_at":"2026-08-14T14:28:22.655134Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.641674Z","title":"The geometry of dissipative evolution equa tions: the porous medium equation","venue":null,"work_id":"1db29695-470e-4755-9c13-310162ed8c7f","year":2001},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.494554Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:e2b4d8163518c87e16d13beefea34d44ce249fb16a2bf1d08abb2e7416ac4260","observation_id":"c4bd98d8-cc37-4b99-aeb0-a02ef3609b82","resolution":{"observed_at":"2026-08-14T14:28:22.645478Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.631058Z","title":"Generalization of an In equality by Talagrand and Links with the Logarithmic Sobolev Inequality","venue":null,"work_id":"4738d1b3-cffb-41d5-b955-9f08bb511731","year":2000},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.497787Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:7aafe0434ee1a41320db9774a69fe90fe7884804f523da77d7f2b7d85b24dccb","observation_id":"2ff0cbe4-488b-4be6-9f0c-8cc8889a552d","resolution":{"observed_at":"2026-08-14T14:28:22.634816Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1811.05954","last_updated":"2019-10-22T21:12:18Z","snapshot_observed_at":"2026-08-14T17:59:13.860850Z","submitted_at":"2018-11-14T18:41:28Z","title":"The exchange-driven growth model: basic properties and longtime behavior","version":3},"cited_work":{"arxiv_id":"1811.05954","doi":null,"metadata_source":"pith","pith_arxiv_id":"1811.05954","snapshot_observed_at":"2026-08-14T14:28:22.564983Z","title":"The exchange-driven growth model: basic properties and longtime behavior","venue":"math-ph","work_id":"25c6528e-5755-443a-bfb5-d7121a19f1b3","year":2018},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.501070Z"},"links":{"cited_paper":"/paper/1811.05954","citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:0df954795146b4e03a259af349be09ee0e84ec9870be3148c1db68464fdfb16a","observation_id":"c57005db-35e8-43fd-8104-78c742a0cd74","resolution":{"observed_at":"2026-08-14T14:28:22.568932Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.620410Z","title":"On the geometry of metric measure s paces","venue":null,"work_id":"6d292fa8-cf89-4b7f-b075-00e56a9bf96c","year":2006},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.505021Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:3bb266f5ecdd05cb0597b87af3cd435bd0bf3b6812140d1609bf0210170013d4","observation_id":"1b23749c-c455-4522-a6ac-27a3ddba425a","resolution":{"observed_at":"2026-08-14T14:28:22.624380Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.609528Z","title":"Topics in propagation of chaos","venue":null,"work_id":"97479dc5-2412-4f50-bd5d-aa66dc332d71","year":1989},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.508858Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:605f3ccfca29470917ca597987119b2993b6f88c032018d361716d385135d467","observation_id":"ad019c17-21ed-474d-a204-2f41e4c341bc","resolution":{"observed_at":"2026-08-14T14:28:22.613264Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.599634Z","title":null,"venue":null,"work_id":"6a6762bb-e9a5-40e1-bed0-2e526070b6ac","year":null},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.512240Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:c9a2a478fb6c785edc7ff12e93932521125990628550264a2bee9040d1a5522f","observation_id":"bb59c785-887b-425a-b346-28d81e173219","resolution":{"observed_at":"2026-08-14T14:28:22.602991Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:28:22.589632Z","title":"Convergence to the equilibria for self- stabilizing processes in double-well landscape","venue":null,"work_id":"3769f28a-6bd2-4c32-aa4f-635c73c0ecf5","year":2013},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.515409Z"},"links":{"citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:5c3ac3c8ec03099386b8d3a436048ace3eb8e33b82e21db6c7172db12ae45d62","observation_id":"c37a3dc0-58fc-49b3-807d-d244ba5daaeb","resolution":{"observed_at":"2026-08-14T14:28:22.593491Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1705.06642","last_updated":"2019-01-04T10:39:37Z","snapshot_observed_at":"2026-08-14T20:59:46.949825Z","submitted_at":"2017-05-18T15:12:54Z","title":"Lower bound for the coarse Ricci curvature of continuous-time pure jump processes","version":4},"cited_work":{"arxiv_id":"1705.06642","doi":null,"metadata_source":"pith","pith_arxiv_id":"1705.06642","snapshot_observed_at":"2026-08-14T14:28:22.548604Z","title":"Lower bound for the coarse Ricci curvature of continuous-time pure jump processes","venue":"math.PR","work_id":"42b6f122-0c56-4182-a99d-c76f4e8a886b","year":2017},"citing_paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-14T14:28:22.518919Z"},"links":{"cited_paper":"/paper/1705.06642","citing_paper":"/paper/1908.03397"},"observation_digest":"sha256:ccbefb24cf41ccb9526dfdca0c23ae7bdaf2bc29df8a8276418d311f91376326","observation_id":"06ec4be8-64ba-4141-b8e4-2535a5e814b5","resolution":{"observed_at":"2026-08-14T14:28:22.554662Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1908.03397","last_updated":"2019-08-09T10:14:39Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-16T04:36:33.927961Z","submitted_at":"2019-08-09T10:14:39Z","title":"Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces"},"reference_resolution":{"displayed":39,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":3,"verified_fuzzy":33},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 39 of 39 outbound references and 0 inbound Pith citation observations for arXiv:1908.03397."}