{"as_of":"2026-08-13T14:52:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f1c99927d79a026a2dc5e45b38545ecece7cc124fb1169ce58264b0494a796cb","coverage":[{"denominator":55,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":55,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T13:15:32.000261Z","state":"measured"},{"denominator":56,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":56,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+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":"2026-05-08T10:20:24.328666Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-11T20:06:08.905770Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"cited_work":{"arxiv_id":"2412.13430","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2412.13430","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"daf8a6db-efe8-4b2d-b0bc-cc66939e25bc","year":null},"citing_paper":{"arxiv_id":"2604.22510","last_updated":"2026-04-24T12:47:35Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-24T12:47:35Z","title":"Asymptotics of Multi-Scale McKean--Vlasov Diffusions with Super-Linear Kernels: a Lifted Semigroup Approach","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-05-08T10:20:24.328666Z"},"links":{"cited_paper":"/paper/2412.13430","citing_paper":"/paper/2604.22510"},"observation_digest":"sha256:e66d01ae5d77ec860f8f87ba892c5b55feae912c77cede62f549331b748eb05f","observation_id":"76a42584-4893-460b-9928-0d639b122108","resolution":{"observed_at":"2026-05-11T20:06:08.910342Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2412.13430/citation-record","integrity":"/paper/2412.13430/integrity","json":"/paper/2412.13430/citation-record.json","paper":"/paper/2412.13430"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:15:32.659381Z","title":"Barbu and M","venue":null,"work_id":"3d2e5d6c-ee4b-44bf-adb0-c8c686c64048","year":2020},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.793158Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:b38f7af415fb995b086e5c01a19636e4d1b1b4bd586e58e7b606509a90f1e48b","observation_id":"17d19389-9a46-48b5-a15c-ee91b6bc0229","resolution":{"observed_at":"2026-08-11T13:15:32.663542Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.648973Z","title":null,"venue":null,"work_id":"93925467-a97c-4b16-9910-ee288160f5b0","year":2023},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.798034Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:42503476cfca51ef8078568945bf556d227e4173980dc1fd31faab439ec27090","observation_id":"987cf31f-2d2c-4ff4-a7e3-011d18652b50","resolution":{"observed_at":"2026-08-11T13:15:32.652400Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.637200Z","title":null,"venue":null,"work_id":"a98cc5d3-b1b0-4c2a-8834-5ca4104d0709","year":2023},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.802151Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:753af34a27ac7772d630478c42c919dc887d5b83dd45038b817bde3535c35a16","observation_id":"dfb53b08-e89d-4bc2-a770-36c1dab0f5f5","resolution":{"observed_at":"2026-08-11T13:15:32.640785Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.625765Z","title":"Buckdahn, J","venue":null,"work_id":"444e4c65-47b0-4e55-a806-11253b085848","year":2017},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.806186Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:f909db0485e972ff891c3bacc0852f27bac5d40ea8a8d33623e08c81b82d725c","observation_id":"a39733b7-c1aa-476a-9fa3-f9ee6ec299be","resolution":{"observed_at":"2026-08-11T13:15:32.629869Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.614762Z","title":"Cardaliaguet, F","venue":null,"work_id":"c5f5937c-1f00-4b66-9432-5eb10e5336e7","year":2019},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.810023Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:368ba4e8ddd9095ac9e3de7aff9523e36eb50e6c043a1c8ef34dd0dac0e06419","observation_id":"1fd3322d-7944-4acd-b48b-93f7e844c8a3","resolution":{"observed_at":"2026-08-11T13:15:32.618164Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.603397Z","title":"Carmona and F","venue":null,"work_id":"6204abf7-7cf2-4443-9561-8f6e10cb926c","year":2018},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.813795Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:c6a2b664e7e93e6aae8e983446172ed1664413ab47527331169aeb030cec1e7f","observation_id":"34bd4115-8034-4c85-afee-8448c11fd385","resolution":{"observed_at":"2026-08-11T13:15:32.606901Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.592860Z","title":null,"venue":null,"work_id":"1a3db6ac-7149-4b9b-9b8b-01e6bf3e8709","year":2020},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.817474Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:91f569e5acf24029b30f5b75124182a89edbdceaddf3f75154ed704155128b62","observation_id":"1ba2965b-1b21-4bcc-bb82-333ad99ea643","resolution":{"observed_at":"2026-08-11T13:15:32.596376Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.582259Z","title":"Cattiaux, A","venue":null,"work_id":"1738c21b-036b-485e-99a3-3fcca8e944a6","year":2008},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.821453Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:d3cfafc9840521bd45a12f67e024d56ae3c153c5ef7bbb71239981e84c177604","observation_id":"91d74cf0-fa0d-4a97-87af-4d226a5dff79","resolution":{"observed_at":"2026-08-11T13:15:32.585745Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.569981Z","title":"Cerrai and M","venue":null,"work_id":"5cad5cec-d761-4655-8158-151ced0ea581","year":2009},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.824634Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:8fa6822ea35240982ca3a91d988ab16f5c7f92e283d35fb8a801e934e5556d2b","observation_id":"ab84f988-0535-4ef3-a5d9-0f4c95c4d5ae","resolution":{"observed_at":"2026-08-11T13:15:32.574036Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.557874Z","title":"Chaudru de Raynal: Strong well posedness of McKean-Vla sov stochastic diﬀerential equations with H¨ older drift.Stoch","venue":null,"work_id":"5bea1152-cacb-430f-b67e-a200fd30ed2e","year":2020},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.827961Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:2baf4c279ff92794d3089280b79405b74be354dcd5921311a22357257642ead1","observation_id":"86ed4b42-79bb-4395-96ab-a844d1dfee41","resolution":{"observed_at":"2026-08-11T13:15:32.561952Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.544954Z","title":"Chaudru de Raynal and N","venue":null,"work_id":"a97383e5-8f9e-4eec-a32e-9d0795f09437","year":2022},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.831243Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:8914dd6e10990b4cc658fbed59c5b9544cdb9e0dae6d24078b18692dd36cd115","observation_id":"08c3665a-5c71-481e-8b28-346b0ae1776a","resolution":{"observed_at":"2026-08-11T13:15:32.549676Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.533909Z","title":"Crisan and E","venue":null,"work_id":"0cec6ff4-426e-4a29-b8fe-c0d4c2a4615e","year":2018},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.834959Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:b0310611e202d7a1f0e19dc76d0e5cd3c7a37461b23b4af70792d42373c079db","observation_id":"a4ef2b2f-bfff-4b54-a858-2d377184c1b1","resolution":{"observed_at":"2026-08-11T13:15:32.537683Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.522539Z","title":null,"venue":null,"work_id":"b734745d-c47e-4b09-abe5-3d3b6fe5daac","year":1983},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.839140Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:219b9dce69d987c10cc95966b086a5259394e2bb4df0eb3ebe890bd9aad572c8","observation_id":"983b606c-a290-4578-a882-fd655b88bb4d","resolution":{"observed_at":"2026-08-11T13:15:32.526098Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.510435Z","title":null,"venue":null,"work_id":"06123c1c-94da-4668-a9d7-0a6f0d57ac3f","year":2023},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.843062Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:1ef78748fc4c19162037fcff2717816c60009fac3618c08b8b1e31d9b5a33bb3","observation_id":"28102aff-8e8e-475a-9e36-035f30e4859c","resolution":{"observed_at":"2026-08-11T13:15:32.514430Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.498881Z","title":null,"venue":null,"work_id":"e0954346-bfdc-4ece-ac66-1c42dfd4109e","year":2022},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.847252Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:109c353ba7ccb10f91b2c497b086891b3b1f1a5bc9b496ad3b789a4979b13b91","observation_id":"bdd51523-a962-44cb-8fad-7acd009aaae9","resolution":{"observed_at":"2026-08-11T13:15:32.502685Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.487329Z","title":null,"venue":null,"work_id":"887b13fa-ec65-4956-a984-59b8895834bb","year":2021},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.850732Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:84a94c8d19dbe18d4ceb0f4417563327ca43b6b310585b6da57a1883f20637a6","observation_id":"033a8f2d-87bd-40fe-99c2-9951797c4f47","resolution":{"observed_at":"2026-08-11T13:15:32.491422Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.476522Z","title":"Eberle, A","venue":null,"work_id":"a67400d0-a859-4b23-b970-ed1c5a925082","year":2019},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.854829Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:369ede4626cfb4e3b8a2c945ac2d095ed4e18848d73ccf2637fbe50766c1bbb6","observation_id":"bf05d000-9d37-4863-9ab4-1c689d273b2b","resolution":{"observed_at":"2026-08-11T13:15:32.479908Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.465929Z","title":"Princeton Univ","venue":null,"work_id":"0e0af912-55fc-489e-a30e-2b2408ac3d6d","year":1985},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.858301Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:9aa80f8339dfdf8ee9157f33f4ac91b9acab347a9029a6d95fa2ea5c07c14691","observation_id":"d53d7932-3641-49d3-b8fd-a40121780731","resolution":{"observed_at":"2026-08-11T13:15:32.469468Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.455834Z","title":null,"venue":null,"work_id":"90bf2d64-9753-4164-bfa9-0ce90f152d0b","year":2018},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.862529Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:0ea3e221b047a7f27e2233544017fb7b3208aa9ce89769f06282e1c350cfb216","observation_id":"95562a6b-0277-4bfb-9ad1-040feb263950","resolution":{"observed_at":"2026-08-11T13:15:32.459009Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.445976Z","title":null,"venue":null,"work_id":"7bae8331-b941-4c67-995b-90436a757423","year":2020},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.866060Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:756701dd384cac4a7e42cac19e2bc1ac63615dc9d6c497e7af13db45bc3ff292","observation_id":"b81a894d-74d9-42e2-a11d-f092af174e5d","resolution":{"observed_at":"2026-08-11T13:15:32.449281Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.433915Z","title":"Hairer and X.-M","venue":null,"work_id":"3210cb2b-3592-4a80-aa34-1c22e878db9e","year":2020},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.869648Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:42d7770ac1ea50a30a0e82ae50b5b1e1c84cdee8b2f12245b0e3f928714761d4","observation_id":"47d281f4-fab9-44e0-a8e6-a74b4b2ac817","resolution":{"observed_at":"2026-08-11T13:15:32.438608Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.421482Z","title":"Hairer and E","venue":null,"work_id":"bfd50a86-9654-4f93-95ce-0376552c082b","year":2021},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.874174Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:81a67da68356b1b2edf8b2691352172dd0afc640142bd78ae94938fd3ed5a178","observation_id":"53f0f1d3-5e8a-47ce-b95a-c0bff5efbe2d","resolution":{"observed_at":"2026-08-11T13:15:32.425589Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.409577Z","title":"Hammersley, D","venue":null,"work_id":"a60e13cb-18fe-442e-9eb7-ce66d7357761","year":2021},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.878729Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:3b076185194a5e1712ef54ec0874756b6499127555d3995cbf8607f3ff80b7c2","observation_id":"dd91f347-74f6-4d61-bb4b-c6b272b20bfa","resolution":{"observed_at":"2026-08-11T13:15:32.413492Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.398149Z","title":null,"venue":null,"work_id":"9368d737-2bea-442a-9ae9-9b2196840d52","year":2023},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.882206Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:f86b0860400cbbd70bfe3c65b804bab45a7a783aeebc741cb0e1e50fbb78e889","observation_id":"333156cd-85e9-4fe5-83de-b9ff477a4fcc","resolution":{"observed_at":"2026-08-11T13:15:32.401757Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.387594Z","title":"Hu and K","venue":null,"work_id":"ef131ee9-c3f5-4f0d-9ca7-1f25bf92c666","year":2017},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.885845Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:d3bf39d53a09bcb50ec4cff7e5635bcc5bb04b7953e45309c7858c4c46608ee3","observation_id":"0750acdf-de74-4f72-a158-6db9a363b5b6","resolution":{"observed_at":"2026-08-11T13:15:32.391132Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.375920Z","title":"Kac: Foundations of kinetic theory","venue":null,"work_id":"d6577be1-03d0-4a0c-83f0-c34042ff224c","year":1956},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.889565Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:c0d3327585b309b9eb8fc0781005f1f7e029f7160798eec62e1782b6a2319861","observation_id":"dd34fdd6-f4bc-40af-9a40-f5cb7683213f","resolution":{"observed_at":"2026-08-11T13:15:32.379654Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.363974Z","title":"Kifer: Averaging and climate models","venue":null,"work_id":"dc8f952a-98b2-4517-8da9-e33834dc0a0c","year":2001},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.894121Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:668c211b42b9ea47c51f797bbac1e4cc9074f994bff500c879d485c0c53fee2d","observation_id":"2fe15799-9d6e-4cd6-9ae0-18722701fd27","resolution":{"observed_at":"2026-08-11T13:15:32.368568Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.351682Z","title":null,"venue":null,"work_id":"ecb9fa65-3d5e-4800-8f15-635611ce22ca","year":2013},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.897862Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:a27f0baf7f239b9fb3789718dd289ac66306033cc9bfc5e65692925f4c75210b","observation_id":"50a10522-2791-485f-bd6d-0215478cfd2a","resolution":{"observed_at":"2026-08-11T13:15:32.356048Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.338653Z","title":null,"venue":null,"work_id":"68a6f35a-4092-41c0-8d15-4582e451e772","year":2004},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.901809Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:1dc785f5a52e90f0a2506d03169921d0042df959250e608612a988443bcd01f9","observation_id":"e7700ecf-a3a4-4292-8d08-76d1fa70b4e1","resolution":{"observed_at":"2026-08-11T13:15:32.343196Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.325477Z","title":"Lions: Mean-ﬁeld games and applications","venue":null,"work_id":"2095824c-302c-4365-9250-06efb9edf4cd","year":2007},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.905029Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:ccf556d35583344194b36e4733228117bc06a2e4ea918270624b94a527aa7911","observation_id":"6e916dd1-36dd-4bd9-a5c8-0920c31c14ae","resolution":{"observed_at":"2026-08-11T13:15:32.329913Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.313924Z","title":null,"venue":null,"work_id":"32bb3998-81df-48db-9da0-011ef975fe78","year":1968},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.908781Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:2b47993ac0731fd53169fa0cfc856701bf07e0c31e9b3992207b67dea8f7a698","observation_id":"ce73ac2b-c6c1-418f-9e34-f15dd7fd14d3","resolution":{"observed_at":"2026-08-11T13:15:32.317791Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.301688Z","title":null,"venue":null,"work_id":"8c347fc3-4c00-4ed5-b8a3-b2ec44cb827b","year":2024},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.913369Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:1d91027860856de910131737c1d301a7576760fa7893a18f09be119c4aed42eb","observation_id":"dfc56ebe-8fef-49f9-b9fa-0e993c5fe844","resolution":{"observed_at":"2026-08-11T13:15:32.306045Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.290040Z","title":"Liu: Strong convergence of principle of averaging for multisc ale stochastic dynamical systems","venue":null,"work_id":"bb070d1b-783f-4d1f-9947-f752475a2b53","year":2010},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.916835Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:d02fb7b2ab6cc3293e5b485ae7d3bf1d75215d0dc226d49ad64cf6c29b9fe23e","observation_id":"62843301-78e4-492f-834e-bc9410e186c9","resolution":{"observed_at":"2026-08-11T13:15:32.293889Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.279003Z","title":null,"venue":null,"work_id":"54fad366-963e-4e5f-81ed-891142b26a93","year":2008},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.919994Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:5a7c9e459e7640fbd1b6a11f79cd1cb6865a6d06692e685357b8eb3a3dcda1f2","observation_id":"2130b9b5-75e0-4cde-a10b-d4e1e31ca590","resolution":{"observed_at":"2026-08-11T13:15:32.282450Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.267937Z","title":null,"venue":null,"work_id":"840c13d1-242b-4e4a-8b44-08c88d74221d","year":1966},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.923648Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:c812b923857319a7a658afdb4185a90ea83ca6c01c3c96e4e380bc6f0e721619","observation_id":"a3a4e195-9e97-4f69-9caa-8d2e078b0e35","resolution":{"observed_at":"2026-08-11T13:15:32.271633Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.256183Z","title":"Mishura and A","venue":null,"work_id":"b9304fdc-78fa-48c5-bc3d-fefdc32ded33","year":2020},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.927353Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:8d6d05b6f5d0f2fff597d4fa1f7a00e1caf6ee9d513f06d44c138d2b9f5498af","observation_id":"59046a8f-fbc0-4064-86c7-2a623925f353","resolution":{"observed_at":"2026-08-11T13:15:32.260478Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.244104Z","title":"Mou and J","venue":null,"work_id":"48f636c5-f8ce-491f-bdea-fc9a6230a615","year":2021},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.931115Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:0db2fdb575ca66cd12d4ee7d31527dfa306bf8f40147c1528f00cb9d837eed04","observation_id":"4845145e-0f1a-4514-90cf-d4e1997fd5ee","resolution":{"observed_at":"2026-08-11T13:15:32.248632Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.231749Z","title":"Otto: The geometry of dissipative evolution equations: the p orous medium equation","venue":null,"work_id":"7d53d188-7980-4b59-a130-1b09720cdeb9","year":2001},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.934799Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:51dc83548fa09ae1acfb6320b9c9347055dd72d9a9f358e992d51b80071a8901","observation_id":"f9d01003-f8b5-4dc6-95b9-4c7d2d7bc9aa","resolution":{"observed_at":"2026-08-11T13:15:32.236588Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.220137Z","title":null,"venue":null,"work_id":"cc9eb062-57e4-45bc-b2b9-b6071c865954","year":2008},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.938967Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:a717ec818709988cd6c6495053480682a8ad4df6fd835df7108bbbd5bcb2ba47","observation_id":"7f5007c5-3f92-4745-aacf-d54dfdf5a89f","resolution":{"observed_at":"2026-08-11T13:15:32.224246Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.207869Z","title":"Pardoux and A","venue":null,"work_id":"4bb6a1f8-61c3-439a-b6c9-a61e768aa59a","year":2001},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.942755Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:1f9bfeb870f8870ec029a5e761f9d144efe42ea1fd5b4573a48f596898b5417e","observation_id":"9b121536-cd24-4e8b-bbba-21fe1913e2e7","resolution":{"observed_at":"2026-08-11T13:15:32.211983Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.197163Z","title":"Pardoux and A","venue":null,"work_id":"25dc573f-9b20-453b-963e-3eec2f2916c0","year":2003},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.946428Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:30e11cca0327f58aa8ea6f34f6d05ab0c256b444b621653db37ddc3840c96890","observation_id":"210fa487-b18e-4a98-b625-c8eafb594e28","resolution":{"observed_at":"2026-08-11T13:15:32.200797Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.185764Z","title":"dos Reis, W","venue":null,"work_id":"bfd869e8-0263-44e9-a8b5-df4b83059c64","year":2019},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.950129Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:3a900b39bc2ff3dba60fc2120a51b612bbc3c39b4f77721f349bcfcd354a3d09","observation_id":"5f832eb6-7511-479e-a5e7-421b67a59102","resolution":{"observed_at":"2026-08-11T13:15:32.189515Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.174984Z","title":"R¨ ockner, X","venue":null,"work_id":"c7943a7d-abf3-4904-86bd-8d5b19b16e64","year":2021},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.953854Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:0e98792a12ca09b838380ac8fd9b9d7c309fab09d7dc76f0b511f7516e4a524e","observation_id":"b29ec71a-7f46-4e80-96c7-0072a7e31515","resolution":{"observed_at":"2026-08-11T13:15:32.178660Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.163416Z","title":"R¨ ockner and L","venue":null,"work_id":"947e0e1b-bf6d-4bf0-a8f0-a74f559e5210","year":2021},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.957788Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:69470ac05307f25f14dd4685838ad415a5f6d0e615b5fea3e27e2dab23f13257","observation_id":"95ff85be-69a2-4c0f-9c6b-b2ca8eb52473","resolution":{"observed_at":"2026-08-11T13:15:32.167470Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.150627Z","title":"R¨ ockner and L","venue":null,"work_id":"e36cd60f-5929-4fb1-a84e-2d4d081f2794","year":2021},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.961543Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:6dbca1f51d8ddd4a30150f2e1d57164e72119f54d5fa4940ff10b05c74e82dfb","observation_id":"03aeb608-84f1-4d16-baef-04dbca38ac76","resolution":{"observed_at":"2026-08-11T13:15:32.155339Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.139849Z","title":"Sznitman: Topics in propagation of chaos, In: P.-L","venue":null,"work_id":"c3363bdf-3f5f-4102-a349-42764c8c4a28","year":1989},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.965197Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:1d935f8beeffce9c3868fa20a19238a3166f5d0012e90bf664520385ef2d78b0","observation_id":"ecdbeebd-a0a3-443e-99d8-90a249035b1f","resolution":{"observed_at":"2026-08-11T13:15:32.143418Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.129451Z","title":"Tugaut: Convergence to the equilibria for self-stabilizing pro cesses in double well landscape","venue":null,"work_id":"3bba07bb-af47-4275-b296-e31297655d93","year":2010},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.969629Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:15a7ad0559084b42374b2ef03f90c550e7610ab55d87af40e0a8c9299239bb97","observation_id":"c7be2e46-1489-41be-9c8f-4e1dc04ab2ff","resolution":{"observed_at":"2026-08-11T13:15:32.133193Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.117226Z","title":"Talay and M","venue":null,"work_id":"d7ff4013-10cf-40f6-afb5-4269c3705bbe","year":2020},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.973364Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:27bcbfd848cd343e4e94fbc900430ec63e8a357bea14ebe97385d677c9884562","observation_id":"baeee11d-0c2b-4b53-ba35-8d9dd546f802","resolution":{"observed_at":"2026-08-11T13:15:32.122076Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.104839Z","title":null,"venue":null,"work_id":"ebecadc8-6a97-464c-95a5-d20aa441dd80","year":1991},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.977005Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:264b921b9658dd49e5592d8c28c6faff34b42ad612edda723035f8305c227954","observation_id":"4c45846e-6f29-4829-826c-de1b3efbcae8","resolution":{"observed_at":"2026-08-11T13:15:32.108807Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.092824Z","title":"Wang: Distribution dependent SDEs for Landau type equa tions","venue":null,"work_id":"d197b9ad-be50-4fad-928f-2cc36013f408","year":2018},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.980792Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:5e15c6f4044777dbbbcaf8caf14007ead23b245c8e4e263dc051518e37378875","observation_id":"294d06df-1c56-40b8-9f58-62b12e749412","resolution":{"observed_at":"2026-08-11T13:15:32.096981Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.080551Z","title":"Wang: Exponential ergodicity for singular reﬂecting McKe an-Vlasov SDEs","venue":null,"work_id":"79bf9e34-34b3-459c-9b3f-c1d306a5b579","year":2023},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.984646Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:83a90e9f983c94025e3a395689694bc0daa56167a7c5dea3198386f3acdfeb13","observation_id":"18249f64-9d0e-4f93-ae0a-d9ac30341248","resolution":{"observed_at":"2026-08-11T13:15:32.084860Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.068610Z","title":null,"venue":null,"work_id":"4f0219d9-1fba-4bb4-a72e-d76da7940637","year":null},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.988259Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:2deb94230664f0c49be98de1088e02411bf4b3433cc6a797d231f86d9e2e68b4","observation_id":"494ba5b1-4e8a-4a2d-a821-02a33a34b63b","resolution":{"observed_at":"2026-08-11T13:15:32.072535Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.057363Z","title":"Xie and X","venue":null,"work_id":"f16b487a-1c39-482a-916b-38aa229b75ef","year":2020},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.992794Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:a4ebc5866e8b742af5ded743aeacadb2a374fda6cb820ce8d880f1104d85d995","observation_id":"e93a0c0a-0d8f-4753-9f14-305007b519fa","resolution":{"observed_at":"2026-08-11T13:15:32.061168Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T13:15:32.042158Z","title":"Zhang: Existence and non-uniqueness of stationary distrib utions for distribution dependent SDEs","venue":null,"work_id":"1601c154-a413-460c-b617-8906849a13f6","year":2023},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:31.996754Z"},"links":{"citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:0e0295e23e3a02152689b967bd8bdd619aa313ce93faac309a67dbcfda6a2b18","observation_id":"4eb164f7-f5ea-4d33-bbcf-663819cee740","resolution":{"observed_at":"2026-08-11T13:15:32.048544Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2308.05874","last_updated":"2023-08-10T23:05:07Z","snapshot_observed_at":"2026-08-13T10:36:56.676483Z","submitted_at":"2023-08-10T23:05:07Z","title":"Homogenization of conditional slow-fast McKean-Vlasov SDEs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2308.05874","snapshot_observed_at":"2026-08-11T13:15:32.000261Z","title":"Zitridis: Homogenization of conditional slow-fast McKean-Vla sov SDEs","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-11T13:15:32.000261Z"},"links":{"cited_paper":"/paper/2308.05874","citing_paper":"/paper/2412.13430"},"observation_digest":"sha256:b0cc119d0d5977bec081573e0ba8098d492014e81b4d4856206b125b8b0663b5","observation_id":"fddfdb7a-ef74-44b7-9051-47e6cc2d20fe","resolution":{"observed_at":"2026-08-11T13:15:32.000261Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2412.13430","last_updated":"2024-12-18T01:46:33Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-11T13:06:03.812048Z","submitted_at":"2024-12-18T01:46:33Z","title":"Asymptotic limit of fully coupled multi-scale non-linear stochastic system: the non-autonomous approximation method"},"reference_resolution":{"displayed":55,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":20,"verified_exact":0,"verified_fuzzy":35},"total_outbound_references":55},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 55 of 55 outbound references and 1 inbound Pith citation observation for arXiv:2412.13430."}