{"as_of":"2026-08-21T16:42:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:1c1922afabda00c4e48c48a30df840beb03dd946e2c9fec1ca7bc24cf604a50c","coverage":[{"denominator":45,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":45,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-14T09:59:50.839181Z","state":"measured"},{"denominator":47,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":47,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-21T06:32:19.484+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T14:51:33.216051Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-15T14:51:33.268688Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2607.10686","snapshot_observed_at":"2026-08-02T07:47:59.993181Z","title":"Nguyen, S","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.08986","last_updated":"2026-07-20T06:11:54Z","snapshot_observed_at":"2026-08-18T04:58:26.153819Z","submitted_at":"2026-07-09T23:17:54Z","title":"A Formalization of the Mean-Field Derivation of the Vlasov Equation","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-02T07:47:59.993181Z"},"links":{"cited_paper":"/paper/2607.10686","citing_paper":"/paper/2607.08986"},"observation_digest":"sha256:1c3fcb3104c914c85593b1db862d02367abe70d9d5d60814222b396dcf1d1ba8","observation_id":"e72c42b2-98a5-437b-9ecb-cc43ec3ca9f8","resolution":{"observed_at":"2026-08-02T07:47:59.993181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"cited_work":{"arxiv_id":"2607.10686","doi":null,"metadata_source":"pith","pith_arxiv_id":"2607.10686","snapshot_observed_at":"2026-08-15T14:51:33.268688Z","title":"Singular mean-field limits via a multiscale mollification metric","venue":"math.AP","work_id":"26308dad-5111-4e99-a058-20171b2fe79c","year":2026},"citing_paper":{"arxiv_id":"2608.04104","last_updated":"2026-08-15T10:58:14Z","snapshot_observed_at":"2026-08-20T23:09:46.138812Z","submitted_at":"2026-08-04T18:01:09Z","title":"Derivation of 2D Vlasov-Poisson for classical particles with Coulomb interactions","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-15T14:51:33.216051Z"},"links":{"cited_paper":"/paper/2607.10686","citing_paper":"/paper/2608.04104"},"observation_digest":"sha256:531166f545f876180e791c9a74a5d80c34a42fda10e6cfb44d27ab0e0001138d","observation_id":"c7fe2ac0-16f4-4b7f-9386-02140bb7c0e7","resolution":{"observed_at":"2026-08-15T14:51:33.276056Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2607.10686/citation-record","integrity":"/paper/2607.10686/integrity","json":"/paper/2607.10686/citation-record.json","paper":"/paper/2607.10686"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Quantitative stochastic homogenization and large-scale regularity , volume 352 of Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:7b4a234965887b55ea001dd17ce618db4f505f23dd47ed57aa9a78840ad6605d","observation_id":"10154d9b-63b5-4906-b81f-a0ac5c244d68","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.04695","last_updated":"2025-02-11T16:01:47Z","snapshot_observed_at":"2026-08-16T14:20:41.704094Z","submitted_at":"2024-02-07T09:34:39Z","title":"A duality method for mean-field limits with singular interactions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.04695","snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"A duality method for mean-field limits with singular interactions, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"cited_paper":"/paper/2402.04695","citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:947640e5d0675a9ef415d88b6226de223c7f513c4d7d206519864b30f1cc844c","observation_id":"758cdec6-0275-4f36-a1f9-3201621f33ae","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Stochastic ODE s and stochastic linear PDE s with critical drift: regularity, duality and uniqueness","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:ec19518713a8dc2cd6b176957b1e95523d5ec22616fc3c9f4e760e4f1515db06","observation_id":"1a5048ce-cab7-4b87-8f50-49ed1adeee05","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"The V lasov dynamics and its fluctuations in the 1/N limit of interacting classical particles","venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:8690621765293b088642a56e2b8be1a20c36b026e599cd312af3fc753415f7e0","observation_id":"62351310-5397-40d7-a2c4-95ce1311b5b6","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"A new approach to the mean-field limit of vlasov--fokker--planck equations","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:8f260e892d953cec9325b24a95bd228310c77490c47d10351622b5d0ba2c20c5","observation_id":"a406b1de-0562-4fbd-bf8d-b4c514da6ee1","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Mean field limit and quantitative estimates with singular attractive kernels","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:98417053f790750032afc350e2c01424dd784a16f0bb75e98efce1e4359c8137","observation_id":"a812055c-435f-44b8-ae67-8722841c0876","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Berman and Magnus \\\" O nnheim","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:28bbe33565cd487423ae3acee98ac85e8ad59ea61051303c8bb0cc6cd2324556","observation_id":"7c1eaac5-d0b4-48a7-9ee3-2de3ead605bb","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Carrillo and Young-Pil Choi","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:eec31202c93fecfe2692809c93fff1252cf747624213e9af109807d8d97773be","observation_id":"867edf18-6f7b-4a23-818f-e3d065f02dac","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2106.14812","last_updated":"2022-05-04T09:16:26Z","snapshot_observed_at":"2026-08-16T20:09:11.212246Z","submitted_at":"2021-06-28T15:34:05Z","title":"Propagation of chaos: a review of models, methods and applications. II. Applications","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2106.14812","snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Propagation of chaos: a review of models, methods and applications","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"cited_paper":"/paper/2106.14812","citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:1d190821b1e38c9f4439c5168ada8673aa8737758084104d2c2bfbf4b1bd7a8a","observation_id":"d573464f-68e3-480f-94d3-a621c717fa27","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"The attractive log gas: stability, uniqueness, and propagation of chaos","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:a0a619bd9a35580e47efc613ddbdb3e3603100a3ca0eab1a6577b3a77337e1e3","observation_id":"12180e33-246d-49eb-9482-5fe8b823cf50","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Carrillo, Lucas C","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:87a9d38085cf8910321138870939abdb6cd43328d8ef5404add442ca75fd512b","observation_id":"15eedbba-d7df-47ac-b26d-7a296de184ba","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Global regularity for critical SQG in bounded domains","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:4c8cb18de1250b6d2d5aa01f31b8c9bb35f5b48a26f0167c902ad4ab0e96c1d0","observation_id":"9064a0ed-0685-4bf2-ba20-a53e0968738a","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Long time dynamics of forced critical SQG","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:0035276cc20654f8ce7ebd31429ea4142f6552fcef9fbf4176909d820d454e8b","observation_id":"fecbf371-b178-424d-b4af-02ff81024677","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Sharp uniform-in-time mean-field convergence for singular periodic Riesz flows","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:0fd6bf6bd2f66b3e10a14e592a038b7cf4c79f355baff5dc56af1a27c9335472","observation_id":"ff747f7a-c953-4f2f-9aa6-82391009fb64","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Correlation estimates for brownian particles with singular interactions, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:341ebaacfc1f2245555824c5d25e254703e8b18bba028cf4e075755b273b01bd","observation_id":"e7a0834f-3693-4612-8f94-b3e884fb87e8","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":null,"venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:d04169b393221cd23687bbf7a968a781a54ec4665c2c0545c036101630ca2de4","observation_id":"7c8ce972-d79e-41ad-8713-500ad82fa6a7","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Mean-field limits for some Riesz interaction gradient flows","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:3db2229957edf53380654cc99a8efe3d99f4e71c6652cad712718a73106ed252","observation_id":"a45f764a-c43f-4d5c-a886-f5d7662f6e3b","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Well-posedness of the transport equation by stochastic perturbation","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:28381265f9c4112a5999be757d423774f961b8bf89e00acb7deb2a5dcd3e4426","observation_id":"6cf1df66-6ed8-4bdd-b3da-8600e20d7380","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"On the dynamics of large particle systems in the mean field limit","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:2630dd2da12a046db1dad74da0e14ed7061283b24a2c872400f16ede3638aea3","observation_id":"164fa877-cd7f-4c3c-9a00-547caeee8528","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2201.02005","last_updated":"2022-01-06T10:45:06Z","snapshot_observed_at":"2026-08-16T17:29:57.015783Z","submitted_at":"2022-01-06T10:45:06Z","title":"Mean-Field Limits in Statistical Dynamics","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2201.02005","snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Mean-field limits in statistical dynamics","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"cited_paper":"/paper/2201.02005","citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:e53e3c63f87a5d523cfb7942f75448731ed843ddf7d6f01ce49ae56ed02f3360","observation_id":"89c89a9e-fbab-411d-a1d8-eb3ea8fe7981","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Wasserstein distances for vortices approximation of E uler-type equations","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:46710912e8d9f5020d30f47553823b6268ce5a79289a7225dd5df01be4a09b09","observation_id":"bead87b1-fd22-4f98-8605-b75ff3db240d","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Higher-order propagation of chaos in L 2 for interacting diffusions","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:9616b58f38c02e710b07c39dfa4d014092ad0a5cc74abf2a76ce92420583ae2e","observation_id":"8becf068-d4b2-4912-bf37-223812cead9f","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"A sharp commutator estimate for sub- C oulomb modulated energies","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:7f45fffad6e892b0cf9fd7f7a0948ba74bed1612f77e1f5b044e3e4eccfa1f11","observation_id":"400e321d-a076-4855-ad97-a9c748d4f7d6","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Another look at regularity in transport-commutator estimates","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:e5e75ec852883e0ad2a45c13ec959d436f370f0b835d7c2856ee308f7fbb152c","observation_id":"b707636f-bcec-4d48-8e79-37ee2daace56","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"N -particles approximation of the V lasov equations with singular potential","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:c2bf6125df173513ce3c5c5bb431af6fb3f5ee0956c65698b32f2e61a79a30e8","observation_id":"77f3aaef-5cfc-40e4-9e2d-937bd31851ef","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"On K ac's chaos and related problems","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:7b4303e6f2fdc8814320729d74a0b51b3120dacd99f17ed8411f399273eeabea","observation_id":"35b4fcb4-f330-4d9d-bf9d-51cd636317a5","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"A review of the mean field limits for V lasov equations","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:bdc10e3611a79cd8e26bbe745cc77596cb236e17762319870e9ebe55c8fcf817","observation_id":"a0e08f4c-a561-4f21-9b3a-5533851bd88b","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Quantitative estimates of propagation of chaos for stochastic systems with W^ -1, kernels","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:9c55626f06026c679cf4e452648800a66d0f108281455baa1bdaa94232565575","observation_id":"a6eeb275-ebb9-4361-a9f3-84491c08ab81","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":null,"venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:079b657c6eb36a95d412e36456006177799a36a3c937000a0d3f60923055b8f2","observation_id":"6ef7f349-958f-4dd6-95aa-cffecf31c097","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Hierarchies, entropy, and quantitative propagation of chaos for mean field diffusions","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:580026017c36da3cd4c7420a181093fedac431d96b15208ededa17e27e0a43d5","observation_id":"c4804098-290d-4bd6-a1f4-45313c820714","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Sharp uniform-in-time propagation of chaos","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:1f0e59d9f2536714c86e05282127a86a74d0b3bc2ec40631f00005e0f68d3606","observation_id":"f6509ac3-974f-4724-ab38-ed6ce6fdb0ec","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"A mean field limit for the V lasov- P oisson system","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:b90a0abd368b1e863efb9162648a3e329545b94d82b3c56079110be6c62dbfcc","observation_id":"49d27945-e222-44e1-a4cc-c6794b3ca260","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":null,"venue":null,"work_id":null,"year":1967},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:b7fac34a7f808e6a30949d2dbc1cbf2d4fedfb7f28cb3511834cbeef5de00dd5","observation_id":"079134df-022d-4a32-8e23-514989593799","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Mathematical Theory of Incompressible Nonviscous Fluids , volume 96 of Applied Mathematical Sciences","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:58c16b94be537388997a1b757235eec260bd92ecebaaa4a7194b64768dcf1ba5","observation_id":"1956dfec-7aa0-45a7-95a4-2f86c292a953","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Mean-field limits of R iesz-type singular flows","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:9873603ac025effb083f1f310db901a575567217f9c90e87768840184f52fe17","observation_id":"d284d454-0947-4246-a2f6-6b26c8204419","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Large systems of interacting particles and the porous medium equation","venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:d045cdbc9aa315c89790d289f5d7ae79a9c2879a3c16bc20966822ecbeac3e54","observation_id":"b94a6bdf-a9b0-4fe2-963a-38007fe30ca7","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Parabolic equations with singular divergence-free drift vector fields","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:677f0a4b2ea933ef5f77f9008be53e9d08ab61db091f9e0b0b5dbc76a56db5c6","observation_id":"f57c897c-9af4-42be-9a33-ee85b1b37ce7","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"The mean-field approximation for higher-dimensional C oulomb flows in the scaling-critical L^ space","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:01a7855f628a40253f79723d1e92c2f194a8479c4a5be4bec0f3d44c225a5042","observation_id":"9fc00472-92db-48cf-aa25-5f261b58d766","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Mean-field convergence of point vortices to the incompressible E uler equation with vorticity in L^","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:ec2f9afe47a5cc7d57bcac5076861472b3baae87cc840acb14d91b86455e0773","observation_id":"fd22d287-282d-43d0-b15a-40ef39e92d85","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Commutators, mean-field, and supercritical mean-field limits for coulomb/riesz gases, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:122198118b38ff73925feb8cd32a18ddd88201d221d22463c4ca774d3fe4c139","observation_id":"2b4d5cec-3997-40ec-8030-ec3f152303f2","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Sharp commutator estimates of all order for C oulomb and R iesz modulated energies","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:9495865062885957c9db09d1530e147f5c93a6b0732c937ef7300d7f6ca82263","observation_id":"9cde2cd9-86a0-4508-8a9e-ac540e437aff","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Mean field limit for Coulomb-type flows","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:b65a524e485b6cf25d4aba0f2a9d632e363d3292ed89b5ed6950559211ae0d6a","observation_id":"27bb238b-c75e-4400-80db-f9ba1a6e0fd5","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Topics in propagation of chaos","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:1b62b122d76742713887aa0c8d703eea50d5b843c5a519e7dcf1b08e95239251","observation_id":"0fea30fc-8bf6-48df-ac30-7e74744bc28c","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Peletier, and Thomas Slangen","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:11ccd747184c5bcd39b9a84ec199d3ef144ef439c942a72abf0ab1d76f212dba","observation_id":"3f83e625-5e88-49f5-8499-cc1583854ef1","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T09:59:50.839181Z","title":"Strong well-posedness of a singular SDE for signed Coulomb particles","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-07-14T09:59:50.839181Z"},"links":{"citing_paper":"/paper/2607.10686"},"observation_digest":"sha256:220c24cb5918240433d5131790182cdbda4cef7f76bb3e29140d6a0bc0d85778","observation_id":"da421c55-3dfa-4b5d-a691-44822245d6ae","resolution":{"observed_at":"2026-07-14T09:59:50.839181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.10686","last_updated":"2026-07-12T10:15:57Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-20T15:20:58.726203Z","submitted_at":"2026-07-12T10:15:57Z","title":"Singular mean-field limits via a multiscale mollification metric"},"reference_resolution":{"displayed":45,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":45,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":45},"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":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"thesis":"As of 21 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 2 inbound Pith citation observations for arXiv:2607.10686."}