{"as_of":"2026-08-11T12:24:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:17365f485b809500eae1c463aab393cabfc237150b16c7f54b28115a2af42904","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":7,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":7,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+00:00","state":"measured"},{"denominator":7,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":7,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T00:26:30.058840Z","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":"2026-06-29T11:03:18.493370Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2402.04695","last_updated":"2025-02-11T16:01:47Z","snapshot_observed_at":"2026-08-11T07:47:50.479636Z","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":"2026-08-07T00:26:30.058840Z","title":"Bresch, M","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.14309","last_updated":"2025-08-18T15:23:45Z","snapshot_observed_at":"2026-08-10T02:40:27.464190Z","submitted_at":"2025-06-17T08:36:37Z","title":"Kac's Program for the Landau Equation","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T00:26:30.058840Z"},"links":{"cited_paper":"/paper/2402.04695","citing_paper":"/paper/2506.14309"},"observation_digest":"sha256:d720e223f157662d5033ca956228dca4d549b875aeda75f95426861aa9e8254c","observation_id":"1343e8cd-2ec7-4a2f-9a30-51ff41bb480e","resolution":{"observed_at":"2026-08-07T00:26:30.058840Z","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":"2026-08-11T07:47:50.479636Z","submitted_at":"2024-02-07T09:34:39Z","title":"A duality method for mean-field limits with singular interactions","version":2},"cited_work":{"arxiv_id":"2402.04695","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2402.04695","snapshot_observed_at":"2026-06-29T11:03:18.493370Z","title":"A duality method for mean-field limits with singular interactions","venue":null,"work_id":"9a6dd050-7e6e-4d74-8996-f58d7e54a414","year":2025},"citing_paper":{"arxiv_id":"2604.13855","last_updated":"2026-04-15T13:24:30Z","snapshot_observed_at":"2026-08-07T17:59:55.302394Z","submitted_at":"2026-04-15T13:24:30Z","title":"Propagation of chaos for the Boltzmann equation with very soft potentials","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-10T12:35:04.930397Z"},"links":{"cited_paper":"/paper/2402.04695","citing_paper":"/paper/2604.13855"},"observation_digest":"sha256:f822f2f90b42b41effbffc46440d9b8406e340bc1d658794a19106aa007df8cb","observation_id":"aef149b6-ae71-4596-a10c-47ca47149596","resolution":{"observed_at":"2026-05-11T11:46:34.339565Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.04695","last_updated":"2025-02-11T16:01:47Z","snapshot_observed_at":"2026-08-11T07:47:50.479636Z","submitted_at":"2024-02-07T09:34:39Z","title":"A duality method for mean-field limits with singular interactions","version":2},"cited_work":{"arxiv_id":"2402.04695","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2402.04695","snapshot_observed_at":"2026-06-29T11:03:18.493370Z","title":"A duality method for mean-field limits with singular interactions","venue":null,"work_id":"9a6dd050-7e6e-4d74-8996-f58d7e54a414","year":2025},"citing_paper":{"arxiv_id":"2605.02058","last_updated":"2026-07-23T23:01:51Z","snapshot_observed_at":"2026-08-02T15:05:34.280346Z","submitted_at":"2026-05-03T21:05:44Z","title":"Quantitative Estimates for Mean-Field Limits and Correlation Functions through a Duality Framework","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-08T19:09:54.683027Z"},"links":{"cited_paper":"/paper/2402.04695","citing_paper":"/paper/2605.02058"},"observation_digest":"sha256:1d3019e2b3fac41dbe6be88777661e6df9ca2fe496717c702c1e85241864aa88","observation_id":"aee5fb83-1f79-4c28-b3b2-48e990d77ed7","resolution":{"observed_at":"2026-05-09T06:00:37.135424Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.04695","last_updated":"2025-02-11T16:01:47Z","snapshot_observed_at":"2026-08-11T07:47:50.479636Z","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":"2026-08-02T15:05:36.281636Z","title":"A duality method for mean- field limits with singular interactions.arXiv preprint arXiv:2402.04695, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2605.02058","last_updated":"2026-07-23T23:01:51Z","snapshot_observed_at":"2026-08-02T15:05:34.280346Z","submitted_at":"2026-05-03T21:05:44Z","title":"Quantitative Estimates for Mean-Field Limits and Correlation Functions through a Duality Framework","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-02T15:05:36.281636Z"},"links":{"cited_paper":"/paper/2402.04695","citing_paper":"/paper/2605.02058"},"observation_digest":"sha256:95bffad61b9961f24087059d5c2d8672c611658369c6372f6f287e97ce53e14d","observation_id":"50b0280e-096e-46c1-a4b0-7705edf50289","resolution":{"observed_at":"2026-08-02T15:05:36.281636Z","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":"2026-08-11T07:47:50.479636Z","submitted_at":"2024-02-07T09:34:39Z","title":"A duality method for mean-field limits with singular interactions","version":2},"cited_work":{"arxiv_id":"2402.04695","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2402.04695","snapshot_observed_at":"2026-06-29T11:03:18.493370Z","title":"A duality method for mean-field limits with singular interactions","venue":null,"work_id":"9a6dd050-7e6e-4d74-8996-f58d7e54a414","year":2025},"citing_paper":{"arxiv_id":"2605.09213","last_updated":"2026-05-09T23:16:19Z","snapshot_observed_at":"2026-08-03T03:45:10.944583Z","submitted_at":"2026-05-09T23:16:19Z","title":"Kinetic theory for Transformers and the lost-in-the-middle phenomenon","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-12T02:36:03.692657Z"},"links":{"cited_paper":"/paper/2402.04695","citing_paper":"/paper/2605.09213"},"observation_digest":"sha256:7929b82eede0c79246233a22338ddd395e53bf9b3cbb546b5544f5cbd67e9a95","observation_id":"dd812830-b876-4ca9-86e5-f4e5a15a3192","resolution":{"observed_at":"2026-05-12T07:31:27.059198Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.04695","last_updated":"2025-02-11T16:01:47Z","snapshot_observed_at":"2026-08-11T07:47:50.479636Z","submitted_at":"2024-02-07T09:34:39Z","title":"A duality method for mean-field limits with singular interactions","version":2},"cited_work":{"arxiv_id":"2402.04695","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2402.04695","snapshot_observed_at":"2026-06-29T11:03:18.493370Z","title":"A duality method for mean-field limits with singular interactions","venue":null,"work_id":"9a6dd050-7e6e-4d74-8996-f58d7e54a414","year":2025},"citing_paper":{"arxiv_id":"2605.28979","last_updated":"2026-05-27T18:34:08Z","snapshot_observed_at":"2026-08-07T20:19:21.735538Z","submitted_at":"2026-05-27T18:34:08Z","title":"Singular mean-field limits for fluctuations around equilibrium","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-29T10:57:42.856994Z"},"links":{"cited_paper":"/paper/2402.04695","citing_paper":"/paper/2605.28979"},"observation_digest":"sha256:c306bb7ccb3162d3d0802ba207b227f7c42d30e457cf26a398c2e3e1912514d5","observation_id":"d9c3ddfb-0cab-417f-b22e-fc9277b90b45","resolution":{"observed_at":"2026-06-29T11:03:18.495204Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.04695","last_updated":"2025-02-11T16:01:47Z","snapshot_observed_at":"2026-08-11T07:47:50.479636Z","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":"2026-08-07T05:23:58.359776Z","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":"sha256:4485ad64a1fc3f553fa860716f6c36812f6e4a5ae0c3f00ab1286a7b7ae1fca4","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"}}],"links":{"evidence":"/evidence","html":"/paper/2402.04695/citation-record","integrity":"/paper/2402.04695/integrity","json":"/paper/2402.04695/citation-record.json","paper":"/paper/2402.04695"},"outbound":[],"paper":{"arxiv_id":"2402.04695","last_updated":"2025-02-11T16:01:47Z","latest_version":2,"primary_category":"math.AP","snapshot_observed_at":"2026-08-11T07:47:50.479636Z","submitted_at":"2024-02-07T09:34:39Z","title":"A duality method for mean-field limits with singular interactions"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 7 inbound Pith citation observations for arXiv:2402.04695."}