{"as_of":"2026-08-14T22:36:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5a93df813c0b40281c1227316671a16eba43fbf6af4be621a614cd0de518074a","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":"2026-08-14T06:32:32.682623+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":"2026-08-12T21:17:57.870967Z","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":"2026-05-23T19:03:21.221875Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2109.11380","last_updated":"2025-03-12T12:59:29Z","snapshot_observed_at":"2026-08-13T18:05:59.443457Z","submitted_at":"2021-09-23T13:51:22Z","title":"Flow equation approach to singular stochastic PDEs","version":3},"cited_work":{"arxiv_id":"2109.11380","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2109.11380","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Duch,Flow equation approach to singular stochastic PDEs,Probab","venue":null,"work_id":"3c859b26-ef40-4d29-9a82-732cf25adf90","year":2021},"citing_paper":{"arxiv_id":"2410.17022","last_updated":"2026-02-27T10:25:41Z","snapshot_observed_at":"2026-08-13T15:07:26.382600Z","submitted_at":"2024-10-22T13:47:47Z","title":"An Additive-Noise Approximation to Keller-Segel-Dean-Kawasaki Dynamics: Small-Noise Results","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-23T19:02:27.187841Z"},"links":{"cited_paper":"/paper/2109.11380","citing_paper":"/paper/2410.17022"},"observation_digest":"sha256:cef3d2651dc0860e0119eabe70bd9c9ba1f58d26ab4924dc81cc8898c6706ccc","observation_id":"71d9377d-87fb-4a56-b9e1-fe9b9f004943","resolution":{"observed_at":"2026-05-23T19:03:21.225177Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.11380","last_updated":"2025-03-12T12:59:29Z","snapshot_observed_at":"2026-08-13T18:05:59.443457Z","submitted_at":"2021-09-23T13:51:22Z","title":"Flow equation approach to singular stochastic PDEs","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.11380","snapshot_observed_at":"2026-08-12T21:17:57.870967Z","title":"Flow equation approach to singular stochastic pdes","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2411.09058","last_updated":"2026-06-15T19:24:40Z","snapshot_observed_at":"2026-08-12T21:03:49.663830Z","submitted_at":"2024-11-13T22:34:54Z","title":"Time-dependent averages of a critical long-range stochastic heat equation","version":2},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-12T21:17:57.870967Z"},"links":{"cited_paper":"/paper/2109.11380","citing_paper":"/paper/2411.09058"},"observation_digest":"sha256:83c58b1c27c9325e916f8d1981b1e605f3cc2ca47a21ec1f5c2a16caa9f36aca","observation_id":"86c4fa4a-a17b-4567-a79b-06236afab351","resolution":{"observed_at":"2026-08-12T21:17:57.870967Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2109.11380","last_updated":"2025-03-12T12:59:29Z","snapshot_observed_at":"2026-08-13T18:05:59.443457Z","submitted_at":"2021-09-23T13:51:22Z","title":"Flow equation approach to singular stochastic PDEs","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.11380","snapshot_observed_at":"2026-08-11T16:17:11.010846Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.10311","last_updated":"2026-05-25T19:07:07Z","snapshot_observed_at":"2026-08-11T15:55:53.363553Z","submitted_at":"2024-12-13T17:51:25Z","title":"The Critical 2d Stochastic Heat Flow and Related Models","version":3},"reference_index":2017,"source":"pdf_text","source_observed_at":"2026-08-11T16:17:11.010846Z"},"links":{"cited_paper":"/paper/2109.11380","citing_paper":"/paper/2412.10311"},"observation_digest":"sha256:8b63a040eb8aa0da34f7cd65619a6d528235142249d3c61bf760b9043798aec1","observation_id":"c3091f5c-4cc1-4151-a3d2-61146acb3ae2","resolution":{"observed_at":"2026-08-11T16:17:11.010846Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2109.11380","last_updated":"2025-03-12T12:59:29Z","snapshot_observed_at":"2026-08-13T18:05:59.443457Z","submitted_at":"2021-09-23T13:51:22Z","title":"Flow equation approach to singular stochastic PDEs","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.11380","snapshot_observed_at":"2026-08-10T21:04:19.485608Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2501.06612","last_updated":"2025-08-16T18:03:48Z","snapshot_observed_at":"2026-08-12T22:40:30.893278Z","submitted_at":"2025-01-11T18:22:35Z","title":"Non-Gaussianity of invariant measures to SPDEs in Da Prato-Debussche regime","version":2},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-10T21:04:19.485608Z"},"links":{"cited_paper":"/paper/2109.11380","citing_paper":"/paper/2501.06612"},"observation_digest":"sha256:5c0ebefe4166a08cbe175e57bf00afeb5061dcb4a348a57dcc035c5ab885b8d4","observation_id":"3a131b5d-b0cb-4cd4-97a9-1ea0c58bb11a","resolution":{"observed_at":"2026-08-10T21:04:19.485608Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2109.11380","last_updated":"2025-03-12T12:59:29Z","snapshot_observed_at":"2026-08-13T18:05:59.443457Z","submitted_at":"2021-09-23T13:51:22Z","title":"Flow equation approach to singular stochastic PDEs","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.11380","snapshot_observed_at":"2026-08-08T21:15:55.393037Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2502.04884","last_updated":"2025-08-19T01:32:11Z","snapshot_observed_at":"2026-08-09T14:14:17.100602Z","submitted_at":"2025-02-07T12:42:56Z","title":"$\\Phi^4_3$ Theory from many-body quantum Gibbs states","version":2},"reference_index":2019,"source":"pdf_text","source_observed_at":"2026-08-08T21:15:55.393037Z"},"links":{"cited_paper":"/paper/2109.11380","citing_paper":"/paper/2502.04884"},"observation_digest":"sha256:8f6c7af69f962939ba26963e33faf6a2012f8c1dc9bff3597967d0b735dc8046","observation_id":"bba3588f-6340-4306-ac86-1a84190bed81","resolution":{"observed_at":"2026-08-08T21:15:55.393037Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2109.11380","last_updated":"2025-03-12T12:59:29Z","snapshot_observed_at":"2026-08-13T18:05:59.443457Z","submitted_at":"2021-09-23T13:51:22Z","title":"Flow equation approach to singular stochastic PDEs","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.11380","snapshot_observed_at":"2026-08-03T23:15:12.939529Z","title":"Duch, Flow equation approach to singular stochastic PDEs, Probab","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2511.07120","last_updated":"2026-05-29T14:55:05Z","snapshot_observed_at":"2026-08-13T10:40:31.716563Z","submitted_at":"2025-11-10T14:10:01Z","title":"Lecture notes on the flow equation approach to singular stochastic PDEs","version":2},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-03T23:15:12.939529Z"},"links":{"cited_paper":"/paper/2109.11380","citing_paper":"/paper/2511.07120"},"observation_digest":"sha256:c313f1ea4bc1edcff6d166c20a3539d19d06de947b605d03fc562282cf0d0ae2","observation_id":"95bf49bd-447d-4908-a748-20a378e515fe","resolution":{"observed_at":"2026-08-03T23:15:12.939529Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2109.11380","last_updated":"2025-03-12T12:59:29Z","snapshot_observed_at":"2026-08-13T18:05:59.443457Z","submitted_at":"2021-09-23T13:51:22Z","title":"Flow equation approach to singular stochastic PDEs","version":3},"cited_work":{"arxiv_id":"2109.11380","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2109.11380","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Duch,Flow equation approach to singular stochastic PDEs,Probab","venue":null,"work_id":"3c859b26-ef40-4d29-9a82-732cf25adf90","year":2021},"citing_paper":{"arxiv_id":"2603.10761","last_updated":"2026-04-08T12:37:24Z","snapshot_observed_at":"2026-07-06T22:48:39.649787Z","submitted_at":"2026-03-11T13:39:07Z","title":"From path integral quantization to stochastic quantization: a pedestrian's journey","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-15T12:51:49.767976Z"},"links":{"cited_paper":"/paper/2109.11380","citing_paper":"/paper/2603.10761"},"observation_digest":"sha256:d715f1a1db605622a39a521ef997820d240c6f8b8a397af1b487610cb06cf5e7","observation_id":"cc041b80-c319-49e8-b679-dbf14453d1f0","resolution":{"observed_at":"2026-05-15T12:55:38.037062Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2109.11380/citation-record","integrity":"/paper/2109.11380/integrity","json":"/paper/2109.11380/citation-record.json","paper":"/paper/2109.11380"},"outbound":[],"paper":{"arxiv_id":"2109.11380","last_updated":"2025-03-12T12:59:29Z","latest_version":3,"primary_category":"math.PR","snapshot_observed_at":"2026-08-13T18:05:59.443457Z","submitted_at":"2021-09-23T13:51:22Z","title":"Flow equation approach to singular stochastic PDEs"},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 7 inbound Pith citation observations for arXiv:2109.11380."}