{"as_of":"2026-08-12T16:43:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:cab9351d361a41d19acfbbb5a832872223f7b5cac1d4b4ae74178c041885390f","coverage":[{"denominator":30,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":30,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-02T03:38:48.560318Z","state":"measured"},{"denominator":30,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":30,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.13849/citation-record","integrity":"/paper/2607.13849/integrity","json":"/paper/2607.13849/citation-record.json","paper":"/paper/2607.13849"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:38:44.802072Z","title":"Billingsley.Convergence of Probability Measures","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:44.802072Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:54539f700f9fa19960d6380aacd22a56dc2829966810d31d0a2751a12d17c1e9","observation_id":"aa854085-67d5-4f0e-8cc7-b9c4a444cff9","resolution":{"observed_at":"2026-08-02T03:38:44.802072Z","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":"2026-08-02T03:38:44.892822Z","title":"Carmona and F","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:44.892822Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:83357db99ad28319d949014b2469a86b7f40d6b41a36e461908032af5444f9ac","observation_id":"679c371a-dc58-4002-9c26-25bf43788c4b","resolution":{"observed_at":"2026-08-02T03:38:44.892822Z","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":"2026-08-02T03:38:45.044577Z","title":"Carmona and F","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:45.044577Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:97900d4bf70be99b23db52e1dc2ad5f688357b680b836c07ee311983707b3191","observation_id":"bf72238c-041c-4214-a0c1-3ec5185f4cdc","resolution":{"observed_at":"2026-08-02T03:38:45.044577Z","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":"2026-08-02T03:38:45.235070Z","title":"Coghi and B","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:45.235070Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:1fe59c19d7f511e391d509025395cfe831891158ad21fae7a8fd872d29d71157","observation_id":"e812c918-684a-466e-a5a4-bfaa60fb98a9","resolution":{"observed_at":"2026-08-02T03:38:45.235070Z","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":"2026-08-02T03:38:45.449288Z","title":"Cornalba, T","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:45.449288Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:0a5ab4d77eb936f2633276787d0c3c87a5b2ea9b26fcb59ec66e8565ca511d97","observation_id":"2ba00c43-a0e7-483b-91c3-0216b8539b64","resolution":{"observed_at":"2026-08-02T03:38:45.449288Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.16140","last_updated":"2024-06-10T15:01:38Z","snapshot_observed_at":"2026-08-11T19:21:20.084018Z","submitted_at":"2024-03-24T13:24:01Z","title":"Rearranged Stochastic Heat Equation: Ergodicity and Related Gradient Descent on ${\\mathcal P}({\\mathbb R})$","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.16140","snapshot_observed_at":"2026-08-02T03:38:45.665684Z","title":"Delarue and W","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:45.665684Z"},"links":{"cited_paper":"/paper/2403.16140","citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:6cd99988582a0ba9732edd10c70ede11c7f22703b85f225a069d352e32d8ed62","observation_id":"d1371307-1443-461e-9e2a-c07a6d3abcf2","resolution":{"observed_at":"2026-08-02T03:38:45.665684Z","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":"2026-08-02T03:38:45.869663Z","title":"Delarue and W","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:45.869663Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:1d90221a1d9603a466854e0b6aa9d7ab68c5545259983b76d624008b199cf0e4","observation_id":"144a2872-1da6-417d-ae73-35791c27bc77","resolution":{"observed_at":"2026-08-02T03:38:45.869663Z","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":"2026-08-02T03:38:46.037903Z","title":"Delarue and W","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:46.037903Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:3d53a546de23ecdfde88e335e6c840500397b76d658d8c625a01163dd3cbf2b9","observation_id":"888265bc-c167-4019-8688-428a6f98074a","resolution":{"observed_at":"2026-08-02T03:38:46.037903Z","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":"2026-08-02T03:38:46.155958Z","title":"Delarue and Y","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:46.155958Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:178037c56d12d2d066b180523eb335c5bfe6851fd433784f93a56e667f06b2c5","observation_id":"c2216537-b9cb-4a70-8245-d500c0ca61a5","resolution":{"observed_at":"2026-08-02T03:38:46.155958Z","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":"2026-08-02T03:38:46.332989Z","title":"Dello Schiavo","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:46.332989Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:c5f5052dfa82f22e2d13f4f4481e2fc4565c464ced0c053291a6df04d1fda06c","observation_id":"37ebb0ba-1613-4761-a006-df7fac4decb3","resolution":{"observed_at":"2026-08-02T03:38:46.332989Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2411.14936","last_updated":"2025-06-08T12:08:08Z","snapshot_observed_at":"2026-08-12T14:39:38.664534Z","submitted_at":"2024-11-22T13:49:02Z","title":"Massive Particle Systems, Wasserstein Brownian Motions, and the Dean-Kawasaki Equation","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.14936","snapshot_observed_at":"2026-08-02T03:38:46.446674Z","title":"Dello Schiavo","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:46.446674Z"},"links":{"cited_paper":"/paper/2411.14936","citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:4f05bbb341a43261221a75126d15d4ceddf46ccac7f121b899e9a7b76c6c4e5b","observation_id":"e1d1bf1f-357f-41a1-a217-1abf0d045add","resolution":{"observed_at":"2026-08-02T03:38:46.446674Z","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":"2026-08-02T03:38:46.555199Z","title":"Djurdjevac, H","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:46.555199Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:3036b92ffa05b626827ec0d53962209bbe47c7ea6fb5b6720d8f165144814713","observation_id":"59ea2809-fee6-44a1-9d0f-6e6b38cb448b","resolution":{"observed_at":"2026-08-02T03:38:46.555199Z","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":"2026-08-02T03:38:46.657723Z","title":"Fehrman and B","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:46.657723Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:6e70bccc42308f702d6eda561d5fbaa49ee25f01269072772784ad2df2aafab6","observation_id":"8adce21d-a1b9-436a-8c65-aea569012d79","resolution":{"observed_at":"2026-08-02T03:38:46.657723Z","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":"2026-08-02T03:38:46.798368Z","title":"Joffe and M","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:46.798368Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:bf993c454d0a3a6db4caa44c384a266585a714af6d73f3bcd6e2961d0ab1360f","observation_id":"990e119b-1a00-418d-bed7-bc71dc1c5350","resolution":{"observed_at":"2026-08-02T03:38:46.798368Z","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":"2026-08-02T03:38:46.872521Z","title":"Konarovskyi","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:46.872521Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:506cf7c19f6c8a0d24e61833cce2aab80d0c91b71c2cb36c68806492c1b06b5b","observation_id":"d197eb36-e3c1-4909-bf7c-7547154ec933","resolution":{"observed_at":"2026-08-02T03:38:46.872521Z","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":"2026-08-02T03:38:46.966568Z","title":"Konarovskyi, T","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:46.966568Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:cfa04fd355e44648c49807286bef41234eb6aeaaefa4c2783cf48e2eeb2f5fc1","observation_id":"80763db1-336e-4fe5-9bab-bd54bdbc797b","resolution":{"observed_at":"2026-08-02T03:38:46.966568Z","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":"2026-08-02T03:38:47.040964Z","title":"Konarovskyi, T","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:47.040964Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:b670d482dc1f65a145604e69422ea1eb4f5a7cc011b28491c0169a3448c18509","observation_id":"32377f92-ac68-408d-a4ed-426baf2e5092","resolution":{"observed_at":"2026-08-02T03:38:47.040964Z","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":"2026-08-02T03:38:47.162361Z","title":"Konarovskyi and M.-K","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:47.162361Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:730a405c3a56441865968fac6052cf0ccdb95c11865c0782a187277b51c4d2c7","observation_id":"b493015f-c533-43c0-b3d5-f8e24b4d1305","resolution":{"observed_at":"2026-08-02T03:38:47.162361Z","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":"2026-08-02T03:38:47.273653Z","title":null,"venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:47.273653Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:4ecde23c4b42016ba45d0eccbcbfe3b566bd2c4f43327cbb805a1d61b0ebaeb0","observation_id":"a3544b42-677b-4d7d-8eaf-0977d1cefec7","resolution":{"observed_at":"2026-08-02T03:38:47.273653Z","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":"2026-08-02T03:38:47.418102Z","title":null,"venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:47.418102Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:5073756b90ff736db5e30af8d67d5baf8956cfcde2095c2e13f6eea455f13135","observation_id":"02332363-9326-44a4-8a68-968090812359","resolution":{"observed_at":"2026-08-02T03:38:47.418102Z","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":"2026-08-02T03:38:47.573376Z","title":null,"venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:47.573376Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:1d7ef61f8cccca602746892a7c9534f4500c7492086cd0747fc6e8110205a773","observation_id":"8aeecaed-f0a0-4279-9284-d19aedde3c43","resolution":{"observed_at":"2026-08-02T03:38:47.573376Z","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":"2026-08-02T03:38:47.667194Z","title":"Lacker, M","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:47.667194Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:1f55d6aa17b5bbba227f11b4a95343158fc7ab81804830d6563e47de377f653e","observation_id":"b69e43d1-0894-4d00-8522-50ce5d1dfe43","resolution":{"observed_at":"2026-08-02T03:38:47.667194Z","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":"2026-08-02T03:38:47.835886Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:47.835886Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:efdf281ed58639738a8192033e115b6766ee130fd0ed2ed5886d59ff740d9f5b","observation_id":"f70a6673-7ee6-4fab-9967-8c162cd2848c","resolution":{"observed_at":"2026-08-02T03:38:47.835886Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.12755","last_updated":"2026-04-28T12:07:38Z","snapshot_observed_at":"2026-08-07T17:53:25.417342Z","submitted_at":"2025-06-15T07:45:38Z","title":"Stochastic intrinsic gradient flows on the Wasserstein space","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.12755","snapshot_observed_at":"2026-08-02T03:38:47.953704Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:47.953704Z"},"links":{"cited_paper":"/paper/2506.12755","citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:2b1012240036309a716b2ffb1ad216c400ea2e676d6df8c5d3d92ab8cf5f4860","observation_id":"88fc41bc-205b-4483-ac74-0d0fe446e53f","resolution":{"observed_at":"2026-08-02T03:38:47.953704Z","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":"2026-08-02T03:38:48.057618Z","title":"Ren and F.-Y","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:48.057618Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:532ebcb75b86333f9a15ba0873ba7c299c58f1721e45cd99105357ef584bed30","observation_id":"35f6ab87-9db5-44d4-9cc4-0f2e310baf55","resolution":{"observed_at":"2026-08-02T03:38:48.057618Z","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":"2026-08-02T03:38:48.180239Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:48.180239Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:9702de5a58ff7cee017286621b38bc24e95d8b8a99b8540dae89fdeb8c968b9c","observation_id":"05d38033-36bd-499d-a52d-eb9347866872","resolution":{"observed_at":"2026-08-02T03:38:48.180239Z","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":"2026-08-02T03:38:48.327951Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:48.327951Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:b2c411d55c2dd86ea96efd3d5ed2edd5c73973539029bef8f490a8fea0a42d13","observation_id":"1cfc6424-b67a-4ed3-bba2-2789ce68c022","resolution":{"observed_at":"2026-08-02T03:38:48.327951Z","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":"2026-08-02T03:38:48.419077Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:48.419077Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:e2704190f6472d4055f485803323db13013b5d4146793bd56b4249992ccbedf1","observation_id":"f95d2f6e-fc53-43bf-a87e-1b59d749ce04","resolution":{"observed_at":"2026-08-02T03:38:48.419077Z","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":"2026-08-02T03:38:48.506296Z","title":"von Renesse, W","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:48.506296Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:4b3a48e776daaba909d54ef1c5498b5655e87471fd90873afa52d7a5e82a6bf8","observation_id":"77feca64-0cf4-44af-8c1c-f6bc6669d0e6","resolution":{"observed_at":"2026-08-02T03:38:48.506296Z","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":"2026-08-02T03:38:48.560318Z","title":"von Renesse and K.-T","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-02T03:38:48.560318Z"},"links":{"citing_paper":"/paper/2607.13849"},"observation_digest":"sha256:fff5537db7890f5a9d0869f192aa60372ee15ad391659ad62e34e18e177b986e","observation_id":"43d64014-01cf-404e-8b5a-205ebcbfca46","resolution":{"observed_at":"2026-08-02T03:38:48.560318Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.13849","last_updated":"2026-07-15T13:58:35Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-07T17:53:53.872214Z","submitted_at":"2026-07-15T13:58:35Z","title":"Rearranged Stochastic Heat Equations with an Entropy Gradient Structure"},"reference_resolution":{"displayed":30,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":30,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":30},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:2607.13849."}