{"as_of":"2026-08-10T10:56:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:4769632a0afcd31be98fddc9d6c340fa4f4ac63a26162926b8bff874961f0240","coverage":[{"denominator":38,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":38,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T15:25:05.605990Z","state":"measured"},{"denominator":39,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":39,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T20:49:33.929911Z","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":[{"citation":{"cited_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.16288","snapshot_observed_at":"2026-08-03T20:49:33.929911Z","title":"Pontryagin maximum principle for mckean–vlasov stochastic reaction–diffusion equations.arXiv preprint arXiv:2507.16288, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2511.18636","last_updated":"2026-07-17T13:03:10Z","snapshot_observed_at":"2026-08-10T06:15:09.130457Z","submitted_at":"2025-11-23T22:22:53Z","title":"Optimal Control of Heterogeneous Mean-Field Stochastic Differential Equations with Common Noise and Applications","version":2},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-03T20:49:33.929911Z"},"links":{"cited_paper":"/paper/2507.16288","citing_paper":"/paper/2511.18636"},"observation_digest":"sha256:9a16ceeb996e57704f2c5c12d42fdce4d191278731cd82b1cbb71616e0f37eb8","observation_id":"6e60b2ba-1401-48af-a2be-a8bf0c020f57","resolution":{"observed_at":"2026-08-03T20:49:33.929911Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2507.16288/citation-record","integrity":"/paper/2507.16288/integrity","json":"/paper/2507.16288/citation-record.json","paper":"/paper/2507.16288"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:25:05.990868Z","title":"The lions derivative in infinite dimensions – ap- plication to higher order expansion of mean-field spdes, 2025","venue":null,"work_id":"81126791-47d2-4330-a6ba-11f70ea1e5a0","year":2025},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.473453Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:50db1c2ff7886e7439a17cf038d195a33206a754ab392e687af7474098c647a4","observation_id":"0553fc1a-73cc-4b0f-863e-5d0d6953c1dc","resolution":{"observed_at":"2026-08-06T15:25:05.994902Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:25:05.980681Z","title":"An introductory approach to duality in optimal stochastic control","venue":null,"work_id":"bfcd84f3-e251-414d-bc1c-1fa90bc53c54","year":1978},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.478072Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:4f212fa7aef835f4e4a548c83135e8a51a80d1702ecc810dedea8dcc0ca5493f","observation_id":"007bb5ff-f396-4b9d-bafa-fe8d2a6dbb8a","resolution":{"observed_at":"2026-08-06T15:25:05.984042Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:25:05.481943Z","title":"A general stochastic maximum principle for optimal control problems.SIAM Journal on Control and Optimization, 28(4):966–979, 1990","venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.481943Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:d6d1c75be1d3ac22820476bbc045705bba3809f3f9f204581da8ad411934aec8","observation_id":"ab6d9635-a6b3-45c7-8c2b-a6086f7e4344","resolution":{"observed_at":"2026-08-06T15:25:05.481943Z","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":"2026-08-06T15:25:05.485799Z","title":"Mean field games.Japanese Journal of Mathe- matics, 2(1):229–260, Mar 2007","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.485799Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:fc9522e7fa98ffeca46deaf11475bc2e583916178d5411323f4dfe5b8a1c879b","observation_id":"b5b30a0a-835d-4937-afb2-6339bac3afbe","resolution":{"observed_at":"2026-08-06T15:25:05.485799Z","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":"2026-08-06T15:25:05.489031Z","title":"Springer International Publishing, Cham, 2018","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.489031Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:d23f4b165885aa6068c999912bd2cef460d4b58befd17c158dd39acf3b549b94","observation_id":"e01820c7-3d98-44e5-958e-eee59b5dd6d8","resolution":{"observed_at":"2026-08-06T15:25:05.489031Z","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":"2026-08-06T15:25:05.492576Z","title":"Mean-field stochastic differential equations and associated pdes","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.492576Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:4c9b7f0de73aa94830c0679d37fb0dd1a13d31f26362a930c70c5f39908e27fd","observation_id":"a1fcf8f6-9785-460e-b840-a23fe04a587e","resolution":{"observed_at":"2026-08-06T15:25:05.492576Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:25:05.969505Z","title":"Dynamic programming for optimal control of stochastic mckean–vlasov dynamics","venue":null,"work_id":"1eb8d3ba-55be-4439-b105-d71e7e6d09bb","year":null},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.496999Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:6ac94692a91179f607fc4db8cca18b9a5f7b8bfbb869f72d2afcc0915dbd8f7f","observation_id":"26485b59-2495-4f67-989d-f1c5593934fe","resolution":{"observed_at":"2026-08-06T15:25:05.974094Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:25:05.504542Z","title":"Ency- clopedia of Mathematics and its Applications","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.504542Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:88b82b916f8571c7e398a5d68f08f59dceb64f0c93ec99f0fecbdfa9f080947b","observation_id":"8b806ad6-bb57-4f32-a897-f9be2f629be2","resolution":{"observed_at":"2026-08-06T15:25:05.504542Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:25:05.957672Z","title":"Stochastic Partial Differential Equations: An Introduc- tion","venue":null,"work_id":"c7ab35c0-1e61-4add-a3fc-5a319345e204","year":2015},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.508160Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:f730bbe78ae98fa30ea5f5c78fd9ee1cd9f2ce9901d4563ebf787500bb219bbc","observation_id":"65912d71-5c8f-4fbe-bf3a-62938cb3250d","resolution":{"observed_at":"2026-08-06T15:25:05.961663Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-3-030-89003-2_2","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T00:03:56.115653Z","title":"Springer International Publishing, Cham, 2021","venue":"SpringerBriefs in mathematics","work_id":"a5b5608a-fa2c-4e27-a8e2-6eac38107810","year":2021},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.512144Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:24106dec8fa90f90011fb3dfdc2e9a828fa9657e334626918a7cefab24e300a4","observation_id":"005efbdd-1dc0-4e6e-9222-0e71c484458c","resolution":{"observed_at":"2026-08-06T15:25:05.804244Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0016-0032(83","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:25:05.791406Z","title":"Stochasticmaximumprinciplefordistributedparametersystems","venue":null,"work_id":"8f18f725-7479-4c34-9ffd-8dd12c0a6fa5","year":1983},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.515217Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:30a56dfe04b389e695c1c8d9a857a711d9490574fe8ce54878625aecf6c917ef","observation_id":"363a9e09-6dfd-4386-a970-4bbdc3b80346","resolution":{"observed_at":"2026-08-06T15:25:05.794609Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.crma.2012.07.009","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Stochastic maximum principle for optimal control of spdes","venue":"Comptes Rendus Mathématique","work_id":"49da70aa-2483-4876-a22d-9194313d228e","year":2012},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.518963Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:60db4a9af34df9abc7b359e5c94e2099054c32cdeeff594337f3f2486ca07d85","observation_id":"4c00d160-6d0b-42e5-b9e8-306635bdff7a","resolution":{"observed_at":"2026-08-06T15:25:05.784056Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-3-030-82331-3_12","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T00:03:56.115653Z","title":"Springer International Publishing, Cham, 2021","venue":"Probability theory and stochastic modelling","work_id":"218e14bb-bb62-4fa9-88f8-5919f3ae5a50","year":2021},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.522440Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:e5d0572629595f180c0818dfe0e7d80406afe11bf1b3949918ae115bca97d2ae","observation_id":"a07dcd6e-5ede-4c75-a866-722a302844f9","resolution":{"observed_at":"2026-08-06T15:25:05.772626Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:25:05.946290Z","title":null,"venue":null,"work_id":"a2a50c38-b48d-4e31-8f5b-780ce9d3a0cb","year":2016},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.525876Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:82432e1b93d4d8d062af001189b9b09bae629bf9130a592794c2024429054b06","observation_id":"58102fe4-5aeb-4594-b8bf-701e9c64ad98","resolution":{"observed_at":"2026-08-06T15:25:05.949835Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10957-018-1243-3","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T00:03:40.895421Z","title":"Stochastic control for mean-field stochastic partial differential equations with jumps.Journal of Optimization Theory and Applications, 176(3):559–584, Mar 2018","venue":"Journal of Optimization Theory and Applications","work_id":"c3e046c9-99db-4d0e-ad60-f5306d5f05e3","year":2018},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.530263Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:869553508710cf40510fb679db9efc451033b97156cd3077ca429c99cd4a2522","observation_id":"a4e99fc5-1749-479a-a8a1-a695b985b312","resolution":{"observed_at":"2026-08-06T15:25:05.760609Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s11401-019-0149-1","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Forward and backward mean-field stochastic partial differential equation and optimal control.Chinese Annals of Mathematics, Series B, 40(4):515–540, Jul 2019","venue":"Chinese Annals of Mathematics Series B","work_id":"d70581eb-6f42-439a-a046-9c6e2397e9fd","year":2019},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.533894Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:607f0199f46d2d8a5d337f40e7718b783164a131010be2664dff5b28621500d2","observation_id":"fcd477bc-e428-4db8-af87-17d1eef7b732","resolution":{"observed_at":"2026-08-06T15:25:05.750354Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1214/22-aap1880","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Op- timal control of path-dependent mckean-vlasov sdes in infinite dimension.The Annals of Applied Probability, 33:2863–2918, 08 2023","venue":"The Annals of Applied Probability","work_id":"cc6c0e80-0ecb-45b2-a695-3b9c0097a877","year":2023},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.537494Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:301912af694569f194c4119f76e0f9b2a6b195c13b1d9f11569e6055980ee9a3","observation_id":"1d5968b5-8072-447d-8e0f-11d974d58db8","resolution":{"observed_at":"2026-08-06T15:25:05.740284Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1142/s0219493722400263","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Distribution-dependent stochastic porous media equations","venue":"Stochastics and Dynamics","work_id":"9c80aa9a-00c4-45d0-8c1a-1ffba06656a3","year":2022},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.540809Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:7fed27316566fb5b765a62f36bc110f583fd0b8029ec00f5a2bc4445739bffc8","observation_id":"0c94ca32-d5d8-4d28-8438-aaaf9d56ae5f","resolution":{"observed_at":"2026-08-06T15:25:05.728353Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:25:05.936584Z","title":"Mckean-vlasov sde and spde with locally monotone coefficients","venue":null,"work_id":"318c1a0e-4eb3-416b-963d-5cb5da5a16fb","year":2024},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.544323Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:586430db0db2b397e8dd56f433d680193c215554e91d65caaa6abb0a0f95deb9","observation_id":"b15008e6-8823-4b16-9a3d-0f3fd87b78ca","resolution":{"observed_at":"2026-08-06T15:25:05.940178Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:25:05.926861Z","title":"Deterministic control of stochastic reaction-diffusion equations","venue":null,"work_id":"4e3640ca-794f-4118-ad22-06eeebe38792","year":2021},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.547595Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:2b8a2e11d7c92b4515fb766005a0031bc657e8bfb07f76e6a07d9b45640a8465","observation_id":"0755f861-f063-45ef-b23b-8acbc55ee230","resolution":{"observed_at":"2026-08-06T15:25:05.930144Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:25:05.550714Z","title":"Optimalcontrolofmeanfieldequationswithmono- tone coefficients and applications in neuroscience.Applied Mathematics & Optimization, 84 (2):1925–1968, Dec 2021","venue":null,"work_id":null,"year":1925},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.550714Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:f51c19e279ba984c2b78fcb66e15ad9ebed1faa9c96599e4256bb4fe139bb03e","observation_id":"58939a23-e873-4cdc-97e4-908cb52746f3","resolution":{"observed_at":"2026-08-06T15:25:05.550714Z","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":"2026-08-06T15:25:05.553763Z","title":"The Wasserstein distances, pages93–111","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.553763Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:fe2b98f21b28abfa979d4caba6e3f452047383795baf84d564c3f66781acaea7","observation_id":"3bc2e90e-d57c-4384-86a6-4d4ea7ad3381","resolution":{"observed_at":"2026-08-06T15:25:05.553763Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:25:05.916875Z","title":null,"venue":null,"work_id":"e2879d90-69b9-4b3a-8828-9fd5428d4167","year":2013},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.557139Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:a6cf9c0e1ee1d0f0d658d5bd52615f425f81da51eefff3709b1f6842a0adb13e","observation_id":"280a7d1b-4a1e-41a8-ae8a-cae0333383a6","resolution":{"observed_at":"2026-08-06T15:25:05.920129Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:25:05.905670Z","title":"Dinculeanu","venue":null,"work_id":"196e2e77-07d2-4e98-b704-eea20c949d8d","year":1967},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.560753Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:64ffba2b8f6958db95832971a8c6abc46a0ff7a340a568deedaeaf43c1cb1223","observation_id":"e0787414-c68c-4870-b8f8-b8b155eace91","resolution":{"observed_at":"2026-08-06T15:25:05.909516Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:25:05.893446Z","title":"Diestel and J.J","venue":null,"work_id":"3b78c1bf-9e8a-4d93-b384-383b74b98b97","year":1977},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.564379Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:f9c5b5816932257f1190d3daded3916820a5ab4af65d80aa66b5b9ff72581ade","observation_id":"ecef8b79-bfcb-43a2-921a-bb47a9452eba","resolution":{"observed_at":"2026-08-06T15:25:05.896798Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-3-031-21912-2","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T00:03:56.115653Z","title":"Springer International Publishing, Cham, 2023","venue":null,"work_id":"e11c51f9-5aad-4fe1-8449-5723ef7d159f","year":2023},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.568039Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:44f8e35ded68e9916be897a9d623a1359ed674a1440a2c63b10c998abd953575","observation_id":"8a20875c-f31c-4411-af9a-1b3a41e9f9b0","resolution":{"observed_at":"2026-08-06T15:25:05.704832Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.2307/2044607","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Proceedings of the American Mathematical Society","work_id":"10d48c1e-3dff-48e4-87df-944bbf99c1df","year":1983},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.571012Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:009ddcfd4e4c900fb6dcc9b1be577c32b8e8dfb1d3ffcc1d8e28abbcc7a1af8a","observation_id":"20374db9-1042-4f03-9f9d-4ee95c17664d","resolution":{"observed_at":"2026-08-06T15:25:05.694353Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-3-319-05714-9_5","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T00:03:56.115653Z","title":"Backward Stochastic Differential Equations, pages 353–515","venue":"Stochastic modelling and applied probability","work_id":"d3403638-9de5-4a66-8caa-12dd27b6ee51","year":2014},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.574209Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:94a4089a274f69e3f7a73de010e6ccba2ca0f585de6c50bb2bbe706f45b1eb5a","observation_id":"55f90ffb-016f-4eba-b0e9-985dd9b16f08","resolution":{"observed_at":"2026-08-06T15:25:05.684394Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.spa.2010.11.008","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"One-dimensional bsdes with finite and infinite time horizons","venue":"Stochastic Processes and their Applications","work_id":"744fce64-2518-44bf-906b-ecc99057adbc","year":2011},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.577572Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:261bf7980324c389523eae2937ffa0db8c9407571797e5657a2ecc27239c166e","observation_id":"ff9c7501-6ed8-428f-acc3-5cd75c55b50e","resolution":{"observed_at":"2026-08-06T15:25:05.674255Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:25:05.580554Z","title":"Jakubowski","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.580554Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:b6440ec9533004a2beae6fa2c3c24ad95f3b9aa4548511098f291ef384aae9e2","observation_id":"b17d198e-d360-4ea8-ba5f-720ea577852e","resolution":{"observed_at":"2026-08-06T15:25:05.580554Z","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":"10.1016/j.spa.2008.08.009","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Martingale solutions and markov selections for stochastic partial differential equations.Stochastic Processes and their Appli- cations, 119(5):1725–1764, 2009","venue":"Stochastic Processes and their Applications","work_id":"02e0942c-4ec9-4d6c-a025-af1cb1f8a47d","year":2009},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.583585Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:6deff49daec62c68ccbaab80e6f856e09ed41162d866adbcd00b24e1b92a9ccd","observation_id":"18c37164-1c2b-4625-8842-3858b99642f8","resolution":{"observed_at":"2026-08-06T15:25:05.656932Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:25:05.881223Z","title":"Adams and J.J.F","venue":null,"work_id":"38cab49f-9617-4f26-bcf2-5b3d1ac7e8b9","year":null},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.587216Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:74d9d496e04dcb2777e2dfbd759d526f3f67c105de8a31ac3124f8be63fdbad1","observation_id":"c79fb648-8ad7-45b8-a47b-26d6129607f0","resolution":{"observed_at":"2026-08-06T15:25:05.885670Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:25:05.870413Z","title":null,"venue":null,"work_id":"fc1a67cc-533f-403d-96f8-40bde1360cc3","year":null},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.590923Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:676547e621d6ea81583e6af6dedbcad587e77da7858b27e0bb3e680a09a0dc6f","observation_id":"de164807-2b78-4fc5-be14-7144969358d3","resolution":{"observed_at":"2026-08-06T15:25:05.873998Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:25:05.860348Z","title":"Handbook of Analysis and Its Foundations","venue":null,"work_id":"88688e27-ac21-490b-9831-df642030c05d","year":null},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.594553Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:a855a1ef16e1bb4a5cc2fdccd1b73524587ea622c2300b78cd7cf40644e6c3ef","observation_id":"9f442283-3cde-433f-a4a2-4711d52545d6","resolution":{"observed_at":"2026-08-06T15:25:05.863573Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:25:05.849536Z","title":null,"venue":null,"work_id":"356e2e6a-3e2c-4b08-bb10-d58b4b0e7575","year":1975},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.602827Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:2650ddd03b97bdabe0bf3d3695a76663eaa72396a8216b4b30576069ebf09734","observation_id":"5e4fffa0-5e7f-49e2-873f-1c909a51ad8b","resolution":{"observed_at":"2026-08-06T15:25:05.852801Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/3-540-29587-9_2","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Topology, pages 21–67","venue":null,"work_id":"cffa4c5d-e442-4500-a3aa-94711e328936","year":2006},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.605990Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:cde056440e0a6b15c821b2b429be290fd58f269a3d41e25850e63fc8c715707b","observation_id":"2660a4b9-383c-4446-b2d0-facb89c9e94d","resolution":{"observed_at":"2026-08-06T15:25:05.632325Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/b978-0-12-622760-4.x5000-6","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"doi: 10.1016/B978-0-12-622760-4.X5000-6","venue":"Elsevier eBooks","work_id":"55ac7524-25be-4510-af2b-ef6b9f29f3d3","year":null},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":1997,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.598432Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:7a28f902c489bf612658de73977a098664e37e48875b5239da2a6cbfb7565a33","observation_id":"6862bd3f-3012-40ab-8ff0-db9c964c19c9","resolution":{"observed_at":"2026-08-06T15:25:05.644519Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:25:05.500580Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations","version":2},"reference_index":2017,"source":"pdf_text","source_observed_at":"2026-08-06T15:25:05.500580Z"},"links":{"citing_paper":"/paper/2507.16288"},"observation_digest":"sha256:f56fa29c3930385ac7814ee6fe7aabde1166707648bf1a4d7fdf19dc0149bbe7","observation_id":"9f109757-dadb-40d2-841d-aeb75fc33a3c","resolution":{"observed_at":"2026-08-06T15:25:05.500580Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2507.16288","last_updated":"2025-08-11T16:26:37Z","latest_version":2,"primary_category":"math.PR","snapshot_observed_at":"2026-08-06T15:11:05.515166Z","submitted_at":"2025-07-22T07:17:28Z","title":"Pontryagin Maximum Principle for McKean-Vlasov Stochastic Reaction-Diffusion Equations"},"reference_resolution":{"displayed":38,"state_counts":{"malformed_identifier":3,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":13,"verified_exact":15,"verified_fuzzy":7},"total_outbound_references":38},"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":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 1 inbound Pith citation observation for arXiv:2507.16288."}