{"as_of":"2026-08-16T22:16:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ee7f8f579c3cef8d8c71705b9021cac802eea8074ab1599d0270c3d7091a1c59","coverage":[{"denominator":41,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":41,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T11:28:38.731358Z","state":"measured"},{"denominator":41,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":41,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+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/1908.09331/citation-record","integrity":"/paper/1908.09331/integrity","json":"/paper/1908.09331/citation-record.json","paper":"/paper/1908.09331"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:28:41.314884Z","title":"Albeverio, M","venue":null,"work_id":"497616b3-e7eb-4a5a-abf4-b5e3a81386a8","year":1991},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:37.508320Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:9d31e916387f7e27eec9149b227273612e8df9ff9b4384cd79d27d0d5b26db75","observation_id":"c3cc24ab-ff4f-4f2a-9a64-09242a0169ce","resolution":{"observed_at":"2026-08-14T11:28:41.375522Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1904.03134","last_updated":"2021-05-07T11:28:53Z","snapshot_observed_at":"2026-08-14T16:51:04.774740Z","submitted_at":"2019-04-05T15:59:45Z","title":"Space-time approximation of stochastic $p$-Laplace systems","version":3},"cited_work":{"arxiv_id":"1904.03134","doi":null,"metadata_source":"pith","pith_arxiv_id":"1904.03134","snapshot_observed_at":"2026-08-14T11:28:39.340440Z","title":"Space-time approximation of stochastic $p$-Laplace systems","venue":"math.AP","work_id":"43316cf6-9d07-4b52-9d6a-487f91bb5a3a","year":2019},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:37.544671Z"},"links":{"cited_paper":"/paper/1904.03134","citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:de4f6543010e642d1636d4680ecee8fe659998c8d73f4de22126fa29b8a91f4d","observation_id":"adffe509-eb4f-418f-bbf1-2d21afc93c7e","resolution":{"observed_at":"2026-08-14T11:28:39.344648Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:41.281660Z","title":"Becker, A","venue":null,"work_id":"88543289-ce47-4a47-a297-9b08c147cbf5","year":2019},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:37.569532Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:7bb0d7b6f0773a83a40f40ce1a3dcd81e20e5f8ab41605818dde99aec6c92713","observation_id":"ed924cc7-6beb-4ba0-98a2-9fb5e3941ad8","resolution":{"observed_at":"2026-08-14T11:28:41.284547Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:41.271896Z","title":"Bahouri, J","venue":null,"work_id":"5ca23134-34dc-4a60-89b6-f0e5c4ed68c5","year":2011},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:37.574222Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:cdfb9165e770d0e05b43b2a5d5ff5af85427528798c68c72e40573053e35cf06","observation_id":"d5c9534c-c7a8-4255-a024-c3c6ff1fde8f","resolution":{"observed_at":"2026-08-14T11:28:41.275264Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:41.260852Z","title":"Becker, B","venue":null,"work_id":"92a79084-641e-4251-a36c-1d8af0bcfbe7","year":2017},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:37.696509Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:53759d0ad546d813e359c2abb11f84e09b3789d82a059d7ae6364b4bb3d9e6c3","observation_id":"12a0e9b5-62d6-460e-9fbd-4fe40db2c360","resolution":{"observed_at":"2026-08-14T11:28:41.264932Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1903.06066","last_updated":"2019-03-14T15:13:31Z","snapshot_observed_at":"2026-08-14T17:02:15.536500Z","submitted_at":"2019-03-14T15:13:31Z","title":"Strong and weak divergence of exponential and linear-implicit Euler approximations for stochastic partial differential equations with superlinearly growing nonlinearities","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1903.06066","snapshot_observed_at":"2026-08-14T11:28:37.764229Z","title":"Beccari, M","venue":null,"work_id":null,"year":1903},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:37.764229Z"},"links":{"cited_paper":"/paper/1903.06066","citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:ed40200e6fa29fbb5066c1bb2e3390a577b63a0e0e46025abb3d286393f0121e","observation_id":"dc3b70ca-65b7-493b-8361-dbcc3b311f20","resolution":{"observed_at":"2026-08-14T11:28:37.764229Z","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":"1806.0156","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:28:39.101550Z","title":"Strong and weak convergence rates of ﬁn ite element method for stochastic partial diﬀerential equation with non-globa lly Lipschitz coeﬃcients","venue":null,"work_id":"988d881f-2a41-49d4-a7e1-00132451328d","year":2018},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:37.901408Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:75625f37a37a33a525b578f59eed1839bd061cd0d26724097e738246fc24365b","observation_id":"3daa8201-e2fd-4e37-8c94-52f664cbd718","resolution":{"observed_at":"2026-08-14T11:28:39.219530Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:41.249578Z","title":null,"venue":null,"work_id":"96c04347-a19d-4548-8f1b-e43ff170fd55","year":2001},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:37.905583Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:6447d317aa7a78cb925bcd2e7f25035926037a91bf99b474e68c51b3e7eebee0","observation_id":"82284183-76f3-4bca-b4a5-b385ed7f9ab7","resolution":{"observed_at":"2026-08-14T11:28:41.254030Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:41.184808Z","title":null,"venue":null,"work_id":"a349ac28-d4d0-43f7-9cfd-354b9b30c3ea","year":2010},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:37.909684Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:6660354d44ab4f74e96009a4f6fde418447882f4a75eb6b6500a6999688d65f2","observation_id":"a37ea93e-db81-45ec-844b-d3b049df8e95","resolution":{"observed_at":"2026-08-14T11:28:41.241810Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:41.059952Z","title":"Furihata, M","venue":null,"work_id":"59870484-e2fb-416f-b2b0-1280ecd437e2","year":2018},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:37.914359Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:aba2d6f79ab9f73ddaed8f44d857150142f3089a3b99dfb66af821d05f595148","observation_id":"4b807981-76ce-4c9e-9fef-fa8d58d0d2a6","resolution":{"observed_at":"2026-08-14T11:28:41.128405Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:41.049264Z","title":"Gy¨ ongy","venue":null,"work_id":"ed85f2a1-e0b8-4b18-81ad-3c9539e92e3e","year":1998},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:37.919515Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:d56fd12feb1d41d4f26cedda29151c1850cd31e047229e30feb538c1a08c01e2","observation_id":"f8ce1f7b-8bd5-47dc-af9e-aa5717a212a4","resolution":{"observed_at":"2026-08-14T11:28:41.053526Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:41.037650Z","title":"Gy¨ ongy","venue":null,"work_id":"3251fde6-17d0-4c23-abfb-7e84a17c9513","year":1999},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:37.926534Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:23da618620cb224602e86d296b1b95801d0d1f9a870dafa8c6bc19ddb7e167ec","observation_id":"eacd93c1-cfc6-4831-9a2d-2ca0f92991e5","resolution":{"observed_at":"2026-08-14T11:28:41.042307Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:41.027158Z","title":"Gubinelli","venue":null,"work_id":"156a5322-595d-4e39-972d-58882c704076","year":2004},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:37.932496Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:54cde6c50d6dcab0d5070fed5b9a80070a5415b8b6ec107b06615c21a8333c03","observation_id":"77744932-f030-47a0-9e04-07776253aec6","resolution":{"observed_at":"2026-08-14T11:28:41.030717Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:41.016010Z","title":"Gubinelli","venue":null,"work_id":"9e777e2f-94e9-47a8-bd20-f0b6b504c6d9","year":2010},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.030296Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:db0c6fe06b7eb596e04dabd6f1a80b696222a98280629e47c7733aa87234fdef","observation_id":"267f60fe-059d-4b07-891b-450edb338482","resolution":{"observed_at":"2026-08-14T11:28:41.020429Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:40.843453Z","title":"Gy¨ ongy, A","venue":null,"work_id":"7a54a5f9-d283-4934-ab1d-2eed41ea70d4","year":2005},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.064164Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:ee60460646e8020bd6823112267af552fa58e9005a3e8b3d2936e6da356f636a","observation_id":"70265bd8-bd4f-427a-ae13-f030f3254fb3","resolution":{"observed_at":"2026-08-14T11:28:40.939742Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:40.830922Z","title":"Gubinelli, P","venue":null,"work_id":"4e44e3cf-22c9-4554-89c6-366ea1da3bbc","year":2015},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.069247Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:b1af122f36b1ee3fc41c347288fabf6cd5b4a525e01b263d64927316fec31c4b","observation_id":"9ce5d304-5d29-41e3-893b-edb11f6458dc","resolution":{"observed_at":"2026-08-14T11:28:40.834752Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:40.820804Z","title":"Gy¨ ongy, S","venue":null,"work_id":"681213e6-0c82-4ff2-89c9-234c628a413d","year":2016},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.072981Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:416f0927820c8d23a7701f57ae83f05649cd8a7d368ed42c418b46f90f3d1f6e","observation_id":"24ee8c24-0dff-43ba-9faa-672eef1520de","resolution":{"observed_at":"2026-08-14T11:28:40.824557Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:40.809901Z","title":null,"venue":null,"work_id":"fa10ceb7-0523-439a-9834-614fd1b405d2","year":2014},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.078983Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:022864866b03dafea1ffecd08aa3dd6a8eeaa4adf9ffe12817d4ad7a521485f8","observation_id":"a60139f2-4bcc-4812-9968-9df3bad6df92","resolution":{"observed_at":"2026-08-14T11:28:40.813249Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1401.0295","last_updated":"2014-01-01T15:25:28Z","snapshot_observed_at":"2026-08-14T23:49:49.182151Z","submitted_at":"2014-01-01T15:25:28Z","title":"On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with non-globally monotone coefficients","version":1},"cited_work":{"arxiv_id":"1401.0295","doi":null,"metadata_source":"pith","pith_arxiv_id":"1401.0295","snapshot_observed_at":"2026-08-14T11:28:39.039533Z","title":"On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with non-globally monotone coefficients","venue":"math.PR","work_id":"0e4dfca1-b6ea-40be-acda-45d43f375f59","year":2014},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.082659Z"},"links":{"cited_paper":"/paper/1401.0295","citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:b9126f03c9aa34b385874bdff46f370b2eeded802f0c98eac1917d47f4dae0ac","observation_id":"e3a8eaf4-ae80-4b39-a78f-56c74bbe24d1","resolution":{"observed_at":"2026-08-14T11:28:39.043539Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:40.726250Z","title":"Hairer, K","venue":null,"work_id":"df7495fd-82c3-480e-9b2e-858d608affd9","year":2016},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.185418Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:7ddb3691bc84a26611d6a795d2dbe8627744edb6b66528e91983613091408935","observation_id":"90b1b6fa-1269-4af8-bd58-3c58df10182b","resolution":{"observed_at":"2026-08-14T11:28:40.802295Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:40.685710Z","title":"Hutzenthaler, A","venue":null,"work_id":"ef65616a-7a21-4b39-8186-b74ed54e2419","year":2018},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.257591Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:d7b2c9c39975ca590741919130c31bda6ec8617b16292d7abd578771d0b84697","observation_id":"b1e21867-b203-48eb-86e0-7aec1d6c9cf3","resolution":{"observed_at":"2026-08-14T11:28:40.689443Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:40.673524Z","title":"Jentzen, P","venue":null,"work_id":"bc77ea22-1649-42b1-8288-f27138b4c137","year":2019},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.270184Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:fbf9fcbe383222404d35479ca00ffcd8a653669b9d6564a004fd15583d2ffca2","observation_id":"cc284049-3389-4b8e-a07b-baa37edf2991","resolution":{"observed_at":"2026-08-14T11:28:40.678189Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:40.605753Z","title":"Jentzen, D","venue":null,"work_id":"cf538d7c-a8af-456f-8df1-eea2360ed41c","year":2017},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.275698Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:ea16efcc87e550b90d0af1443f79814319554a2935e03ea99c701e645f0963f6","observation_id":"21b241a6-68d3-4e38-b101-1044a12f03d7","resolution":{"observed_at":"2026-08-14T11:28:40.665435Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:40.371594Z","title":"Kovacs, S","venue":null,"work_id":"456a9167-84bc-4cb9-add1-299ae906b153","year":2018},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.279619Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:0eff33f69834c931ffaf67469719447c31d131af3ea1bdd291b7d25ca30940bc","observation_id":"8e3dd358-fbf4-45d3-8297-dab699ba6bd1","resolution":{"observed_at":"2026-08-14T11:28:40.485094Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:38.283646Z","title":null,"venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.283646Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:04844acc18047d58892abb60b3ad8119b69c0c57102e518e156e00a22b278d1e","observation_id":"7ce98672-d479-4c86-af91-c972b557aae1","resolution":{"observed_at":"2026-08-14T11:28:38.283646Z","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":"2026-08-14T11:28:40.361511Z","title":null,"venue":null,"work_id":"3fa1098d-09f4-4e58-a50f-d2c31cadc85a","year":2015},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.286753Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:8a14b2779bd42942d1080863b678638a299a140b80331b1fa27df8680914499a","observation_id":"d0fec28a-b40c-406b-8108-5444f947b688","resolution":{"observed_at":"2026-08-14T11:28:40.365327Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:40.351111Z","title":null,"venue":null,"work_id":"5438a37c-1b45-443a-84db-a73aacbe3c73","year":2017},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.291762Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:407903993e4398f9a4f0c0e1dd708bdd6e17fb54a5afea5d437f73fe4b74e4cc","observation_id":"4c1f8175-087a-4c5a-a269-e307f45b0139","resolution":{"observed_at":"2026-08-14T11:28:40.354741Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:40.293305Z","title":null,"venue":null,"work_id":"9a42a922-4bb0-4613-9758-1c8ac667e9f6","year":2006},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.297142Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:28176eabc70b898932c63365cbb93b3d2058df569421c935d1182d2bc52d125e","observation_id":"e112b745-8a5f-4402-94a3-5b841b8b8f95","resolution":{"observed_at":"2026-08-14T11:28:40.343887Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:40.079245Z","title":null,"venue":null,"work_id":"dadc7b51-ad16-49c1-888a-205748baee2e","year":1900},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.301339Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:d36fa89cdf8ec98d979d927b25219ad9e70aef1af2cbf40302e0d9cd8b9da99b","observation_id":"8390e17e-b8f4-4b72-8e3b-ce792c5a635f","resolution":{"observed_at":"2026-08-14T11:28:40.197513Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:40.068337Z","title":"Revuz, M","venue":null,"work_id":"deeeb9ac-73a7-40b9-9392-d6617cc97a48","year":1999},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.401253Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:f142f36b59b2d0bf99d7a49db66575faf81be2248793ff6c5f167d1fc5868edd","observation_id":"01385ccb-619b-4c3d-8fde-ab2236ea7004","resolution":{"observed_at":"2026-08-14T11:28:40.072295Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:40.057976Z","title":"R¨ ockner, R","venue":null,"work_id":"610d8c20-c90a-43da-8bee-6ebfedbcacf5","year":2017},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.530946Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:a8151bb308a271fb2fbe0035a14338d00aa41a8b06fd49ccd1540773f743fd87","observation_id":"742cf686-fe07-48d4-9205-d56e48cd91ef","resolution":{"observed_at":"2026-08-14T11:28:40.061505Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:39.891016Z","title":null,"venue":null,"work_id":"b8967f30-af9f-4e43-9bf9-88b61cb395fd","year":1985},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.535469Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:225d21c87f6b5fa75e80c359c6b0d31b49f20176bbcfb1d2528619143abed58b","observation_id":"b6f61be5-6027-4bf7-92f9-086ceb10eca8","resolution":{"observed_at":"2026-08-14T11:28:39.992134Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:39.797979Z","title":null,"venue":null,"work_id":"5293a72e-c54d-438d-96a4-f902c8c147bc","year":1971},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.539904Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:fd3fb6d006f2a514d88cb21f30e96efe87bc4fe01df504cfebe665c1df823d4d","observation_id":"d9bad3fe-cddc-4f53-a76a-e0f2d29496d0","resolution":{"observed_at":"2026-08-14T11:28:39.801734Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:39.786171Z","title":null,"venue":null,"work_id":"bc5b0cd0-4638-45e6-9a9c-066567492ff5","year":1978},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.543761Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:e8f0737e1f777b4c24827032a3508addaaddbf69e74cecd66efa0a1e140dab46","observation_id":"4469fb62-dadf-48b2-86db-16f6618fc34d","resolution":{"observed_at":"2026-08-14T11:28:39.790142Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:39.774389Z","title":null,"venue":null,"work_id":"5646b447-740f-4d80-84c4-f74b794d5405","year":1983},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.547355Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:40c5869ae4e92edcce7a5b58df411f417f8fd14b1e4a06c58f9198aa2ac11d2a","observation_id":"0aaff0bc-71b7-4c1b-8a2e-1c13d78fa9e8","resolution":{"observed_at":"2026-08-14T11:28:39.778194Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:39.560427Z","title":null,"venue":null,"work_id":"1f625b36-6e97-4915-b814-b71de1a99e85","year":2006},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.551358Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:db7a4565909c7601244e56dd1c9f19f679a116d652127aaf1c39abda544016dd","observation_id":"84d0f0af-b87b-4995-8807-4281b6cfed9c","resolution":{"observed_at":"2026-08-14T11:28:39.670353Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:39.548784Z","title":"Tsatsoulis, H","venue":null,"work_id":"50b620e5-5408-47d5-97bd-1f9e2767c411","year":2018},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.554761Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:c90cb69c8244d148289aa07798ea657b093f883f5f20eca86017f29f2c5d3c95","observation_id":"2bd1032b-15b2-4366-856a-2dafa7dd78bd","resolution":{"observed_at":"2026-08-14T11:28:39.552880Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:39.537932Z","title":"Tsatsoulis, H","venue":null,"work_id":"dde42413-db20-4a43-a659-1143050a5006","year":2018},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.558527Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:3c0496b93c8f3b9e7b45b632164a9e5b600ee89d169507a1ca2b0fb1a90a8514","observation_id":"ad2b10ac-4d03-4e0f-8c89-1d9026035172","resolution":{"observed_at":"2026-08-14T11:28:39.541678Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:39.440825Z","title":"Galerkin ﬁnite element methods for stochastic parab olic partial diﬀerential equations","venue":null,"work_id":"5cdae42d-07ab-490a-bbcd-5c100f383ee9","year":null},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.562274Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:7683933336eaa78733758c6db5a2f250f8a81620369f0074436f9db65aedf7e3","observation_id":"cff2f7c4-0ed6-4649-8f2e-9df7b3637cd2","resolution":{"observed_at":"2026-08-14T11:28:39.530679Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T11:28:39.352962Z","title":null,"venue":null,"work_id":"2cbf3f8e-ee76-49cd-aade-2f7d554277e9","year":2015},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.590566Z"},"links":{"citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:903536ac25220f8993b49e492651e5aa09f19d5dad46b0dc14efac94c1c514cc","observation_id":"efe2fb99-3997-459d-9162-0395fcf1730f","resolution":{"observed_at":"2026-08-14T11:28:39.356349Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1504.04143","last_updated":"2017-10-22T14:33:54Z","snapshot_observed_at":"2026-08-14T22:52:13.675077Z","submitted_at":"2015-04-16T08:54:07Z","title":"Piecewise linear approximation for the dynamical $\\Phi^4_3$ model","version":2},"cited_work":{"arxiv_id":"1504.04143","doi":null,"metadata_source":"pith","pith_arxiv_id":"1504.04143","snapshot_observed_at":"2026-08-14T11:28:38.828910Z","title":"Piecewise linear approximation for the dynamical $\\Phi^4_3$ model","venue":"math.PR","work_id":"c40b6c45-0183-4d13-9f69-13297b8b4a49","year":2015},"citing_paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-14T11:28:38.731358Z"},"links":{"cited_paper":"/paper/1504.04143","citing_paper":"/paper/1908.09331"},"observation_digest":"sha256:941d703c1c84d5f5b3ecd09b5cac35d423618ff9437508ee3497e40edd247da0","observation_id":"7571c8cc-c01c-4579-b413-b8b9e513cd18","resolution":{"observed_at":"2026-08-14T11:28:38.935206Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1908.09331","last_updated":"2019-08-25T14:03:16Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-16T16:49:35.801092Z","submitted_at":"2019-08-25T14:03:16Z","title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus"},"reference_resolution":{"displayed":41,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":15,"verified_exact":4,"verified_fuzzy":22},"total_outbound_references":41},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 0 inbound Pith citation observations for arXiv:1908.09331."}