{"as_of":"2026-08-07T08:01:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fc512ce81b43865ea700adfff9db3e4c331d388aa6bce4998b9b063e0ce332d9","coverage":[{"denominator":37,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":37,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T11:52:43.573539Z","state":"measured"},{"denominator":37,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":37,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+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/2608.05007/citation-record","integrity":"/paper/2608.05007/integrity","json":"/paper/2608.05007/citation-record.json","paper":"/paper/2608.05007"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:52:44.311985Z","title":"Ammari, K","venue":null,"work_id":"41a9966d-a9ea-46cc-945d-d11a360354fb","year":2012},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.391741Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:2ca4ed4b1e563657f6f8c6aeaf2ef6ba1ce3418f3f84131d28dcf9a6d8abaa9f","observation_id":"58b3c6e5-6ca8-46e1-bb8a-045f93e15f73","resolution":{"observed_at":"2026-08-06T11:52:44.316979Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:44.295717Z","title":"Ammari, H","venue":null,"work_id":"66cfb731-c356-4029-bf3b-0a835851f311","year":2009},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.397422Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:de1c21974b28b4784af7c81dda998a6d837ad3546ac40fb039f926e08cfa2ce3","observation_id":"a862b10c-7dce-4b76-af22-d480bfee929b","resolution":{"observed_at":"2026-08-06T11:52:44.301092Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:44.277230Z","title":null,"venue":null,"work_id":"f18b19d9-2e28-437c-833f-ae43998be8fa","year":2018},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.403026Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:4c475b4e92441a33300278f692ee0147af661e42b86cb4ce4674c8270c51fd4d","observation_id":"e62c49d1-fa49-4a5d-8710-9049fc01c0cf","resolution":{"observed_at":"2026-08-06T11:52:44.282333Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:44.260789Z","title":"B´ enichou and R","venue":null,"work_id":"ecda4c77-aae0-4ea9-bc22-4207e1040a8f","year":2008},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.407936Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:8a085bf6fb46472d47213153f67d7e3a62190ed548c83e0a61b34ef0726def13","observation_id":"87a8f9c6-0a96-400d-ba64-01eba09256e4","resolution":{"observed_at":"2026-08-06T11:52:44.266155Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:44.243758Z","title":"Br´ ezis,Functional analysis, sobolev spaces and partial differential equations, Vol","venue":null,"work_id":"b4f0fe2c-3c40-43df-8ffc-4258b278891a","year":2011},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.412628Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:8df86bca0a162e11af223ce122e55c4681ac2775aa7002ff966ee58684872395","observation_id":"a3d6163f-a586-4cda-a1a7-05c1a218fb11","resolution":{"observed_at":"2026-08-06T11:52:44.248873Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:44.227678Z","title":"Carillo, T","venue":null,"work_id":"4cc35b79-d0f7-4877-9486-4585490a516f","year":2026},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.417449Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:c7cc7724cf12cba3b63c119c64f92986441c690cf07223c159c9c82c020ea1ae","observation_id":"3527030e-461b-433c-8364-3ae4960fafac","resolution":{"observed_at":"2026-08-06T11:52:44.232882Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:44.210383Z","title":"Champagnat and D","venue":null,"work_id":"7829d561-0567-41ae-a18b-e2184bacd709","year":2023},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.422649Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:6e55f00401208f72fd52477a1819f4d46f5a5ec1d8867f6d7d964ee123739288","observation_id":"655b9a22-b17c-4e7d-ba46-ad0cf2cae00b","resolution":{"observed_at":"2026-08-06T11:52:44.215421Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:44.191413Z","title":"Chen and A","venue":null,"work_id":"dece6b93-98f1-430c-a3f1-122ea8687d17","year":2011},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.427951Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:cc89a636f47da6ef9a84934eae3e795a8969cd6c1c08888b8a5ec4648887605d","observation_id":"22439de2-6ab6-4c7d-9c0c-b7dcb9bc85c6","resolution":{"observed_at":"2026-08-06T11:52:44.198677Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:44.173291Z","title":null,"venue":null,"work_id":"225d1737-e7c7-4079-a587-32189760999a","year":2010},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.432580Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:39f575c2dc53dc8c03b678e2574f29998bc19e47bf37421e73f5a919f266fe20","observation_id":"1f932ac2-fcfe-4bfc-acff-d3aa14ddb023","resolution":{"observed_at":"2026-08-06T11:52:44.178993Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:44.154831Z","title":"Collet, S","venue":null,"work_id":"33e91c28-de3b-4a31-b105-2b0ed36674fb","year":2013},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.437494Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:97cccbab56902a76ec26f9ff706108399839ccfa5a08974a034287f698ce42f2","observation_id":"246893fe-02d5-4b2e-bdb7-f82e1d30e7ab","resolution":{"observed_at":"2026-08-06T11:52:44.160801Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:44.137923Z","title":"Di Ges` u, T","venue":null,"work_id":"1ae3516d-87df-4db6-adbc-24a710e39982","year":2016},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.442381Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:9d05a4e5ba48e1240ba049bdf25a1419d5b3cfb76b5524de5f97d03faa8b6f61","observation_id":"f9141dea-015a-4b8d-8a9f-d1e801fc63e4","resolution":{"observed_at":"2026-08-06T11:52:44.143422Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:44.121754Z","title":null,"venue":null,"work_id":"170a3db2-90fc-4b2a-94cc-112417e9494f","year":2010},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.447148Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:2726b0f97def46ea691a20190f97cf237da8b7778b335c9bedcca067e49c5a1f","observation_id":"2888703d-a714-4a5b-9475-bbd15c42c286","resolution":{"observed_at":"2026-08-06T11:52:44.127109Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:44.105107Z","title":"I Freidlin and A","venue":null,"work_id":"40b96dac-280b-444a-98e3-278c2b8e5082","year":1993},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.451765Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:2e8db01ca01db5a5b62a36151f353d8598b2744b4bc0a8b560cdf89be3da9401","observation_id":"d0b484b3-af09-46c5-92b7-d062b21f9243","resolution":{"observed_at":"2026-08-06T11:52:44.110082Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:44.080422Z","title":null,"venue":null,"work_id":"d2ad1342-a49f-4517-8c8d-3252eef6f195","year":1985},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.456454Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:533a1b3f2757eb69fea0590510ee7684f3ec0a884cac44ad068aed69d4838810","observation_id":"6ec38f21-4dbe-467e-b9cc-05487e6a3082","resolution":{"observed_at":"2026-08-06T11:52:44.085456Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:44.062304Z","title":null,"venue":null,"work_id":"f7bca425-a62f-4110-a349-4fff6a2c6dee","year":2019},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.461243Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:d73c5f2abd4d947ed45139a83ecbbb236818139013ccec3af7dcdf54aef1f2ee","observation_id":"ef55162c-cc57-4208-831a-bbb3e3ebc1ae","resolution":{"observed_at":"2026-08-06T11:52:44.067825Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:44.043168Z","title":"Gilbarg and N","venue":null,"work_id":"c634d689-e80d-4bc6-b582-f2bd4a243a61","year":2001},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.465816Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:75ca90d4e3913db05fdae8ceb9e629365444683f9b3c30daef875bd38fc9f7fc","observation_id":"6ea246a0-204b-418d-b756-d4724f6d253e","resolution":{"observed_at":"2026-08-06T11:52:44.049792Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:44.025570Z","title":"S Grebenkov, R","venue":null,"work_id":"f9f9de6b-0e7a-427c-ab44-27f81473c087","year":2019},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.470574Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:39333db65f192395c772d7aa37e3cdb68a46c484200d971f83d3a97a8aa741c0","observation_id":"c87cffc0-b337-4e9d-ad56-169eff7637e1","resolution":{"observed_at":"2026-08-06T11:52:44.031311Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:44.009608Z","title":"V Grigoriev, Y","venue":null,"work_id":"31a94a9d-42b7-4a0f-8fb6-9679f43a916b","year":2002},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.475334Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:50467e42bd8f7722b331239d8ecdf0a25b0f3d4336194466b430a1caa6ba6f24","observation_id":"1aaf490a-1698-48fd-a77e-4f02f647d0b6","resolution":{"observed_at":"2026-08-06T11:52:44.014535Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:43.993542Z","title":"Holcman and Z","venue":null,"work_id":"4368faec-6ffd-4d59-8208-95c59931b463","year":2004},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.480267Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:ece2bb5a3eae5d8f646bf2b91e5238823eae2236285a1e20618312cc5e78346f","observation_id":"4d2649c7-ff32-4ce0-8209-36db6f5891c1","resolution":{"observed_at":"2026-08-06T11:52:43.998195Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2508.15060","last_updated":"2025-09-03T05:35:01Z","snapshot_observed_at":"2026-08-05T18:19:14.930660Z","submitted_at":"2025-08-20T20:48:17Z","title":"Asymptotic analysis on narrow tubes: narrow escape problems and diffusion processes","version":2},"cited_work":{"arxiv_id":"2508.15060","doi":null,"metadata_source":"pith","pith_arxiv_id":"2508.15060","snapshot_observed_at":"2026-08-06T11:52:43.718639Z","title":"Asymptotic analysis on narrow tubes: narrow escape problems and diffusion processes","venue":"math.PR","work_id":"2e3c828a-896d-4fa8-8e9f-5da3f0e499a0","year":2025},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.484954Z"},"links":{"cited_paper":"/paper/2508.15060","citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:1b2ad01a7d452280284a765ae143c94c776bd110adef47102ee61efd95538aab","observation_id":"8b7b1196-4bf3-4db7-b200-feee7fd3a1af","resolution":{"observed_at":"2026-08-06T11:52:43.725127Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2511.21548","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:52:43.689720Z","title":"https://arxiv.org/abs/2511.21548v2","venue":null,"work_id":"3e5a8c75-4070-4683-8e8e-e9436d9b80a1","year":2025},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.490207Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:bc366c80bf1128943081d2ed8a340e71d58a69d8fca695a21d3987b1eb8eb8e1","observation_id":"21efa938-649e-4d6b-845f-2841355abab4","resolution":{"observed_at":"2026-08-06T11:52:43.699820Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:43.977511Z","title":"Leli` evre, D","venue":null,"work_id":"1c9171e3-dcae-43aa-b896-8c7132d8e765","year":2025},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.495164Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:9f4e62185a3ecc2d0d29e5eb2773a95ecaa7333112052c9a79e834516cac75fb","observation_id":"fa05e793-2293-4ce9-80ae-753544f3d321","resolution":{"observed_at":"2026-08-06T11:52:43.982544Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2401.06903","last_updated":"2024-04-08T16:23:27Z","snapshot_observed_at":"2026-07-06T17:15:01.812342Z","submitted_at":"2024-01-12T21:40:01Z","title":"A spectral approach to the narrow escape problem in the disk","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2401.06903","snapshot_observed_at":"2026-08-06T11:52:43.500113Z","title":"Leli` evre, M","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.500113Z"},"links":{"cited_paper":"/paper/2401.06903","citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:a9f9ed669ef00235f22c37c8c42a307b0c29690bff04ca3020e0ebf341783e59","observation_id":"3cf1f2f5-0161-4291-b1aa-73a0fd48b0e3","resolution":{"observed_at":"2026-08-06T11:52:43.500113Z","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":"2026-08-06T11:52:43.961445Z","title":null,"venue":null,"work_id":"fead634c-cb8a-44d1-a850-712af620265b","year":2012},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.506355Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:7ead4e635af7b7d2b0b139190a74db9fd2b48523b83bd61f6ffe68a4cfc33e27","observation_id":"6a907934-6868-4eff-973f-2d6a223cc71d","resolution":{"observed_at":"2026-08-06T11:52:43.966254Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:43.944313Z","title":"Lions and A.-S","venue":null,"work_id":"7f6d890b-c745-4b58-82f2-9309f580c286","year":1984},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.511267Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:8e5780ee91933e32ac3507baf7682348dc00e1389c9fe89089e95d0ab34a9c6d","observation_id":"3c1779b5-5ac3-4824-8fbb-1280c85c2058","resolution":{"observed_at":"2026-08-06T11:52:43.949178Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:43.927535Z","title":null,"venue":null,"work_id":"b18618fb-5173-46d6-9738-b3f2f53905cf","year":1953},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.516279Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:6f182785398face55864fbf704b969f941768fe16786dd8337728a0c458c6157","observation_id":"1551e533-a656-410b-ab7c-95fe37589d49","resolution":{"observed_at":"2026-08-06T11:52:43.933604Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:43.911414Z","title":"Nursultanov, J","venue":null,"work_id":"6cad94f7-9736-4eae-ab0c-346111f8587a","year":2021},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.520889Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:ed24d4a69500cc9f8b5e555ed07e62c8eadb1c890fd7f970a337cd559985599c","observation_id":"59721e93-1af7-47b6-8115-a71fba0d105f","resolution":{"observed_at":"2026-08-06T11:52:43.917031Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:43.894080Z","title":"Pillay, M","venue":null,"work_id":"3f99552d-8c46-4e93-86ae-e534d1c47ee8","year":2010},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.527539Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:19fe46e27a566dd67f6b1f7d77bd62175a4e76fc25b4f719f02a4b0d11fc4612","observation_id":"b248cc64-ed04-4255-acc4-f799df23e3ee","resolution":{"observed_at":"2026-08-06T11:52:43.899171Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:43.874864Z","title":"Rudin,Real and complex analysis(1974)","venue":null,"work_id":"1cec82d3-fc14-45a2-8dc9-09031f898355","year":1974},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.532962Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:c3e2e5b6cb047327b7d09b5110fa9a59a7ff97663a3a0b0384a92c7f33fa9d51","observation_id":"324465d1-9843-4d7a-99e7-5b7774ffda7e","resolution":{"observed_at":"2026-08-06T11:52:43.880048Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:43.857784Z","title":"Schuss, A","venue":null,"work_id":"30c93db2-afd7-46dd-8eb5-109dd04b1645","year":2007},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.537778Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:90622a73e4f664c1af2dd0b33e1d48d542f63b23bab77e98997fb9b1613d2f0e","observation_id":"7e112bd2-ff4b-4a60-9bff-21be4885acca","resolution":{"observed_at":"2026-08-06T11:52:43.863163Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:43.841883Z","title":"Singer, Z","venue":null,"work_id":"0adab7c2-7cb2-4ef6-a08e-68b0bdeee022","year":2006},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.542674Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:d3c9c4cae64395efb7f476cadf9ae9c38a89dfaf60d9bb9d83e49de7743789ba","observation_id":"6bd30286-587b-4714-b9d4-71caa3f181c1","resolution":{"observed_at":"2026-08-06T11:52:43.846829Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:43.826271Z","title":"Singer, Z","venue":null,"work_id":"e6f2933c-8316-414d-a312-c8ffc3a1c068","year":2006},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.547182Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:6df70c41c5cadbc13ccd9335daccbb25e55669d847c9240d5bc689603302b023","observation_id":"c8f557b4-c780-4919-a1d3-66f21f853b84","resolution":{"observed_at":"2026-08-06T11:52:43.831201Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:43.810261Z","title":"Singer, Z Schuss, and D","venue":null,"work_id":"60b30531-6b1d-4873-af9c-9a3dfc0a8f3c","year":2008},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.551846Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:7b998af2a98d65ba034b4381b36714184cdc5309fdf127fc2c30f7a99a83d668","observation_id":"153294b5-3cb0-44f1-9e17-6dd8185f4fa2","resolution":{"observed_at":"2026-08-06T11:52:43.815108Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:43.791013Z","title":"S Strichartz,A guide to distribution theory and fourier transforms, World Scientific Publishing Company, 2003","venue":null,"work_id":"dcefaf54-78fc-4af2-b20a-7eb84d94cf87","year":2003},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.558053Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:b58860dafe0ab48c7cda6455486261aba38a0dc61644b8c4b526b5f8ebf77891","observation_id":"bdd7b814-a120-47bb-a00c-80d9f6630643","resolution":{"observed_at":"2026-08-06T11:52:43.797397Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:43.773895Z","title":"W Stroock and S","venue":null,"work_id":"b3b98af7-49cb-4d74-b09b-9adc34c67990","year":1971},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.563337Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:9017f4f11dc8d8d3fd0c4cf65b96ea3bfe966e81bc2aa68c99261b6487f1d6f3","observation_id":"a1bb977e-9653-4491-9323-c2059372e132","resolution":{"observed_at":"2026-08-06T11:52:43.779288Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:43.756234Z","title":null,"venue":null,"work_id":"b041dae9-b49f-46db-bad7-f64f728f7b2f","year":1967},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.568539Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:aa51b3c6d2bfd49b349d3eb1e5b731c0ac1a6b80d3e399f55708dbb0f2739656","observation_id":"b4f44a7f-913c-48f1-8b34-18cc25570404","resolution":{"observed_at":"2026-08-06T11:52:43.761766Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T11:52:43.737431Z","title":"Watanabe,On stochastic differential equations for multi-dimensional diffusion processes with boundary conditions, Journal of Mathematics of Kyoto University11(1971), no","venue":null,"work_id":"1a43d098-63f1-483e-b39f-52d328916266","year":1971},"citing_paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T11:52:43.573539Z"},"links":{"citing_paper":"/paper/2608.05007"},"observation_digest":"sha256:b594aecd1393636c95f972c28e5f06d7268aec1781e69bf9683e1439f01d883b","observation_id":"2c234fbd-04b3-408b-91ac-7a5256b49b5e","resolution":{"observed_at":"2026-08-06T11:52:43.743858Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2608.05007","last_updated":"2026-08-05T16:13:19Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-07T06:32:51.780407Z","submitted_at":"2026-08-05T16:13:19Z","title":"A spectral approach to the narrow escape problem in two-dimensional domains"},"reference_resolution":{"displayed":37,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":9,"verified_exact":2,"verified_fuzzy":26},"total_outbound_references":37},"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":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 7 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2608.05007."}