{"as_of":"2026-08-22T01:04:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:020dd244f59d18a3bf0d68ed7c9fa860a36659ff30ef5307f19358ad94ae0764","coverage":[{"denominator":38,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":38,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T15:09:56.595192Z","state":"measured"},{"denominator":38,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":38,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-21T06:32:19.484+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/2505.16345/citation-record","integrity":"/paper/2505.16345/integrity","json":"/paper/2505.16345/citation-record.json","paper":"/paper/2505.16345"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:09:53.318915Z","title":null,"venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:53.318915Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:167951760a327b317706c2a27a29fad0bc7e3b5dbde22f9aa739496a1955b465","observation_id":"d84a07df-e303-4dc0-8f3a-b204f27456ab","resolution":{"observed_at":"2026-08-07T15:09:53.318915Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf02684380","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T00:03:45.533247Z","title":"Bastian, G","venue":"Computing","work_id":"d7bd49cd-7b33-49d9-bf0b-35e2a0d3fc22","year":1998},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:53.357267Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:93895392f69a215e4de6cff9060571e0d62d9e7e86af1ec7d02d85c4c2db1ce9","observation_id":"04f46177-adf0-40a2-85c9-1f7393375095","resolution":{"observed_at":"2026-08-07T15:09:59.115214Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/040618849","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Beckermann, S","venue":"SIAM Journal on Matrix Analysis and Applications","work_id":"d01e4b8d-9988-4b5f-8153-0ca15cca548a","year":2005},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:53.419804Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:b46e0dc3e5b5afd35e8d48f75d8fd6eeef49fc65b6574fa4f1ae8db58bbee462","observation_id":"a8dd7434-0670-4c4b-8dcd-86398f17f9e4","resolution":{"observed_at":"2026-08-07T15:09:58.982651Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T15:09:53.491424Z","title":"Berenger , A perfectly matched layer for the absorption of electromagnetic waves , Journal of Computational Physics, 114 (1994), pp","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:53.491424Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:aff855e2eb3cc860ac9b086f4bbb0b33a64b050a345dcd1f70f0fa20f04a9f36","observation_id":"df8be3e6-70ef-4c9f-9a5b-5c4c0cba9407","resolution":{"observed_at":"2026-08-07T15:09:53.491424Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:09:53.574118Z","title":"B \\' e riot and A","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:53.574118Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:4deb49733a0c47f1172feb09c28eefbc916c930b2f560d6df0134c34b03a69f3","observation_id":"e693ad42-b25e-424f-9bfe-6e6040495117","resolution":{"observed_at":"2026-08-07T15:09:53.574118Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:09:53.675246Z","title":"Berm \\' u dez, L","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:53.675246Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:b8e3b351bc31869de8a3114df815218edca092a33fbfaa485dcb2bc3ca46115c","observation_id":"6aff32e0-89c7-4577-a926-4fc6be48713a","resolution":{"observed_at":"2026-08-07T15:09:53.675246Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:09:53.784027Z","title":"Berm \\' u dez, L","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:53.784027Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:ad5a4b20c4f310fd62c7eb0385dd1581d57698ca07a8323c70918a8d48a121a7","observation_id":"ecee0274-1a8f-4809-9e83-d1335dcd4884","resolution":{"observed_at":"2026-08-07T15:09:53.784027Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/040617741","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Bécache, A","venue":"SIAM Journal on Numerical Analysis","work_id":"52c990dd-c75d-4d36-8a5e-795b400294e0","year":2006},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:53.899083Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:021fa65b067866e0a50ab40f0207795987577fe14be7845e4b6e5d0673985f36","observation_id":"47608739-f686-4047-99fa-07ee755d8648","resolution":{"observed_at":"2026-08-07T15:09:58.840382Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf01733786","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T00:03:45.533247Z","title":null,"venue":"BIT Numerical Mathematics","work_id":"dcfeea7f-7cce-4d62-9d6f-5a6913be801a","year":1996},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:53.995010Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:5154c264545a4963ccbe9335bf4596f5699f8656900536f2c8a5ffb4d23dae8f","observation_id":"92bbc300-6b50-4deb-98be-c16c046ca955","resolution":{"observed_at":"2026-08-07T15:09:58.718694Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/s0168-9274(97)00039-1","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Cao , A note on the convergence behavior of GMRES , Applied Numerical Mathematics, 25 (1997), pp","venue":"Applied Numerical Mathematics","work_id":"ff45eb7b-fd54-4518-a1de-2d57734633bd","year":1997},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:54.126825Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:6ecd08a5914804a60b68faf488414250e88bf65fd7de09a43a1e13c9cc1eef19","observation_id":"8dbf3e54-1221-49ac-aa66-2316f84cdb8a","resolution":{"observed_at":"2026-08-07T15:09:58.571491Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1216/jie-2009-21-2-229","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Journal of Integral Equations and Applications","work_id":"050c5e36-cbc6-4d49-9d47-ecb8a4b6df38","year":2009},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:54.269348Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:50f8302eeba730c605312dc35c3a530e579f521dd8160d14710cd3a7ccc0d2d1","observation_id":"9a2cc0fc-9016-49ac-a1a0-0eda4fac38da","resolution":{"observed_at":"2026-08-07T15:09:58.449721Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T15:09:54.395917Z","title":"Crouzeix and C","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:54.395917Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:34b678b661a1b5e858944d3984def9d66cbd5527d54e3c50228c0920872e8cf7","observation_id":"1fb91cd1-aadc-4184-be3f-aef0a8955d0f","resolution":{"observed_at":"2026-08-07T15:09:54.395917Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0377-0427(93)90028-a","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Journal of Computational and Applied Mathematics","work_id":"7ad25dfc-d603-4401-b210-fcca15b1981a","year":1993},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:54.535142Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:fd7d938d67d14de64eb76dac96762ba264e676dde78d19304609c045aa3f3fa6","observation_id":"bb5b0b31-9614-4b39-9ca8-96e68591a8e2","resolution":{"observed_at":"2026-08-07T15:09:58.277520Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T15:09:54.619176Z","title":"Dolean, P","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:54.619176Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:611b34a5942f1f3ec8bc4f7aeaf3a6d14159c19e10ae7ff7c78e560b3560d700","observation_id":"d02f4bbb-cdbf-441a-86d3-fb26687b6888","resolution":{"observed_at":"2026-08-07T15:09:54.619176Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2209.01231","last_updated":"2022-09-02T18:24:32Z","snapshot_observed_at":"2026-08-19T04:45:31.155201Z","submitted_at":"2022-09-02T18:24:32Z","title":"How Descriptive are GMRES Convergence Bounds?","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2209.01231","snapshot_observed_at":"2026-08-07T15:09:54.712074Z","title":"Embree , How Descriptive are GMRES Convergence Bounds? , 2022, https://doi.org/10.48550/ARXIV.2209.01231","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:54.712074Z"},"links":{"cited_paper":"/paper/2209.01231","citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:0ee2cb9ae2c7007025ff36356df78c54a11a702f73bb5df59b80b3ef3dafdf5a","observation_id":"e9266035-10e3-4920-a5d2-b38c46a66046","resolution":{"observed_at":"2026-08-07T15:09:54.712074Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2312.15022","last_updated":"2025-02-21T19:41:04Z","snapshot_observed_at":"2026-08-16T14:32:06.523257Z","submitted_at":"2023-12-22T19:08:25Z","title":"Extending Elman's Bound for GMRES","version":2},"cited_work":{"arxiv_id":"2312.15022","doi":"10.48550/arxiv.2312.15022","metadata_source":"pith","pith_arxiv_id":"2312.15022","snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Extending Elman's Bound for GMRES","venue":"math.NA","work_id":"d9b55c69-16bf-4b62-902c-668bd8452923","year":2023},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:54.810547Z"},"links":{"cited_paper":"/paper/2312.15022","citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:c0349a1b0ed20baf61cee9bd28d60146b2cf65ea79295f510365325a561f6316","observation_id":"01079e5c-590e-4268-aefb-874a6385538c","resolution":{"observed_at":"2026-08-07T15:09:58.155863Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T15:09:54.910470Z","title":"Engquist and A","venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:54.910470Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:853d5a376a5fe73bfd78c0d40011f13168fe04e33d6be4e7b3b88be40f80253c","observation_id":"2c5cc087-a42e-4e44-91e3-45d9ccb0ee4e","resolution":{"observed_at":"2026-08-07T15:09:54.910470Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:09:54.999088Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:54.999088Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:255386c75991db52f3d541a6024458866bafbac1fe203e253753094d5e780fb3","observation_id":"3d556d5d-f4b1-43a0-983e-7c5d870f2b73","resolution":{"observed_at":"2026-08-07T15:09:54.999088Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/060678257","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"SIAM Journal on Matrix Analysis and Applications","work_id":"34d28087-5be5-4e65-ac2e-1c4001bd4979","year":2008},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:55.138935Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:39f09a155934bc08ab841085ead07cef48c97e4d47572ebe8aa3c245ad2c63ff","observation_id":"48d70e2f-56a3-4002-bb2d-a9f06455a7e2","resolution":{"observed_at":"2026-08-07T15:09:57.975788Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T15:09:55.278028Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:55.278028Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:1ecdf41445260f21f08b77d629f486afd05059c5752d0729deb9a41974b7eedc","observation_id":"c0831396-1ae1-451d-8f05-f80f6cd97f14","resolution":{"observed_at":"2026-08-07T15:09:55.278028Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/21m1399658","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Galkowski, P","venue":"SIAM Journal on Mathematical Analysis","work_id":"dbcc2b6b-0753-4856-acdc-ea886419b3ca","year":2021},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:55.387126Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:7b70b581d882894c6cc6df74f222fa87a577c0125fb097daf4f2f7d61e1dbf99","observation_id":"f5e06fd4-3aeb-421e-bfe1-d9363a36e43f","resolution":{"observed_at":"2026-08-07T15:09:57.823261Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T15:09:55.486695Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:55.486695Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:7b809be282aef6f699cc2b9ae5951e1ced2addfa132347913085975bb66dcd6f","observation_id":"6ffb05fa-236d-4a6d-b5a2-d5869e111af7","resolution":{"observed_at":"2026-08-07T15:09:55.486695Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:09:55.546572Z","title":"García Ramos, R","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:55.546572Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:f15bd027d840ae84f3b4c2f3f7e1c49a24040cea77a98ac8e21672ba2de4545a","observation_id":"d71c8af7-6d6b-4c4e-b3ce-1b97327526b6","resolution":{"observed_at":"2026-08-07T15:09:55.546572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10444-022-09931-9","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T00:03:40.895421Z","title":"Marchand, J","venue":"Advances in Computational Mathematics","work_id":"39185032-1afd-4023-b91f-1275573835e8","year":2022},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:55.606226Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:0ffcb09356f24310a1f1f4c75fd298b4d7041d479fc57636fb8076dd6db367e1","observation_id":"ca811cf1-1334-4c9d-9dde-987ec6c16401","resolution":{"observed_at":"2026-08-07T15:09:57.619962Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2021.11018","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:09:59.507950Z","title":"Marchner, H","venue":null,"work_id":"4e44dfc1-8c25-4f03-b15c-dc9b22cefe4a","year":2021},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:55.682755Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:4256156d51c8f3040abdec154c734a6422bb41eb7113339f54a78c94fd9ea42c","observation_id":"c4d548f3-024f-4db3-9f90-681e06691187","resolution":{"observed_at":"2026-08-07T15:09:59.566518Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T15:09:59.703016Z","title":null,"venue":null,"work_id":"863b5909-47aa-49bb-8098-b551d35d61f9","year":1999},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:55.753358Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:45e85e452d16eda28cbb6cc954e620c32319837b2fdfdc00580503935cbcde0f","observation_id":"df1c1da4-6784-4107-a057-11efd085e81f","resolution":{"observed_at":"2026-08-07T15:09:59.777689Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T15:09:55.831144Z","title":"Modave, C","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:55.831144Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:a98e88c7406340b2e69a046ca3f95f356d1710606602a4baa0436b4196f7e10b","observation_id":"3ba09231-c9e6-4d27-8b5c-a6b604ed0698","resolution":{"observed_at":"2026-08-07T15:09:55.831144Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2006.08750","last_updated":"2020-06-17T14:46:50Z","snapshot_observed_at":"2026-07-06T09:29:24.597783Z","submitted_at":"2020-06-15T20:43:30Z","title":"A two-level shifted Laplace preconditioner for Helmholtz problems: Field-of-values analysis and wavenumber-independent convergence","version":2},"cited_work":{"arxiv_id":"2006.08750","doi":"10.48550/arxiv.2006.08750","metadata_source":"pith","pith_arxiv_id":"2006.08750","snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"A two-level shifted Laplace preconditioner for Helmholtz problems: Field-of-values analysis and wavenumber-independent convergence","venue":"math.NA","work_id":"a80de2e6-457e-4535-9a22-3c8d6c0e05ab","year":2020},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:55.909802Z"},"links":{"cited_paper":"/paper/2006.08750","citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:ea68da1aaf67656d3b6a22edc9620c7cb626d5dcd84ca6dbe9a8abd9e7f62975","observation_id":"93171f9d-0a26-48df-b1eb-8035db2d44f1","resolution":{"observed_at":"2026-08-07T15:09:57.445578Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1553/etna_vol54s534","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"ETNA - Electronic Transactions on Numerical Analysis","work_id":"aade01af-2dd8-4749-9178-c5c4285986ea","year":2021},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:55.988182Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:9d97283d36a1f27e24813a0f494be6db95f6371b45f44cbc02a8007b1943783c","observation_id":"39f3a483-d9b0-430c-8481-a4b8c4c308a8","resolution":{"observed_at":"2026-08-07T15:09:57.304256Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T15:09:56.045001Z","title":"Saad , Iterative Methods for Sparse Linear Systems , Society for Industrial and Applied Mathematics, 2003, https://doi.org/10.1137/1.9780898718003","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:56.045001Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:38ce682fe92213461da0b1fead804f7631878328011535a619fcc62a837939a7","observation_id":"b632f0c2-c574-4ba8-aa90-bbb3ad597324","resolution":{"observed_at":"2026-08-07T15:09:56.045001Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:09:56.118833Z","title":"Saad , Numerical Methods for Large Eigenvalue Problems , Society for Industrial and Applied Mathematics, 2011, https://doi.org/10.1137/1.9781611970739","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:56.118833Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:21d33488744fb7c968947150406881f33d3a6df63134dfd232d3fd16164fd8d2","observation_id":"e2b6f178-f9ac-4f4d-af63-f33a3507fb95","resolution":{"observed_at":"2026-08-07T15:09:56.118833Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:09:56.195482Z","title":"Saad and M","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:56.195482Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:9e251e417d46ab73961187b89c0ab6910af2292bd11055b9a415a4095854896f","observation_id":"06a05c0b-566b-41c6-b128-1db21bbd6ad0","resolution":{"observed_at":"2026-08-07T15:09:56.195482Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2312.13625","last_updated":"2024-06-10T11:42:11Z","snapshot_observed_at":"2026-08-16T14:32:43.128088Z","submitted_at":"2023-12-21T07:36:33Z","title":"New Convergence Analysis of GMRES with Weighted Norms, Preconditioning and Deflation, Leading to a New Deflation Space","version":2},"cited_work":{"arxiv_id":"2312.13625","doi":"10.48550/arxiv.2312.13625","metadata_source":"pith","pith_arxiv_id":"2312.13625","snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"New Convergence Analysis of GMRES with Weighted Norms, Preconditioning and Deflation, Leading to a New Deflation Space","venue":"math.NA","work_id":"9c2c0067-a0ab-4728-8e30-2e729c5268ac","year":2023},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:56.264110Z"},"links":{"cited_paper":"/paper/2312.13625","citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:0931df3b6bd7c8f57b38160d84d0dc2c1edcedbc5ecc57a7c2c8a53a0413ce08","observation_id":"3f9ba500-f321-4f63-8447-976c2d5530ca","resolution":{"observed_at":"2026-08-07T15:09:57.137662Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1515/9780691213101","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Princeton University Press eBooks","work_id":"df3b8232-a5dd-48c6-8b01-212e000077b7","year":2005},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:56.308079Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:1d86e841e201aaac85e6bbc5854bb97bbc643b7c3d3f0071ee8a19517cfcf5be","observation_id":"43d5dae2-28f1-462a-b323-1d7866dce187","resolution":{"observed_at":"2026-08-07T15:09:57.005488Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/s0168-9274(98)00026-9","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Turkel and A","venue":"Applied Numerical Mathematics","work_id":"44f41828-a3fb-456d-99bd-927f1103668a","year":1998},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:56.376501Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:24e8eb4a84c317a460c5c4ce0e01f1fe5b8ee6efbd96d152540eb90cee61c386","observation_id":"31cb69fd-b40f-4aad-bf7d-57c04c008a43","resolution":{"observed_at":"2026-08-07T15:09:56.888410Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf01389450","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T00:03:45.533247Z","title":"van der Sluis and H","venue":"Numerische Mathematik","work_id":"d517ad92-19b7-49a3-b869-1ae2cc02e86b","year":1986},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:56.424362Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:bcbd56de75d22a28d12509052e7f7700cbf0d31524d34f82585a68bbf00e40c6","observation_id":"594e31ac-714d-4fd2-b41a-539ddce1fba2","resolution":{"observed_at":"2026-08-07T15:09:56.760891Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"proc/2018630","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:09:59.273300Z","title":"Vuik , Krylov Subspace Solvers and Preconditioners , ESAIM: Proceedings and Surveys, 63 (2018), pp","venue":null,"work_id":"2278ea77-402c-4060-9eee-a3ea1f7174f6","year":2018},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:56.497433Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:577dee74dab14ccfae2937461de81eb23b1b03b8b5d253461e53766e23a439a4","observation_id":"9039ea06-ca53-46d8-a86b-33b023fc9a5d","resolution":{"observed_at":"2026-08-07T15:09:59.351251Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T15:09:56.595192Z","title":"write newline","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances","version":2},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:56.595192Z"},"links":{"citing_paper":"/paper/2505.16345"},"observation_digest":"sha256:faf4079187d9bdf9691407507e8da934abdb2d14cf0ffc2ed2d3bdbc3213f20e","observation_id":"c0067d24-78db-4257-beb3-26df5164d1dc","resolution":{"observed_at":"2026-08-07T15:09:56.595192Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2505.16345","last_updated":"2026-06-11T15:06:04Z","latest_version":2,"primary_category":"math.NA","snapshot_observed_at":"2026-08-16T22:48:04.064364Z","submitted_at":"2025-05-22T07:59:18Z","title":"Convergence analysis of GMRES applied to Helmholtz problems near resonances"},"reference_resolution":{"displayed":38,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":19,"verified_exact":18,"verified_fuzzy":0},"total_outbound_references":38},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"thesis":"As of 22 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2505.16345."}