{"as_of":"2026-08-08T04:43:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:e69b086120d30db1e8c837e2b3ade032425f85d52633025604c160370c9f50c0","coverage":[{"denominator":47,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":47,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T11:49:01.393430Z","state":"measured"},{"denominator":47,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":47,"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/2506.01644/citation-record","integrity":"/paper/2506.01644/integrity","json":"/paper/2506.01644/citation-record.json","paper":"/paper/2506.01644"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:48:55.553932Z","title":"Multilevel Monte Carlo path simulation,","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:55.553932Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:9c3d12100edd6aff21dfe40195142f2c447ee226300cf2c0f947e1d02e030334","observation_id":"03619c33-26e3-45b5-ace0-38cf4a0f4089","resolution":{"observed_at":"2026-08-07T11:48:55.553932Z","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":"2026-08-07T11:49:10.004169Z","title":"Multilevel Monte Carlo methods,","venue":null,"work_id":"b5d43f9d-d860-4fd2-8808-757e5617b8b6","year":2001},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:55.663524Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:69a8db5228fb09d5847ea5dd0730f24c0b19e00a8096a755c184d407b6d7eac5","observation_id":"e40b3e12-2160-4aac-ad7d-31760b5f9ad4","resolution":{"observed_at":"2026-08-07T11:49:10.105193Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:48:55.750360Z","title":"Multilevel Monte Carlo Finite Element Method for elliptic PDEs with stochastic coefficients,","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:55.750360Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:4104468bb1ac8ff7548871d65d144b1f433b81d0e5a52e4dba1b8ccd95365d0a","observation_id":"3030a44f-b7ba-4523-ae10-fb819c19d782","resolution":{"observed_at":"2026-08-07T11:48:55.750360Z","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":"2026-08-07T11:48:55.830009Z","title":"Finite element error analysis of elliptic PDEs with random coefficients and its application to multilevel Monte Carlo methods,","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:55.830009Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:3058633c76f7ea495f47371a6b5d54e1249503ce1538c7ff500a9834d3e14410","observation_id":"14381ffa-6cf2-47e3-92e2-f207da9696ca","resolution":{"observed_at":"2026-08-07T11:48:55.830009Z","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":"2026-08-07T11:48:55.897894Z","title":"Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients,","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:55.897894Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:cd619f46c292c3fd0c726fe5f3b988675e2bb6d5021a086ad216ca8b6f5047f2","observation_id":"6f38294f-a8ab-4b2a-bc0f-13fc28f2bc01","resolution":{"observed_at":"2026-08-07T11:48:55.897894Z","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":"2026-08-07T11:48:56.000574Z","title":"Further analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients,","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:56.000574Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:43489e41421d925268f222f5f92f319bb8f56975be472a9c9d46774217c2e847","observation_id":"84854772-18a1-47e2-abf9-8d116a630299","resolution":{"observed_at":"2026-08-07T11:48:56.000574Z","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":"2026-08-07T11:49:09.713508Z","title":"Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions,","venue":null,"work_id":"4862dcda-9a47-4f3e-91fb-e134766441c8","year":2012},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:56.109156Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:e0758f7f785af5456108d5f0ed029d5f15f383f85f984d5149aef3f401ac9f02","observation_id":"bafbda09-a83e-4519-8fc1-7787fe59f453","resolution":{"observed_at":"2026-08-07T11:49:09.842287Z","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":"2026-08-07T11:49:09.500512Z","title":"Multi-level Monte Carlo finite volume methods for uncertainty quantification of acoustic wave propagation in random heterogeneous layered medium,","venue":null,"work_id":"bd5a732c-88f3-4401-974c-ac0a706160c4","year":2016},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:56.195473Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:2c93d1ee52a31f44c237ceff10e31bf1fab85eb355b83f9396042a32b24ebb4d","observation_id":"b3dc5957-0b80-469d-a66b-277f5875b173","resolution":{"observed_at":"2026-08-07T11:49:09.629105Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:48:56.242350Z","title":"Convergence analysis of multilevel monte carlo variance estimators and appli- cation for random obstacle problems,","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:56.242350Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:609cbb3b042ad855e0c1c976348de1115be34261ae66bb67e710b0bfb072d3d9","observation_id":"5b49641e-b07c-44cc-96cb-2de2274528d7","resolution":{"observed_at":"2026-08-07T11:48:56.242350Z","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":"2026-08-07T11:49:09.012007Z","title":"Estimation of arbitrary order central statistical moments by the multilevel monte carlo method,","venue":null,"work_id":"138a2e86-5209-439a-b63a-357daf99131c","year":2016},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:56.326288Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:4b5c9a50ce9e28049005cf25dfaaaf3d65186cab37e5f08030a25938718cca55","observation_id":"0cee1b2e-a872-47e6-9072-1ced6a97da3c","resolution":{"observed_at":"2026-08-07T11:49:09.142353Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:48:56.389545Z","title":"A fully parallelized and budgeted multilevel monte carlo method and the application to acoustic waves,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:56.389545Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:822e9ab9e14d32f936b8b5f9a5e3fc4cc37b86946d350b36cc3dddbc09b83af7","observation_id":"598f7b69-56e6-41ef-b793-13e3b9970823","resolution":{"observed_at":"2026-08-07T11:48:56.389545Z","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":"2026-08-07T11:48:56.475288Z","title":"A continuation multilevel Monte Carlo algorithm,","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:56.475288Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:c7ef959b4205af1d3c5d308a11a5ecdca626ae4a2208b73e56934fbdbd96d502","observation_id":"02c47d47-90d1-4c7e-984f-42891eefdd88","resolution":{"observed_at":"2026-08-07T11:48:56.475288Z","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":"2026-08-07T11:49:08.651527Z","title":"Multilevel Monte Carlo methods,","venue":null,"work_id":"c6e3e763-8a96-4919-af09-6db5eba162c6","year":2015},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:56.576143Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:66f338000b3bb5197d72906144b7ff96c4c66984a9dbdc9da4f88581ae4a37ed","observation_id":"f0e86a40-5f03-4e04-81ac-0b4be8e18eff","resolution":{"observed_at":"2026-08-07T11:49:08.842609Z","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":"2026-08-07T11:49:08.352498Z","title":"On multilevel best linear unbiased estimators,","venue":null,"work_id":"e1177ebc-5447-4f7e-bbc1-e82f45e590cc","year":2020},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:56.658588Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:01c7de3ed56606d12aa735c26460eb8c66ad47bba6a7300db735280409518563","observation_id":"96d99b18-1e50-4f2c-b148-c3f4d8c05ab1","resolution":{"observed_at":"2026-08-07T11:49:08.444983Z","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":"2026-08-07T11:49:08.034557Z","title":"Survey of multifidelity methods in uncertainty propa- gation, inference, and optimization,","venue":null,"work_id":"5e82fad9-d661-48ed-9c0e-f72e7f851bbf","year":2018},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:56.813425Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:6c6ab6058e2989aea230636f821bd19f974e3eebda35fd1ed55a492a5fb80f24","observation_id":"2eb1b626-8a4c-443c-9bfd-9f35fb8728b6","resolution":{"observed_at":"2026-08-07T11:49:08.220337Z","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":"2026-08-07T11:49:07.701616Z","title":"Algorithms for computing the sample variance: analysis and recommendations,","venue":null,"work_id":"236c3520-3f00-4fc0-a430-80d695b80345","year":1983},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:56.934037Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:71b2f5d57cd7ef977cc48f6f66eb9e375e7dca61f1d8ee33023026c6becb2a42","observation_id":"85936f6d-d975-45e0-ba2c-4db69e8f4e0b","resolution":{"observed_at":"2026-08-07T11:49:07.844335Z","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":"2026-08-07T11:49:07.450260Z","title":"Note on a method for calculating corrected sums of squares and products,","venue":null,"work_id":"e2bd5578-c8ac-4106-8ebd-39dbc0356397","year":1962},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:57.064270Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:ce0bc54be855270a32e249f0bbc5687dbf7154fd17ebb9f053abd62595610bd2","observation_id":"e3063dfe-06f0-4780-95d4-d7696bc90b67","resolution":{"observed_at":"2026-08-07T11:49:07.552717Z","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":"2026-08-07T11:49:07.267666Z","title":"Numerically stable, scalable formulas for parallel and online computation of higher-order multivariate central moments with arbitrary weights,","venue":null,"work_id":"f31a7098-7e20-4af7-a9a6-02db4003a080","year":2016},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:57.192545Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:1539db66366a6e4fdc444b7f470137ef276eae772122483625bf382ed8bd56a7","observation_id":"0d5b65a0-8a75-4e24-b9b1-cbee82ecdcee","resolution":{"observed_at":"2026-08-07T11:49:07.342714Z","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":"2026-08-07T11:49:07.054391Z","title":"Improved efficiency of a multi-index FEM for computational uncer- tainty quantification,","venue":null,"work_id":"be263524-a36c-444a-ab4c-9d7d45f9ec14","year":2019},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:57.331582Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:01872e72c8505a175f9c6a52b408f4542a8c0d9cefa27f1f5e3b823c328483cd","observation_id":"3cdf3ab6-8661-41ca-a422-221bb0f82ae6","resolution":{"observed_at":"2026-08-07T11:49:07.162762Z","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":"2026-08-07T11:49:06.923344Z","title":"Multi-index Monte Carlo: when sparsity meets sampling,","venue":null,"work_id":"98f83e9e-124d-45e5-899c-e1fb0d15bbe8","year":2016},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:57.460337Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:6e310ffd087fa48aa1ef03f235a613e10e48b6fa7634c7535c000207708db6fc","observation_id":"b35c4e95-f6c3-41c2-9ed5-7f8cd366ec65","resolution":{"observed_at":"2026-08-07T11:49:06.990636Z","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":"2026-08-07T11:49:06.740145Z","title":"Multilevel and multi-index Monte Carlo methods for the McKean-Vlasov equation,","venue":null,"work_id":"1762da2c-1ca4-478e-8a44-cb77e2bc53ae","year":2018},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:57.609492Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:75373dc052fd00ac23815a8c0f7ab3cdfd42417c7a37e8eb8f838e0ab01c5c73","observation_id":"926256c6-bc1d-4827-ac3a-77f786ea6a8c","resolution":{"observed_at":"2026-08-07T11:49:06.844939Z","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":"2026-08-07T11:49:06.592546Z","title":"Sparse grids,","venue":null,"work_id":"5287d1f6-511c-4bc6-8636-75ff6d2be67e","year":2004},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:57.736587Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:97160bf48acdd9a1b2fccf0104dc4ed796653dd5af750965d263de6f27e37e97","observation_id":"e6d11c35-c7a9-4057-88ee-099f71d3a4e3","resolution":{"observed_at":"2026-08-07T11:49:06.668863Z","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":"2026-08-07T11:49:06.358911Z","title":"The parallel finite element system M++ with integrated multilevel preconditioning and multilevel Monte Carlo methods,","venue":null,"work_id":"a04ab8ee-c83e-40d9-8689-73695c6e03bd","year":2021},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:57.898740Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:fcf610e61d133a72d91137014b2ca9eb4e5b17ba9e24e4377837335befe603d1","observation_id":"bef064ca-a514-4024-b389-d3e979d24b0e","resolution":{"observed_at":"2026-08-07T11:49:06.465113Z","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":"2026-08-07T11:49:06.112103Z","title":"A multigrid multilevel Monte Carlo method for transport in the Darcy-Stokes system,","venue":null,"work_id":"ad66463c-0212-4392-ae2a-3d0a5a3801fd","year":2018},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:58.079383Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:08e8c000edef8513e8540e373347489fa4554894638a6e9bbf91eba6d74a6d16","observation_id":"ce99b214-3845-4072-baab-97c8c2a49590","resolution":{"observed_at":"2026-08-07T11:49:06.224954Z","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":"2026-08-07T11:49:05.876039Z","title":"Multilevel Monte Carlo for two phase flow and Buckley-Leverett transport in random heterogeneous porous media,","venue":null,"work_id":"78d3a3ec-fd6e-40d1-8305-a5cc7e1745b8","year":2013},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:58.227049Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:fd5d6c87036f503ade9e62812f0f0e576c8d98f97999619b25527a1316c166e4","observation_id":"b158ccf0-d43c-4f08-a6b3-32fbfeae68c7","resolution":{"observed_at":"2026-08-07T11:49:05.966351Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:48:58.414378Z","title":"An explicit link between gaussian fields and gaussian markov random fields: the stochastic partial differential equation approach,","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:58.414378Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:8f50186901b61c071ded08c5c56f15743961c2d831752257b8dcb79d18e6642b","observation_id":"bf119018-72d0-4898-8135-cf0d591d1d00","resolution":{"observed_at":"2026-08-07T11:48:58.414378Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.07929","last_updated":"2024-12-10T21:18:08Z","snapshot_observed_at":"2026-07-06T20:04:57.037551Z","submitted_at":"2024-12-10T21:18:08Z","title":"Dirichlet-Neumann Averaging: The DNA of Efficient Gaussian Process Simulation","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.07929","snapshot_observed_at":"2026-08-07T11:48:58.581429Z","title":"Dirichlet-neumann averaging: The dna of efficient gaussian process simulation,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:58.581429Z"},"links":{"cited_paper":"/paper/2412.07929","citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:f0a6ca40be2714e05ebddab70e555750029446b9ef89581a678b9121ead81354","observation_id":"0c37fb79-f8f8-4024-b00f-6cf033ad09e5","resolution":{"observed_at":"2026-08-07T11:48:58.581429Z","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":"2026-08-07T11:49:05.627358Z","title":"hp-multilevel monte carlo methods for uncertainty quantification of compressible navier–stokes equations,","venue":null,"work_id":"13041d92-3880-42e6-a6d1-1c938b169a31","year":2020},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:58.782196Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:b7a6d643261b5883b7329271075f66481991b432e7867cb187ca476f711600f0","observation_id":"23a042be-6d3b-4e25-933f-155c377753b4","resolution":{"observed_at":"2026-08-07T11:49:05.784156Z","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":"2026-08-07T11:49:05.294428Z","title":"Flexi: A high order discontinuous galerkin framework for hyperbolic–parabolic con- servation laws,","venue":null,"work_id":"6763185c-7a36-4164-9815-a741ff1059fa","year":2021},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:58.890970Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:b3499b6901f72e43d3911ed7762414991a01f453f98858cc02e3c89e2f1540d6","observation_id":"58a99fb8-7d09-46f3-b5e0-7a395762900e","resolution":{"observed_at":"2026-08-07T11:49:05.486845Z","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":"2026-08-07T11:49:05.188553Z","title":"A statistical framework for generating microstructures of two-phase random materials: application to fatigue analysis,","venue":null,"work_id":"3c68f5b0-a905-425f-9f2f-4e3c6904cfd3","year":2020},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:59.077656Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:0e6574cccbb7efc9f111c624c0fbd3e466755fcce978b5342918223a9c41566a","observation_id":"426af0bc-2cbf-406a-acfe-bdf56b3af0a0","resolution":{"observed_at":"2026-08-07T11:49:05.233361Z","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":"2026-08-07T11:49:05.031800Z","title":"Finite elements for mat´ ern-type random fields: Uncertainty in computational mechanics and design optimization,","venue":null,"work_id":"442460cd-0141-446c-9ffc-bb27a43aaed2","year":2024},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:59.212151Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:6847700e10234aea5658b0da8c3f481411014996ca42a70c9d0320505c91edee","observation_id":"9cf8b3d0-c30f-4b40-8fc9-9883b4663dfd","resolution":{"observed_at":"2026-08-07T11:49:05.124146Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:48:59.312979Z","title":"A stochastic gradient method with mesh refinement for PDE-constrained optimization under uncertainty,","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:59.312979Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:24d08627393d0f3302478234f066a9e757ddfba8f5ce8a507c0069717da4aaa5","observation_id":"35058a09-33bb-42c4-8ec5-b9c1c24b412d","resolution":{"observed_at":"2026-08-07T11:48:59.312979Z","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":"2026-08-07T11:48:59.478616Z","title":"Complexity analysis of stochastic gradient methods for PDE- constrained optimal control problems with uncertain parameters,","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:59.478616Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:e922a2af70b79dccc8160f172edf69c8163174a169f860baf535390f6405a59a","observation_id":"44bec246-dbb2-4009-9451-d9c5ac49a6d1","resolution":{"observed_at":"2026-08-07T11:48:59.478616Z","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":"2026-08-07T11:49:04.732218Z","title":"Mpp 3.4.1,","venue":null,"work_id":"27c202ca-23a1-4232-9dee-7f0d8972bd1e","year":2024},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:59.653510Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:184bcaa22fe44196e59b5fe7ab8b99e7cf3d590da1451d417c78494d7e6245ce","observation_id":"fcac0918-a4cf-4c2c-b109-f3502d9d31fb","resolution":{"observed_at":"2026-08-07T11:49:04.833550Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:48:59.727394Z","title":"Baumgarten, A Fully Parallelized and Budgeted Multi-level Monte Carlo Framework for Partial Differential Equations","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:59.727394Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:be29a4cba9599065a39f75959ab77ee19ae67c5f92d74c4b79a3bb679fddc8d5","observation_id":"2282f8e0-bae2-4605-86bf-f6b1955b6f24","resolution":{"observed_at":"2026-08-07T11:48:59.727394Z","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":"2311.06069","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:49:01.633372Z","title":"A filtered multilevel monte carlo method for estimating the expectation of discretized random fields,","venue":null,"work_id":"bf894e9c-cca0-4169-9a4a-4d3c5eaa20da","year":2023},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T11:48:59.876252Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:a7785bf982d8a843834c4479cfcda00b279bfba26c5da866a2ce443f0f9a0834","observation_id":"5a655340-03d0-4ae8-8fe3-7c4d6fa72c86","resolution":{"observed_at":"2026-08-07T11:49:01.703982Z","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":"2026-08-07T11:49:04.441364Z","title":"Application of hierarchical matrices for computing the Karhunen–Lo` eve expansion,","venue":null,"work_id":"d4ea6686-4402-4000-9312-ac8eb86e51e0","year":2009},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-07T11:49:00.058882Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:ace8468ea02c309fc391d80e88a64479ecfd663de8d1f1dbee675cf853737b8f","observation_id":"7f99e42c-f7ea-4748-b7b2-38ef2c9d05f2","resolution":{"observed_at":"2026-08-07T11:49:04.576803Z","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":"2026-08-07T11:49:04.062658Z","title":"Karhunen–lo` eve approximation of random fields by generalized fast multipole methods,","venue":null,"work_id":"24af8769-6559-4271-a776-220a4050689c","year":2006},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-07T11:49:00.193931Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:98007b02ae6ed54b7ef0561a86e8b959a15ba77a8276a45d9e393e0eddaccfac","observation_id":"30f420be-5c81-4c52-9bfb-84972cd2745f","resolution":{"observed_at":"2026-08-07T11:49:04.249532Z","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":"2026-08-07T11:49:03.766376Z","title":"On the low-rank approximation by the pivoted cholesky decomposition,","venue":null,"work_id":"64f6d5e1-a31f-4e67-bf6b-2de9c1fe4186","year":2012},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-07T11:49:00.288633Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:6eb80913b778701e51c9f4bc1139885d4a577127b62d1ddf039224e8b33a66b3","observation_id":"02d5f2a8-66e1-4f1f-98d2-6ec8e6a8d062","resolution":{"observed_at":"2026-08-07T11:49:03.888778Z","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":"2026-08-07T11:49:03.514349Z","title":"Fast and exact simulation of stationary Gaussian processes through circulant embedding of the covariance matrix,","venue":null,"work_id":"03142a82-1747-4d1c-881c-27d2742159bf","year":1997},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-07T11:49:00.426144Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:0c6e733eca3d3f3e45b6131c49c8b30236b4562035f32ddb6065169cef28248d","observation_id":"9763e8e5-fd34-47c5-827f-9a2844112ddf","resolution":{"observed_at":"2026-08-07T11:49:03.666570Z","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":"2026-08-07T11:49:03.260671Z","title":"Unified analysis of periodization-based sampling methods for mat´ ern covariances,","venue":null,"work_id":"a5f8131e-4cd9-447b-b20f-7de824615bca","year":2020},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-07T11:49:00.536984Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:417d13bfb9812825a7f0b073476de34ee4f766b06fad8dab7e59fff734ae9171","observation_id":"816fadef-021d-4c4e-a08e-a2706fc21f38","resolution":{"observed_at":"2026-08-07T11:49:03.409409Z","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":"2026-08-07T11:49:03.079513Z","title":"Efficient white noise sampling and coupling for multilevel monte carlo with nonnested meshes,","venue":null,"work_id":"ad90eab6-eeb6-401a-9d5c-99327c0f26f1","year":2018},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-07T11:49:00.712893Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:201dfc86c4955f1526b6afc34cade381012fed83222a4e53c912225645cf9dcc","observation_id":"ccdf8e77-ec70-434d-8222-f72c8d542b30","resolution":{"observed_at":"2026-08-07T11:49:03.169759Z","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":"2026-08-07T11:49:02.828714Z","title":"Analysis of boundary effects on pde-based sampling of whittle–matern random fields,","venue":null,"work_id":"2675b0ba-12c5-42f2-9c98-0eab1b60773e","year":2019},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-07T11:49:00.848766Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:87dce45f8ad0c19366da3fb1f82ac66bae20b110a707f85cb59fe234c266d9c5","observation_id":"6508ba09-7582-440c-8d2d-24d682f3725c","resolution":{"observed_at":"2026-08-07T11:49:02.963838Z","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":"2026-08-07T11:49:02.591732Z","title":"Numerical solution of fractional elliptic stochastic pdes with spatial white noise,","venue":null,"work_id":"4a0070e8-bb0d-4c06-ba84-4a57e7ab4174","year":2020},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-07T11:49:00.984225Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:c2f354819a225b6fd7654c05ff69f66ba07bca0fe96b49aa0d80e39e6b7c6581","observation_id":"70dff636-1edb-41de-bc9a-b60fadb5ec10","resolution":{"observed_at":"2026-08-07T11:49:02.690976Z","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":"2026-08-07T11:49:02.331580Z","title":"Boffi, F","venue":null,"work_id":"eabf5559-a309-41df-bd40-47d770bd4757","year":2013},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-07T11:49:01.122015Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:7bffacf5656dc950231e7f2d98769d980b32b943e809e57438153fe32f0f95c0","observation_id":"967ff2ff-0014-4765-8659-52a6370062f4","resolution":{"observed_at":"2026-08-07T11:49:02.441072Z","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":"2026-08-07T11:49:02.109130Z","title":"Hochbruck, T","venue":null,"work_id":"ce09184a-ec09-44d6-bcac-b1c8ff68d2a7","year":2012},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-07T11:49:01.263337Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:ded3a48273e1e68f8f0c77b17de9cc6bc5f5bad7b651b33c9de5626670631efe","observation_id":"9281afae-f7ba-4e72-98a5-c75a33454aab","resolution":{"observed_at":"2026-08-07T11:49:02.222489Z","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":"2026-08-07T11:49:01.826655Z","title":null,"venue":null,"work_id":"d119ee76-2188-4dd7-be9d-a1e8a3c791f7","year":2012},"citing_paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-07T11:49:01.393430Z"},"links":{"citing_paper":"/paper/2506.01644"},"observation_digest":"sha256:f47056873e7b2df6b9e2c80b7564593784660cb919aad198469c4370c9e47f10","observation_id":"10cf66bf-a598-4a53-b377-4f93510cb5df","resolution":{"observed_at":"2026-08-07T11:49:01.945879Z","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"}}],"paper":{"arxiv_id":"2506.01644","last_updated":"2025-06-08T17:42:46Z","latest_version":2,"primary_category":"math.NA","snapshot_observed_at":"2026-08-07T11:34:24.638263Z","submitted_at":"2025-06-02T13:17:23Z","title":"A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems"},"reference_resolution":{"displayed":47,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":14,"verified_exact":1,"verified_fuzzy":32},"total_outbound_references":47},"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 8 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 0 inbound Pith citation observations for arXiv:2506.01644."}