{"as_of":"2026-08-16T20:05:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f5524124f961adaa91026c2a7f335170ba142e51274648a18eb3a89ed7e70b59","coverage":[{"denominator":40,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":40,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-15T00:05:31.854903Z","state":"measured"},{"denominator":40,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":40,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2603.09728/citation-record","integrity":"/paper/2603.09728/integrity","json":"/paper/2603.09728/citation-record.json","paper":"/paper/2603.09728"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-15T00:05:31.854903Z","title":null,"venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:4efdd75637cf7e45ead98826031178ea919cd26b8f816e449924da9866e9abeb","observation_id":"aa122bfd-be88-4b6a-8bdd-29a9a2628dc7","resolution":{"observed_at":"2026-07-15T00:05:31.854903Z","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":"2026-07-15T00:05:31.854903Z","title":"Miehe, F","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:d151c0bf469472ffab3383cdc733482ced967dfd7acb0067a5e50a9b32cd408b","observation_id":"3891f60f-b526-4c9e-b487-c9cc12b0fb93","resolution":{"observed_at":"2026-07-15T00:05:31.854903Z","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":"2026-07-15T00:05:31.854903Z","title":"Ambati, T","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:8d9fc8e82a8622f0a457b9019b988640cf6a9037556304e9b6b78cf82bed1906","observation_id":"5a45075e-ae09-469a-8207-2d894cc1e450","resolution":{"observed_at":"2026-07-15T00:05:31.854903Z","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":"2026-07-15T00:05:31.854903Z","title":"Kalina, T","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:5c2a8b78e8253fdcc8a54cbc6d14e13f5d1bc311c76b6d644e90caf63179e7f0","observation_id":"37960631-8b37-43de-b521-8dff3dbc2fa5","resolution":{"observed_at":"2026-07-15T00:05:31.854903Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2020.113353","doi":"10.1016/j.cma.2020.113353","metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Gerasimov, U","venue":"Computer Methods in Applied Mechanics and Engineering","work_id":"f5723b05-1a10-4c86-87fa-4b089c226f76","year":2020},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:0cb7106888ce2d2c157f53c7b5582ebfe38cf0674a8371b1c52c6cc1cc21df5d","observation_id":"3b3695ba-f1c1-4a5b-a4d3-f62e9a6ae486","resolution":{"observed_at":"2026-07-15T00:10:52.312765Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2023.115960","doi":"10.1016/j.cma.2023.115960","metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Nagaraja, U","venue":"Computer Methods in Applied Mechanics and Engineering","work_id":"e3139992-9396-46c1-a100-7c88ec8ca938","year":2023},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:453993fe1ca545ac30bdf67e8b2a71c4f61e55c00a91c11de942e3fa0de5d4a0","observation_id":"280a38ee-987d-4b28-addd-ba4966a581d1","resolution":{"observed_at":"2026-07-15T00:10:52.302889Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-15T00:05:31.854903Z","title":null,"venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:8a5814c8b3c32b70b9c15e42f7cc854df3498b3f383645bd94cb7e2fe6aaf239","observation_id":"09c39e5b-97f7-48dc-8b1c-96755227582b","resolution":{"observed_at":"2026-07-15T00:05:31.854903Z","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":"2020.113533","doi":"10.1016/j.cma.2020.113533","metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Girolami, E","venue":"Computer Methods in Applied Mechanics and Engineering","work_id":"6f976e6b-52eb-4ef5-9ade-c1a6c68107db","year":2021},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:a0fa91a23ea33d261878e2a52ee6eca49f9ac2ef78cd33c9d11213a9185d7007","observation_id":"61b276f5-e997-4714-bbbb-ed4611ccd166","resolution":{"observed_at":"2026-07-15T00:10:52.278946Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-15T00:05:31.854903Z","title":"Duffin, E","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:ebd409e215b7f87df5e5f83cba0d7c86f34311d7dad474874ef617c1a87167b9","observation_id":"7d405a2a-c04d-4485-9445-2fc32c3e04fb","resolution":{"observed_at":"2026-07-15T00:05:31.854903Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-07-15T00:05:31.854903Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:4b2b8e015ef044c6562e9af6994eee83948c2510a5e17c558689dab34aa6f892","observation_id":"95bec573-7eeb-4598-85af-b4d86a4c3787","resolution":{"observed_at":"2026-07-15T00:05:31.854903Z","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/s00466-022-02240-4","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Pulikkathodi, E","venue":"Computational Mechanics","work_id":"fc1c4935-f0cd-40c0-b2ff-de6eb54ec1d4","year":2023},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:ac2c12be83ae3b6054bccf8cd5a4df21f04386b63aa8104f378bfb079cf5af58","observation_id":"216dc43b-8ba9-4b5c-b2bb-5bf7d3f2c3fe","resolution":{"observed_at":"2026-07-15T00:10:52.249220Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1088/0266-5611/26/2/025009","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Inverse Problems","work_id":"b79ede02-4a19-4755-8aff-2644690c2e79","year":2010},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:2521e64bc5beb5c89afa7222fd794ef43dedc2c9d8653db8864946fd9c037cb7","observation_id":"8f91660c-0d60-4ca1-88eb-882f8bd251ff","resolution":{"observed_at":"2026-07-15T00:10:52.324239Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2021.103143","doi":"10.1016/j.tafmec.2021.103143","metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kuncham, S","venue":"Theoretical and Applied Fracture Mechanics","work_id":"3dfe3951-8ee0-4c8b-9de8-2694d50550a3","year":2022},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:56e6d2de4e74f0e65c4af18f4119ce1f738504ace0496fd95c0a6ce2adcba4ca","observation_id":"22084834-3433-4750-a01b-6b61b324dc0a","resolution":{"observed_at":"2026-07-15T00:10:52.293516Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.petrol.2013.04.018","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Journal of Petroleum Science and Engineering","work_id":"9200b842-540a-428f-b00c-21c243c7c40e","year":2013},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:7e9cda718f28eae21f2efa6b93693d5c4cabdd3216b5f946893cde12d2e9dafb","observation_id":"089b7aae-5aa2-4e52-b155-c7524fff3e55","resolution":{"observed_at":"2026-07-15T00:10:52.315573Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-15T00:05:31.854903Z","title":"Cervera, G","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:bc1a6b9a3e65a2663fa41696c6a1f58c3aa492479a0ca0af06bac6b25ebe32a7","observation_id":"da266d51-2e43-46a2-8fc7-2f7047c573a1","resolution":{"observed_at":"2026-07-15T00:05:31.854903Z","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/s00466-023-02380-1","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Bharali, F","venue":"Computational Mechanics","work_id":"7bff371a-fdce-4af4-aed6-148c06c85fa8","year":2024},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:c6f1c3f45e8e6bcda64bb56f248e74e43e023a1ec9e2c61fc7fa11033c0ffcab","observation_id":"f987c820-dabd-48a4-9341-87d9cf723974","resolution":{"observed_at":"2026-07-15T00:10:52.362907Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-15T00:05:31.854903Z","title":"De Lorenzis, T","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:5a7632471e0ab15f9a8d82b030cae745b0198318c77b22970b58253e27c6f1fa","observation_id":"df9f7b51-633f-4f73-b42c-87091e3d2139","resolution":{"observed_at":"2026-07-15T00:05:31.854903Z","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":"10.15488/15172","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Khimin, L","venue":"Institutional Repository of Leibniz Universität Hannover (Leibniz Universität Hannover)","work_id":"e1d0eeb7-d452-4092-b8bc-bfa351913515","year":2023},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:df42f61df4c5cf7ee58d50cdf0eeb732d4fdcd909394b416fa2ed7e2f547120f","observation_id":"3193b26c-31cf-4887-9606-f4cb05ae14ac","resolution":{"observed_at":"2026-07-15T00:10:52.284990Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.cma.2015.03.009","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Heister, M","venue":"Computer Methods in Applied Mechanics and Engineering","work_id":"dcdd5342-397c-46ad-a594-a8e6fd16d372","year":2015},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:af5f9fc81a4eb96c5ed72e2b573caf33787ebb3ec1694b956f6410694ca5fe1b","observation_id":"3e5c907a-dc0c-43f6-8857-7337f25a52cd","resolution":{"observed_at":"2026-07-15T00:10:52.305155Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-15T00:05:31.854903Z","title":"Kristensen, Phase field methods for fracture - With a special focus on hydrogen assisted fracture, Ph.D","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:a039a534c264e3624e760c13b9cd631db48edc0f37e361ba1a62b5bbc39d8c6b","observation_id":"059f67db-b640-4c41-bffc-83de768d2450","resolution":{"observed_at":"2026-07-15T00:05:31.854903Z","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":"2026-07-15T00:05:31.854903Z","title":"Evensen, Data Assimilation: The Ensemble Kalman Filter, Springer, Berlin, Heidelberg, 2009.doi: 10.1007/978-3-642-03711-5","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:866943691a3b416d2caacaca3c5475e9d4792424851e76e194804891879939a2","observation_id":"00820daa-300e-4916-8197-c5d0e53a271c","resolution":{"observed_at":"2026-07-15T00:05:31.854903Z","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":"2026-07-15T00:05:31.854903Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:9b55994fce4de592710b13b13731f050be64f00619dfcc97e381187d698ce217","observation_id":"27eace1c-02de-43db-ba5a-0f2f951c582c","resolution":{"observed_at":"2026-07-15T00:05:31.854903Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1810.06191","last_updated":"2023-02-14T18:51:59Z","snapshot_observed_at":"2026-08-14T18:14:48.074750Z","submitted_at":"2018-10-15T06:09:12Z","title":"Inverse Problems and Data Assimilation","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1810.06191","snapshot_observed_at":"2026-07-15T00:05:31.854903Z","title":"Sanz-Alonso, A","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"cited_paper":"/paper/1810.06191","citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:a926947e70f3a89c82b7c2967fab03a75d432141690d3a2e40126dcd58a9704a","observation_id":"a83f9b99-bc31-46eb-9679-ed27f0ed4d97","resolution":{"observed_at":"2026-07-15T00:05:31.854903Z","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":"2026-07-15T00:05:31.854903Z","title":"Evensen, The Ensemble Kalman Filter: Theoretical formulation and practical implementation, Ocean Dynamics 53 (4) (2003) 343–367.doi:10.1007/s10236-003-0036-9","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:47d9b2aa8586bac244795e7674a1de8a642435690e5ccf7777e59c51e0338715","observation_id":"20559c5d-8af5-4eee-99d6-ac69eba160b1","resolution":{"observed_at":"2026-07-15T00:05:31.854903Z","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":"2026-07-15T00:05:31.854903Z","title":"Gordon, D","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:14a354a7b4bf38c911f0410e7455fc8e8034579b0491687c2eeb8eb0c57ce6dc","observation_id":"2943ce93-b864-44b0-95aa-ea9f4b45664e","resolution":{"observed_at":"2026-07-15T00:05:31.854903Z","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":"2026-07-15T00:05:31.854903Z","title":null,"venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:303275576d0a9892b1684f342723c3683699e79f884cc181ea393ed41ee324e3","observation_id":"d6be9a31-5393-45c2-afc4-e281c6d1fcc4","resolution":{"observed_at":"2026-07-15T00:05:31.854903Z","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":"2026-07-15T00:05:31.854903Z","title":null,"venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:12f34bda6a19a0f72e6e365a01e6a7b409036b26a9ea0658046173c1944fae1b","observation_id":"c718c5df-52bc-4e46-84e9-675fb7543d89","resolution":{"observed_at":"2026-07-15T00:05:31.854903Z","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":"2026-07-15T00:05:31.854903Z","title":"Doucet, S","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:6fb43cae0cce079f3822bb3b877797162fd04fdcffe4c8b92be13c9578d8a6ff","observation_id":"efba0551-e6c6-4b8a-bfbf-adaac3c73b08","resolution":{"observed_at":"2026-07-15T00:05:31.854903Z","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":"10.5194/gmd-2023-38","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Giles, M","venue":null,"work_id":"6f2ba901-b1a2-494d-b2ea-1d5359974717","year":2024},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:49a7a7a81c897f51ffe022db952a271d97da732fc20f2b5ed64f7e8a965373a1","observation_id":"6fd59d0c-11dc-459d-984e-cfd71d86d2ed","resolution":{"observed_at":"2026-07-15T00:10:52.269454Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-15T00:05:31.854903Z","title":"Bengtsson, P","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:54b573629ce8cdefad383e4f5150c77132f86367beff804d039fc8cdde35339d","observation_id":"81cedcb8-c20e-45e7-beaf-eb9e2cd00050","resolution":{"observed_at":"2026-07-15T00:05:31.854903Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2503.16154","last_updated":"2025-03-20T13:55:41Z","snapshot_observed_at":"2026-08-16T12:48:16.169073Z","submitted_at":"2025-03-20T13:55:41Z","title":"Statistical accuracy of the ensemble Kalman filter in the near-linear setting","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.16154","snapshot_observed_at":"2026-07-15T00:05:31.854903Z","title":"Calvello, J","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"cited_paper":"/paper/2503.16154","citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:a572b39dd66b29a8dbc01324e44890b7ea09a48b04e4201d91c9dbff80590169","observation_id":"c660da24-9193-4578-9d76-265b41cbdef7","resolution":{"observed_at":"2026-07-15T00:05:31.854903Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2409.09800","last_updated":"2025-02-07T01:48:22Z","snapshot_observed_at":"2026-08-16T13:18:24.102682Z","submitted_at":"2024-09-15T17:29:03Z","title":"Accuracy of the Ensemble Kalman Filter in the Near-Linear Setting","version":2},"cited_work":{"arxiv_id":"2409.09800","doi":"10.48550/arxiv.2409.09800","metadata_source":"pith","pith_arxiv_id":"2409.09800","snapshot_observed_at":"2026-08-05T02:49:54.815029Z","title":"Accuracy of the Ensemble Kalman Filter in the Near-Linear Setting","venue":"math.ST","work_id":"e9cdec6b-915b-41de-ab09-82dcd9180740","year":2024},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"cited_paper":"/paper/2409.09800","citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:c63dc55268f8393234fe72566f511f2694de6f4c4cbc7615798cceb67b99e56f","observation_id":"66532caa-7261-49dd-a957-773cf63b9511","resolution":{"observed_at":"2026-07-15T00:10:52.335437Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2019.112752","doi":"10.1016/j.cma.2019.112752","metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Kirkesæther Brun, T","venue":"Computer Methods in Applied Mechanics and Engineering","work_id":"d468eb55-9769-4351-a13c-3be0bbfad33f","year":2020},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:fa7480842f1c7d725b22ac081abd9a3b2095299f0edd933ec0647f7f066923ae","observation_id":"cd62c66d-fcba-4285-aae5-a34924058c76","resolution":{"observed_at":"2026-07-15T00:10:52.256369Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10704-012-9753-8","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Hofacker, C","venue":"International Journal of Fracture","work_id":"8349d6b8-459f-4888-89e5-990b55facc27","year":2012},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:70b63cb167bcc2233a1928b1e4ad78b1e6f43ed10c289dba1ebdedad81889b9e","observation_id":"8c613f76-878e-447b-8de2-4be3c81fe412","resolution":{"observed_at":"2026-07-15T00:10:52.275153Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-15T00:05:31.854903Z","title":"Schillings, A","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:c1e05dfae24bc2a04dae9c0a7ec9f221262626708199ce5be59e63bbe4ff4ced","observation_id":"167e7244-9be2-4594-9e5a-40cd80a07c99","resolution":{"observed_at":"2026-07-15T00:05:31.854903Z","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":"10.1175/mwr3020.1","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Monthly Weather Review","work_id":"cb627f03-806f-4936-badb-f87b1f7bb032","year":2005},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:cca7d69a77fda5c852b8e03a33cd36cac6222b7cd767c693da739a20a5b325fd","observation_id":"c6352ccd-4cf4-46d1-9c91-3ab37c34db0a","resolution":{"observed_at":"2026-07-15T00:10:52.334831Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-15T00:05:31.854903Z","title":null,"venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:1c86070f9d53d5cd72ea0ddf9420d2db007d3bce5e6506a005bc94fddb810bef","observation_id":"6b0e712d-6637-4fbe-accc-7aa649a5a39a","resolution":{"observed_at":"2026-07-15T00:05:31.854903Z","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":"2026-07-15T00:05:31.854903Z","title":"Gaspari, S","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:f7db5efadf773a160a4a1d8d9d2afc8ecb8688a92056552e3b86de01eeafe2a9","observation_id":"d3abe89e-bc18-43df-8ecd-2efbd0a67b3c","resolution":{"observed_at":"2026-07-15T00:05:31.854903Z","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":"2026-07-15T00:05:31.854903Z","title":"Bezanson, A","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:3c52e2a425b9f7a362df21074d9689b85e11dc39619819e63bb79184928ca074","observation_id":"0c83e3fd-90a1-4536-85ee-9f94b0d1967a","resolution":{"observed_at":"2026-07-15T00:05:31.854903Z","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":"2026-07-15T00:05:31.854903Z","title":"Carlsson, F","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-07-15T00:05:31.854903Z"},"links":{"citing_paper":"/paper/2603.09728"},"observation_digest":"sha256:21d122101faf7670a9b04b182114f66f97c9ae8787835f7fb81f445eed68b7b8","observation_id":"e7745186-e805-4799-a4fb-c1835c6e00a9","resolution":{"observed_at":"2026-07-15T00:05:31.854903Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2603.09728","last_updated":"2026-03-10T14:33:11Z","latest_version":1,"primary_category":"cs.CE","snapshot_observed_at":"2026-08-15T06:05:34.118468Z","submitted_at":"2026-03-10T14:33:11Z","title":"A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture"},"reference_resolution":{"displayed":40,"state_counts":{"malformed_identifier":5,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":21,"verified_exact":14,"verified_fuzzy":0},"total_outbound_references":40},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 0 inbound Pith citation observations for arXiv:2603.09728."}