{"as_of":"2026-08-12T08:33:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5c46f9bc6194b523e69de539b2905248a84bbfa9febef1c4fa766461449b7e24","coverage":[{"denominator":38,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":38,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-08T19:29:47.895711Z","state":"measured"},{"denominator":38,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":38,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+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/2502.06865/citation-record","integrity":"/paper/2502.06865/integrity","json":"/paper/2502.06865/citation-record.json","paper":"/paper/2502.06865"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T19:29:48.292109Z","title":"Bhattacharya, Microstructure of martensite: why it forms and how it gives rise to the shape-memory effect, V ol","venue":null,"work_id":"4cd15d4d-d7ba-4f7d-9312-a2dadc89bd7f","year":2003},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.783521Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:4237a5c79f744853d2b5cd3e96ce9fee6aad72a2c400c61b1a66eeeea1947086","observation_id":"4aae807d-5242-4708-8211-99b591a7a8ad","resolution":{"observed_at":"2026-08-08T19:29:48.295094Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-08T19:29:48.282638Z","title":"Dacorogna, Direct methods in the calculus of variations, V ol","venue":null,"work_id":"7d44f42c-9c69-4bca-95a9-a982a2f2a876","year":2007},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.786970Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:97447b863ec154119c54f73996e70a491492c8e1585d0c3065274cd8821145e1","observation_id":"f6269a25-098d-4350-8303-e90b314249fb","resolution":{"observed_at":"2026-08-08T19:29:48.285560Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-08T19:29:48.273372Z","title":"Luskin, On the computation of crystalline microstructure, Acta numerica 5 (1996) 191–257","venue":null,"work_id":"9b8d818c-41f9-497c-be8f-baa60014f77d","year":1996},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.789804Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:8ebaa9a823243fa23034de444cde0a9f0d2dd40bf5febb8a76cd1e99b471cb6d","observation_id":"f5edfc11-8711-44c2-b83e-09f265b08d66","resolution":{"observed_at":"2026-08-08T19:29:48.276449Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-08T19:29:48.263018Z","title":"Carstensen, Ten remarks on nonconvex minimisation for phase transition simulations, Computer Methods in Applied Mechanics and Engineering 194 (2) (2005) 169–193","venue":null,"work_id":"5a01fb87-3c0b-4d5f-b9f4-7a490115f59c","year":2005},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.792992Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:5a298dda2adc264f1057adb43e40a6088af69aa49f8431f82d8ecfaf28d10cab","observation_id":"499fbce8-fa55-4bf1-94b6-0c51dace4cdd","resolution":{"observed_at":"2026-08-08T19:29:48.266616Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-08T19:29:48.253586Z","title":null,"venue":null,"work_id":"d7880606-8c0c-4635-b1eb-2d1c10f93a18","year":1999},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.796007Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:3e36ef055a2d64f4435adb9ee5e6f8a908ee4695ff22106737b71890a507ed8c","observation_id":"cea96b5e-1aaf-4a7a-94f3-8cb6e65f2332","resolution":{"observed_at":"2026-08-08T19:29:48.256556Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-08T19:29:48.243422Z","title":"Carstensen, Numerical analysis of microstructure, Theory and Numerics of Differential Equations: Durham 2000 (2001) 59–126","venue":null,"work_id":"6f613c59-50e7-4616-a1df-4fee162e5551","year":2001},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.798848Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:6c9a5a88b504fe5b7cec4d1a6ec21bd06690050a04f5c0c1214663ffe31c6bb3","observation_id":"a5b7452c-492c-4bfb-a9d4-65a9d995e709","resolution":{"observed_at":"2026-08-08T19:29:48.246739Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-08T19:29:48.232855Z","title":"Bartels, C","venue":null,"work_id":"a1e84d93-a2b7-4839-8dc4-b5f9d0cb58b8","year":2004},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.801982Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:72d191a484055d569cc00b9a444609f8c317dc0355db8e567642e8992c82f84c","observation_id":"03c7666e-7a2e-4572-a2df-9230046dd093","resolution":{"observed_at":"2026-08-08T19:29:48.235955Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-08T19:29:48.222754Z","title":"Carstensen, P","venue":null,"work_id":"6ba42436-cb91-421b-842f-1af4ca66e069","year":1997},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.804679Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:f6021336f60de4c835089a69607ac3b2a87d865e70f002b92ef0dcf890ca4c08","observation_id":"d6a2bba4-709b-4279-a84a-a4fdabd1d053","resolution":{"observed_at":"2026-08-08T19:29:48.225964Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-08T19:29:48.213511Z","title":null,"venue":null,"work_id":"a4fe135a-fa10-4abe-9ae6-341a7dd61a37","year":1993},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.807509Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:673c0296c116c10af8e207a6449634529c7b637f1f1a393779f2a1cafd4884b1","observation_id":"7c4fd29c-7079-41c4-970f-404fb7a835b5","resolution":{"observed_at":"2026-08-08T19:29:48.216421Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-08T19:29:48.204164Z","title":"Aranda, P","venue":null,"work_id":"dfdc4e2e-9c67-47e7-b723-d6ec30a20b9c","year":2001},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.810161Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:a56de6d83f6306bca2d401a499bd03c916b2c54dabec7eff3710ef31838933e8","observation_id":"9eac9fdf-f625-4b07-8576-eca58340595f","resolution":{"observed_at":"2026-08-08T19:29:48.206996Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-08T19:29:48.195292Z","title":"Carstensen, T","venue":null,"work_id":"26f9b44e-23f9-4ab3-bf5b-84e2804b2075","year":2000},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.813144Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:034892c91990e04e64dccfbd37dafe7997d1c379942eb626f44635a9fa5564f3","observation_id":"0eeef94e-fd94-4b52-aef1-e83c177d6f9b","resolution":{"observed_at":"2026-08-08T19:29:48.198029Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-08T19:29:48.185827Z","title":"Hornik, M","venue":null,"work_id":"5e5a2969-20db-4394-b2f1-2ac1ac6eae61","year":1990},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.816216Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:35808a268e14d93f590a525234be36fbcae2ab4531dc2e36adaafc8baef9cc15","observation_id":"cd51efdd-a27b-4d3b-b245-40cb60402c33","resolution":{"observed_at":"2026-08-08T19:29:48.189022Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-08T19:29:47.818986Z","title":"Hornik, Approximation capabilities of multilayer feedforward networks, Neural networks 4 (2) (1991) 251–257","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.818986Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:82085200e521627130e5038daf069223360eabb6da195f6ee25d65a6479b7ecb","observation_id":"5a1b424a-c7bc-42c3-843d-dc4d9e06136c","resolution":{"observed_at":"2026-08-08T19:29:47.818986Z","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":"2026-08-08T19:29:48.169558Z","title":"Raissi, P","venue":null,"work_id":"cbc1a349-8cff-4ac5-a15b-c3549ff61f03","year":2019},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.822150Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:6ef320abf1dca721e9d61b3abaf1116b02e2cff8ab7953a114e542d91ca8c09d","observation_id":"c1b8cb50-400f-4224-b3c9-5417fc63f7d1","resolution":{"observed_at":"2026-08-08T19:29:48.172805Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-08T19:29:47.824892Z","title":"Sirignano, K","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.824892Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:d1cb55edb2411476a9f486a2d2d8f17bd6ead1f53c9893b94e1d8820743f1ec6","observation_id":"68cd2fb6-28a8-421b-9313-0b83b3a97b73","resolution":{"observed_at":"2026-08-08T19:29:47.824892Z","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":"2026-08-08T19:29:47.827842Z","title":"Yu, et al., The deep ritz method: a deep learning-based numerical algorithm for solving variational problems, Communications in Mathematics and Statistics 6 (1) (2018) 1–12","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.827842Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:48d372965deb5555d21fa8a4861bdf618dca0b2f0ec2218048288ea17c9dec65","observation_id":"686c45ab-f5db-41ae-b6ef-8f73563b4c13","resolution":{"observed_at":"2026-08-08T19:29:47.827842Z","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":"2026-08-08T19:29:47.830561Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.830561Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:530a88f1391f83c91708eec3d74f5610abf414373e55afb864b56da685f8434f","observation_id":"7551554b-15c1-4d6c-bbc4-70ff7f870925","resolution":{"observed_at":"2026-08-08T19:29:47.830561Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1809.02362","last_updated":"2023-01-26T04:45:04Z","snapshot_observed_at":"2026-07-06T06:59:44.822737Z","submitted_at":"2018-09-07T09:03:55Z","title":"A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1809.02362","snapshot_observed_at":"2026-08-08T19:29:47.833466Z","title":"Grohs, F","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.833466Z"},"links":{"cited_paper":"/paper/1809.02362","citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:a858050796f776d1496ca6d0486c73a322842050e6aa0d34eb5c1cb78b8f15d3","observation_id":"773acfb8-c205-4eb0-85b9-501c54ce97d6","resolution":{"observed_at":"2026-08-08T19:29:47.833466Z","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":"2026-08-08T19:29:48.138436Z","title":"Rahaman, A","venue":null,"work_id":"8413ea11-1d3c-4804-9b75-58cbd5de535d","year":2019},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.836828Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:25178486fedf88eb9393105d21ae477e759728ddc9df895fa1f0b128637626e1","observation_id":"453068f4-5ee2-49d4-b3f8-a2118a5f0bee","resolution":{"observed_at":"2026-08-08T19:29:48.141770Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-08T19:29:47.840190Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.840190Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:34fa92e7506053a26c7f39d42b2dfac4d8efe079eb4bfae69c05784f0fc43f57","observation_id":"fd1f0171-8346-4e28-a97c-c3e4b35be6eb","resolution":{"observed_at":"2026-08-08T19:29:47.840190Z","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":"2026-08-08T19:29:48.122541Z","title":null,"venue":null,"work_id":"fb84bf86-200c-48c6-ad4f-42718d33442c","year":2023},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.842928Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:df291863dbf6ea35abcf84eb3d23407a459907ebaedc45f0b704affe76743655","observation_id":"e2d81eaf-e4c3-4ee2-824e-03adaf273deb","resolution":{"observed_at":"2026-08-08T19:29:48.125639Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-08T19:29:48.111112Z","title":"Tancik, P","venue":null,"work_id":"5c0b763d-9511-4d07-ac8f-74e11ffd3152","year":2020},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.846190Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:194901dabd2be9ec3a2b5c25310e0e5353e924611ac910531b01092232b14443","observation_id":"792bce73-1579-459b-a7db-8c14fb39043a","resolution":{"observed_at":"2026-08-08T19:29:48.114174Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-08T19:29:48.101571Z","title":"Geifman, A","venue":null,"work_id":"1803d9cd-a87b-449a-8cb4-aa7e578abe10","year":2020},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.849140Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:11e0c7c2ca93595ceaa57f4aaaea0291b71b97c52422a3692fe64e6103df1bd4","observation_id":"338a0a20-d4e6-44d7-8c90-12f02164d6e7","resolution":{"observed_at":"2026-08-08T19:29:48.104678Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2009.10683","last_updated":"2021-03-18T14:56:31Z","snapshot_observed_at":"2026-08-11T21:55:29.860664Z","submitted_at":"2020-09-22T16:58:26Z","title":"Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHS","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2009.10683","snapshot_observed_at":"2026-08-08T19:29:47.852242Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.852242Z"},"links":{"cited_paper":"/paper/2009.10683","citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:64324b73bd0f0a2f5950b4b6c29db95641733342f61cd345399d0b833c2448e2","observation_id":"ed07b979-db5d-4582-b33b-c260fffe33ea","resolution":{"observed_at":"2026-08-08T19:29:47.852242Z","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":"2026-08-08T19:29:48.090318Z","title":"Weinan, B","venue":null,"work_id":"45f96e80-6067-4dd0-a2c6-0afae851664e","year":2018},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.855631Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:0622332c0955d59176ce47a6c65437337c76461cf916cd5b5e79e6edec5273fd","observation_id":"11a773c2-218e-44e5-96dd-529c2adfca5c","resolution":{"observed_at":"2026-08-08T19:29:48.093676Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1412.6980","last_updated":"2017-01-30T01:27:54Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2014-12-22T13:54:29Z","title":"Adam: A Method for Stochastic Optimization","version":9},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1412.6980","snapshot_observed_at":"2026-08-08T19:29:47.858382Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.858382Z"},"links":{"cited_paper":"/paper/1412.6980","citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:4e5dd094db61939cb43d9b61f283d3bb75bb26bc1dc8ac19746882b6f404a1f4","observation_id":"65673a9f-2a07-47bb-81b2-991b133d47e8","resolution":{"observed_at":"2026-08-08T19:29:47.858382Z","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":"2026-08-08T19:29:47.861466Z","title":"Jacot, F","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.861466Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:3721320b0d9640cd9f1365f217e3c9743fc0be38c19e955a03fc0c336a090ce5","observation_id":"e54a4fa9-c918-4c4e-b0e0-de87edd44647","resolution":{"observed_at":"2026-08-08T19:29:47.861466Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1810.02054","last_updated":"2019-02-05T01:59:59Z","snapshot_observed_at":"2026-08-08T10:07:26.425335Z","submitted_at":"2018-10-04T04:47:47Z","title":"Gradient Descent Provably Optimizes Over-parameterized Neural Networks","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1810.02054","snapshot_observed_at":"2026-08-08T19:29:47.864952Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.864952Z"},"links":{"cited_paper":"/paper/1810.02054","citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:9cbf507683b08714ec03c0c630d611cee1010af9ed6fd863000dae104b018fde","observation_id":"2e4b5aa2-0426-41e1-9fa8-7508d601c8bb","resolution":{"observed_at":"2026-08-08T19:29:47.864952Z","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":"2026-08-08T19:29:48.072227Z","title":"Chizat, E","venue":null,"work_id":"9dbaa19c-4709-4b60-8f29-4572d6ed9a32","year":2019},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.868259Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:b613207a61489c3f056835747076f6205ba2fd6d2119b4c33883ea7f55a2555b","observation_id":"51d1afc3-2511-4b16-82ab-b8ef0c577c4c","resolution":{"observed_at":"2026-08-08T19:29:48.075483Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-08T19:29:48.060787Z","title":null,"venue":null,"work_id":"0fd04a48-c2ed-4bcc-ba60-cbb5451b05d9","year":2019},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.871302Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:63796e7e9a8cfe0fb80e838b0257cd14c9329c800239a4952f1902a0f4b6d648","observation_id":"2150d0bc-ca16-4abd-b1aa-ca34501a6c3d","resolution":{"observed_at":"2026-08-08T19:29:48.064278Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-08T19:29:47.874173Z","title":"Arora, S","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.874173Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:f7c4337e4ab9678f60bb42ce84ac1ef09d71453eb404f8cd046fd67dfd7cf376","observation_id":"bf423686-a842-4804-b0a9-381b960eb58e","resolution":{"observed_at":"2026-08-08T19:29:47.874173Z","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":"2026-08-08T19:29:48.040933Z","title":"Rahimi, B","venue":null,"work_id":"3edc2311-e048-4a9b-b172-a4f19fd27c0f","year":2007},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.877136Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:1425792dd6c53c7841c34782c8197ff6c21db17dcbba7b694d5aa3a71840d563","observation_id":"66728b02-5b04-402e-ad94-045f768667ee","resolution":{"observed_at":"2026-08-08T19:29:48.044745Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-08T19:29:48.029113Z","title":"Muller, Singular perturbations as a selection criterion for periodic minimizing sequences, Calc","venue":null,"work_id":"1990ea05-823b-4ad1-abf2-b93937427885","year":1993},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.879959Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:e04883be7891208b4dc5614ce50e22ca2f6eecce5e0dc14637d8eb5f57dc6231","observation_id":"332bb91e-664e-4a84-81f0-d315a7ac5b6b","resolution":{"observed_at":"2026-08-08T19:29:48.033026Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-08T19:29:48.018668Z","title":null,"venue":null,"work_id":"928e23be-855f-48f8-b0f1-1afe812c896a","year":1997},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.882948Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:58535c65420739acfce3681f3f29785d50f103283888c101792ec9eb22da955c","observation_id":"bc4815dc-95cb-46b1-84c7-706406b6b8a4","resolution":{"observed_at":"2026-08-08T19:29:48.021832Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-08T19:29:48.007249Z","title":"Müller, Variational models for microstructure and phase transitions, Lecture Notes in Math","venue":null,"work_id":"e434ab89-02ea-44a4-90f2-085fac3ad83a","year":1999},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.885943Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:49ca52eed68ad97d7617e31a0141af460a59209f9dbe67b6f7f668decc794f2e","observation_id":"a65b9d4f-c4ff-4e3c-8bc8-9792c7b9a316","resolution":{"observed_at":"2026-08-08T19:29:48.011385Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-08T19:29:47.996529Z","title":null,"venue":null,"work_id":"5fe66b84-3b30-498b-b3e3-9aa2bfbf136c","year":1992},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.889177Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:0c5f7acc542f68f523d3b226f893dd48037689c8480c915ce2d8e4fb151ba53e","observation_id":"890f7d11-42f3-4ca4-a2e9-99c3688f3fe9","resolution":{"observed_at":"2026-08-08T19:29:47.999721Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-08T19:29:47.984253Z","title":"Dondl, B","venue":null,"work_id":"274bf11c-001e-4e98-84c4-79dd347aee5c","year":2016},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.892356Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:4f474a69f590e8a58ffad8ae9090d7c4da2885660eb2ffd476c135aeb90afbef","observation_id":"39e16500-51a2-405b-ab3f-9040d2d025c5","resolution":{"observed_at":"2026-08-08T19:29:47.988570Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-08T19:29:47.895711Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-08T19:29:47.895711Z"},"links":{"citing_paper":"/paper/2502.06865"},"observation_digest":"sha256:7be70f137f388a3ea33049482ad3d1de939485b1abd69cd7c019f79945c434a7","observation_id":"23dc9bae-9179-481a-9d5e-7064665e48fd","resolution":{"observed_at":"2026-08-08T19:29:47.895711Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2502.06865","last_updated":"2025-02-08T02:37:03Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-09T22:57:07.444733Z","submitted_at":"2025-02-08T02:37:03Z","title":"Deep Ritz method with Fourier feature mapping: A deep learning approach for solving variational models of microstructure"},"reference_resolution":{"displayed":38,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":18,"verified_exact":0,"verified_fuzzy":20},"total_outbound_references":38},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2502.06865."}