{"as_of":"2026-08-14T00:34:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:eb5819db55ebf9433a4e8454ce91dabed8f53e7b3c1ca080fd876887b537b1bf","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":"2026-08-06T17:04:31.855309Z","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":"2026-08-13T06:32:02.005865+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/2507.11870/citation-record","integrity":"/paper/2507.11870/integrity","json":"/paper/2507.11870/citation-record.json","paper":"/paper/2507.11870"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:04:36.916983Z","title":"Aldirany, R","venue":null,"work_id":"067f82ae-2577-4900-816c-8c59bb1210d9","year":2024},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:28.420800Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:f0346df6c0dbc87cd0eeb81cfcdb49151a7cf6840592658329a0271e0f4376e8","observation_id":"babac7c7-8d7c-415f-8c42-7f2f67dbec9e","resolution":{"observed_at":"2026-08-06T17:04:37.045316Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T17:04:36.654192Z","title":null,"venue":null,"work_id":"e8dc0d84-f8d2-4a8f-893f-a255b9c8a103","year":2003},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:28.483884Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:04820c23e0dd426713323f26996bf7051d6a788d212d6c18ed4a58614c7265ad","observation_id":"042a510f-f481-48f2-b3e0-0c26aa1f7822","resolution":{"observed_at":"2026-08-06T17:04:36.745373Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T17:04:36.385822Z","title":null,"venue":null,"work_id":"d32238a3-de36-4e08-8e52-86cdeee94951","year":2021},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:28.577460Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:3104448125ba20366246e01e164c14a2fc41d234d714f66a3e0e1522b53392b2","observation_id":"4dd34305-a13b-415d-ae47-7d9331df76b1","resolution":{"observed_at":"2026-08-06T17:04:36.522328Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T17:04:36.217054Z","title":"Chandrasekaran, P","venue":null,"work_id":"61c5f338-768e-4ef0-b1c0-18806c879ab5","year":2003},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:28.639875Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:ca8fa33ccf1b033ec98bffcb5219c9b0bff615fcec7c13c4d1a2cfc4a4e1dc54","observation_id":"b109ff4c-333b-4dca-ba2d-386556d7dad3","resolution":{"observed_at":"2026-08-06T17:04:36.301317Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T17:04:35.981134Z","title":"Chandrasekaran, P","venue":null,"work_id":"17dfef67-a3c1-400c-9f6b-76309c472069","year":2010},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:28.679396Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:2e56c21478a49f86f794283877814e9baf78a96c3ce7f9098681b1bf2a4d23a1","observation_id":"e3d1e20c-146a-46e3-a19c-f937be5705d3","resolution":{"observed_at":"2026-08-06T17:04:36.119700Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T17:04:35.748375Z","title":null,"venue":null,"work_id":"5964ee57-d88f-4015-95fc-dfd0a18a42be","year":2024},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:28.730531Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:4486abc35e95c26c24372f8b860e58127511e7d87bfc4596be01f1fe037af07c","observation_id":"40d8f3e0-e62d-446c-a780-9450f4da40ed","resolution":{"observed_at":"2026-08-06T17:04:35.861877Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T17:04:35.617369Z","title":null,"venue":null,"work_id":"6f3877f3-dce8-474e-a77b-8e1c93384f34","year":2024},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:28.779040Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:977471d26dbd0ab2b89cde892c0eb3b5338bfa3045be64034e559a9706298326","observation_id":"89d5adfd-eefc-46a2-916c-ea98e7ce74ea","resolution":{"observed_at":"2026-08-06T17:04:35.676323Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T17:04:35.341051Z","title":null,"venue":null,"work_id":"f1b70ee0-0d55-4d99-832d-69325921ff12","year":2019},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:28.815022Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:d8d8d0615d5a9b01b67eb03c96967deca95b9a79411bd16394c56b2ceb8f5091","observation_id":"11d1124b-7811-449e-9edc-259ba6814a9a","resolution":{"observed_at":"2026-08-06T17:04:35.515236Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T17:04:35.125067Z","title":"Gómez-Castro","venue":null,"work_id":"e89d4a84-7b01-4639-8177-ff693529a944","year":2024},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:28.875536Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:664ee5b048a57a913c26fd73bf252b2999b9c1db0a3e7006d10d5856ffbc5c21","observation_id":"e64365bb-eb0a-48e6-9304-b46195419597","resolution":{"observed_at":"2026-08-06T17:04:35.219052Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T17:04:34.906664Z","title":"Greengard and V","venue":null,"work_id":"746c3a82-2225-45a8-8131-c3f2f1e5baa8","year":1987},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:28.940452Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:f8422d997f2760012c39edc58085851138e56655843e1da418bc1dc749bd14b1","observation_id":"4e67b1d1-29f4-4185-9363-a86d8034fdab","resolution":{"observed_at":"2026-08-06T17:04:35.003051Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.13459","last_updated":"2021-10-10T04:30:49Z","snapshot_observed_at":"2026-08-13T18:03:53.288620Z","submitted_at":"2021-09-28T03:21:47Z","title":"Multiwavelet-based Operator Learning for Differential Equations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.13459","snapshot_observed_at":"2026-08-06T17:04:28.984914Z","title":"Gupta, X","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:28.984914Z"},"links":{"cited_paper":"/paper/2109.13459","citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:c46a10eb0a444e357025189652e0fed7df7710990bcb2a79ebbbe5b655f9ea7a","observation_id":"2808d7a3-b66e-4012-9616-7d1304b7bfdb","resolution":{"observed_at":"2026-08-06T17:04:28.984914Z","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":"2026-08-06T17:04:34.736747Z","title":null,"venue":null,"work_id":"2ee16f03-2eb5-49ed-b2f4-b6faf5f6f2cf","year":2023},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:29.054339Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:b385b2cafda48f45dbed39d829df44947fb9026807653a0c3b6314a4e8dd31e2","observation_id":"a1db66a0-0d0f-41d9-a0cc-838025997d84","resolution":{"observed_at":"2026-08-06T17:04:34.835404Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2401.02398","last_updated":"2025-05-02T17:02:22Z","snapshot_observed_at":"2026-08-13T04:48:52.506408Z","submitted_at":"2024-01-04T18:31:21Z","title":"Generating synthetic data for neural operators","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2401.02398","snapshot_observed_at":"2026-08-06T17:04:29.108661Z","title":"Hasani and R","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:29.108661Z"},"links":{"cited_paper":"/paper/2401.02398","citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:508953d733fe9966450fb56183b2c4b7202a9dcc22dddbf362412007ba2f7b13","observation_id":"1dd7dfde-5898-4440-ab8b-ac62a5525b1e","resolution":{"observed_at":"2026-08-06T17:04:29.108661Z","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":"2026-08-06T17:04:34.534774Z","title":"Helwig, X","venue":null,"work_id":"96e105a9-d59b-4713-be8a-c3430f6e0587","year":2023},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:29.143131Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:3d3465a943fadcc234ba5647633087b30136396a12af72c16e9982bf07a7443a","observation_id":"962ca2f7-07ef-4786-a51c-0968c11e1cd5","resolution":{"observed_at":"2026-08-06T17:04:34.630064Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T17:04:29.223922Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:29.223922Z"},"links":{"cited_paper":"/paper/1412.6980","citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:e714af4afa6801906b39d061af8611d198053a1fef036af88f97044647d7c668","observation_id":"80049576-21e1-4578-bad5-ee00371d2ea5","resolution":{"observed_at":"2026-08-06T17:04:29.223922Z","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":"2026-08-06T17:04:29.270789Z","title":"Kovachki, Z","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:29.270789Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:17e078d1f047117511efc63ac50366a3343881f11538f446a6e187a6fc911f9e","observation_id":"1965a119-88c4-460e-b577-736c5903686b","resolution":{"observed_at":"2026-08-06T17:04:29.270789Z","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":"2026-08-06T17:04:34.333190Z","title":"Lerer, I","venue":null,"work_id":"4bf80358-3471-4f6f-ae8d-a03ab7eb3daf","year":2024},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:29.359986Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:9fcbcc091e60478f37bd39378e9f0ec332dc8db62551e8c4c766c02efe4c1a9b","observation_id":"0be1e384-b1e3-4c57-bc33-8ab8c5875c21","resolution":{"observed_at":"2026-08-06T17:04:34.425831Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T17:04:29.465767Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:29.465767Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:8ea222e15007ecfb840be2d7ca7e83fe35b9dcbe1c72c6b443749f4a06f5713c","observation_id":"939548b7-82ff-4ad9-b3fd-c9ea14fde4f1","resolution":{"observed_at":"2026-08-06T17:04:29.465767Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2006.09535","last_updated":"2020-10-19T20:28:04Z","snapshot_observed_at":"2026-08-13T22:24:15.535726Z","submitted_at":"2020-06-16T21:56:22Z","title":"Multipole Graph Neural Operator for Parametric Partial Differential Equations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2006.09535","snapshot_observed_at":"2026-08-06T17:04:29.557029Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:29.557029Z"},"links":{"cited_paper":"/paper/2006.09535","citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:545d34052c15eb6f593e75ce5178c480514a2c6970f6fab5605e45c36434bfc5","observation_id":"c09207a3-f632-47df-b466-5496ea964b76","resolution":{"observed_at":"2026-08-06T17:04:29.557029Z","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":"2026-08-06T17:04:34.132116Z","title":null,"venue":null,"work_id":"dcbc34c7-b4e2-4eec-92f5-36d7c8c29e4e","year":2018},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:29.618309Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:18566a0c6db9dae981b665b9bb7a493cafa784016345a95e3383dfca955597c4","observation_id":"f11e181e-1178-48d3-b616-20205d98f6e4","resolution":{"observed_at":"2026-08-06T17:04:34.222143Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T17:04:29.670632Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:29.670632Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:fac4e24640ee262be313b73fefa5daa8f071b7c24c7f7868e47321ccd7cc2761","observation_id":"23b9a73e-c1a8-4824-b39e-1bedf0e1eca1","resolution":{"observed_at":"2026-08-06T17:04:29.670632Z","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":"2026-08-06T17:04:34.008109Z","title":null,"venue":null,"work_id":"d9f7c07f-3064-446c-be38-15b507cd0af7","year":2021},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:29.726126Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:34cf5ae81a0b4890b2aaa1e8cf2d420b883a7c8404714ce0f376e8a9f41d1b8a","observation_id":"ebb672bc-e62b-437c-bc4f-72d5257c920a","resolution":{"observed_at":"2026-08-06T17:04:34.065242Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1907.06732","last_updated":"2020-02-04T11:25:30Z","snapshot_observed_at":"2026-08-13T01:23:59.718727Z","submitted_at":"2019-07-15T20:24:22Z","title":"Pad\\'e Activation Units: End-to-end Learning of Flexible Activation Functions in Deep Networks","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1907.06732","snapshot_observed_at":"2026-08-06T17:04:29.782258Z","title":"Molina, P","venue":null,"work_id":null,"year":1907},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:29.782258Z"},"links":{"cited_paper":"/paper/1907.06732","citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:98432653dce82056b3920e4c7d48db44e71fe994e8074e238f872efa768f6468","observation_id":"497d088c-361b-43d9-86c2-d272c32dc5e5","resolution":{"observed_at":"2026-08-06T17:04:29.782258Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2202.11214","last_updated":"2022-02-22T22:19:35Z","snapshot_observed_at":"2026-08-02T21:09:07.860947Z","submitted_at":"2022-02-22T22:19:35Z","title":"FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2202.11214","snapshot_observed_at":"2026-08-06T17:04:29.844579Z","title":"Pathak, S","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:29.844579Z"},"links":{"cited_paper":"/paper/2202.11214","citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:2ff580d7f3e91bc0c601108b8ad5d6b336dfa46b8e4c9ad1bdbc74426f76e2cd","observation_id":"6a10009c-19fb-4124-b72b-c6aa3ae892ff","resolution":{"observed_at":"2026-08-06T17:04:29.844579Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:04:33.831198Z","title":"Raissi, P","venue":null,"work_id":"e540b923-f63f-49e5-a150-8dd3590c981f","year":2019},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:29.932980Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:894c35c88d39221a31b243d83a51e121bee13a433f151f9f73d8103589dfce8c","observation_id":"b129d997-7943-4817-a66a-a35ab9d42e47","resolution":{"observed_at":"2026-08-06T17:04:33.907208Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T17:04:33.624161Z","title":"Raoni’c, R","venue":null,"work_id":"7e1595d5-eb6c-48c8-815b-60aeb9e20d8c","year":2023},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:29.961926Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:4e5879bb5780fcef76f992766f5c99f796d7db3f3a6dd528ffa250583c8fd23d","observation_id":"a662548e-88de-4841-9f09-e72a913af30f","resolution":{"observed_at":"2026-08-06T17:04:33.722511Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T17:04:33.450757Z","title":"Ronneberger, P","venue":null,"work_id":"983833e1-0755-4069-8d98-a83337892645","year":2015},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:30.155652Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:75791eafd73e3e5024cb3751544013f34d021666eb08d41f1d2121c0a8defee7","observation_id":"f0c0aedc-dfda-4e27-b53f-19884a24ce95","resolution":{"observed_at":"2026-08-06T17:04:33.540470Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.00442","last_updated":"2024-07-20T12:35:00Z","snapshot_observed_at":"2026-08-12T23:32:10.981975Z","submitted_at":"2024-06-29T13:50:23Z","title":"A Review of Neural Network Solvers for Second-order Boundary Value Problems","version":2},"cited_work":{"arxiv_id":"2407.00442","doi":null,"metadata_source":"pith","pith_arxiv_id":"2407.00442","snapshot_observed_at":"2026-08-06T17:04:32.447917Z","title":"A Review of Neural Network Solvers for Second-order Boundary Value Problems","venue":"math.NA","work_id":"305cf738-ddb5-44bd-b594-2f97ded38af9","year":2024},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:30.379555Z"},"links":{"cited_paper":"/paper/2407.00442","citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:d3cf2880a0f1214bff6de70f776097810b74399a8f70c85fc0f28540716b76c1","observation_id":"f5a5495d-f15b-4167-b6e3-1d04ab83cde5","resolution":{"observed_at":"2026-08-06T17:04:32.565480Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T17:04:33.316073Z","title":null,"venue":null,"work_id":"7ecdf1f7-7410-4ae6-bc98-1ea9069c9aa4","year":2024},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:30.524876Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:4662e2ed7cfbe96179175811916daa64861a4c41ff5d5775fa61eda13161a26b","observation_id":"4fc59cd1-031d-4821-8347-af78cff9afbd","resolution":{"observed_at":"2026-08-06T17:04:33.390788Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2212.12899","last_updated":"2022-12-25T13:08:09Z","snapshot_observed_at":"2026-08-13T13:14:34.472635Z","submitted_at":"2022-12-25T13:08:09Z","title":"FMM-Net: neural network architecture based on the Fast Multipole Method","version":1},"cited_work":{"arxiv_id":"2212.12899","doi":null,"metadata_source":"pith","pith_arxiv_id":"2212.12899","snapshot_observed_at":"2026-08-06T17:04:32.209874Z","title":"FMM-Net: neural network architecture based on the Fast Multipole Method","venue":"math.NA","work_id":"e850b79d-d249-4e52-8f41-61a2fc2368c8","year":2022},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:30.684236Z"},"links":{"cited_paper":"/paper/2212.12899","citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:91cb425f73c6f2428bb4ec63d87a95fa8adcd538e7f7e3c929c1b919faeed83c","observation_id":"3cbad813-693b-4f24-8f03-9ae2f0175d34","resolution":{"observed_at":"2026-08-06T17:04:32.339811Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T17:04:30.856681Z","title":"Telgarsky","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:30.856681Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:2f5c91afbfbf2b68a26bcac64a302a87ac5b65097713f39b61378183e26d5bf2","observation_id":"482fae2a-be44-4bbe-8f04-ebf7f9eb002a","resolution":{"observed_at":"2026-08-06T17:04:30.856681Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2503.19081","last_updated":"2025-03-24T19:12:39Z","snapshot_observed_at":"2026-08-12T12:59:22.854613Z","submitted_at":"2025-03-24T19:12:39Z","title":"Paving the way for scientific foundation models: enhancing generalization and robustness in PDEs with constraint-aware pre-training","version":1},"cited_work":{"arxiv_id":"2503.19081","doi":null,"metadata_source":"pith","pith_arxiv_id":"2503.19081","snapshot_observed_at":"2026-08-06T17:04:31.995504Z","title":"Paving the way for scientific foundation models: enhancing generalization and robustness in PDEs with constraint-aware pre-training","venue":"cs.LG","work_id":"fa9300de-9727-4541-bb51-97665bb770f2","year":2025},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:31.015004Z"},"links":{"cited_paper":"/paper/2503.19081","citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:cfd632e51d9120888b8adf1d6a18a8b81d2c299db33061425509348af56e2511","observation_id":"b69d25f0-578f-46b6-a9db-8e387a8a88d7","resolution":{"observed_at":"2026-08-06T17:04:32.082181Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T17:04:33.124175Z","title":"Vaswani, N","venue":null,"work_id":"aac11db4-f6c3-4ef6-bb56-16d71c65285c","year":2017},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:31.175109Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:d524a4a605744d5d8805533a14fe23464df714ce3292942f1fcac832c4017635","observation_id":"50ce88ab-3f14-4a8a-9c1b-ec0aa76f0df1","resolution":{"observed_at":"2026-08-06T17:04:33.233026Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2401.09323","last_updated":"2024-01-17T16:47:39Z","snapshot_observed_at":"2026-08-13T04:40:30.164850Z","submitted_at":"2024-01-17T16:47:39Z","title":"BENO: Boundary-embedded Neural Operators for Elliptic PDEs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2401.09323","snapshot_observed_at":"2026-08-06T17:04:31.328960Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:31.328960Z"},"links":{"cited_paper":"/paper/2401.09323","citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:9b1570efec36a3e9d23356aa57c4e1a7881326e210767b4f7b5f7f37d7284e7d","observation_id":"b18c85af-e9fe-4b34-8444-3f8e4f748048","resolution":{"observed_at":"2026-08-06T17:04:31.328960Z","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":"2026-08-06T17:04:31.486302Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:31.486302Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:81d0e247347f7d5cd66d13d52f1d839073bdb63db0378d87f26aeb63da63a98c","observation_id":"7b8c928f-0fbb-488f-98e3-5291712dc259","resolution":{"observed_at":"2026-08-06T17:04:31.486302Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.02366","last_updated":"2024-06-01T15:33:37Z","snapshot_observed_at":"2026-08-13T23:44:28.996307Z","submitted_at":"2024-02-04T06:37:38Z","title":"Transolver: A Fast Transformer Solver for PDEs on General Geometries","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.02366","snapshot_observed_at":"2026-08-06T17:04:31.637581Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:31.637581Z"},"links":{"cited_paper":"/paper/2402.02366","citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:d7a71705ecc2cbfa0e8fb7c90918f8169bdea11a5e310a58aa7df4c76ea67518","observation_id":"e01fce39-afdd-4084-ba69-1509c002ec19","resolution":{"observed_at":"2026-08-06T17:04:31.637581Z","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":"2026-08-06T17:04:32.916117Z","title":null,"venue":null,"work_id":"af5cac4c-b915-4a04-9238-49bd46fa26fb","year":2010},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:31.772911Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:55807611ad78a301cd5a7b02c03dd0a6a55b1734a709cee42b77dc33e5f56f10","observation_id":"29ef7f89-5766-495d-9b93-d1da92a54e1e","resolution":{"observed_at":"2026-08-06T17:04:33.010800Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-06T17:04:32.711664Z","title":"Zhang, A","venue":null,"work_id":"d7621dd7-2d55-4fe5-b710-b4747e01eed4","year":2024},"citing_paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T17:04:31.855309Z"},"links":{"citing_paper":"/paper/2507.11870"},"observation_digest":"sha256:406de5f12c2a6db02ad5dd565aacfafc554a561b9b11ee2955051033383b8d85","observation_id":"13a98cb1-998f-49f7-bb07-5c067566baf1","resolution":{"observed_at":"2026-08-06T17:04:32.809392Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.11870","last_updated":"2025-07-16T03:32:46Z","latest_version":1,"primary_category":"cs.CE","snapshot_observed_at":"2026-08-12T16:53:45.423515Z","submitted_at":"2025-07-16T03:32:46Z","title":"MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs"},"reference_resolution":{"displayed":38,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":22,"verified_exact":3,"verified_fuzzy":12},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2507.11870."}