{"as_of":"2026-08-18T06:43:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:0f327dcc2796f20a15cd148d92d966b23432ee3e930c384c3575e1279f4d37a2","coverage":[{"denominator":44,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":44,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T05:20:03.562464Z","state":"measured"},{"denominator":44,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":44,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+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/2412.17695/citation-record","integrity":"/paper/2412.17695/integrity","json":"/paper/2412.17695/citation-record.json","paper":"/paper/2412.17695"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T05:20:04.284036Z","title":"Rozza, D","venue":null,"work_id":"576691ae-0e4e-43cf-9ab9-fa12bfa09bdc","year":2007},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.345853Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:d2e1685f96bae9f7628e3e8b15342c9cf241f9f736a122c739fdda16c0c3a637","observation_id":"f467893d-43b6-4277-83db-26e842d1d6ff","resolution":{"observed_at":"2026-08-11T05:20:04.288371Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:04.269547Z","title":"Benner, S","venue":null,"work_id":"f1a8c388-6afe-458b-b3a9-1249f2bc02b7","year":2015},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.352965Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:d865c80d0e7a112676a6a4928de6b85711113673c9c773456b1a13075b02a6f4","observation_id":"35952286-40ba-43fc-b8c5-d372478af031","resolution":{"observed_at":"2026-08-11T05:20:04.274225Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:04.253740Z","title":null,"venue":null,"work_id":"7088a962-eb63-4023-87e5-b72a66ecb8b8","year":2021},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.358074Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:1e0236fb0158432cce3b9672a1130f1590e38a08d77a69599d155742e624c728","observation_id":"f23e2858-7b54-4fb1-a64d-42a7edc35287","resolution":{"observed_at":"2026-08-11T05:20:04.258505Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:04.236464Z","title":"Peherstorfer, Breaking the Kolmogorov barrier with nonlinear model reduction, Notices of the American Mathematical Society 69 (5) (2022) 725–733","venue":null,"work_id":"abc5b789-bcac-4061-9129-96a600cdc77b","year":2022},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.363114Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:04d37c5d646ac9091b9fa94af42ffec9eceb8bc18e9880b5eeef55b090081c62","observation_id":"54955e62-d17f-4969-b17b-a6c0d9573f84","resolution":{"observed_at":"2026-08-11T05:20:04.241807Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:04.220160Z","title":"Bruna, B","venue":null,"work_id":"fd506398-c617-4a35-81dc-bfb4f99f036f","year":2024},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.368631Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:703d20dbdc5882482eedb53440ba9db5fef51abb1876e3862eebb775825052e7","observation_id":"36e0aab9-8dcb-4989-b46c-d46c198f196f","resolution":{"observed_at":"2026-08-11T05:20:04.224864Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:04.205272Z","title":"Berman, P","venue":null,"work_id":"e2813f51-1183-4225-ba50-271fa4b6ee77","year":2024},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.373688Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:5478daa262796eec846c6266fc80396df9bd36554e54514c78b3ff86a07c8086","observation_id":"e71b64b6-a737-4aa9-aa1a-701f001b7a1a","resolution":{"observed_at":"2026-08-11T05:20:04.209887Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2404.01145","last_updated":"2024-04-01T14:45:16Z","snapshot_observed_at":"2026-08-16T14:04:38.470926Z","submitted_at":"2024-04-01T14:45:16Z","title":"Sequential-in-time training of nonlinear parametrizations for solving time-dependent partial differential equations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.01145","snapshot_observed_at":"2026-08-11T05:20:03.378888Z","title":"Zhang, Y","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.378888Z"},"links":{"cited_paper":"/paper/2404.01145","citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:2fa5abf37edb567ee3efba65fb94e29487da40ffbba11b51eddd54169f876089","observation_id":"dfb6194f-5b95-4b6e-86d5-f2a8764b19dd","resolution":{"observed_at":"2026-08-11T05:20:03.378888Z","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":"2026-08-11T05:20:04.189417Z","title":null,"venue":null,"work_id":"0ea90b7b-9b2e-4b38-9109-32502ebe1bba","year":2017},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.384257Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:76347cfbb57fcaa06adfda1d59d3d9f0a4a57529e0ba2a22c647b32b97eb74be","observation_id":"e8177ae1-1c36-4466-bdd9-e66585a891d8","resolution":{"observed_at":"2026-08-11T05:20:04.194747Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:04.173402Z","title":"Geelen, S","venue":null,"work_id":"c914d141-8b05-408b-9f95-1cfbe27ad422","year":2023},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.389407Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:c4bc173f97f6cddf8da8bc272ef1de95ed4c77557a76106a57cbd8ad025a36c0","observation_id":"7cdba884-c4ce-4acd-9f09-709084cbe3b4","resolution":{"observed_at":"2026-08-11T05:20:04.178693Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:04.155908Z","title":"Barnett, C","venue":null,"work_id":"8f5e7607-54ca-4479-9577-26e6dd7b4bf0","year":2022},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.393985Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:24e15f5a5d65e3887caa3b471517fd6e7c635f13c06f11377808212c491e5b49","observation_id":"a150371d-4fe1-4c9b-a10f-344fe64f578f","resolution":{"observed_at":"2026-08-11T05:20:04.160702Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:04.140909Z","title":"Barrault, Y","venue":null,"work_id":"8f7d583b-8ca6-4686-92b5-fbd63ba114c8","year":2004},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.398689Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:36480a81c5eae5e8d160a5d7fc9ea063042cf23c36d4e5dc205e775bbf1c8d0e","observation_id":"40f025ca-f4cc-407c-8cee-b8ebd61d9b61","resolution":{"observed_at":"2026-08-11T05:20:04.145728Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:04.125282Z","title":null,"venue":null,"work_id":"243423b4-3ab0-431d-af22-3fd1e6ff4ff5","year":1930},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.403417Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:718f763669e871bafae67e03b469a7d2d2e7e994e6fac29577258431e35c92f0","observation_id":"d38b5069-e442-4295-9eaf-0ff968e0cacf","resolution":{"observed_at":"2026-08-11T05:20:04.130223Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:04.109214Z","title":"Frenkel, Wave Mechanics, Advanced General Theory, Clarendon Press, Oxford, 1934","venue":null,"work_id":"02321cc9-da53-484d-9e71-1ee0013ebde4","year":1934},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.408019Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:69a42d5b8d4ab7844f80699c51d07d33084879f1a3ffebe0286d3cc210fa147e","observation_id":"4d98002f-f4e4-4ef6-8bcb-e08d8bb4ceaf","resolution":{"observed_at":"2026-08-11T05:20:04.115207Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:04.094738Z","title":"Lubich, From quantum to classical molecular dynamics: reduced models and numerical anal- ysis, Vol","venue":null,"work_id":"36c08249-40f6-4458-aba6-e5ff7c544601","year":2008},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.413048Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:fabfbfd8dc3dba8eaaf5876b60a54c16b50de87e77cb0cdd7d24f8c16ce3eb28","observation_id":"1ee25dbf-0ad0-4988-8ec4-8e88d7dbab55","resolution":{"observed_at":"2026-08-11T05:20:04.099356Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:03.417656Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.417656Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:9e835f5ae4bc06963987563199e5569b0925564c8d5b94d0ba7f64325b2d04ee","observation_id":"6f924bd0-0605-4678-92a5-5f13f1f750d7","resolution":{"observed_at":"2026-08-11T05:20:03.417656Z","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":"2026-08-11T05:20:04.070803Z","title":"Black, P","venue":null,"work_id":"d1fe3592-6b82-4da6-9085-8cac1826e0b4","year":2020},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.422276Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:1f4af723e67c7bef27b835f775893195c709c0eee8616de98654e68a557b306a","observation_id":"80ae422f-13f1-4f55-9f49-992d6b0981b3","resolution":{"observed_at":"2026-08-11T05:20:04.075899Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:04.056229Z","title":null,"venue":null,"work_id":"b37a0db6-d66d-4136-ace8-5187d42fd051","year":2021},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.426992Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:48a482ace1a1e71e5f6d34eea5948a402eae98a610208b69aea27216cb5b693d","observation_id":"eabe9731-ed08-4070-8f77-4f7849cf922e","resolution":{"observed_at":"2026-08-11T05:20:04.060710Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:04.041521Z","title":"Anderson, M","venue":null,"work_id":"53da2eb0-41e7-42bb-9079-fd4e5c88eefb","year":2022},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.432146Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:93f37d308635248abf4be5f54a0093127cca131808c39c0cdb8de85f0a75320b","observation_id":"fda954d0-d8a8-447c-9f17-a5d06cbcbe30","resolution":{"observed_at":"2026-08-11T05:20:04.046450Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2308.03461","last_updated":"2023-08-07T10:39:40Z","snapshot_observed_at":"2026-08-16T15:10:19.934207Z","submitted_at":"2023-08-07T10:39:40Z","title":"Positional Embeddings for Solving PDEs with Evolutional Deep Neural Networks","version":1},"cited_work":{"arxiv_id":"2308.03461","doi":null,"metadata_source":"pith","pith_arxiv_id":"2308.03461","snapshot_observed_at":"2026-08-11T05:20:03.708326Z","title":"Positional Embeddings for Solving PDEs with Evolutional Deep Neural Networks","venue":"math.NA","work_id":"ed6a01cf-8a67-46ed-9291-79cd6922baab","year":2023},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.436944Z"},"links":{"cited_paper":"/paper/2308.03461","citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:44608d60cd4971b17abee6e957f49531d297e01aa860c0ee65d5d56ebf6a1bb7","observation_id":"202b83a8-872f-401b-b024-26105fb76c9d","resolution":{"observed_at":"2026-08-11T05:20:03.715232Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2302.06479","last_updated":"2023-05-15T16:15:43Z","snapshot_observed_at":"2026-08-16T15:55:42.073734Z","submitted_at":"2023-02-13T15:56:01Z","title":"Structure-Preserving Model Reduction for Port-Hamiltonian Systems Based on a Special Class of Nonlinear Approximation Ansatzes","version":2},"cited_work":{"arxiv_id":"2302.06479","doi":null,"metadata_source":"pith","pith_arxiv_id":"2302.06479","snapshot_observed_at":"2026-08-11T05:20:03.687530Z","title":"Structure-Preserving Model Reduction for Port-Hamiltonian Systems Based on a Special Class of Nonlinear Approximation Ansatzes","venue":"math.NA","work_id":"ab3739a0-a177-417f-94d6-64d9500f6f4b","year":2023},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.442158Z"},"links":{"cited_paper":"/paper/2302.06479","citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:cf4cff1320b0adffb7b62a334974581f6364392dd71b1aa748a96661a5a128a2","observation_id":"a80c5513-f361-49bf-be68-11640edec1bc","resolution":{"observed_at":"2026-08-11T05:20:03.693204Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:04.027139Z","title":"Lasser, C","venue":null,"work_id":"f3776e57-27cb-4334-952d-d087a09f9ded","year":2020},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.447645Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:6ed627bab478b7c229ceb0e8deaee43f78ced1134972a6058b385a4aea940e07","observation_id":"ac3a5fa3-a1cc-4989-be00-f19a6da7ebca","resolution":{"observed_at":"2026-08-11T05:20:04.031897Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:04.012537Z","title":null,"venue":null,"work_id":"04adf70c-739e-4f41-8b8d-df766c9cd4f5","year":2022},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.452516Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:d0a7bfe3635ddf80bb6cc426bd0ac3158105a5a8f8a1f9f33703c6c946a246da","observation_id":"08507a60-13d5-42f5-8bd9-9334238de91b","resolution":{"observed_at":"2026-08-11T05:20:04.017230Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:03.997658Z","title":null,"venue":null,"work_id":"e855d372-203c-43b0-bfb5-ac64d72508ba","year":2020},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.457334Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:bc6c3a87007a07f0d73db5d7bca9b9e7b7e2d4e456f203b6b4c76f9580ddd27f","observation_id":"69865119-8dda-490f-817f-14e813beeb23","resolution":{"observed_at":"2026-08-11T05:20:04.002761Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:03.981971Z","title":null,"venue":null,"work_id":"2365b34a-c983-4632-87b2-1611a05d81a6","year":2022},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.462140Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:2f8ad0d04a2126006bbceaba00c670c6bf4229ded8d776729ffb101af6e4aa0c","observation_id":"bf6d7b33-6fe7-4e0c-a7e6-ea76666143f9","resolution":{"observed_at":"2026-08-11T05:20:03.987470Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:03.966870Z","title":null,"venue":null,"work_id":"442dbbf2-bebf-4a83-bf53-023b139bbb98","year":2021},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.466555Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:65fda7b6946cbfb84d2180732e57027bc6dbb6b4b0388dd9d5011fd00014ee77","observation_id":"fc2373dd-9492-48bc-9371-f4cbadee7b29","resolution":{"observed_at":"2026-08-11T05:20:03.971986Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2303.09630","last_updated":"2023-03-16T20:18:33Z","snapshot_observed_at":"2026-08-17T20:48:30.260710Z","submitted_at":"2023-03-16T20:18:33Z","title":"Hyper-Reduced Autoencoders for Efficient and Accurate Nonlinear Model Reductions","version":1},"cited_work":{"arxiv_id":"2303.09630","doi":null,"metadata_source":"pith","pith_arxiv_id":"2303.09630","snapshot_observed_at":"2026-08-11T05:20:03.665016Z","title":"Hyper-Reduced Autoencoders for Efficient and Accurate Nonlinear Model Reductions","venue":"physics.comp-ph","work_id":"263d0288-0a24-452f-85bc-17c371c62da2","year":2023},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.470975Z"},"links":{"cited_paper":"/paper/2303.09630","citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:300ad329f96ce7f82f57863c57fa39bc59373d43b4c15711d50b697acc77f4c6","observation_id":"5d336e85-83cb-46a7-8039-0492a824c646","resolution":{"observed_at":"2026-08-11T05:20:03.670711Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:03.950032Z","title":"Romor, G","venue":null,"work_id":"ab7fd2cb-4d9e-4f5e-8f8e-6c97753824ff","year":2023},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.475619Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:c1658c440d2ecda7f34ef5813f4e1d30b33bd799b0be93bcbf7c7c3e5c03a78f","observation_id":"daedffeb-15af-40b4-a24f-75fdd53799b0","resolution":{"observed_at":"2026-08-11T05:20:03.955867Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:03.932965Z","title":"Berman, B","venue":null,"work_id":"3fa222ca-e707-47ed-a53b-97197c83b29d","year":2024},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.480225Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:20bb6ec51ca437e1016488ccf5bc529d7ffd63badf77375e70c2f54e0717d3f8","observation_id":"b1dc5f60-fd4d-4c4d-9015-fbbb0652f924","resolution":{"observed_at":"2026-08-11T05:20:03.937565Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:03.918519Z","title":"Berman, B","venue":null,"work_id":"70b647a7-b2ec-4967-920d-258a3db33dc2","year":2023},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.484968Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:7c7cd267b59e08e6b1135699cbd86c0a5754741b2efee553e73c0ba0e7c335bc","observation_id":"bbf95fea-b5dc-4d75-af13-5ac8ed19f831","resolution":{"observed_at":"2026-08-11T05:20:03.923367Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:03.902623Z","title":"Rutzmoser, D","venue":null,"work_id":"94f37e84-2bcb-4b94-b8e4-efa66cffd97c","year":2017},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.490835Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:e6713acf48906d5549453f407f5a2497b8196c16653f12430a9cf42e7a58e861","observation_id":"b918bc82-7db4-48be-bc00-acf74191ef5d","resolution":{"observed_at":"2026-08-11T05:20:03.908327Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:03.887584Z","title":"Geelen, L","venue":null,"work_id":"0e86e3d2-a67b-4b79-9d40-689264e93486","year":2023},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.495415Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:1fdd67c94fbb64cc2226179a3ad0d8520ebcf5257cd69fccc825624448c468cb","observation_id":"e1b87b95-badb-402d-a652-203e88369dfc","resolution":{"observed_at":"2026-08-11T05:20:03.892435Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:03.870606Z","title":"Geelen, L","venue":null,"work_id":"f59b54cc-5f12-401c-8465-c40c445a93a4","year":2023},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.500663Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:a4177cf53bb239ccd90139c6daaee4173e1cbd650a14c5396530c2a9963564d5","observation_id":"af8b1f27-7809-42cd-a96e-fc5c0180430e","resolution":{"observed_at":"2026-08-11T05:20:03.875348Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:03.507259Z","title":"Sharma, H","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.507259Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:5c2e214f01375318e432289e1c31ab50f2ea96f42ea40ed688d0ba52a67468c5","observation_id":"2295908a-6f88-4b5a-abb3-aa05f24a1b90","resolution":{"observed_at":"2026-08-11T05:20:03.507259Z","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":"2026-08-11T05:20:03.844244Z","title":"Cohen, C","venue":null,"work_id":"260351f1-04cb-414b-bd51-48064560f30d","year":2023},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.512440Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:954969352e87fac4b14e8c9ed6c3498469b1a58d652b2809029da4f1bba10d57","observation_id":"5a2a3555-53c6-406e-8efb-80f08f9e27c7","resolution":{"observed_at":"2026-08-11T05:20:03.849555Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:03.827518Z","title":"Benner, P","venue":null,"work_id":"b99c04db-fce6-4086-a90c-1019e9c58588","year":2023},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.517431Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:b1ec5369b04ebd563c8d6d6a4ee165b8d9e89b85efaee7e061ebcc1f2df7a341","observation_id":"04144724-92b8-46e2-8474-1df94300246b","resolution":{"observed_at":"2026-08-11T05:20:03.832258Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2403.06732","last_updated":"2024-12-12T16:31:43Z","snapshot_observed_at":"2026-08-17T19:07:34.553180Z","submitted_at":"2024-03-11T13:53:12Z","title":"Greedy construction of quadratic manifolds for nonlinear dimensionality reduction and nonlinear model reduction","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.06732","snapshot_observed_at":"2026-08-11T05:20:03.522527Z","title":"Schwerdtner, B","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.522527Z"},"links":{"cited_paper":"/paper/2403.06732","citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:edd08448a521ae4e27da5b61063868486aa5449979acdf09cd71ba286e05c9f7","observation_id":"061fb1d2-0b6d-4ad2-9ad3-742a05983a6f","resolution":{"observed_at":"2026-08-11T05:20:03.522527Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2409.02703","last_updated":"2024-09-04T13:40:45Z","snapshot_observed_at":"2026-08-16T13:21:24.870211Z","submitted_at":"2024-09-04T13:40:45Z","title":"Online learning of quadratic manifolds from streaming data for nonlinear dimensionality reduction and nonlinear model reduction","version":1},"cited_work":{"arxiv_id":"2409.02703","doi":null,"metadata_source":"pith","pith_arxiv_id":"2409.02703","snapshot_observed_at":"2026-08-11T05:20:03.628026Z","title":"Online learning of quadratic manifolds from streaming data for nonlinear dimensionality reduction and nonlinear model reduction","venue":"math.NA","work_id":"87a16bbd-4af2-4cc4-8f97-1512a108ccfd","year":2024},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.528537Z"},"links":{"cited_paper":"/paper/2409.02703","citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:fd14d3019aeadc7c629c846a3f42bae93a94f715074847d6e785978937a705a5","observation_id":"1e5553f3-5e88-4001-9b1b-5e78e8c3756e","resolution":{"observed_at":"2026-08-11T05:20:03.633455Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:03.811877Z","title":"Goyal, P","venue":null,"work_id":"9e631973-d27b-4a55-925a-f26b8b5c2d22","year":2024},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.534088Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:42071b4ad7e125a755b809610ad6c5a2c2fc82cbbd00b93f1a62dcf75785aad9","observation_id":"6aa94880-20b5-477e-8274-10c96d472316","resolution":{"observed_at":"2026-08-11T05:20:03.817084Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:03.796782Z","title":"Ballout, Y","venue":null,"work_id":"6ec7ef1c-8a07-4a86-941d-7d9bf098dce0","year":2024},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.538930Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:f7d95f48fa69278d9862be37f722de9c383cbd2c7af3c8774f2a474c7f86c131","observation_id":"c28daa2a-1c28-4229-9ce9-075c53a55f81","resolution":{"observed_at":"2026-08-11T05:20:03.801880Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.09746","last_updated":"2024-12-12T22:33:32Z","snapshot_observed_at":"2026-08-12T01:00:09.868337Z","submitted_at":"2024-12-12T22:33:32Z","title":"Empirical sparse regression on quadratic manifolds","version":1},"cited_work":{"arxiv_id":"2412.09746","doi":null,"metadata_source":"pith","pith_arxiv_id":"2412.09746","snapshot_observed_at":"2026-08-11T05:20:03.602763Z","title":"Empirical sparse regression on quadratic manifolds","venue":"math.NA","work_id":"1f8a1129-8750-40e2-a7de-37f1c1d3c541","year":2024},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.543515Z"},"links":{"cited_paper":"/paper/2412.09746","citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:dbbf028a081c4b8b174a16b83ac1e5f98039555dc16ddf535489ed75cd3da9d2","observation_id":"f5845be9-7230-416d-9ef1-5c69c91e2357","resolution":{"observed_at":"2026-08-11T05:20:03.610704Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:03.781753Z","title":"Barnett, C","venue":null,"work_id":"5434ff07-2c1b-4da0-9b08-3a2ba7026e04","year":2023},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.548238Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:e49acd0406f28ee8760365caaf77079f40b583e1b6a1417b070f089cf81c97e6","observation_id":"fd93e608-adbc-4a6a-9e43-f01307e1cbf1","resolution":{"observed_at":"2026-08-11T05:20:03.786759Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:03.766363Z","title":null,"venue":null,"work_id":"7e2e9a1f-f6c5-4119-97fa-83bbc8824c14","year":2024},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.552870Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:27314ffc9607d00da77db19d15f02246536da3a26eeb340a26d470ff39f01e6b","observation_id":"a3908a55-6709-4059-ae31-b5f55b6feb61","resolution":{"observed_at":"2026-08-11T05:20:03.771292Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-11T05:20:03.557451Z","title":null,"venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.557451Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:e67ad29be1eda718640ceb1115768de92fbac83d97ffa3a2029378af927c10a2","observation_id":"3d01fb61-a649-460f-9e12-c34f9b10dd3e","resolution":{"observed_at":"2026-08-11T05:20:03.557451Z","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":"2026-08-11T05:20:03.742463Z","title":"Schwerdtner, P","venue":null,"work_id":"544e122b-85a7-4c16-9ccb-1897df8212d1","year":2024},"citing_paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-11T05:20:03.562464Z"},"links":{"citing_paper":"/paper/2412.17695"},"observation_digest":"sha256:469be005ed8e0993141ce28fd0184e3de457e0bdd207ec4b00be04d2b5839c8f","observation_id":"732d88d5-611d-45be-8a28-4d41f32a65e3","resolution":{"observed_at":"2026-08-11T05:20:03.747017Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.17695","last_updated":"2024-12-23T16:20:04Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-15T17:36:19.783337Z","submitted_at":"2024-12-23T16:20:04Z","title":"Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds"},"reference_resolution":{"displayed":44,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":14,"verified_exact":5,"verified_fuzzy":25},"total_outbound_references":44},"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":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 0 inbound Pith citation observations for arXiv:2412.17695."}