{"as_of":"2026-08-19T09:14:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:b0c6a04c7fd80eab1f231f6710fa1e182f83c0623972dfcb403791f3a13ff4d1","coverage":[{"denominator":32,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":32,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T19:11:56.793977Z","state":"measured"},{"denominator":32,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":32,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-19T06:32:44.657259+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2506.17582/citation-record","integrity":"/paper/2506.17582/integrity","json":"/paper/2506.17582/citation-record.json","paper":"/paper/2506.17582"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T19:11:57.115357Z","title":null,"venue":null,"work_id":"720c3c50-2bd4-4bef-845b-c7da8b1b8979","year":2022},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.694598Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:f42c1d23d43cab1bd5b0139afbf1a70451703c598828e0b356e0e6c5f6bf2dae","observation_id":"3f022929-154d-4d34-a00f-3e0c0a55f5b8","resolution":{"observed_at":"2026-08-15T19:11:57.119011Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T19:11:57.107802Z","title":null,"venue":null,"work_id":"af70527f-4760-4532-8b2a-1caa6166c2bb","year":2018},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.697653Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:fab8a70d8d9aa8df88abcaa9be75459db5a77e584e0d7d2be18edcdc541b0b5e","observation_id":"131281d3-9fce-43d5-be1a-eaf3062c9050","resolution":{"observed_at":"2026-08-15T19:11:57.110785Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T19:11:57.099892Z","title":"Zienkiewicz, R","venue":null,"work_id":"0f2288dd-da13-4b63-9cd5-2e201ef53118","year":2013},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.700736Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:f17141bb9dd19d6eaf249a739eef4fdaa57b0e53d3d9af45d2d7ddb1be4cbf96","observation_id":"c74a4cbc-69eb-49dd-9351-5baf9af04c1c","resolution":{"observed_at":"2026-08-15T19:11:57.103145Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T19:11:57.090327Z","title":"Godunov and I","venue":null,"work_id":"fa5e1aa7-ed02-4955-b99e-ca26917b53f6","year":1959},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.704392Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:51ebbe093838e337e1f4704abe15efe0cee6e13d1e797d37a1d4a96e5e2d8ed3","observation_id":"1ab49e87-7a76-4438-8ff7-4f2e4439cbae","resolution":{"observed_at":"2026-08-15T19:11:57.093370Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T19:11:57.082218Z","title":"Eymard, T","venue":null,"work_id":"0cb6ba2e-23fe-4721-b094-f065750030e5","year":2000},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.707571Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:563c4b35cfb1556209cc6aaccc5e0b5acc1aee0d12dd0e36aafa51ddd7408cc6","observation_id":"6c189fe2-5254-4219-9423-560ce6d45482","resolution":{"observed_at":"2026-08-15T19:11:57.085699Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T19:11:57.073891Z","title":null,"venue":null,"work_id":"d7b085bf-669a-4b78-8f9a-808829b97e57","year":2021},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.711210Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:0ef360b43414783d19d1aff129a3d025f0eef4ff723eca3a323ad39afea97ac3","observation_id":"b3fa2936-084b-46f3-8932-3b61444038dc","resolution":{"observed_at":"2026-08-15T19:11:57.077370Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T19:11:57.065198Z","title":null,"venue":null,"work_id":"0da2dca3-2763-479d-a8ee-03be6ee5f154","year":2021},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.714673Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:ac9dc85bb1c26a24f30712da54ddc11d6f7ce72d763cc8de59834c8b13bbc1fe","observation_id":"881ec914-b394-4468-9403-df1896ba123b","resolution":{"observed_at":"2026-08-15T19:11:57.067870Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2103.10974","last_updated":"2021-03-19T18:15:42Z","snapshot_observed_at":"2026-08-18T10:24:59.042584Z","submitted_at":"2021-03-19T18:15:42Z","title":"Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2103.10974","snapshot_observed_at":"2026-08-15T19:11:56.717464Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.717464Z"},"links":{"cited_paper":"/paper/2103.10974","citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:60b2f2e31a19cfee79a293471f5ff30152e5ba251d27fbc4c353b0ef816bf86b","observation_id":"e36e7f52-50bd-4a3a-863e-18fe39559412","resolution":{"observed_at":"2026-08-15T19:11:56.717464Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2111.08823","last_updated":"2022-11-19T01:19:30Z","snapshot_observed_at":"2026-08-19T09:00:12.050859Z","submitted_at":"2021-11-15T02:51:42Z","title":"Meta-Auto-Decoder for Solving Parametric Partial Differential Equations","version":3},"cited_work":{"arxiv_id":"2111.08823","doi":null,"metadata_source":"pith","pith_arxiv_id":"2111.08823","snapshot_observed_at":"2026-08-15T19:11:56.904646Z","title":"Meta-Auto-Decoder for Solving Parametric Partial Differential Equations","venue":"cs.LG","work_id":"c7380fb0-6497-47e6-a654-d90a43ded343","year":2021},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.720998Z"},"links":{"cited_paper":"/paper/2111.08823","citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:a4558dc15607efa64b1b8a3de3d8fe40da9088953a57c9a7027fe99b03e7d4ec","observation_id":"2f8a00ac-3e74-4bf0-9b8f-96dda81738e2","resolution":{"observed_at":"2026-08-15T19:11:56.910003Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T19:11:57.056624Z","title":"Belbute-Peres, F","venue":null,"work_id":"11a8c934-1ac0-4ae1-93e5-5296cc5f1b39","year":null},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.724146Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:d0c60012d5d3cc952a81e500f74f00503bcb2fb1a9c3d3756127b5911b41c497","observation_id":"de819b62-000a-421a-8f60-5ee6ad53f550","resolution":{"observed_at":"2026-08-15T19:11:57.060469Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T19:11:57.048729Z","title":null,"venue":null,"work_id":"68f7e788-d3c9-4277-b463-589ff24469b9","year":2019},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.728178Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:563874b8dd9478248dd812a653658a7c57ac5238e7207e31d45e52dd0e0a9b31","observation_id":"a636db74-f3fd-4d82-803c-8fdfeecf8e36","resolution":{"observed_at":"2026-08-15T19:11:57.051623Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1808.04295","last_updated":"2018-11-29T03:20:18Z","snapshot_observed_at":"2026-08-14T18:41:45.177033Z","submitted_at":"2018-08-13T15:40:41Z","title":"Understanding training and generalization in deep learning by Fourier analysis","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1808.04295","snapshot_observed_at":"2026-08-15T19:11:56.732531Z","title":"Xu,Understanding training and generalization in deep learning by fourier anal- ysis, CoRR abs/1808.04295 (2018), Available athttp://arxiv.org/abs/1808","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.732531Z"},"links":{"cited_paper":"/paper/1808.04295","citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:5dd76b8c6f5c579d93c1bf0d2caf6b83349d1aa55a3efb4fc80792f57e123303","observation_id":"1c5661f3-ffbc-4f0b-a347-f62f2737dc74","resolution":{"observed_at":"2026-08-15T19:11:56.732531Z","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":"2026-08-15T19:11:57.040212Z","title":"LeCun, Y","venue":null,"work_id":"dbd650bb-07be-42c4-8d51-84f9a7463276","year":2015},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.736212Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:0d9a59c59f72cd9de914a19a8f2cd95430d03feaa21d2ef3ab4ca6fa7aa0dcbb","observation_id":"e967798d-8ba5-412a-bf3d-26f411ca8a64","resolution":{"observed_at":"2026-08-15T19:11:57.043507Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T19:11:57.032743Z","title":"Raissi, P","venue":null,"work_id":"b4a575ac-1528-4139-86d9-309e0398d58a","year":2019},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.739565Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:643214dd1bb85542514e8ff486d7968e4f094de793f16e11a92a70a48c47461b","observation_id":"6d115a96-bd06-460e-8439-41eb1f3d6828","resolution":{"observed_at":"2026-08-15T19:11:57.035333Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T19:11:57.023784Z","title":"Sirignano and K","venue":null,"work_id":"ff8e6829-29c4-47fb-a7ea-10d9405fbfe5","year":2018},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.743481Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:2211c2e896907f749175c0bd4619abc57de5847f79da1685ddf29c81e1ad6255","observation_id":"dbd5399c-6590-4241-b1f0-1b51bdf70b0c","resolution":{"observed_at":"2026-08-15T19:11:57.026737Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T19:11:57.015410Z","title":"Yu,et al.,The deep ritz method: a deep learning-based numerical algorithm for solving variational problems, Communications in Mathematics and Statistics 6 (2018), pp","venue":null,"work_id":"4f489596-355c-45eb-882d-376cc472d336","year":2018},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.746404Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:36dc878315c344c88f9d9b5eb1376f0be5ad16c36d364a29b4f5e45d0f7cf309","observation_id":"dc3d40c2-c73d-4c16-8ab6-e3787b760e18","resolution":{"observed_at":"2026-08-15T19:11:57.018851Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T19:11:57.006582Z","title":null,"venue":null,"work_id":"1827c2f6-c200-4ded-b247-458c422cfbcf","year":2023},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.750062Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:1a6d943e7522c8f3154bb0027e9110e739a427b7405fe33b8ed80c45b2e3c512","observation_id":"551f0b87-41b2-4a63-bddb-c55dea2d5b78","resolution":{"observed_at":"2026-08-15T19:11:57.009742Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T19:11:56.998347Z","title":"Raissi, A","venue":null,"work_id":"7e4bede2-41ab-4902-8a28-4ab7a7175dcd","year":2020},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.753126Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:4a1eea5b519aceac031b4a4a3e51b363ab894cebbfa2b74ab46fe82072202042","observation_id":"e957f737-d050-4a57-9354-6dce8901a4b0","resolution":{"observed_at":"2026-08-15T19:11:57.001654Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T19:11:56.989601Z","title":null,"venue":null,"work_id":"ac29fb12-ce9b-4f39-a95d-f87c04d3c66a","year":2021},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.756322Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:8fdd3a16e9393194bf09bb09b071bbc26b12c27ed696b24e4ede27a4cb67b50b","observation_id":"78e0de77-8567-4d6c-a227-0d7b788cfecd","resolution":{"observed_at":"2026-08-15T19:11:56.993246Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T19:11:56.981468Z","title":null,"venue":null,"work_id":"f1050fd9-4a5d-4911-9061-921fe0db70d1","year":2018},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.759442Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:de0be53f9f74e1bf5fa25f3dee3882c1946024e45374a7308e1cfbdadf7e2178","observation_id":"a1229dba-a834-4ac8-bca9-f36589668669","resolution":{"observed_at":"2026-08-15T19:11:56.984416Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2003.03485","last_updated":"2020-03-07T01:56:20Z","snapshot_observed_at":"2026-08-15T17:57:12.049079Z","submitted_at":"2020-03-07T01:56:20Z","title":"Neural Operator: Graph Kernel Network for Partial Differential Equations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2003.03485","snapshot_observed_at":"2026-08-15T19:11:56.763344Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.763344Z"},"links":{"cited_paper":"/paper/2003.03485","citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:670e7f98d5d1786f8827b516c879d597a184192511c7b864fdcbafaec1459df0","observation_id":"b60ca831-241a-44cf-bd5a-c99e7c5a759e","resolution":{"observed_at":"2026-08-15T19:11:56.763344Z","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":"2026-08-15T19:11:56.973118Z","title":null,"venue":null,"work_id":"6b0b9838-55bd-4147-bab6-a58c6ec0a97f","year":2023},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.766286Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:5f3e6d59d0fcc5c81f285a10e13078550332922adf9c1d0e0d1b091c3674e988","observation_id":"f01ee33d-cf7c-4082-80f5-dd972a644999","resolution":{"observed_at":"2026-08-15T19:11:56.976052Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T19:11:56.964925Z","title":"Penwarden, S","venue":null,"work_id":"3f3e700a-d789-4288-b075-79d499703592","year":null},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.768929Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:fcb45fb8b077bc3ee7b68f43c61683b5266cbeb5d43ff0a812aa4f55c81a6693","observation_id":"4c6c164d-9855-4c18-a394-fa362425c5a6","resolution":{"observed_at":"2026-08-15T19:11:56.967811Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T19:11:56.772276Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.772276Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:e61d6b17f9469fd86e9f3688d1e25cc72a699bcc3bc32355fc5b9f2898b5b8e8","observation_id":"a78bbfbc-88b7-43cb-826c-5f42177e8b48","resolution":{"observed_at":"2026-08-15T19:11:56.772276Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1088/1674-1056/ad0bf4","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Chinese Physics B","work_id":"9245f25e-6ca3-498c-acae-1ebc43a9c970","year":null},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.775261Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:45b4119f4691446416f5546e76d9606609c7309baa598fcda3d12ebce857a7ff","observation_id":"967c107a-18aa-49bc-ae37-8ccbf708aac0","resolution":{"observed_at":"2026-08-06T23:36:19.416689Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T19:11:56.777931Z","title":"Zou and G.E","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.777931Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:63ad339d7ddc24057e4149064727394da5a5cec7811768a9d69ec8337b4a310e","observation_id":"3dc6ff8c-5919-40ca-85e0-c8dfaf764d33","resolution":{"observed_at":"2026-08-15T19:11:56.777931Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1609.09106","last_updated":"2016-12-01T10:08:15Z","snapshot_observed_at":"2026-08-14T14:43:47.411225Z","submitted_at":"2016-09-27T05:57:00Z","title":"HyperNetworks","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1609.09106","snapshot_observed_at":"2026-08-15T19:11:56.780379Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.780379Z"},"links":{"cited_paper":"/paper/1609.09106","citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:c82530729f9b4b7d1da3284edb20eace6a27ee624858d531ccc00815a929c6b2","observation_id":"345a8d4f-2090-421e-a865-7bb5939d2d06","resolution":{"observed_at":"2026-08-15T19:11:56.780379Z","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":"2026-08-15T19:11:56.954930Z","title":null,"venue":null,"work_id":"6dd3d015-fc7b-4eda-a404-76907b7c9aff","year":2024},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.784339Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:b6a7e2d6e3ca124dcddfae6f0f890cd24b243c79e9f69dcc2f640432de479069","observation_id":"690cfc24-e6df-41b9-9d7c-2218d25c98c6","resolution":{"observed_at":"2026-08-15T19:11:56.958756Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T19:11:56.947026Z","title":"Xiang, W","venue":null,"work_id":"5c0e7d25-e6fd-4589-9e57-8b74ba7948ae","year":2022},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.787138Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:f18d3ee7ab666f700d8e9b4429f4f59c8055d76a043b6814d6d99872ee1bb711","observation_id":"02ed87ec-9148-4de1-94ad-dd90b7d80ea4","resolution":{"observed_at":"2026-08-15T19:11:56.949763Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T19:11:56.939130Z","title":null,"venue":null,"work_id":"9280b7f2-34b5-49a7-9aab-4548a44c05a3","year":2022},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.790688Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:6cc7e983825f88d7b76d7011c39d11d9bf62dd9db0f6794cc887417f742792c3","observation_id":"a72139ed-41a4-40b6-ba9c-b86b6b4c98d0","resolution":{"observed_at":"2026-08-15T19:11:56.942349Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T19:11:56.931040Z","title":"Iserles,A first course in the numerical analysis of differential equations, 44, Cambridge university press, 2009","venue":null,"work_id":"81ba91cd-26ce-4031-ba99-d29847468c07","year":2009},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T23:36:19.026539Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:2f27e1c7a33fd3fce2de0a822e34b27459839a6ea61d5d2c1771654480b6d992","observation_id":"26326323-6e54-4b47-b0db-f190b99dda5c","resolution":{"observed_at":"2026-08-15T19:11:56.934267Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T19:11:56.922051Z","title":"Iserles,A first course in the numerical analysis of differential equations, 44, Cambridge university press, 2009","venue":null,"work_id":"1b9abd5c-ec0a-449e-a73a-36877fecca89","year":2009},"citing_paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:56.793977Z"},"links":{"citing_paper":"/paper/2506.17582"},"observation_digest":"sha256:a71a3ff9c3a3687bbeff7248fd9a1de6abb6cf40751483052bfc05669f3f7d10","observation_id":"a22814ba-665b-45e9-8fce-de16ae5a8764","resolution":{"observed_at":"2026-08-15T19:11:56.925229Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.17582","last_updated":"2025-06-21T04:28:03Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-17T22:33:43.763560Z","submitted_at":"2025-06-21T04:28:03Z","title":"LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs"},"reference_resolution":{"displayed":32,"state_counts":{"malformed_identifier":2,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":17,"verified_exact":2,"verified_fuzzy":11},"total_outbound_references":32},"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":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2506.17582."}