{"as_of":"2026-08-18T16:04:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:e6aeaec660aed5976cb2d02513f8c38ff3557aa2bb1778fe41367eac74de6757","coverage":[{"denominator":47,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":47,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T11:20:55.587449Z","state":"measured"},{"denominator":47,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":47,"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/2504.15897/citation-record","integrity":"/paper/2504.15897/integrity","json":"/paper/2504.15897/citation-record.json","paper":"/paper/2504.15897"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"1607.06450","last_updated":"2016-07-21T19:57:52Z","snapshot_observed_at":"2026-08-15T04:53:45.483331Z","submitted_at":"2016-07-21T19:57:52Z","title":"Layer Normalization","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1607.06450","snapshot_observed_at":"2026-08-16T11:20:55.350035Z","title":"R., and Hinton, G","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.350035Z"},"links":{"cited_paper":"/paper/1607.06450","citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:3ffa018e874db98fa0c89208156912df2a7d7b595aa12909a91f3aa1cc116f33","observation_id":"439981b7-d0cb-448a-a4f2-d81d6c095a86","resolution":{"observed_at":"2026-08-16T11:20:55.350035Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:20:55.356170Z","title":"A survey of projection-based model reduction methods for parametric dynamical systems","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.356170Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:9c55a06cadf666f9e3229c403268207d02e2fd0f50264a007c4019a1aee082a3","observation_id":"a76f910e-4717-4f9d-b87e-d6bb59c515d3","resolution":{"observed_at":"2026-08-16T11:20:55.356170Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:20:55.361665Z","title":"Model Reduction and Approximation","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.361665Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:b048f2538c8d43865bd5aba05c4dbffcaeed04903c4efe30dfd9672444039331","observation_id":"87e670b7-1af6-4d40-906b-f7e57d389063","resolution":{"observed_at":"2026-08-16T11:20:55.361665Z","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":"2026-08-16T11:20:56.597786Z","title":"and Maday, Y","venue":null,"work_id":"951f858e-aed6-4f8a-a168-41ea36ef0e1e","year":1997},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.367309Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:fda9c164a246a1bfaf6f6ee8af914d22cd037a7dd29681c1a3177236dd62cd4f","observation_id":"57ddd16a-ffec-4479-8304-ac3999a72aa2","resolution":{"observed_at":"2026-08-16T11:20:56.602378Z","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":"2026-08-16T11:20:56.581741Z","title":"Spherical fourier neural operators: Learning stable dynamics on the sphere","venue":null,"work_id":"05874ecc-be99-404d-adfd-a1fefcf9f3c3","year":2023},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.372254Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:2b46d77abe8a1c1e35e7faa03fd3abf27344dcdb16317b3d4afc324d883898e3","observation_id":"ed84be20-8d18-4705-8cd2-5de55fb07982","resolution":{"observed_at":"2026-08-16T11:20:56.586913Z","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":"2026-08-16T11:20:55.377503Z","title":"and Scott, R","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.377503Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:57216b1defbda148f34d4f8a8aeb5fe269dd71e80e4429f4f045f9be929ea9e9","observation_id":"4c9b247e-94ae-455f-a000-2f994561e758","resolution":{"observed_at":"2026-08-16T11:20:55.377503Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1905.11075","last_updated":"2020-01-04T11:27:06Z","snapshot_observed_at":"2026-08-17T08:03:09.102030Z","submitted_at":"2019-05-27T09:26:17Z","title":"Machine Learning for Fluid Mechanics","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1905.11075","snapshot_observed_at":"2026-08-16T11:20:55.383738Z","title":"L., Noack, B","venue":null,"work_id":null,"year":1905},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.383738Z"},"links":{"cited_paper":"/paper/1905.11075","citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:3ae8e4838fbc68c7d1c4ca2ed70a6d464a43f05846e96f88b243de6f99c7ac5f","observation_id":"0794f175-a044-4623-8989-ab4e74f74519","resolution":{"observed_at":"2026-08-16T11:20:55.383738Z","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":"2026-08-16T11:20:56.563791Z","title":"Choose a transformer: Fourier or galerkin","venue":null,"work_id":"22bfdeb3-b688-4c9d-a601-60bf5e6fd3ed","year":2021},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.388704Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:f74d91f1e481383aa2f72de98098b28ce0f1b76034c744a3cac16553267929bf","observation_id":"d57c31c3-d817-4735-9262-f4298579a56d","resolution":{"observed_at":"2026-08-16T11:20:56.569373Z","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":"2026-08-16T11:20:55.393503Z","title":"Gradient-based constrained optimization using a database of linear reduced-order models","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.393503Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:fea0ca806ca87127bdd070221c743ca54d544a3cbd0bfaee85ebbe5219d171b6","observation_id":"e3ae2aa0-c3e0-4946-aa3a-614862faf459","resolution":{"observed_at":"2026-08-16T11:20:55.393503Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:20:55.398165Z","title":"Fluid simulation using laplacian eigenfunctions","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.398165Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:2981be6a6b56160e4ad87e59f7ecc035f79547fad3e9d4681f8895047828f199","observation_id":"68c9f1ec-e662-4a64-8fed-f38bb0c14b23","resolution":{"observed_at":"2026-08-16T11:20:55.398165Z","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":"2026-08-16T11:20:56.545778Z","title":"Partial Differential Equations","venue":null,"work_id":"a0c09e3d-03f2-4321-8b82-9bea3043636f","year":2010},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.402579Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:9d0de08c103975b563ca8056baeaa8ca8c785b49cb0e80b387512ede53fa67b9","observation_id":"c4cd1971-b9a0-419a-8bb3-67f77d2a6b37","resolution":{"observed_at":"2026-08-16T11:20:56.551163Z","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":"2026-08-16T11:20:56.530046Z","title":"and Trudinger, N","venue":null,"work_id":"aac7da3f-d599-4332-9543-15b2684bedbd","year":2013},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.407296Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:577d977eb4665fb587876c0367645be5362881d088bc3eb19ca3e91c2de7e15b","observation_id":"4fbdef62-c31a-43e5-8b2b-d9cb5df0ecdc","resolution":{"observed_at":"2026-08-16T11:20:56.534880Z","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":"2026-08-16T11:20:56.513539Z","title":"Gnot: A general neural operator transformer for operator learning","venue":null,"work_id":"6acfc426-97cd-4194-b86a-8e22c0700b81","year":2023},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.411949Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:1faf1b2c56f765e6919e0e46cfc488153a9f440628c40b9117bca0e90c8e1bab","observation_id":"eb6fa11c-1928-4536-a7d1-c10fe066647f","resolution":{"observed_at":"2026-08-16T11:20:56.518448Z","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":"2026-08-16T11:20:55.416310Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.416310Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:50c756112934a7a6771daddfb73d6888292a0222f8ed34dcf95997857f11f28d","observation_id":"eb1ce69e-5cc8-4f2e-a2c7-9c6499a83f11","resolution":{"observed_at":"2026-08-16T11:20:55.416310Z","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":"2026-08-16T11:20:56.497905Z","title":"and Mitsume, N","venue":null,"work_id":"32183900-5603-4cd1-ba88-dff75f05d453","year":2024},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.428200Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:c2ebf8dec8db9df6d6875473b487f3befe12c14b66299428c76e00e0d9ed4f0c","observation_id":"1c2660b6-b1f0-43d8-a83d-f04213e088eb","resolution":{"observed_at":"2026-08-16T11:20:56.502668Z","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":"2026-08-16T11:20:56.481357Z","title":"E., Kevrekidis, I","venue":null,"work_id":"fefbd1d9-97b6-468d-8ef8-836c4ed87671","year":2021},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.432960Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:d5edff72581c9791ec46cb4f7ba78ba803e0ed24b030c7281a2362c64b6c9ddb","observation_id":"8f12f30d-74a4-4563-97b6-3cac6ad29688","resolution":{"observed_at":"2026-08-16T11:20:56.486064Z","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":"2310.00120","last_updated":"2023-09-29T20:18:52Z","snapshot_observed_at":"2026-08-16T14:56:22.894933Z","submitted_at":"2023-09-29T20:18:52Z","title":"Multi-Grid Tensorized Fourier Neural Operator for High-Resolution PDEs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2310.00120","snapshot_observed_at":"2026-08-16T11:20:55.438933Z","title":"B., Azizzadenesheli, K., and Anandkumar, A","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.438933Z"},"links":{"cited_paper":"/paper/2310.00120","citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:55f233b6871dbd71d78271c45d04ddcb309750e71dbd624919c8e68594402ca1","observation_id":"f834e9f3-28b7-420a-859e-47e90a7e02cf","resolution":{"observed_at":"2026-08-16T11:20:55.438933Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:20:55.443979Z","title":"Neural operator: Learning maps between function spaces with applications to pdes","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.443979Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:edfbc7edd3042f92a3ecc9bf784e66ba023e3ed9ac7c0b28e0e586b0cca1c53e","observation_id":"5fa660d3-9b0c-4c84-b1f6-9ec90d39c067","resolution":{"observed_at":"2026-08-16T11:20:55.443979Z","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":"7101.18371","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:20:55.972300Z","title":"and Zhang, H","venue":null,"work_id":"12a31498-a844-424d-b640-b31cf3edec1b","year":2010},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.449415Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:d377490d5c711f132febb9624e2a87c12f30be1e71c371b3d33500d5ac06179f","observation_id":"4eda61d4-b36f-4488-90b7-10cfcffeacfc","resolution":{"observed_at":"2026-08-16T11:20:55.980541Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"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":"2026-08-16T11:20:56.454009Z","title":null,"venue":null,"work_id":"e003ccde-2005-4d2b-b154-2691f46f1368","year":2023},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.454363Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:0d48fa17f2505325a5b0012478ffe4c337f27bd136819bc61f3c79c77bd56f57","observation_id":"48f68de2-57ad-475e-9870-6f7a91c72f30","resolution":{"observed_at":"2026-08-16T11:20:56.458921Z","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":"2026-08-16T11:20:56.436963Z","title":"Scalable transformer for pde surrogate modeling","venue":null,"work_id":"40463e42-e3dd-44b1-b09c-ace8767420b6","year":2023},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.459198Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:cbbcecaaf8a48bc7c6e5e360e0cd73fb5d586239d5a84a8f1b3e93639c6808cb","observation_id":"b9710b3c-9175-4b51-be88-443310bb2ee1","resolution":{"observed_at":"2026-08-16T11:20:56.442662Z","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":"2010.08895","last_updated":"2021-05-17T03:12:33Z","snapshot_observed_at":"2026-08-14T20:53:04.124337Z","submitted_at":"2020-10-18T00:34:21Z","title":"Fourier Neural Operator for Parametric Partial Differential Equations","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2010.08895","snapshot_observed_at":"2026-08-16T11:20:55.464301Z","title":"B., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.464301Z"},"links":{"cited_paper":"/paper/2010.08895","citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:698586611ed86fa9deaeb05a8d9291c0042897f7cb6c81aeb009b08137a04d5e","observation_id":"c558f876-b0a2-4c98-8768-33bf2dfba2b3","resolution":{"observed_at":"2026-08-16T11:20:55.464301Z","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":"2026-08-16T11:20:56.420717Z","title":"Z., Liu, B., and Anandkumar, A","venue":null,"work_id":"7bb6655f-86a0-4a18-9c2b-8a7682f665d0","year":2022},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.469813Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:4747e1210172dc04e3869e45939c80ba130edb084ae37ce5ef73e9fcd6836d1a","observation_id":"5bb495e1-b414-4d5b-9c8d-91b75a6fd1de","resolution":{"observed_at":"2026-08-16T11:20:56.425772Z","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":"2309.00583","last_updated":"2023-09-01T16:59:21Z","snapshot_observed_at":"2026-08-18T11:01:08.167287Z","submitted_at":"2023-09-01T16:59:21Z","title":"Geometry-Informed Neural Operator for Large-Scale 3D PDEs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2309.00583","snapshot_observed_at":"2026-08-16T11:20:55.474625Z","title":"B., Choy, C., Li, B., Kossaifi, J., Otta, S","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.474625Z"},"links":{"cited_paper":"/paper/2309.00583","citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:ade05da06ad0a5a33d90b64af802527d62e16562d9159162a094e36335c3265c","observation_id":"f1ad6c49-8096-4b98-a60e-b7a967e9bf94","resolution":{"observed_at":"2026-08-16T11:20:55.474625Z","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":"2026-08-16T11:20:56.405184Z","title":"E., Michelis, M","venue":null,"work_id":"a9f93f75-95c9-430f-93dd-c61a0873cd5a","year":2024},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.479887Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:631516f4db74d8100cdb46473c32c6805ce2f1bb8d3fb700847796f429525824","observation_id":"2c27759f-89b0-460c-9bad-5a7f71dce60d","resolution":{"observed_at":"2026-08-16T11:20:56.409772Z","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":"2026-08-16T11:20:56.389578Z","title":"and Hutter, F","venue":null,"work_id":"aee5bdb7-8054-4b41-bb83-6a31eb81b0a6","year":2017},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.484878Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:e6d6aabeb1f5f046ecad85d156b9f28704b4f7eb35b231e58eba458ad8835c95","observation_id":"116a5e25-d621-4d7b-8b28-f9f30f7408e3","resolution":{"observed_at":"2026-08-16T11:20:56.394829Z","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":"2026-08-16T11:20:56.374205Z","title":null,"venue":null,"work_id":"857b245d-654d-4ff1-a840-4c9433e71a55","year":2019},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.489531Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:ed8bc87e230a85bac8ce6b1187b954b048f2145d9df0a9445c56334da4294fa0","observation_id":"daca4482-539d-4dd8-962f-8c780a932218","resolution":{"observed_at":"2026-08-16T11:20:56.378710Z","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":"2026-08-16T11:20:56.358496Z","title":"A., George, R","venue":null,"work_id":"4a73ba81-8d25-4321-969d-76989d57f41d","year":2024},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.494504Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:5c9104efea23926286f4ee9e3201ab4ba2f72aeeb177ff555d1b5c08caa4c053","observation_id":"ba8864bd-df8c-4407-8ab1-cf481ea21a91","resolution":{"observed_at":"2026-08-16T11:20:56.363611Z","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":"1711.10561","last_updated":"2017-11-28T21:21:59Z","snapshot_observed_at":"2026-08-15T08:52:31.204350Z","submitted_at":"2017-11-28T21:21:59Z","title":"Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1711.10561","snapshot_observed_at":"2026-08-16T11:20:55.499295Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.499295Z"},"links":{"cited_paper":"/paper/1711.10561","citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:f9355c9afb86f7179153ff23cfe982cdcaf831b37b971740953778fda89aa3df","observation_id":"7c4f682c-6e2f-46ad-964e-81c7e35e1dcd","resolution":{"observed_at":"2026-08-16T11:20:55.499295Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:20:55.504797Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.504797Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:4d2e672847b8d84e6e38c081802fcd1c4e51f6f5c38320e32cb82d59b43b19ec","observation_id":"68e4e117-96f2-4a48-ac32-f04495fbba82","resolution":{"observed_at":"2026-08-16T11:20:55.504797Z","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":"2026-08-16T11:20:56.331408Z","title":"Challenges in training PINN s: A loss landscape perspective","venue":null,"work_id":"851ab987-c331-411c-b332-7f6b12077458","year":2024},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.509588Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:92cc613cf46fcdab8c77ad159e565d2aeb54a5dc8f778003d659c51051456bb8","observation_id":"6de97b17-d1a7-457a-89a2-fd76d132efc3","resolution":{"observed_at":"2026-08-16T11:20:56.336791Z","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":"10.1007/s10915-021-01491-2","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:20:55.643396Z","title":"Efficient spectral methods for pdes with spectral fractional laplacian","venue":null,"work_id":"1229daf4-53c1-44d5-a962-dabd9657c709","year":2021},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.514419Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:191304eedded8eaa12f3fdf9a11910382a72da60423268721960e63fc9f8a7db","observation_id":"3c42c909-0077-4588-9b80-24b7e509c74f","resolution":{"observed_at":"2026-08-16T11:20:55.649079Z","resolver_source":"doi","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:20:55.519150Z","title":"and Barbic, J","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.519150Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:9ae383219c31a949c8979b45956229a2bd25891f1878ebff779222f4d5e91bed","observation_id":"78239498-48ef-4430-8567-de94775027c2","resolution":{"observed_at":"2026-08-16T11:20:55.519150Z","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":"2026-08-16T11:20:56.314461Z","title":"Turbulence and the dynamics of coherent structures","venue":null,"work_id":"eca84bcd-1ec7-4c6b-880f-bfa3d2ebcd7d","year":1987},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.523972Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:a4c19ab5606681d80174bafae426cbf568aeeaccb8b5a391ecb9a753eb2f93d2","observation_id":"1e165b39-9536-4bc2-9aa3-c40f5db0f1e1","resolution":{"observed_at":"2026-08-16T11:20:56.320400Z","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":"2026-08-16T11:20:56.298830Z","title":"F., Bj rstad, P","venue":null,"work_id":"db9fe640-3222-4e09-a4ca-89315f0ea952","year":1996},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.528753Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:6e54205c6db0cb209716fd275f0b22a8fbc5ee534fff017c1807342d8b93e6f6","observation_id":"6d97f569-cf0a-43f4-be3c-4ffe2e59ce1e","resolution":{"observed_at":"2026-08-16T11:20:56.304142Z","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":"2026-08-16T11:20:55.533769Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.533769Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:ccf6aef4cbdbf6a6d15e917088a6a25b5d23da73ad13966fa3ef38d82d62b197","observation_id":"5df2d377-1c73-4d2f-9b0c-c879adb7d747","resolution":{"observed_at":"2026-08-16T11:20:55.533769Z","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":"2026-08-16T11:20:56.270560Z","title":"and Shakarchi, R","venue":null,"work_id":"ff4b285a-9a23-4494-9670-fd7e2e3039f9","year":2009},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.539024Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:bae8796be77b5aade5abfd4d25ea8ba9160dc90c38390ca4552ffdd60087ce77","observation_id":"d6a98eae-c26b-412b-8aa4-e94e131cfd70","resolution":{"observed_at":"2026-08-16T11:20:56.276532Z","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":"2026-08-16T11:20:56.253686Z","title":null,"venue":null,"work_id":"48898dce-5fb5-4dd3-90bb-2ebe9666b984","year":2013},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.543766Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:f62fe9faf4542436806627b5e3b72eb2f88eb9fa4b11fb06bc3c676ad30e954d","observation_id":"1d011611-348a-46a2-80d6-dec3b1a888ff","resolution":{"observed_at":"2026-08-16T11:20:56.258457Z","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":"1607.08022","last_updated":"2017-11-06T14:21:43Z","snapshot_observed_at":"2026-08-15T14:21:42.814056Z","submitted_at":"2016-07-27T10:23:00Z","title":"Instance Normalization: The Missing Ingredient for Fast Stylization","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1607.08022","snapshot_observed_at":"2026-08-16T11:20:55.548596Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.548596Z"},"links":{"cited_paper":"/paper/1607.08022","citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:a20080dec4e5ce1b5eacb764129f4379ef926b8241f2b6c417461d60ba7984b3","observation_id":"12e19bcf-7c34-4cb6-a7d0-471c3e3cc1d7","resolution":{"observed_at":"2026-08-16T11:20:55.548596Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:20:55.554119Z","title":"M., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.554119Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:050f7fc663bb0b7e264336d92c90428ca1114f65c821d64ba4feb45c8d840efd","observation_id":"0ff3d159-331b-4623-9518-07121981dc1b","resolution":{"observed_at":"2026-08-16T11:20:55.554119Z","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":"2026-08-16T11:20:56.226791Z","title":"BENO : Boundary-embedded neural operators for elliptic PDE s","venue":null,"work_id":"1141b788-c375-4c08-9521-ebae816b2d46","year":2024},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.559011Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:1e3cacc72c640c5898208c1d09a94bd02fca8f65fe3881d0f703d92168071065","observation_id":"00d41a2a-a60b-4d2d-92ba-9975dde05a88","resolution":{"observed_at":"2026-08-16T11:20:56.231953Z","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":"2026-08-16T11:20:56.210323Z","title":"and Wang, C","venue":null,"work_id":"62e637fa-8f9d-429d-849e-89787b93885e","year":2024},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.563684Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:c41f2d2265b252434ecaf0719a9d4166c86836a7b9163fd7a1dc30eed1afde90","observation_id":"dd00b684-7b0d-447e-9fd7-dbb37dce55e3","resolution":{"observed_at":"2026-08-16T11:20:56.215073Z","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":"2026-08-16T11:20:55.568364Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.568364Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:5d8a04f4fa25a69d2165fe3471eac06ab3a54fc960e0936a904c09b9602aead3","observation_id":"8fa874df-736c-4e40-a46b-e9b90f52bd09","resolution":{"observed_at":"2026-08-16T11:20:55.568364Z","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":"10.1137/141001007","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:20:55.624865Z","title":"B., Javed, M., Montanelli, H., and Trefethen, L","venue":null,"work_id":"113b64ca-5081-47e6-a9c5-5996dc3173ec","year":2015},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.573293Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:5d86397d79aeb5570cfc98ce8a1301835d070b28d19a4704e22618619b6a0917","observation_id":"5e958ee7-d348-4617-90bc-3cdfb8602432","resolution":{"observed_at":"2026-08-16T11:20:55.631936Z","resolver_source":"doi","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":"2026-08-16T11:20:56.193676Z","title":"Transolver: A fast transformer solver for PDE s on general geometries","venue":null,"work_id":"835ce0e0-3963-4c4e-a569-311e0433a608","year":2024},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.578077Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:17614293e9a1cd50dfa5a08a5e20bade6c26b2dcecdfca8a92e2e6c583b4c654","observation_id":"8488c2c9-d71d-400e-be45-5b466c24f50f","resolution":{"observed_at":"2026-08-16T11:20:56.198883Z","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":"2310.12487","last_updated":"2024-12-26T07:56:34Z","snapshot_observed_at":"2026-08-18T11:49:55.666507Z","submitted_at":"2023-10-19T05:47:28Z","title":"Improved Operator Learning by Orthogonal Attention","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2310.12487","snapshot_observed_at":"2026-08-16T11:20:55.582600Z","title":"Improved operator learning by orthogonal attention","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.582600Z"},"links":{"cited_paper":"/paper/2310.12487","citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:966cbc22346c47d2753e2828e80e4cca4ba6c445fbcd0c2a48bd7078cbe6fa0f","observation_id":"60f73612-51de-419c-a244-2c5714d210b1","resolution":{"observed_at":"2026-08-16T11:20:55.582600Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:20:55.587449Z","title":"write newline","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-16T11:20:55.587449Z"},"links":{"citing_paper":"/paper/2504.15897"},"observation_digest":"sha256:d0edf6c7ec49f26e6baa4bed6096169515d8711a866b71b225ec2a18762b100b","observation_id":"510deb16-6dc1-4592-b4b8-cbd799cc933a","resolution":{"observed_at":"2026-08-16T11:20:55.587449Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2504.15897","last_updated":"2025-04-22T13:40:04Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-18T11:50:41.320430Z","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains"},"reference_resolution":{"displayed":47,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":24,"verified_exact":2,"verified_fuzzy":20},"total_outbound_references":47},"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 47 of 47 outbound references and 0 inbound Pith citation observations for arXiv:2504.15897."}