{"as_of":"2026-08-08T03:05:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5eb06b0c68155bee79869101dba03fc7e490a6d99e6d0d63c564452a61e7a34d","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":7,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":7,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+00:00","state":"measured"},{"denominator":7,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":7,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T14:27:43.397479Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-07-02T02:16:26.938225Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2306.05697","last_updated":"2023-07-27T09:24:31Z","snapshot_observed_at":"2026-07-06T15:40:35.255445Z","submitted_at":"2023-06-09T06:34:16Z","title":"Group Equivariant Fourier Neural Operators for Partial Differential Equations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2306.05697","snapshot_observed_at":"2026-08-07T14:27:43.397479Z","title":"Group equivariant fourier neural operators for partial differential equations.arXiv preprint arXiv:2306.05697, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.18857","last_updated":"2025-05-24T20:27:16Z","snapshot_observed_at":"2026-08-07T14:22:12.717536Z","submitted_at":"2025-05-24T20:27:16Z","title":"Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T14:27:43.397479Z"},"links":{"cited_paper":"/paper/2306.05697","citing_paper":"/paper/2505.18857"},"observation_digest":"sha256:4df2e7c02064ff93a574d13abef77831ae131a63d2935da735cc790825a9afdb","observation_id":"b32cd65e-098e-460f-9ce4-e22f07b9a4b0","resolution":{"observed_at":"2026-08-07T14:27:43.397479Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2306.05697","last_updated":"2023-07-27T09:24:31Z","snapshot_observed_at":"2026-07-06T15:40:35.255445Z","submitted_at":"2023-06-09T06:34:16Z","title":"Group Equivariant Fourier Neural Operators for Partial Differential Equations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2306.05697","snapshot_observed_at":"2026-08-07T04:19:40.117818Z","title":"Group equivariant Fourier neural operators for partial differential equations","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.10973","last_updated":"2025-06-12T17:59:31Z","snapshot_observed_at":"2026-08-07T16:26:20.683246Z","submitted_at":"2025-06-12T17:59:31Z","title":"Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-07T04:19:40.117818Z"},"links":{"cited_paper":"/paper/2306.05697","citing_paper":"/paper/2506.10973"},"observation_digest":"sha256:a3dd0c9ed63ca80b99434121cdeec4e05939856aa51d5e53131aa280cb12aa1f","observation_id":"e8064189-2563-491e-ac45-4425bded670c","resolution":{"observed_at":"2026-08-07T04:19:40.117818Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2306.05697","last_updated":"2023-07-27T09:24:31Z","snapshot_observed_at":"2026-07-06T15:40:35.255445Z","submitted_at":"2023-06-09T06:34:16Z","title":"Group Equivariant Fourier Neural Operators for Partial Differential Equations","version":2},"cited_work":{"arxiv_id":"2306.05697","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2306.05697","snapshot_observed_at":"2026-07-02T02:16:26.938225Z","title":"Group equivariant fourier neural operators for partial differential equations","venue":null,"work_id":"3c1db0fb-8c20-4849-b3d4-039cfbd7aa8f","year":2023},"citing_paper":{"arxiv_id":"2605.02597","last_updated":"2026-05-04T13:47:45Z","snapshot_observed_at":"2026-07-06T23:15:37.099197Z","submitted_at":"2026-05-04T13:47:45Z","title":"Isotropic Fourier Neural Operators","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-05-08T18:28:14.933578Z"},"links":{"cited_paper":"/paper/2306.05697","citing_paper":"/paper/2605.02597"},"observation_digest":"sha256:286ab5b3bc8789680a80db2802150718b0792c81ebce83eaad3c9567630d49c1","observation_id":"ac660249-f722-4fa3-8045-911f41bdaa10","resolution":{"observed_at":"2026-05-09T06:25:46.048277Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2306.05697","last_updated":"2023-07-27T09:24:31Z","snapshot_observed_at":"2026-07-06T15:40:35.255445Z","submitted_at":"2023-06-09T06:34:16Z","title":"Group Equivariant Fourier Neural Operators for Partial Differential Equations","version":2},"cited_work":{"arxiv_id":"2306.05697","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2306.05697","snapshot_observed_at":"2026-07-02T02:16:26.938225Z","title":"Group equivariant fourier neural operators for partial differential equations","venue":null,"work_id":"3c1db0fb-8c20-4849-b3d4-039cfbd7aa8f","year":2023},"citing_paper":{"arxiv_id":"2605.04198","last_updated":"2026-05-05T18:40:59Z","snapshot_observed_at":"2026-07-06T23:16:59.568304Z","submitted_at":"2026-05-05T18:40:59Z","title":"Deep Wave Network for Modeling Multi-Scale Physical Dynamics","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-05-08T17:33:24.661591Z"},"links":{"cited_paper":"/paper/2306.05697","citing_paper":"/paper/2605.04198"},"observation_digest":"sha256:d31da160dbcc642d2fb2bb943449608becec212278cddd49c44b46cdafebe548","observation_id":"33a3cd7f-d701-4ed2-9243-9de8b3b973b2","resolution":{"observed_at":"2026-05-11T17:31:04.681435Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2306.05697","last_updated":"2023-07-27T09:24:31Z","snapshot_observed_at":"2026-07-06T15:40:35.255445Z","submitted_at":"2023-06-09T06:34:16Z","title":"Group Equivariant Fourier Neural Operators for Partial Differential Equations","version":2},"cited_work":{"arxiv_id":"2306.05697","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2306.05697","snapshot_observed_at":"2026-07-02T02:16:26.938225Z","title":"Group equivariant fourier neural operators for partial differential equations","venue":null,"work_id":"3c1db0fb-8c20-4849-b3d4-039cfbd7aa8f","year":2023},"citing_paper":{"arxiv_id":"2605.14546","last_updated":"2026-05-14T08:25:16Z","snapshot_observed_at":"2026-07-06T23:25:58.895612Z","submitted_at":"2026-05-14T08:25:16Z","title":"Discovering Physical Directions in Weight Space: Composing Neural PDE Experts","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-05-15T02:03:50.528627Z"},"links":{"cited_paper":"/paper/2306.05697","citing_paper":"/paper/2605.14546"},"observation_digest":"sha256:abd186edf3f3a5324d6d87e0559d208ed7f1ed991768272c7da2cec1d783ee9e","observation_id":"94e4369a-f819-4c0c-a47e-383c29313803","resolution":{"observed_at":"2026-05-15T02:08:29.748802Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2306.05697","last_updated":"2023-07-27T09:24:31Z","snapshot_observed_at":"2026-07-06T15:40:35.255445Z","submitted_at":"2023-06-09T06:34:16Z","title":"Group Equivariant Fourier Neural Operators for Partial Differential Equations","version":2},"cited_work":{"arxiv_id":"2306.05697","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2306.05697","snapshot_observed_at":"2026-07-02T02:16:26.938225Z","title":"Group equivariant fourier neural operators for partial differential equations","venue":null,"work_id":"3c1db0fb-8c20-4849-b3d4-039cfbd7aa8f","year":2023},"citing_paper":{"arxiv_id":"2606.03260","last_updated":"2026-06-02T07:23:06Z","snapshot_observed_at":"2026-08-03T02:25:23.001125Z","submitted_at":"2026-06-02T07:23:06Z","title":"EqGINO: Equivariant Geometry-Informed Fourier Neural Operators for 3D PDEs","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-06-28T11:03:59.241935Z"},"links":{"cited_paper":"/paper/2306.05697","citing_paper":"/paper/2606.03260"},"observation_digest":"sha256:b44cd9a999eac242d82f26bb1c9d3b7dd99352841f64807ee162a88f3589e473","observation_id":"c9445aed-78b3-4d8a-a028-4310cbabea31","resolution":{"observed_at":"2026-07-02T02:16:26.939527Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2306.05697","last_updated":"2023-07-27T09:24:31Z","snapshot_observed_at":"2026-07-06T15:40:35.255445Z","submitted_at":"2023-06-09T06:34:16Z","title":"Group Equivariant Fourier Neural Operators for Partial Differential Equations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2306.05697","snapshot_observed_at":"2026-07-31T01:28:50.569807Z","title":"Group equi- variant fourier neural operators for partial differential equations.arXiv preprint arXiv:2306.05697,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.25100","last_updated":"2026-07-27T21:58:13Z","snapshot_observed_at":"2026-08-07T08:20:14.884654Z","submitted_at":"2026-07-27T21:58:13Z","title":"Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method","version":1},"reference_index":1999,"source":"pdf_text","source_observed_at":"2026-07-31T01:28:50.569807Z"},"links":{"cited_paper":"/paper/2306.05697","citing_paper":"/paper/2607.25100"},"observation_digest":"sha256:5d3f45541bb8f9d7890049c40ccfb421e84b7ddfec2b9fc0753d9ebef2e5bed1","observation_id":"7fa3f1a2-dd12-470e-adfc-7b203a9cb2b9","resolution":{"observed_at":"2026-07-31T01:28:50.569807Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2306.05697/citation-record","integrity":"/paper/2306.05697/integrity","json":"/paper/2306.05697/citation-record.json","paper":"/paper/2306.05697"},"outbound":[],"paper":{"arxiv_id":"2306.05697","last_updated":"2023-07-27T09:24:31Z","latest_version":2,"primary_category":"cs.LG","snapshot_observed_at":"2026-07-06T15:40:35.255445Z","submitted_at":"2023-06-09T06:34:16Z","title":"Group Equivariant Fourier Neural Operators for Partial Differential Equations"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"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":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 7 inbound Pith citation observations for arXiv:2306.05697."}