{"as_of":"2026-08-10T08:00:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:1f2e5a5ac97fefea518d2d88dba376bbdc23c00589af12760ea94898ca3f55c6","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":6,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":6,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+00:00","state":"measured"},{"denominator":6,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":6,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T10:46:04.915849Z","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":"2026-06-29T23:54:03.215770Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2109.03697","last_updated":"2022-05-04T23:21:02Z","snapshot_observed_at":"2026-07-06T11:45:39.359567Z","submitted_at":"2021-09-03T17:52:25Z","title":"U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.03697","snapshot_observed_at":"2026-08-06T10:46:04.915849Z","title":"Wen , author Z","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.23662","last_updated":"2025-07-31T15:40:14Z","snapshot_observed_at":"2026-08-10T03:00:32.375289Z","submitted_at":"2025-07-31T15:40:14Z","title":"Modeling turbulent and self-gravitating fluids with Fourier neural operators","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-06T10:46:04.915849Z"},"links":{"cited_paper":"/paper/2109.03697","citing_paper":"/paper/2507.23662"},"observation_digest":"sha256:a5119e4158416302015a60fad8cd50e07080d4dd1bbd3412e477e25731afc842","observation_id":"bcc79742-18d0-4197-afff-3d6b1eb7ba9b","resolution":{"observed_at":"2026-08-06T10:46:04.915849Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03697","last_updated":"2022-05-04T23:21:02Z","snapshot_observed_at":"2026-07-06T11:45:39.359567Z","submitted_at":"2021-09-03T17:52:25Z","title":"U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow","version":3},"cited_work":{"arxiv_id":"2109.03697","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2109.03697","snapshot_observed_at":"2026-06-29T23:54:03.215770Z","title":null,"venue":null,"work_id":"41171355-4bff-4fd0-8ad4-c44dc74bb0ce","year":2022},"citing_paper":{"arxiv_id":"2604.27158","last_updated":"2026-04-29T20:04:20Z","snapshot_observed_at":"2026-08-02T10:11:32.769739Z","submitted_at":"2026-04-29T20:04:20Z","title":"Hybrid Fourier Neural Operator-Lattice Boltzmann Method","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-07T08:13:46.567661Z"},"links":{"cited_paper":"/paper/2109.03697","citing_paper":"/paper/2604.27158"},"observation_digest":"sha256:3ee524f9cba2dccaec78963b692b232176a5f726b80f698bf910d0dc90db0c74","observation_id":"70f0e934-c545-4231-bd1b-f711dc4e241f","resolution":{"observed_at":"2026-05-12T10:01:29.195366Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03697","last_updated":"2022-05-04T23:21:02Z","snapshot_observed_at":"2026-07-06T11:45:39.359567Z","submitted_at":"2021-09-03T17:52:25Z","title":"U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow","version":3},"cited_work":{"arxiv_id":"2109.03697","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2109.03697","snapshot_observed_at":"2026-06-29T23:54:03.215770Z","title":null,"venue":null,"work_id":"41171355-4bff-4fd0-8ad4-c44dc74bb0ce","year":2022},"citing_paper":{"arxiv_id":"2605.10451","last_updated":"2026-05-11T12:20:57Z","snapshot_observed_at":"2026-08-02T17:41:13.014171Z","submitted_at":"2026-05-11T12:20:57Z","title":"Don't Fix the Basis -- Learn It: Spectral Representation with Adaptive Basis Learning for PDEs","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-05-12T04:26:28.481470Z"},"links":{"cited_paper":"/paper/2109.03697","citing_paper":"/paper/2605.10451"},"observation_digest":"sha256:14c9311f99c2e8a175f08035c35eb1176980fac43b89031cbefc28e978395ecb","observation_id":"ada86a5e-43f2-4ec6-8a49-5405bc45e67c","resolution":{"observed_at":"2026-05-12T06:16:27.728951Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03697","last_updated":"2022-05-04T23:21:02Z","snapshot_observed_at":"2026-07-06T11:45:39.359567Z","submitted_at":"2021-09-03T17:52:25Z","title":"U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow","version":3},"cited_work":{"arxiv_id":"2109.03697","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2109.03697","snapshot_observed_at":"2026-06-29T23:54:03.215770Z","title":null,"venue":null,"work_id":"41171355-4bff-4fd0-8ad4-c44dc74bb0ce","year":2022},"citing_paper":{"arxiv_id":"2605.24876","last_updated":"2026-05-24T05:37:11Z","snapshot_observed_at":"2026-08-06T04:35:55.990288Z","submitted_at":"2026-05-24T05:37:11Z","title":"IV-Net: A neural network for elliptic PDEs with random and highly varying coefficients","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-06-29T23:53:30.631124Z"},"links":{"cited_paper":"/paper/2109.03697","citing_paper":"/paper/2605.24876"},"observation_digest":"sha256:3aa6165ccbed85f0680a62871e8e2bd69858695560dc736dceabee0c51e877cb","observation_id":"55562982-1c32-4959-b211-335e99b335ec","resolution":{"observed_at":"2026-06-29T23:54:03.217203Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03697","last_updated":"2022-05-04T23:21:02Z","snapshot_observed_at":"2026-07-06T11:45:39.359567Z","submitted_at":"2021-09-03T17:52:25Z","title":"U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.03697","snapshot_observed_at":"2026-07-11T19:51:56.544026Z","title":"arXiv , author =","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.06587","last_updated":"2026-07-05T15:21:12Z","snapshot_observed_at":"2026-08-08T18:54:56.054217Z","submitted_at":"2026-07-05T15:21:12Z","title":"CoFINN: Conservation Flux Informed Neural Networks for Physics Problems Governed by Conservation Laws","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-07-11T19:51:56.544026Z"},"links":{"cited_paper":"/paper/2109.03697","citing_paper":"/paper/2607.06587"},"observation_digest":"sha256:ce52eb3e25ccbc86bd33eb0c7b59f4bba85f644e1239d7672c10217c20217e30","observation_id":"4343f9c8-74bd-4ba8-a181-1fcd4c6edda8","resolution":{"observed_at":"2026-07-11T19:51:56.544026Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2109.03697","last_updated":"2022-05-04T23:21:02Z","snapshot_observed_at":"2026-07-06T11:45:39.359567Z","submitted_at":"2021-09-03T17:52:25Z","title":"U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.03697","snapshot_observed_at":"2026-08-02T02:17:07.946065Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.14394","last_updated":"2026-07-15T22:17:25Z","snapshot_observed_at":"2026-08-09T11:02:52.638150Z","submitted_at":"2026-07-15T22:17:25Z","title":"DRIFT: Direct Reduced Fourier Transforms for Distributed Spectral Neural Operators","version":1},"reference_index":2022,"source":"pdf_text","source_observed_at":"2026-08-02T02:17:07.946065Z"},"links":{"cited_paper":"/paper/2109.03697","citing_paper":"/paper/2607.14394"},"observation_digest":"sha256:2b815a4d59c784f4e1583f1aa36a02f36fb4feb09c5de8115acc6b3fb498e7f9","observation_id":"3bde103f-08e6-40a0-a81d-82a25365a0f0","resolution":{"observed_at":"2026-08-02T02:17:07.946065Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2109.03697/citation-record","integrity":"/paper/2109.03697/integrity","json":"/paper/2109.03697/citation-record.json","paper":"/paper/2109.03697"},"outbound":[],"paper":{"arxiv_id":"2109.03697","last_updated":"2022-05-04T23:21:02Z","latest_version":3,"primary_category":"physics.geo-ph","snapshot_observed_at":"2026-07-06T11:45:39.359567Z","submitted_at":"2021-09-03T17:52:25Z","title":"U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow"},"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":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 6 inbound Pith citation observations for arXiv:2109.03697."}