{"as_of":"2026-08-08T18:56:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c49137c1a7d4115fef78f03b2936958dbb852b90ae35261949e34784ed3cdbba","coverage":[{"denominator":48,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":48,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T15:38:33.034749Z","state":"measured"},{"denominator":53,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":53,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":5,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":5,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-22T07:32:11.942427Z","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":"2026-05-22T07:34:42.670311Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"cited_work":{"arxiv_id":"2507.15409","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.15409","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Pdeformer-2: A versatile foundation model for two- dimensional partial differential equations","venue":null,"work_id":"fbb69a2d-bf7d-4092-b229-692353be42f8","year":2025},"citing_paper":{"arxiv_id":"2509.00867","last_updated":"2026-05-15T10:46:55Z","snapshot_observed_at":"2026-08-02T10:00:26.415365Z","submitted_at":"2025-08-31T14:24:23Z","title":"Self-supervised neural operator for solving partial differential equations","version":3},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-05-21T22:08:10.516224Z"},"links":{"cited_paper":"/paper/2507.15409","citing_paper":"/paper/2509.00867"},"observation_digest":"sha256:e5f7dc0139df7c212167e1e6b13d4099df77a89499d00f192ff58b927c7c7a43","observation_id":"3b60c3ea-dc7c-42fc-89a5-dbaa825d0de9","resolution":{"observed_at":"2026-05-21T22:10:42.351001Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"cited_work":{"arxiv_id":"2507.15409","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.15409","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Pdeformer-2: A versatile foundation model for two- dimensional partial differential equations","venue":null,"work_id":"fbb69a2d-bf7d-4092-b229-692353be42f8","year":2025},"citing_paper":{"arxiv_id":"2604.00333","last_updated":"2026-04-06T23:06:42Z","snapshot_observed_at":"2026-08-04T01:50:45.202906Z","submitted_at":"2026-04-01T00:11:47Z","title":"MVNN: A Measure-Valued Neural Network for Learning McKean-Vlasov Dynamics from Particle Data","version":2},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-05-13T22:45:53.377753Z"},"links":{"cited_paper":"/paper/2507.15409","citing_paper":"/paper/2604.00333"},"observation_digest":"sha256:95ca73b45621a865c3ef070ff387c93fdf02ae680743bfe72d664608d56f34cc","observation_id":"aaf1a791-b4b6-48c0-876d-e03b30b2fe60","resolution":{"observed_at":"2026-05-13T22:48:23.056937Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"cited_work":{"arxiv_id":"2507.15409","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.15409","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Pdeformer-2: A versatile foundation model for two- dimensional partial differential equations","venue":null,"work_id":"fbb69a2d-bf7d-4092-b229-692353be42f8","year":2025},"citing_paper":{"arxiv_id":"2605.10159","last_updated":"2026-05-11T08:05:54Z","snapshot_observed_at":"2026-08-06T22:49:59.052985Z","submitted_at":"2026-05-11T08:05:54Z","title":"jNO: A JAX Library for Neural Operator and Foundation Model Training","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-12T03:08:15.825182Z"},"links":{"cited_paper":"/paper/2507.15409","citing_paper":"/paper/2605.10159"},"observation_digest":"sha256:2d7ed642dfd2988c6d025041a569b4d00e1d20bf77dd512ef471a777afabb18e","observation_id":"7c78fc8c-6f05-4f0e-9c2c-8736042fcc76","resolution":{"observed_at":"2026-05-12T03:11:19.405443Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"cited_work":{"arxiv_id":"2507.15409","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.15409","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Pdeformer-2: A versatile foundation model for two- dimensional partial differential equations","venue":null,"work_id":"fbb69a2d-bf7d-4092-b229-692353be42f8","year":2025},"citing_paper":{"arxiv_id":"2605.15284","last_updated":"2026-05-14T18:00:58Z","snapshot_observed_at":"2026-08-02T11:48:08.944568Z","submitted_at":"2026-05-14T18:00:58Z","title":"Tadpole: Autoencoders as Foundation Models for 3D PDEs with Online Learning","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-19T16:41:24.644385Z"},"links":{"cited_paper":"/paper/2507.15409","citing_paper":"/paper/2605.15284"},"observation_digest":"sha256:99824c352e47005ea4275dca1302f6141485fd0f159cbf791f263a8fbd9371f7","observation_id":"db6d685f-a88d-43c0-8464-2437f03ad671","resolution":{"observed_at":"2026-05-19T16:42:39.702380Z","resolver_source":"arxiv_id","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"cited_work":{"arxiv_id":"2507.15409","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.15409","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Pdeformer-2: A versatile foundation model for two- dimensional partial differential equations","venue":null,"work_id":"fbb69a2d-bf7d-4092-b229-692353be42f8","year":2025},"citing_paper":{"arxiv_id":"2605.22724","last_updated":"2026-05-21T16:57:33Z","snapshot_observed_at":"2026-08-02T10:11:30.865561Z","submitted_at":"2026-05-21T16:57:33Z","title":"Multiple Neural Operators Achieve Near-Optimal Rates for Multi-Task Learning","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-05-22T07:32:11.942427Z"},"links":{"cited_paper":"/paper/2507.15409","citing_paper":"/paper/2605.22724"},"observation_digest":"sha256:db2429c1e8b8468d36ce6d2ba0a694197c6dcd49c09d9a2295c6b60dadfe5c7b","observation_id":"28c3b99f-6d40-44ed-86f2-64cc526fe7bf","resolution":{"observed_at":"2026-05-22T07:34:42.673068Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2507.15409/citation-record","integrity":"/paper/2507.15409/integrity","json":"/paper/2507.15409/citation-record.json","paper":"/paper/2507.15409"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:38:27.998798Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:27.998798Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:77ff6b57781c8d165893af022f3f7ea6949482f761e12c20c0412f1fe007236d","observation_id":"847e3e4d-0384-43c4-8ef0-f7a0a7747a69","resolution":{"observed_at":"2026-08-06T15:38:27.998798Z","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":"2026-08-06T15:38:39.908932Z","title":null,"venue":null,"work_id":"68f8e64f-3a51-44cc-9e46-c67926996e89","year":2021},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:28.253197Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:b302b7e9864fc4ae27e1a221cac0f63f3eda4e33c01c5caca43a96f80139acbb","observation_id":"2f69a4f5-23f4-453a-95a9-5ec1179aafc5","resolution":{"observed_at":"2026-08-06T15:38:39.985884Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T15:38:39.778339Z","title":"Nature Machine Intelligence3(3), 218–229 (2021) https://doi.org/10.1038/ s42256-021-00302-5","venue":null,"work_id":"8834d709-52d2-4082-abfa-113d6dfd4a5f","year":2021},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:28.407685Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:1a0e690f99dcce30259849f18e7a2d579305bfdf14d22c8f3d9317103611e24d","observation_id":"1f64720e-6643-4e6e-a781-63ec7c36ad92","resolution":{"observed_at":"2026-08-06T15:38:39.861436Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T15:38:39.611704Z","title":null,"venue":null,"work_id":"9a28706e-2cab-4ac1-ab4e-6eb1835f37e9","year":2023},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:28.554746Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:5ba038796c2e590a6deeab68c058e3ec3f37698a9dd87af74316a3fe89adcfd7","observation_id":"80ad6b96-0bdd-4f5c-a41e-c0eaf90186ff","resolution":{"observed_at":"2026-08-06T15:38:39.684148Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T15:38:39.440821Z","title":null,"venue":null,"work_id":"b2e4a978-ca32-4fdc-9e53-4ee3b33e9d95","year":2024},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:28.641636Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:57fefda955c8f257d9b55ef19214c466e73468a9f7d84e2a288665ec03ff138b","observation_id":"644f9756-fe1b-4eda-916f-3579ea5ae2b2","resolution":{"observed_at":"2026-08-06T15:38:39.530551Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.17527","last_updated":"2025-09-04T14:38:34Z","snapshot_observed_at":"2026-07-06T18:20:48.343830Z","submitted_at":"2024-05-27T15:34:35Z","title":"Unisolver: PDE-Conditional Transformers Towards Universal Neural PDE Solvers","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.17527","snapshot_observed_at":"2026-08-06T15:38:28.758931Z","title":"CoRRabs/2405.17527(2024)","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:28.758931Z"},"links":{"cited_paper":"/paper/2405.17527","citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:5a83c19bdf1f81ad5c1d888e448826d12f6153b1af917feeb8ff1c695c8f99e2","observation_id":"8709ba4d-202b-46b8-a303-e15a5489ea02","resolution":{"observed_at":"2026-08-06T15:38:28.758931Z","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":"2026-08-06T15:38:39.312804Z","title":"Transactions on Machine Learning 26 Research (2024)","venue":null,"work_id":"ac54a234-7f4d-486e-98f1-ae45d793a71f","year":2024},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:28.842565Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:6e1a71b95863d4d6acb7684651218fc71375d4e527adf67c1a74501b7473408b","observation_id":"f8701d8c-e09b-49e8-821e-07d11db04e85","resolution":{"observed_at":"2026-08-06T15:38:39.390885Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.06026","last_updated":"2025-02-09T20:50:28Z","snapshot_observed_at":"2026-08-08T16:57:04.034225Z","submitted_at":"2025-02-09T20:50:28Z","title":"A Multimodal PDE Foundation Model for Prediction and Scientific Text Descriptions","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.06026","snapshot_observed_at":"2026-08-06T15:38:28.954297Z","title":"arXiv preprint arXiv:2502.06026 (2025)","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:28.954297Z"},"links":{"cited_paper":"/paper/2502.06026","citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:14de618784a09cd223dccca0ea13659d42e1220f9b3223f9394c6933be547f80","observation_id":"e33942ed-01d7-43f8-a7e5-afbe7f6e5d3c","resolution":{"observed_at":"2026-08-06T15:38:28.954297Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.01137","last_updated":"2025-02-21T21:42:35Z","snapshot_observed_at":"2026-08-07T14:58:34.922672Z","submitted_at":"2024-10-02T00:19:20Z","title":"Explain Like I'm Five: Using LLMs to Improve PDE Surrogate Models with Text","version":5},"cited_work":{"arxiv_id":"2410.01137","doi":null,"metadata_source":"pith","pith_arxiv_id":"2410.01137","snapshot_observed_at":"2026-08-06T15:38:34.510077Z","title":"Explain Like I'm Five: Using LLMs to Improve PDE Surrogate Models with Text","venue":"cs.LG","work_id":"e4321919-e975-4739-bc5f-b1134e7afa15","year":2024},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:29.087235Z"},"links":{"cited_paper":"/paper/2410.01137","citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:f5d41ce6e966b3a306d2ab1f10b9141f2089d93a8cf7faba7e066e02e56f6a87","observation_id":"9244c1b4-1edb-4530-b1eb-a316dc336c95","resolution":{"observed_at":"2026-08-06T15:38:34.552707Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T15:38:39.106601Z","title":null,"venue":null,"work_id":"a2cec5a9-5727-4f02-846e-b52a00f923ff","year":2023},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:29.180411Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:9d2359a2eaacbd81f3555bf46703469809e62169b0d3684b7fa783104534c9c5","observation_id":"2c7198bc-b5bc-493a-b956-703d7c00565a","resolution":{"observed_at":"2026-08-06T15:38:39.237446Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T15:38:38.905893Z","title":"Physical Review E111(3), 035304 (2025)","venue":null,"work_id":"808773a3-32ae-4b0e-9431-04f5f6fa56f8","year":2025},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:29.264863Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:9be37a405668561a77298b5dd37fa1fa26fb5606b36a3e18442acbeee7c0091f","observation_id":"9a74aff6-5fca-4717-85da-bbb5e7589482","resolution":{"observed_at":"2026-08-06T15:38:39.003405Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2408.16168","last_updated":"2025-06-12T20:31:59Z","snapshot_observed_at":"2026-08-06T17:19:08.115509Z","submitted_at":"2024-08-28T23:20:03Z","title":"LeMON: Learning to Learn Multi-Operator Networks","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2408.16168","snapshot_observed_at":"2026-08-06T15:38:29.377486Z","title":"arXiv preprint arXiv:2408.16168 (2024)","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:29.377486Z"},"links":{"cited_paper":"/paper/2408.16168","citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:f5b5fdea629fe5feee09243378906bc415dd54784fb9f8e56841a08dd4bb9c32","observation_id":"02dd2bb6-5324-4e0d-ad5d-321c7eda74bf","resolution":{"observed_at":"2026-08-06T15:38:29.377486Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2409.09811","last_updated":"2024-09-15T18:20:15Z","snapshot_observed_at":"2026-07-06T19:15:43.173430Z","submitted_at":"2024-09-15T18:20:15Z","title":"PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.09811","snapshot_observed_at":"2026-08-06T15:38:29.575921Z","title":"arXiv preprint arXiv:2409.09811 (2024)","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:29.575921Z"},"links":{"cited_paper":"/paper/2409.09811","citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:c07d72c85dad58e57dac3bf766743eee9fcfca58ee668740e5c3474af6e600e2","observation_id":"5a1df786-3914-4563-bb75-fc0103931644","resolution":{"observed_at":"2026-08-06T15:38:29.575921Z","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":"2026-08-06T15:38:38.755045Z","title":"Proceedings of the National Academy of Sciences120(39), 2310142120 (2023)","venue":null,"work_id":"1391e966-a412-46dd-a546-7b46b9eeeeae","year":2023},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:29.653757Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:912b43232412711a752f8ab15db716c4871fc3d94bc151bed7e33a019f0abb28","observation_id":"7434b054-f141-4e6b-9f91-e6bfa1df8e7c","resolution":{"observed_at":"2026-08-06T15:38:38.826809Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2024.11337","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:38:34.313503Z","title":"Journal of Computational Physics519, 113379 (2024) https://doi.org/10.1016/j.jcp.2024.113379","venue":null,"work_id":"61afc6ef-5f41-44dc-bac5-7fd949227778","year":2024},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:29.787555Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:f6a93b76ee11bd5b02f24afdfa893d0a4a42c8ad1b4f33743f0dca7722c59c3f","observation_id":"5aac4e2e-6468-4120-9e85-bab93b5a5654","resolution":{"observed_at":"2026-08-06T15:38:34.400313Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T15:38:29.887878Z","title":"https://arxiv.org/abs/2411.16063","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:29.887878Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:8993b5f8c1180fdef38dac7e737887125d98aa4f88b5e594c686a45fa1bba607","observation_id":"2df9fac9-57e4-4442-8827-6d24506dd9e8","resolution":{"observed_at":"2026-08-06T15:38:29.887878Z","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":"2026-08-06T15:38:38.544086Z","title":null,"venue":null,"work_id":"6359dbd0-f63c-4fc0-96b1-d9bfb0cbf675","year":2023},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:30.015833Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:39f2e8a14728a2ed190e728dc41090757ac02572aa00f28f07de8d385d4e9c1f","observation_id":"a8917ab3-f853-4464-aef6-3756c65c9b22","resolution":{"observed_at":"2026-08-06T15:38:38.668108Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T15:38:38.357522Z","title":"In: Salakhutdinov, R., Kolter, Z., Heller, K., Weller, A., Oliver, N., Scarlett, J., Berkenkamp, F","venue":null,"work_id":"eb872485-5703-4f47-8655-8c3183efa620","year":2024},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:30.089042Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:8a37d36493d94280437e1fe1e9be59dbd8572b63f6e190ad6015e8e1f4e39cd2","observation_id":"843566d4-4122-46cb-a941-ffc7a5e93ca8","resolution":{"observed_at":"2026-08-06T15:38:38.487758Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.16014","last_updated":"2025-05-29T06:25:04Z","snapshot_observed_at":"2026-07-31T09:33:18.309545Z","submitted_at":"2024-02-25T07:19:01Z","title":"OmniArch: Building Foundation Model For Scientific Computing","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.16014","snapshot_observed_at":"2026-08-06T15:38:30.174457Z","title":"CoRRabs/2402.16014 (2024)","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:30.174457Z"},"links":{"cited_paper":"/paper/2402.16014","citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:00a6c92f0ebd3c191e92e9e91449c7e2910b6de1c127b21ba28e664c4a0ab76a","observation_id":"b3b2b716-2411-47d2-8a64-f45b8863be32","resolution":{"observed_at":"2026-08-06T15:38:30.174457Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.18972","last_updated":"2025-04-30T03:02:41Z","snapshot_observed_at":"2026-07-06T20:28:52.880548Z","submitted_at":"2025-01-31T09:07:56Z","title":"BCAT: A Block Causal Transformer for PDE Foundation Models for Fluid Dynamics","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.18972","snapshot_observed_at":"2026-08-06T15:38:30.253398Z","title":"arXiv preprint arXiv:2501.18972 (2025)","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:30.253398Z"},"links":{"cited_paper":"/paper/2501.18972","citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:c75ce02eb391d0eb7f7a6d74e65b87de1bd9d685109c9a1b29fe4258ef3c55a2","observation_id":"bdf2cbbf-c642-4836-808a-68ecc2caf6b7","resolution":{"observed_at":"2026-08-06T15:38:30.253398Z","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":"2026-08-06T15:38:38.215429Z","title":"Advances in Neural Information Processing Systems36, 71242–71262 (2023)","venue":null,"work_id":"3aceb06e-2a52-4df0-a2b4-0841656c41c0","year":2023},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:30.330090Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:b10fc6dbe8d02517ced106e2e527b25092ea08f2a01278ac5fb2982c7d8c280b","observation_id":"0d7b9860-e248-47ad-b6af-0aec2db49238","resolution":{"observed_at":"2026-08-06T15:38:38.276449Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T15:38:38.056049Z","title":"Advances in Neural Information Processing Systems37, 104035–104064 (2024)","venue":null,"work_id":"830f5774-45db-43f1-b0d0-dc29643c0913","year":2024},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:30.410383Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:824634a12b239f642e4ef92356af1af21738780cbcb77ca5703fd5f1555d13be","observation_id":"9939dd1e-4efb-4750-9c9e-beb782e5451c","resolution":{"observed_at":"2026-08-06T15:38:38.129608Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T15:38:37.922343Z","title":"In: Advances in Neural Information Processing Systems, vol","venue":null,"work_id":"53a2791f-f485-45a3-925f-a0e1825d1fa8","year":2024},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:30.492552Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:677ec372e6d6d92317e3c6ee605f260510a55fd7248862c3864e88ff70f604e4","observation_id":"c1156a1e-a66f-48ba-9483-c9931896c197","resolution":{"observed_at":"2026-08-06T15:38:37.981565Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.06664","last_updated":"2025-01-27T12:18:51Z","snapshot_observed_at":"2026-08-05T15:39:45.754412Z","submitted_at":"2024-07-09T08:41:13Z","title":"PDEformer-1: A Foundation Model for One-Dimensional Partial Differential Equations","version":2},"cited_work":{"arxiv_id":"2407.06664","doi":null,"metadata_source":"pith","pith_arxiv_id":"2407.06664","snapshot_observed_at":"2026-08-06T15:38:34.018179Z","title":"PDEformer-1: A Foundation Model for One-Dimensional Partial Differential Equations","venue":"math.NA","work_id":"397614ab-2fc9-4a74-8f49-9c0f8fead959","year":2024},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:30.605354Z"},"links":{"cited_paper":"/paper/2407.06664","citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:f5104332ca7b758bb43c1ed23e0a6cbcaa179f2cd8a5a1495914ca261061fb71","observation_id":"11a03e85-e2fb-49b6-914e-0a87a75a8371","resolution":{"observed_at":"2026-08-06T15:38:34.092759Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1905.10388","last_updated":"2019-12-02T19:00:08Z","snapshot_observed_at":"2026-07-06T07:55:20.243031Z","submitted_at":"2019-05-24T18:01:01Z","title":"Dedalus: A Flexible Framework for Numerical Simulations with Spectral Methods","version":2},"cited_work":{"arxiv_id":"1905.10388","doi":null,"metadata_source":"pith","pith_arxiv_id":"1905.10388","snapshot_observed_at":"2026-08-06T15:38:33.845530Z","title":"Dedalus: A Flexible Framework for Numerical Simulations with Spectral Methods","venue":"astro-ph.IM","work_id":"1d77d333-2bd4-473a-8994-b19e04bed903","year":2019},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:30.709334Z"},"links":{"cited_paper":"/paper/1905.10388","citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:86bbf8b5d9a68a7297de88bd337e4e6f01b323c68a6ffc2e51002bc72dd5ccca","observation_id":"5fc7288c-b8bf-42e2-9b8d-66174cd9ca8b","resolution":{"observed_at":"2026-08-06T15:38:33.897176Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T15:38:30.786287Z","title":"preprint (2023)","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:30.786287Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:efddc974a77c5d78141e3ab46397191d37af6a3cad2f7ea9cb9103eafde7b2fc","observation_id":"72f40a45-71e4-4205-833b-ead29a223937","resolution":{"observed_at":"2026-08-06T15:38:30.786287Z","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":"2026-08-06T15:38:30.865163Z","title":"In: Medical Image Computing and Computer-Assisted Intervention–MICCAI 2015: 18th International Conference, Munich, Germany, October 5-9, 2015, Proceedings, Part III 18, pp","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:30.865163Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:ec6ad1d1993d038d67e78e49f3ca78994751624a9caaf72f85407dbfae6f93cb","observation_id":"0c91efa6-49f0-4c66-b105-a95f0541ad47","resolution":{"observed_at":"2026-08-06T15:38:30.865163Z","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":"2026-08-06T15:38:37.703936Z","title":"Journal of Machine Learning Research24(388), 1–26 (2023)","venue":null,"work_id":"579e7bb7-dce7-4774-aecd-729b6c9300f6","year":2023},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:30.901545Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:4cd3502f609be46f9984e80c538a5e368770819816a2d96ddd11865e8f7521e1","observation_id":"e7b6347c-e1d3-4ede-956a-ccff45935122","resolution":{"observed_at":"2026-08-06T15:38:37.810057Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T15:38:31.057031Z","title":"arXiv preprint arXiv:2501.19205 (2025)","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:31.057031Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:46f2b9dda1b2613603ac592af620d53473be665efd08164565ae9a15ee098896","observation_id":"0183a6a5-4991-4134-8da1-4cf970f25567","resolution":{"observed_at":"2026-08-06T15:38:31.057031Z","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":"2026-08-06T15:38:31.167063Z","title":"In: Proceed- ings of ICNN’95 - International Conference on Neural Networks, vol","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:31.167063Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:d67583f06c4b31ca5aa5a06be105b93a031c3386e4db0e85684d75a57a72df89","observation_id":"9b30e30e-27c2-45de-ba26-f1189c9a032d","resolution":{"observed_at":"2026-08-06T15:38:31.167063Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1412.6980","last_updated":"2017-01-30T01:27:54Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2014-12-22T13:54:29Z","title":"Adam: A Method for Stochastic Optimization","version":9},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1412.6980","snapshot_observed_at":"2026-08-06T15:38:31.283879Z","title":"arXiv preprint arXiv:1412.6980 (2014)","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:31.283879Z"},"links":{"cited_paper":"/paper/1412.6980","citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:40f92dc3e759c5832a0fcee6b19906d4cf6c0861f104e9320e797c2771f0f556","observation_id":"ff2b8337-ecd7-4c1b-80ca-1a156f7f18fc","resolution":{"observed_at":"2026-08-06T15:38:31.283879Z","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":"2026-08-06T15:38:37.548389Z","title":null,"venue":null,"work_id":"2bb8bf49-d11f-4401-884e-bf9820dd32a1","year":2021},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:31.426009Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:cc1d036c5849312baaef2e5147717c48e883a5b5fd356cb644270a17b7004a64","observation_id":"e2ab798c-5ae4-46aa-9a8c-7086ca03b0ac","resolution":{"observed_at":"2026-08-06T15:38:37.617502Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T15:38:37.350965Z","title":"In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp","venue":null,"work_id":"6d6a77e3-995f-450d-bf16-0451bc9acd32","year":2023},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:31.613075Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:b4c219dd5dc273aadf8ec3820cf1eec605c2efd41b3bb239486d180d1632c1a5","observation_id":"9c110dd6-e0f3-456f-9809-8389418893a2","resolution":{"observed_at":"2026-08-06T15:38:37.431466Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T15:38:31.711933Z","title":"In: 2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:31.711933Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:2b6b5e699f68807a434d63e9360ec65d7993dfd54743c6b2aef4943123d6afa9","observation_id":"dc52d176-553b-4c5e-b37a-fb254a1f5cb0","resolution":{"observed_at":"2026-08-06T15:38:31.711933Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-06T15:38:31.808206Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:31.808206Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:e56fa13d6c6fd66b378b1463d137264026084e9dc3e03ded9df412c14ea75468","observation_id":"f90c9a32-7199-420e-b794-e03e4ec2cb45","resolution":{"observed_at":"2026-08-06T15:38:31.808206Z","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":"2026-08-06T15:38:37.176198Z","title":null,"venue":null,"work_id":"7a042b06-9b20-4a04-96de-f6d5eeffdfdd","year":null},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:31.885697Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:1d8d6701a5e8df566cc9e2fad1ea5f50d1e835e006eeb4780f7abf5354c9935a","observation_id":"45df7769-8db3-4e2a-909b-bc4180b2fd5b","resolution":{"observed_at":"2026-08-06T15:38:37.240218Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T15:38:36.985533Z","title":null,"venue":null,"work_id":"13347514-4ae4-48c4-bd6a-49bdb9bf9408","year":null},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:32.010049Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:7329b291f220107785b4ae7937e44b8a2ce2dae5fef593d8dcd8161799962cfa","observation_id":"e40af7d0-39ef-4cab-ad11-d98408708155","resolution":{"observed_at":"2026-08-06T15:38:37.096561Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T15:38:36.806567Z","title":null,"venue":null,"work_id":"a2a7cd55-67e8-40c4-ba9d-40814267fb6e","year":null},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:32.095836Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:511fa3ec8fd2b7742f2ca8aa56451beba88cfda8d85471e0f79bf6d607c24974","observation_id":"5620c8b9-d06b-4c2e-8cff-7465cfdf88b7","resolution":{"observed_at":"2026-08-06T15:38:36.888622Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T15:38:36.611887Z","title":null,"venue":null,"work_id":"322b2b95-75c7-4a3f-9e8a-d2806859ce47","year":null},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:32.204380Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:0b564cce8e361be8e78aae2c62a5490256e145224121d872e3345bbd3fa51fa6","observation_id":"73e51f65-38b0-43e8-a033-3098c018856e","resolution":{"observed_at":"2026-08-06T15:38:36.699348Z","resolver_source":"raw_fallback","status":"parse_uncertain"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T15:38:36.430127Z","title":null,"venue":null,"work_id":"23fc351c-6334-4e84-9dde-ec2a4910e988","year":null},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:32.283796Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:3805f56d49054e9c4b4d9343e2b570163d40287e5342f4712841f6cc908702ff","observation_id":"d43a40a2-80f9-416e-880f-b63bb78e3206","resolution":{"observed_at":"2026-08-06T15:38:36.514027Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T15:38:36.243717Z","title":null,"venue":null,"work_id":"61f70503-5aee-4120-b216-fa21e4f9a781","year":null},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:32.337674Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:84fe549fcae5c2c879b192f777884f4f20fb7bd86200553e7d025e1698c121e0","observation_id":"2fef922b-8b40-40ee-902b-2073213e9c37","resolution":{"observed_at":"2026-08-06T15:38:36.348714Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T15:38:35.990827Z","title":"DeepONet (MLP)","venue":null,"work_id":"4b065da0-1f2e-4003-84bf-74f2b8ee0ee7","year":null},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:32.416942Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:f2289a3db5408553e633a1202c0c28a4819d3b08dcc3e437d0ad9a7bd86002b6","observation_id":"7764352d-06f3-4124-af19-ac27a26fd405","resolution":{"observed_at":"2026-08-06T15:38:36.126062Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T15:38:35.705037Z","title":null,"venue":null,"work_id":"117770c8-69a7-4b9f-a86f-8c757d28a57e","year":null},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:32.583191Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:8bef06c624e8a2d9373f4879ff139c5db744783c827b3d465ae46045f7c3ebdd","observation_id":"f9719195-f2a8-4d6c-9ef6-81e992b2d3c3","resolution":{"observed_at":"2026-08-06T15:38:35.845181Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"0000.0001","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:38:33.300666Z","title":null,"venue":null,"work_id":"5a1c71c3-8d05-454a-b48e-97b0d6a01227","year":null},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:32.683116Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:dae0028b473adb9ef7279e5ead4ea358f17a976f49374e2e34192e3e52957b3b","observation_id":"9bb625ba-24e0-4f3d-9e55-0caec5bb6e0e","resolution":{"observed_at":"2026-08-06T15:38:33.395418Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T15:38:35.494519Z","title":null,"venue":null,"work_id":"1a7944c8-044a-4473-bb16-40b9c0f46641","year":null},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:32.765293Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:f1ee0d6d8aa3625fa3d3997b679e0d82ce4e28acc909e68edc0af51093e155f3","observation_id":"f29d10ac-bde5-4a39-9757-244cd36b03d2","resolution":{"observed_at":"2026-08-06T15:38:35.581758Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T15:38:35.204961Z","title":"39: Visualization of the divergence-constrained DCR equation on a square domain periodic along both axes and initial conditions violating the divergence constraint","venue":null,"work_id":"1bebca60-e9ee-4f20-a6bb-9c8af62ae5c0","year":null},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:32.867066Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:f487014fe37ea7ad461667980955cd3d645b10e07a96f2377dddf114a18d2fdb","observation_id":"28ead5e2-dad6-4396-9acc-e5041683f7cb","resolution":{"observed_at":"2026-08-06T15:38:35.352881Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T15:38:34.948776Z","title":null,"venue":null,"work_id":"68c69658-94a6-4611-b529-d8d3f7b656ae","year":null},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:32.950871Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:d223dd16df491f582dbd6e68bb11652bc5936d449692ffa8f6cf1af5f417447e","observation_id":"31175195-53b5-4c6f-be6c-45c0aba828fb","resolution":{"observed_at":"2026-08-06T15:38:35.063086Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T15:38:34.696331Z","title":"41: Visualization of the divergence-constrained wave equation on a square domain periodic along both axes and initial conditions satisfying the divergence constraint","venue":null,"work_id":"cb589d06-c2ba-49ed-9df9-fed474685555","year":null},"citing_paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-06T15:38:33.034749Z"},"links":{"citing_paper":"/paper/2507.15409"},"observation_digest":"sha256:2eebe32b8ad5a59727d392d89e17aadd62f1df98f3bdbe3ebd393e39e401f9fc","observation_id":"5ca67765-be73-496e-a436-9305bf47956b","resolution":{"observed_at":"2026-08-06T15:38:34.810721Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.15409","last_updated":"2025-08-13T13:21:08Z","latest_version":2,"primary_category":"math.NA","snapshot_observed_at":"2026-08-06T15:30:21.069577Z","submitted_at":"2025-07-21T09:08:48Z","title":"PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations"},"reference_resolution":{"displayed":48,"state_counts":{"malformed_identifier":2,"metadata_mismatch":4,"parse_uncertain":1,"unresolved":28,"verified_exact":1,"verified_fuzzy":12},"total_outbound_references":48},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 48 of 48 outbound references and 5 inbound Pith citation observations for arXiv:2507.15409."}