{"as_of":"2026-08-10T02:54:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c333340c5aa0e528176e88e5793426faa2f887f246e300cd989fe1c3e1d95d4e","coverage":[{"denominator":45,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":45,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T20:18:51.054789Z","state":"measured"},{"denominator":45,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":45,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2507.03272/citation-record","integrity":"/paper/2507.03272/integrity","json":"/paper/2507.03272/citation-record.json","paper":"/paper/2507.03272"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00521-020-05543-w","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T00:03:40.895421Z","title":"Kiranyaz, J","venue":"Neural Computing and Applications","work_id":"4a6b159b-d04a-47ab-bdd2-229f7d65295c","year":2021},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:44.713332Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:a651fe71bc3289534ab0144a812966a6c9e80541934da96f4fb3681d48065ced","observation_id":"fb65415b-9bf6-4f44-95da-5a624720d1f2","resolution":{"observed_at":"2026-08-06T20:18:52.692604Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T20:18:44.838617Z","title":"doi:10.1126/sciadv.abd7416","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:44.838617Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:1d031078b95396abd755946a4037deb954ed560b6604c7e46b739c2c9f6a6c11","observation_id":"ead7dd9d-2bea-43e2-936d-744f8813eae6","resolution":{"observed_at":"2026-08-06T20:18:44.838617Z","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":"2021.30893","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:18:54.152745Z","title":null,"venue":null,"work_id":"dc0f2c17-2a40-47bc-af92-81fb0c5a8a4c","year":2021},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:44.934521Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:0625dc86f011205dad3d9810b67daf626854dc42cd1c6c4bf263faf44f7a5b46","observation_id":"601d8c5b-704a-47eb-8f16-a5aaabb3c3a6","resolution":{"observed_at":"2026-08-06T20:18:54.219366Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2022.32225","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:18:53.940895Z","title":null,"venue":null,"work_id":"7ecb7313-e0a6-4c95-9f4c-559bab71dcfc","year":2022},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:45.020136Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:f6321bd4315130f002d9a367bcc3e404979eb05d2aaf1863c013ef31288ecd1c","observation_id":"c3de31db-5016-43b4-9fe5-b7164246768b","resolution":{"observed_at":"2026-08-06T20:18:54.039678Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.3997/2214-4609","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:18:52.445971Z","title":"Konuk, J","venue":null,"work_id":"a1d3b8a8-2c7e-4e3b-a13d-375a4bc7fd73","year":2021},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:45.121576Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:60f3f3b90c5077f539a769b4d2d47d196ae4a2cc7328dbaf87098a4d0055bf13","observation_id":"66146975-19ac-4359-8b9a-63897b2d94b0","resolution":{"observed_at":"2026-08-06T20:18:52.501064Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T20:18:45.203273Z","title":"Borrel-Jensen, S","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:45.203273Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:12c368ddcdebc69771c476bd9198ffaf5de0f63bfacd5374e59c58dd0d4c840e","observation_id":"bfc5718d-1f2b-4960-976c-2256c95a9ed4","resolution":{"observed_at":"2026-08-06T20:18:45.203273Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1021/acs.jpcb.3c07714","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:18:52.290120Z","title":"doi:10.1021/acs.jpcb.3c07714","venue":null,"work_id":"8a969b06-0d9c-49b9-92b6-b87d36227f7a","year":2024},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:45.317124Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:a1dca1b2f03dc99700e237fed35fe5c10dc4ff11c892cbe95b9a088c963d9f99","observation_id":"31dfe5e7-3b0a-4eb1-94b4-99270f806f64","resolution":{"observed_at":"2026-08-06T20:18:52.348190Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T20:18:58.094910Z","title":null,"venue":null,"work_id":"9f63c1e3-0154-490f-a6a8-feba42642ab7","year":null},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:45.487197Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:d8b4f694a36de257acf149450358af7888107f3222ef5e98fa571a34d34859a4","observation_id":"9d1096b3-c794-4d10-93a6-372a2b9b64ba","resolution":{"observed_at":"2026-08-06T20:18:58.183779Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T20:18:45.759594Z","title":"Abdar, F","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:45.759594Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:8108e91d7e95a7f39d7f740ce4f69ea648a0ae71aa6944dddcc381ad1e882c74","observation_id":"439d5d3c-614a-409b-b852-78a537fb20da","resolution":{"observed_at":"2026-08-06T20:18:45.759594Z","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":"2026-08-06T20:18:57.745102Z","title":"Cheng, C","venue":null,"work_id":"d0f04c76-23f2-464a-9f9c-be57578eb61d","year":2023},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:45.884403Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:925787389397f6b0e5c12d5658853d888ee0bc69b27dc9d8871dcab6f436dbce","observation_id":"2b2df35b-b2d4-4481-b91b-551e96391947","resolution":{"observed_at":"2026-08-06T20:18:57.811930Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"5533.00038","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:18:53.575659Z","title":"doi:/10.1061/(ASCE)MT.1943-5533.0003843","venue":null,"work_id":"92122289-d894-4417-9566-30bdbb7b109e","year":2021},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:46.000448Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:a31fb566ced6a1c241d997d50920e1b472dc4c210a4da12759dec9703bbf31ae","observation_id":"da9ca8a5-094e-442d-9ddf-0328cf813a97","resolution":{"observed_at":"2026-08-06T20:18:53.710914Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2023.13883","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:18:53.372125Z","title":"doi:10.1016/j.chemosphere.2023.138830","venue":null,"work_id":"a85b31b5-fd9c-47d8-bf5e-341eaf7105e3","year":2023},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:46.101530Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:27be2bd856522b4f3946a01e613bfcf125999aaaf1fac25e9a97385488ac98fb","observation_id":"b21e4b4f-2ac3-45f4-83b8-4d2bcbc5d331","resolution":{"observed_at":"2026-08-06T20:18:53.459891Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2018.87692","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:18:53.175540Z","title":null,"venue":null,"work_id":"3ee2e6d0-db95-463c-ab48-51bc5509a21f","year":2018},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:46.230057Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:fa87154c52cffd3e016c7b074c9988994bc8d82b226c2d00499d0b6958edf0eb","observation_id":"f1a95fe8-3867-40da-b548-f3599180ec35","resolution":{"observed_at":"2026-08-06T20:18:53.255393Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s11831-022-09872-y","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:18:51.969684Z","title":null,"venue":null,"work_id":"027c5d4e-a281-4b73-8636-7d4fab26f5ce","year":2023},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:46.367119Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:6a3e9b8feb3d3a3db9f8318e448794125de584b67edff2adb1149b37c9a35c82","observation_id":"a6ff9e34-471c-4150-a09b-dbc65a30a65e","resolution":{"observed_at":"2026-08-06T20:18:52.177049Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2025.11784","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:18:52.913345Z","title":null,"venue":null,"work_id":"61ff8830-7a91-4bcd-b75d-12e49300603e","year":2025},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:46.479534Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:9f2f6404e6d33e566aadc0cbbf5b8293848d5ed364f7e10ebb05aa59ce2fb3b8","observation_id":"5fd4b332-8700-4d9c-b5a8-8f767803a9d6","resolution":{"observed_at":"2026-08-06T20:18:53.001751Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2504.01195","last_updated":"2025-05-28T02:54:12Z","snapshot_observed_at":"2026-08-07T16:16:22.018914Z","submitted_at":"2025-04-01T21:17:41Z","title":"Towards Signed Distance Function based Metamaterial Design: Neural Operator Transformer for Forward Prediction and Diffusion Model for Inverse Design","version":3},"cited_work":{"arxiv_id":"2504.01195","doi":"10.48550/arxiv.2504.01195","metadata_source":"pith","pith_arxiv_id":"2504.01195","snapshot_observed_at":"2026-08-07T06:16:28.064256Z","title":"Towards Signed Distance Function based Metamaterial Design: Neural Operator Transformer for Forward Prediction and Diffusion Model for Inverse Design","venue":"physics.comp-ph","work_id":"22c68b6a-04ca-4069-b7f3-d33ed4947762","year":2025},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:46.609145Z"},"links":{"cited_paper":"/paper/2504.01195","citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:a0e969b6013e3dc7cf0839eb305af79582bd97a5ddd97f589ec7ccae43c90375","observation_id":"da04b964-9875-4d75-a5c1-6e3d362a4faa","resolution":{"observed_at":"2026-08-06T20:18:51.747343Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T20:18:57.536932Z","title":null,"venue":null,"work_id":"fc20d07d-3e21-4f6f-bec9-2c29106bdc44","year":2021},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:46.740073Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:71a5eeae84ce7c3edceefce37ce3d6295476ba120bf21e304f729396644341c0","observation_id":"cc7b48d0-75bc-4a28-a8b5-e3346a5202d3","resolution":{"observed_at":"2026-08-06T20:18:57.618113Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T20:18:57.334080Z","title":"Koric, A","venue":null,"work_id":"40d918a8-c2fc-4a60-9cc0-2862c35f1783","year":2024},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:46.911295Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:1fca17e7dc591689eddfdc749c6544a0d6e6d6c40cee03cc05a97478b2152f05","observation_id":"a001c59b-a090-443c-87f6-212fff633078","resolution":{"observed_at":"2026-08-06T20:18:57.419632Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T20:18:57.189342Z","title":"Goswami, M","venue":null,"work_id":"9295371c-1642-4bc0-8090-65122b88d675","year":2022},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:47.085261Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:2766e2f0b41bfce6efe6aac75c271619d9b8ec5b760007c80ad292bc946fcdd9","observation_id":"66059299-fd82-426f-b849-a4355165ff48","resolution":{"observed_at":"2026-08-06T20:18:57.250863Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T20:18:57.034089Z","title":null,"venue":null,"work_id":"bd90b396-65ff-40e9-945e-561665519c43","year":2023},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:47.202852Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:282d424e29f93b34610e6c79799b751ef8f0ecd8ece0d22951ab6100255c380a","observation_id":"39a483df-01bd-425c-93c9-c4ec1abf41d6","resolution":{"observed_at":"2026-08-06T20:18:57.107493Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T20:18:56.833053Z","title":null,"venue":null,"work_id":"a4e699c4-644e-4902-9f22-fc412bbc666e","year":2023},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:47.311428Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:3ac3f97590c3e1306827c6aa652f9f7cb5a1bb521bd48b0c3379debf35af8b57","observation_id":"88a5e6dc-d653-428b-bbb5-5d1f985e2bbd","resolution":{"observed_at":"2026-08-06T20:18:56.930341Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T20:18:56.692439Z","title":"Haghighat, U","venue":null,"work_id":"7e301a48-0738-4c54-9abb-d087ec64a65d","year":2024},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:47.502065Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:d5f76e6af002d1d96f20cbe1c8ad62a93e35574ff40c343294d4718813b75962","observation_id":"a1c5e6c6-d024-48c7-8707-0fa03edfed3c","resolution":{"observed_at":"2026-08-06T20:18:56.747128Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T20:18:56.544881Z","title":"Kobayashi, J","venue":null,"work_id":"5b7f0779-3fbb-4206-9b58-70c61d0d57bf","year":2024},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:47.655207Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:5ac4ab56c16002114d55eaff037335d76def5a414054c00df52f9ad310718e16","observation_id":"3c7dd0e9-7ef5-4f75-b8c3-8c11e68899c4","resolution":{"observed_at":"2026-08-06T20:18:56.606829Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T20:18:56.402545Z","title":"Sahin, C","venue":null,"work_id":"4c01449a-d87d-488b-9bce-8dbc678e2524","year":2024},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:47.808810Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:0b83158b4112bc85b9c89b7f58e812600a994a07e2d174c08bb8c5d340bd975d","observation_id":"d0c4a284-cfbd-4bad-bb94-4e7b122c09fb","resolution":{"observed_at":"2026-08-06T20:18:56.467679Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T20:18:56.254298Z","title":null,"venue":null,"work_id":"036f8b49-86c4-4a0c-807c-76b523c765e2","year":2023},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:48.016761Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:a415835308310c10eca06321c4589e9558174c84ded92fe11a18e798fb1d76e2","observation_id":"8caec51e-7420-413f-a511-8003aca670d3","resolution":{"observed_at":"2026-08-06T20:18:56.321834Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T20:18:56.094004Z","title":null,"venue":null,"work_id":"3e23a845-b86a-47fa-897b-dc6813eb1e2f","year":2025},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:48.173479Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:a69486f0a9d51baf0db10d43547f068d083ae8a151152833c8f6cf6ad5e5972b","observation_id":"caa3a35d-7337-45ef-b0c1-56dc5d4f3384","resolution":{"observed_at":"2026-08-06T20:18:56.183855Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T20:18:55.971973Z","title":null,"venue":null,"work_id":"0c352c66-0d72-4852-93ae-69e8604824a1","year":2024},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:48.303813Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:552c79a60099a67d97cb4f425fa1606c963bdc16cac00b7ff400739954fb2700","observation_id":"0a250661-7f35-4893-9254-0d5bb6b73363","resolution":{"observed_at":"2026-08-06T20:18:56.032754Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T20:18:55.831842Z","title":"Vaswani, N","venue":null,"work_id":"b3bcc4ca-b71c-4d94-999c-8561228e03e4","year":2017},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:48.473456Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:15b4cf606a82ca5930193bc261518bd8390c542123cef2f19c4fb862b25caeab","observation_id":"08f7263c-0f27-4cea-b4e2-2a390fffc5df","resolution":{"observed_at":"2026-08-06T20:18:55.884456Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T20:18:48.678936Z","title":"Cao, Choose a transformer: Fourier or galerkin, Advances in neural information processing systems 34 (2021) 24924–24940","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:48.678936Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:3086d40002f31c81e92d08809231b2aab77ca513c97f66f3c77a74a03606898e","observation_id":"527f4c66-a2ad-43a0-a488-842120ad6529","resolution":{"observed_at":"2026-08-06T20:18:48.678936Z","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":"2026-08-06T20:18:55.651483Z","title":null,"venue":null,"work_id":"73f4ec31-c734-4cd4-8141-2e1630d7c476","year":2022},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:48.809044Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:1ba0948406734a1fada8cd5b3bfd5f141e92e4af6872007f4fe968a97b00c2ee","observation_id":"0cb9a7ac-c975-49e7-a031-0373bf469915","resolution":{"observed_at":"2026-08-06T20:18:55.743263Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2205.13671","last_updated":"2023-04-27T21:01:23Z","snapshot_observed_at":"2026-07-06T13:14:29.961613Z","submitted_at":"2022-05-26T23:17:53Z","title":"Transformer for Partial Differential Equations' Operator Learning","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2205.13671","snapshot_observed_at":"2026-08-06T20:18:48.906392Z","title":"Farimani, Transformerforpartial differentialequations’ operatorlearning, arXiv preprintarXiv:2205.13671(2022)","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:48.906392Z"},"links":{"cited_paper":"/paper/2205.13671","citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:23944bca21fd9d58889002ff2ee7a565e5c76afe9a2cb02a1c6fb47ba2d0353e","observation_id":"0227d9c1-c850-4db4-b88b-a06cb591db59","resolution":{"observed_at":"2026-08-06T20:18:48.906392Z","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":"2026-08-06T20:18:55.489673Z","title":"12556–12569","venue":null,"work_id":"7249e8f9-a7ff-44dc-a974-e9a98f0eae55","year":2023},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:49.104454Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:f8c0949c439d646cc8faa07cf25335704dd393188f26670b8989e8ed27d0e77c","observation_id":"b2cacf4f-7898-4c04-98ba-e89b92cecdc7","resolution":{"observed_at":"2026-08-06T20:18:55.563310Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.48550/arxiv.2504.19452","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:18:51.328199Z","title":null,"venue":null,"work_id":"e4e39477-959a-4a49-953e-7d2d787b3545","year":2025},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:49.273553Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:a7873de94b4d75103e0a08938ef5c23b1976542c925fb316c4236dc4ece9e550","observation_id":"da9d7b43-c0c9-456d-af0e-0c1057869e1c","resolution":{"observed_at":"2026-08-06T20:18:51.426355Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T20:18:49.494330Z","title":"doi:10.1016/j.cma.2024.117560","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:49.494330Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:522595579ffcf4c498bda0388694bfabc2fc18ef45e7b02a8d28fce0cd2dbbba","observation_id":"0cb6322d-4bd8-478d-ab5e-4839d1f125f4","resolution":{"observed_at":"2026-08-06T20:18:49.494330Z","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":"2026-08-06T20:18:55.366182Z","title":"Kushwaha, J","venue":null,"work_id":"8ea78afc-a646-4135-a690-b68636eb8035","year":2024},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:49.658549Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:01257c1b756679439d7dd963e9801ac2d560d6982ed08233054135991f601230","observation_id":"4c2d0e47-b160-449f-a70d-c65b8c3b9093","resolution":{"observed_at":"2026-08-06T20:18:55.417962Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2003.08934","last_updated":"2020-08-03T22:17:31Z","snapshot_observed_at":"2026-08-07T21:12:33.939201Z","submitted_at":"2020-03-19T17:57:23Z","title":"NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2003.08934","snapshot_observed_at":"2026-08-06T20:18:49.810193Z","title":"doi:10.48550/arXiv.2003.08934","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:49.810193Z"},"links":{"cited_paper":"/paper/2003.08934","citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:e0ebf0452c3b8e09626ed02e71d5a573f01b23986c0e7371f2e7c2523bad9252","observation_id":"ea3e8d79-3284-45e4-b767-ceca12531f09","resolution":{"observed_at":"2026-08-06T20:18:49.810193Z","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":"2026-08-06T20:18:55.201113Z","title":"Kozlowski, B","venue":null,"work_id":"258e07f7-1d9e-4f82-b727-362cfa17a7a9","year":1992},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:49.964409Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:f39c21ef243c0d0597fb5e997773240e8bfe079487da5eec5fcb1783eba21ba2","observation_id":"a9c4899e-1ede-4625-8500-c6b138bacdfd","resolution":{"observed_at":"2026-08-06T20:18:55.281368Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T20:18:55.058877Z","title":"Zhu, Coupled Thermo-Mechanical Finite-Element Model with Application to Initial Solidification, Ph.D","venue":null,"work_id":"9e59d09c-de68-43f3-b625-4772fe71f09c","year":1996},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:50.112921Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:876bf21de28f3e6d6984bbbf3e9086e9b76bb9122a79ee8e31cf71370982aec0","observation_id":"c683cd54-db2e-4b3f-b048-abf35a8ea290","resolution":{"observed_at":"2026-08-06T20:18:55.126634Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T20:18:54.931594Z","title":null,"venue":null,"work_id":"014921da-c359-49ef-86e2-476c0ec2b4dd","year":2022},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:50.270852Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:0308330865812e5556c743af12276bc43366ed482b3f32dd238931181a6fe767","observation_id":"09d52e38-80de-4c2a-a5a7-7636791bddeb","resolution":{"observed_at":"2026-08-06T20:18:54.987366Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T20:18:54.782434Z","title":"Koric, B","venue":null,"work_id":"463a0875-faa6-49a8-a657-b61a91abed02","year":2006},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:50.407500Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:1b1022f3e7c204cfcb6e1038db7211412a9e77b0ea87a6b9aa8d6e58edcea1bd","observation_id":"b1c4c32c-2839-4c89-b559-637407bc0e2c","resolution":{"observed_at":"2026-08-06T20:18:54.861787Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T20:18:54.619188Z","title":null,"venue":null,"work_id":"31a10400-ab67-43d7-992d-2beda0397baa","year":2020},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:50.534747Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:84ec6e525692877a3e20da102017e6a9493ad577005b32d7cc2785818190999f","observation_id":"a0b0ccf2-945f-421f-8c45-5cbced10f73e","resolution":{"observed_at":"2026-08-06T20:18:54.689878Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T20:18:54.499931Z","title":null,"venue":null,"work_id":"74c491d4-5ffc-46d6-96a5-6fe58aa85918","year":2021},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:50.755751Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:72253c9070cda5587170e27566f50032eb83703c0d9651663e1bd2cceb87555f","observation_id":"31557612-8af5-48d4-97f3-fe0d864003af","resolution":{"observed_at":"2026-08-06T20:18:54.553056Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T20:18:54.390428Z","title":null,"venue":null,"work_id":"3d453ea5-b434-44ac-86f5-7765a4f1bf9f","year":2025},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:50.902232Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:8fe7c9592718398a21cded54b08122cac2b1db7b45237be904d6eaf1e404e3be","observation_id":"fd01894b-3334-4ea7-9ce2-788a06be68f7","resolution":{"observed_at":"2026-08-06T20:18:54.449898Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T20:18:54.271005Z","title":null,"venue":null,"work_id":"5ebdb4e3-31ae-4783-ad17-0d845de9a1fd","year":2025},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:51.054789Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:f6a837dd73cc23d0cd85a8f3f7617f8230fbbe6ac4f19f26c431daec908e949a","observation_id":"8a2e564d-8b3f-4300-9d8c-4e7d82c7b945","resolution":{"observed_at":"2026-08-06T20:18:54.317279Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T20:18:57.921694Z","title":null,"venue":null,"work_id":"cb68ab56-52a3-474a-a6b8-44b23e53934b","year":null},"citing_paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations","version":1},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-06T20:18:45.634864Z"},"links":{"citing_paper":"/paper/2507.03272"},"observation_digest":"sha256:cedd7ef81c9c162bc2190659b4aa3a19701bf4fa31642a5fc71ef6df4058f135","observation_id":"b54e8a24-d23e-4187-9831-368a46940cc8","resolution":{"observed_at":"2026-08-06T20:18:57.994821Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.03272","last_updated":"2025-07-04T03:06:51Z","latest_version":1,"primary_category":"physics.comp-ph","snapshot_observed_at":"2026-08-08T22:13:14.294579Z","submitted_at":"2025-07-04T03:06:51Z","title":"Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations"},"reference_resolution":{"displayed":45,"state_counts":{"malformed_identifier":0,"metadata_mismatch":6,"parse_uncertain":0,"unresolved":21,"verified_exact":6,"verified_fuzzy":12},"total_outbound_references":45},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 0 inbound Pith citation observations for arXiv:2507.03272."}