{"as_of":"2026-08-22T10:43:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:12c8ac0042dc03f2d9364ea889b6fb59057451a3b9a0844eb1232302691aef94","coverage":[{"denominator":44,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":44,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T18:29:14.499710Z","state":"measured"},{"denominator":46,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":46,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-22T06:32:14.747728+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-09T15:42:31.757357Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-07T06:05:53.675825Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.15178","snapshot_observed_at":"2026-08-09T15:42:31.757357Z","title":"Harnessing scale and physics: A multi-graph neural operator framework for pdes on arbitrary geometries.CoRR, abs/2411.15178, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.01337","last_updated":"2025-02-07T13:59:37Z","snapshot_observed_at":"2026-08-18T11:04:22.836945Z","submitted_at":"2025-02-03T13:25:55Z","title":"Neural Preconditioning Operator for Efficient PDE Solves","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-09T15:42:31.757357Z"},"links":{"cited_paper":"/paper/2411.15178","citing_paper":"/paper/2502.01337"},"observation_digest":"sha256:d82786c3587bb5c1d1ec08746b423f544d096f764c7d7a07aa45daf6a3c2630b","observation_id":"5472448d-dd21-4962-9c47-5550ae9b0003","resolution":{"observed_at":"2026-08-09T15:42:31.757357Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"cited_work":{"arxiv_id":"2411.15178","doi":null,"metadata_source":"pith","pith_arxiv_id":"2411.15178","snapshot_observed_at":"2026-08-07T06:05:53.675825Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","venue":"cs.LG","work_id":"97994c73-ebf8-4a84-acec-e80d640705aa","year":2024},"citing_paper":{"arxiv_id":"2506.06001","last_updated":"2025-06-06T11:47:37Z","snapshot_observed_at":"2026-08-14T10:35:59.189376Z","submitted_at":"2025-06-06T11:47:37Z","title":"LaDEEP: A Deep Learning-based Surrogate Model for Large Deformation of Elastic-Plastic Solids","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T06:05:53.390798Z"},"links":{"cited_paper":"/paper/2411.15178","citing_paper":"/paper/2506.06001"},"observation_digest":"sha256:c82ba239007d40952a397da3efe5efd14740b84cd405618828b977ed7dc2e010","observation_id":"ee4122de-0413-4506-a7eb-08419cee3dc4","resolution":{"observed_at":"2026-08-07T06:05:53.681741Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2411.15178/citation-record","integrity":"/paper/2411.15178/integrity","json":"/paper/2411.15178/citation-record.json","paper":"/paper/2411.15178"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2210.05495","last_updated":"2022-10-11T14:52:20Z","snapshot_observed_at":"2026-08-18T11:25:41.593107Z","submitted_at":"2022-10-11T14:52:20Z","title":"MAgNet: Mesh Agnostic Neural PDE Solver","version":1},"cited_work":{"arxiv_id":"2210.05495","doi":null,"metadata_source":"pith","pith_arxiv_id":"2210.05495","snapshot_observed_at":"2026-08-12T18:29:14.773917Z","title":"MAgNet: Mesh Agnostic Neural PDE Solver","venue":"cs.LG","work_id":"1b446946-06de-46ed-b1e3-3bb8d976ed32","year":2022},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.254240Z"},"links":{"cited_paper":"/paper/2210.05495","citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:b9898dff9e35484cfc12f74c472f2c0064907c7f7f9c3cb14b4efc6437778ea7","observation_id":"a06aa44c-1786-4b68-9de8-e2c1d15c42b0","resolution":{"observed_at":"2026-08-12T18:29:14.783479Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:15.314292Z","title":null,"venue":null,"work_id":"068e9baa-ef47-4a9e-ae19-57701a1f0d14","year":2022},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.260513Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:46f67770d54aa7928d7088d828abe22b668318b379effc7e5561c73f9afcf431","observation_id":"4f7159a7-75b2-43d0-b94b-aaa3834ead65","resolution":{"observed_at":"2026-08-12T18:29:15.319044Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:15.299047Z","title":"Bronstein, Joan Bruna, Yann LeCun, Arthur Szlam, and Pierre Van- dergheynst","venue":null,"work_id":"328a3c5b-025b-4d98-9800-d65a0b7b4d95","year":2016},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.265452Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:a66a2522158fee42d031973f9e02a8315f134b626d4a64a221d2ddd8258080b0","observation_id":"75a25189-8b9f-4261-b6eb-de0dd5e230b5","resolution":{"observed_at":"2026-08-12T18:29:15.303914Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:15.283426Z","title":null,"venue":null,"work_id":"756acc01-e34a-40cb-acbd-749e12029170","year":2021},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.271272Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:9f1eab2c96138c239c00d7ececde1267a01cb2fa7272c8323add92e84e22d966","observation_id":"bd161689-1226-4040-bb60-ad04096d739c","resolution":{"observed_at":"2026-08-12T18:29:15.288623Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:15.268470Z","title":null,"venue":null,"work_id":"38f06125-65e4-482e-99c5-a617356736bc","year":2023},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.282483Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:d680658614a98aec7c7d356cc26594f50480b4be5478dffed42af232f95053df","observation_id":"3d449ff3-9a3c-4deb-a2fc-e2a37d410f5f","resolution":{"observed_at":"2026-08-12T18:29:15.273103Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:15.253781Z","title":null,"venue":null,"work_id":"bf3f7824-0f87-47f8-b955-e5440228d04e","year":2020},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.288348Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:e7f38d75bca01cab6a0677d91f625e6adedf36b30ac2ad3f4be991d386f2725e","observation_id":"3e2525d5-74b1-4f7c-b1e0-8beb28a1c6cf","resolution":{"observed_at":"2026-08-12T18:29:15.258447Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:15.237474Z","title":null,"venue":null,"work_id":"9572aa19-df87-4cc4-99b3-717c7fa10cc0","year":2019},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.294393Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:c9f1f2ff6a735206eead7aaa01a458b362c2d073029e3e975c0392c9cbeaf0f1","observation_id":"f89457c9-20ab-4f61-9f51-87acd38ece81","resolution":{"observed_at":"2026-08-12T18:29:15.242326Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:15.222482Z","title":"Schoenholz, Patrick F","venue":null,"work_id":"0d98636b-3c6c-46d4-8a5f-8147f6047aaa","year":2017},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.299304Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:12e2afd57f287a4b95c82466c94ed7db31612bed42e3955d849bccd041d5e8d1","observation_id":"528d2607-34ea-41c6-96ab-ef70ae1be0cf","resolution":{"observed_at":"2026-08-12T18:29:15.227229Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:14.304289Z","title":null,"venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.304289Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:92a090d4d57beef4dadd22707a3072384ac0dda0d3ea9c8d9b42c39c0094a5fc","observation_id":"f3221af7-fd62-406b-ac05-666cdc459007","resolution":{"observed_at":"2026-08-12T18:29:14.304289Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T18:29:15.207366Z","title":null,"venue":null,"work_id":"fd8a1524-37cc-4370-855d-ccae1460b1b9","year":2023},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.309168Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:3dc94d1d6bfeb7bcfbc229de7713a5d62e4a20536ff5a61f498d6008a6a34148","observation_id":"0931ea3a-356c-44f2-bf5c-14d6ac4ac26e","resolution":{"observed_at":"2026-08-12T18:29:15.212127Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:15.191186Z","title":null,"venue":null,"work_id":"25a41d82-f6e7-4c8f-8e02-6f32dd917e2b","year":2021},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.314544Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:82e502338695c3b4ee0613cb7ba38f1311b1286425ef3f7547f992f0f64ecb8e","observation_id":"5b910a79-4330-44b1-8f57-9ebba461831c","resolution":{"observed_at":"2026-08-12T18:29:15.196026Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:15.175402Z","title":"Hamilton, Zhitao Ying, and Jure Leskovec","venue":null,"work_id":"e2d5bce6-892e-4bca-b2d0-411caf6241ee","year":2017},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.320012Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:dff4f880d2350abb4e44bc67fa8f4cd9cca142ae95b4bb447d92b62b025a705d","observation_id":"202a9ea6-9f19-482b-8df0-cedb26f07fce","resolution":{"observed_at":"2026-08-12T18:29:15.180208Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2302.14376","last_updated":"2023-06-14T12:26:03Z","snapshot_observed_at":"2026-08-20T11:32:02.799534Z","submitted_at":"2023-02-28T07:58:49Z","title":"GNOT: A General Neural Operator Transformer for Operator Learning","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2302.14376","snapshot_observed_at":"2026-08-12T18:29:14.325375Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.325375Z"},"links":{"cited_paper":"/paper/2302.14376","citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:0794709f0d74f03fd23483bb890e93e822fa3c1db26a5b412001037896c3518c","observation_id":"2758819e-1951-4218-b4f4-d8d90fdd5f0c","resolution":{"observed_at":"2026-08-12T18:29:14.325375Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2310.19809","last_updated":"2024-06-26T02:00:14Z","snapshot_observed_at":"2026-08-19T20:37:37.451093Z","submitted_at":"2023-10-16T13:01:35Z","title":"MgNO: Efficient Parameterization of Linear Operators via Multigrid","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2310.19809","snapshot_observed_at":"2026-08-12T18:29:14.330942Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.330942Z"},"links":{"cited_paper":"/paper/2310.19809","citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:796d13ae2119695919d7813e87e0b38dad922ee8bd09be6f20d4802c1feef423","observation_id":"51844214-c8e7-4855-985e-e7c6642d1fa4","resolution":{"observed_at":"2026-08-12T18:29:14.330942Z","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":"2026-08-12T18:29:15.158811Z","title":"Kingma and Jimmy Ba","venue":null,"work_id":"581787e4-fb7f-45bb-87db-68cfc90f9c44","year":2015},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.336730Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:45dd210a13978a439df3e26cb71240d22dbdeeb3ba8178dc9c398b5f8d7f0236","observation_id":"450f3f30-dbd2-477f-a6cf-71f906d909e5","resolution":{"observed_at":"2026-08-12T18:29:15.164326Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:15.141396Z","title":"Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew M","venue":null,"work_id":"df92bd6b-9d4f-4af3-8ffd-f69207323a43","year":2023},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.341640Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:c2a1e3c5b6d9441ed55dd8320aa936b5c9ee988f88e6040be158f233f11bda94","observation_id":"a57aa467-1786-427b-962a-de3490c33aad","resolution":{"observed_at":"2026-08-12T18:29:15.146551Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:15.125525Z","title":null,"venue":null,"work_id":"f6ab9a17-1591-44dd-b82f-12a2f6d24370","year":2024},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.346331Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:bc514e0843d4e606896b3615fa1fd7e62573d6bfd28be347d56e3bf9da3c1cfc","observation_id":"e5f928bd-8f29-4c4c-8e0c-2a3740a1612f","resolution":{"observed_at":"2026-08-12T18:29:15.130348Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:15.108450Z","title":"Stuart, and Anima Anandkumar","venue":null,"work_id":"3e268216-3171-4f21-9081-f5a2f5c46e9d","year":2021},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.352665Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:f355c894a57d16a83d504d71d2e1448b770eb54e48a58987f1ff6d6a3c34975e","observation_id":"82a05c58-1f82-464b-84f0-67498cec2572","resolution":{"observed_at":"2026-08-12T18:29:15.113559Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:15.091423Z","title":"Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Andrew M","venue":null,"work_id":"b0f67422-7aca-4800-aca7-f163c29f75ff","year":2020},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.357786Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:b07e4c35a7452e105b80e717124fdcaa600ff296f4bd357f98d146fea60d994b","observation_id":"b053190b-0200-4504-8763-4163382d8394","resolution":{"observed_at":"2026-08-12T18:29:15.096571Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:14.362467Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.362467Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:274d8753b2f15a6288db6f6fa9592b4b6fb857aff83f6ff02338befac3235f8a","observation_id":"6880d4a3-687e-4229-8157-456806bf7d9b","resolution":{"observed_at":"2026-08-12T18:29:14.362467Z","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":"2026-08-12T18:29:15.074486Z","title":null,"venue":null,"work_id":"bc0a6b5f-2e2e-4896-86a4-bc8137f76ea6","year":2023},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.368633Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:6288bc93622a1952e680654f293fae172b8b05462b1b76b939758f398f7f0523","observation_id":"15725c69-2d4c-499b-a077-d32f721e0e9a","resolution":{"observed_at":"2026-08-12T18:29:15.079294Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2003.03485","last_updated":"2020-03-07T01:56:20Z","snapshot_observed_at":"2026-08-15T17:57:12.049079Z","submitted_at":"2020-03-07T01:56:20Z","title":"Neural Operator: Graph Kernel Network for Partial Differential Equations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2003.03485","snapshot_observed_at":"2026-08-12T18:29:14.373169Z","title":"Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew M","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.373169Z"},"links":{"cited_paper":"/paper/2003.03485","citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:f450f9172a65b3165c5f308e479fcd75fbe71ae0adb82f74f5f5a197629a4f8f","observation_id":"e6796525-f1cd-45ba-9d76-0586c53d6053","resolution":{"observed_at":"2026-08-12T18:29:14.373169Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2309.00583","last_updated":"2023-09-01T16:59:21Z","snapshot_observed_at":"2026-08-18T11:01:08.167287Z","submitted_at":"2023-09-01T16:59:21Z","title":"Geometry-Informed Neural Operator for Large-Scale 3D PDEs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2309.00583","snapshot_observed_at":"2026-08-12T18:29:14.379042Z","title":"Kovachki, Chris Choy, Boyi Li, Jean Kossaifi, Shourya Prakash Otta, Mohammad Amin Nabian, Maximilian Stadler, Christian Hundt, Kamyar Azizzadenesheli, and Anima Anandkumar","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.379042Z"},"links":{"cited_paper":"/paper/2309.00583","citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:8e67e0bfa66c1713f5e8fa28bed46d155637c326b42947d5024eda86fd6a7717","observation_id":"25aaed13-c39d-4ef6-b212-d10fd31c1a77","resolution":{"observed_at":"2026-08-12T18:29:14.379042Z","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":"2026-08-12T18:29:14.386322Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.386322Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:7a2ace8e57c7fc0b31eab7abad8f7d3dcc9524844e23453f50741fb26977adc0","observation_id":"d050fc98-fa96-451b-a9a6-c01a864ed350","resolution":{"observed_at":"2026-08-12T18:29:14.386322Z","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":"2026-08-12T18:29:15.046589Z","title":null,"venue":null,"work_id":"92c34e4b-0bce-4bb3-bd4d-2483167390f5","year":2021},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.390928Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:850f023181f5be96c3ae55808648556366c91ca73f5d779426654dfb8dd5231d","observation_id":"cb7ca429-93d1-4e2b-8a38-744e50726fc6","resolution":{"observed_at":"2026-08-12T18:29:15.052109Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:15.028740Z","title":null,"venue":null,"work_id":"2d96aaf6-48d5-487c-9915-3486e4e468a6","year":1998},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.395729Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:8210f033451a17b9b9267656acaa9e83077f5865eeb795d85f1ea75e11541da8","observation_id":"ad7a4fdd-abad-41e5-8618-6e6dbbdd91c5","resolution":{"observed_at":"2026-08-12T18:29:15.033986Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:15.012788Z","title":null,"venue":null,"work_id":"62dce14c-3f75-4cfe-91c2-65081c308367","year":1998},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.400880Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:3ad1dd8fdf35f7a8a22d8086965393dafd59dcf43888900b3ed644d302777455","observation_id":"16ef8533-171a-4276-a2cb-e1ecbabface1","resolution":{"observed_at":"2026-08-12T18:29:15.017848Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:14.995571Z","title":"Brunton, and J","venue":null,"work_id":"4a6b76c2-772c-465e-9d0b-41012e4c7540","year":2023},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.405964Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:9566d254b4ba3ddc115905e4f4651d3a3905363d4c93e25efb8e22bf730e1a1f","observation_id":"b84aa9ee-b5af-4465-a127-312f44411935","resolution":{"observed_at":"2026-08-12T18:29:15.000487Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:14.979347Z","title":null,"venue":null,"work_id":"ffa3fb8b-6862-47f0-abf9-b9138161e56f","year":2021},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.411055Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:cdb63fa31ca028e703ec10009534e70948c701cae05d66bc7f407d91bbd92126","observation_id":"c824f1af-661c-404d-9d1b-4c3ca78fb014","resolution":{"observed_at":"2026-08-12T18:29:14.984034Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:14.964208Z","title":"Qi, Hao Su, Kaichun Mo, and Leonidas J","venue":null,"work_id":"028cccbf-38af-4ac8-a4e3-3b1cc1c057ed","year":2016},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.416471Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:d79fc065114a9d1e03af547ac171a09b4da8a3bcddbe92d30a790806062a5623","observation_id":"60e0805c-3afe-4cd0-a5c6-6570a2ce52c3","resolution":{"observed_at":"2026-08-12T18:29:14.969021Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:14.421742Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.421742Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:c22225688c49a46894f0c55117379363f75dc63caa60d16d16ffa22d9d02b8ae","observation_id":"f829e309-0050-4148-b008-80b7ebff81d3","resolution":{"observed_at":"2026-08-12T18:29:14.421742Z","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":"2026-08-12T18:29:14.938175Z","title":null,"venue":null,"work_id":"e87cfad2-f1ff-41ec-9ae4-68e861ccd8ca","year":2015},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.426401Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:b32816eaa040261b997dbc6f9327a7205ad36c19e723a8c2466ed928f41a5a4a","observation_id":"2ea941be-5583-482d-a66a-3df71b3566de","resolution":{"observed_at":"2026-08-12T18:29:14.943258Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:14.431960Z","title":"Rumelhart, Geoffrey E","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.431960Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:2f490461712f13dfbb9672604e1d6f84b3915d5edf6420d433eb1637601d64ac","observation_id":"7a240054-b040-44cf-835c-f1e9149302c9","resolution":{"observed_at":"2026-08-12T18:29:14.431960Z","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":"2026-08-12T18:29:14.910771Z","title":null,"venue":null,"work_id":"0cf44548-c77f-4b9a-a42f-4794a0e856e8","year":2018},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.438509Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:90ed57e2814cd40c8cafea3d41e11f07fc9f1dd16d90673a85b763ea1117e8c7","observation_id":"f8911be7-0de8-4dd6-b996-8afa651abef3","resolution":{"observed_at":"2026-08-12T18:29:14.916071Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:14.893234Z","title":null,"venue":null,"work_id":"10cdef7f-6402-43c5-9a69-be78c32e6f9f","year":2017},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.443435Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:646ceef76401acfb42fa30b2118290a0316ab05c91fc2f406abce697a1806601","observation_id":"d1abacd1-05b8-435a-8ac0-46b79e4e9423","resolution":{"observed_at":"2026-08-12T18:29:14.899259Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:14.877243Z","title":null,"venue":null,"work_id":"169ea47a-b51d-4209-af6f-f55f82dc964f","year":2023},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.448400Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:39edeeccb8ca307bff68f3d9742827d555a3128e30dede271c016405a897f3d7","observation_id":"b56c7d49-de5f-4a51-9cc6-d7f4e0e53091","resolution":{"observed_at":"2026-08-12T18:29:14.882006Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:14.860315Z","title":null,"venue":null,"work_id":"7d730b49-62ac-4ee8-b226-fdcc2f279fa3","year":null},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.458360Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:44df279ff3d992468f92919cdce29b5906a20c9119d524a8c7231762a469af99","observation_id":"d413e7b4-04f7-4d67-b3a0-cfd00fb74c00","resolution":{"observed_at":"2026-08-12T18:29:14.865706Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:14.470136Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.470136Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:889bb4d35159c8cc366e153dc8466ffabc144a70b5bc39d0434a4868b7ae2c0c","observation_id":"cf800c40-9a3c-44b1-bd23-2bb5fb54d2c9","resolution":{"observed_at":"2026-08-12T18:29:14.470136Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2310.12487","last_updated":"2024-12-26T07:56:34Z","snapshot_observed_at":"2026-08-21T09:23:22.726797Z","submitted_at":"2023-10-19T05:47:28Z","title":"Improved Operator Learning by Orthogonal Attention","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2310.12487","snapshot_observed_at":"2026-08-12T18:29:14.483419Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.483419Z"},"links":{"cited_paper":"/paper/2310.12487","citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:99ab87df1742708497bb473cc0e06cb73dd9e0594813856dda46e1c2825c4285","observation_id":"b1ec9ac8-6fe8-4dea-b03a-a046fc042324","resolution":{"observed_at":"2026-08-12T18:29:14.483419Z","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":"2026-08-12T18:29:14.831758Z","title":null,"venue":null,"work_id":"af0fa0a1-6bff-4ee0-9e6e-d86481279f58","year":2023},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.489251Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:bf268e59a3f36fca5c6e76a5d277811aaf16271ad7b204807ad8bf652eeec67a","observation_id":"7fc005db-b140-4244-8d43-d89541b3da12","resolution":{"observed_at":"2026-08-12T18:29:14.837169Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:14.811411Z","title":null,"venue":null,"work_id":"8afbd29b-4636-4797-9e64-c4b559725f08","year":2022},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.494181Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:66db767ec0e65918404ac45de0f5a5d0195449778df30cbf47bf9e2d484953e4","observation_id":"ede481bb-efae-4c6c-baa2-9c49490c587e","resolution":{"observed_at":"2026-08-12T18:29:14.816822Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-12T18:29:14.795510Z","title":null,"venue":null,"work_id":"06c98d82-0fee-4349-8af5-6eca018ba965","year":2022},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.499710Z"},"links":{"citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:14c0aa2543191b979bf9408686a2d9ec3c7a7129fc4f21325d12b3bbc49460df","observation_id":"3b7d043e-60df-4e9d-8c9f-01c62af97086","resolution":{"observed_at":"2026-08-12T18:29:14.800354Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2301.12664","last_updated":"2023-05-29T16:30:47Z","snapshot_observed_at":"2026-08-22T00:16:19.509600Z","submitted_at":"2023-01-30T04:58:40Z","title":"Solving High-Dimensional PDEs with Latent Spectral Models","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2301.12664","snapshot_observed_at":"2026-08-12T18:29:14.464477Z","title":"ArXiv abs/2301.12664 (2023)","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":2023,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.464477Z"},"links":{"cited_paper":"/paper/2301.12664","citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:f989c50889204515797522aaafa5ea5b9e46e84f11289f8a2744494a87d27a13","observation_id":"131bca14-f8d3-4a04-8d1c-4bdebf0f7d34","resolution":{"observed_at":"2026-08-12T18:29:14.464477Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.02366","last_updated":"2024-06-01T15:33:37Z","snapshot_observed_at":"2026-08-18T09:48:19.058609Z","submitted_at":"2024-02-04T06:37:38Z","title":"Transolver: A Fast Transformer Solver for PDEs on General Geometries","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.02366","snapshot_observed_at":"2026-08-12T18:29:14.475401Z","title":"ArXiv abs/2402.02366 (2024)","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","version":3},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-12T18:29:14.475401Z"},"links":{"cited_paper":"/paper/2402.02366","citing_paper":"/paper/2411.15178"},"observation_digest":"sha256:fda0ef6969807a13e18f66ec8b6304c2b4d8ab30e436cf28eba8151f478f505e","observation_id":"5ec920af-a4bd-4076-b063-cee2ce142e3f","resolution":{"observed_at":"2026-08-12T18:29:14.475401Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2411.15178","last_updated":"2025-02-07T13:53:41Z","latest_version":3,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-18T11:03:42.596553Z","submitted_at":"2024-11-18T12:35:03Z","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries"},"reference_resolution":{"displayed":44,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":33,"verified_exact":1,"verified_fuzzy":9},"total_outbound_references":44},"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":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"thesis":"As of 22 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 2 inbound Pith citation observations for arXiv:2411.15178."}