{"as_of":"2026-08-23T08:30:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:176286271b64257a931470180aa56dc9687d22d01c217fedb9fee28a582d8198","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":"2026-08-23T06:30:58.430688+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":"sha256:4cad4eaf49064053227d2091557b40323d15bcecc7ddf6a04ba64a3ba59d5fd4","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"sha256:52c82f5b7ef608f3250c0a63129f6dd7163c11060a4f58446c3798c0073a96ff","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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:c5e48831503531413e47a56d327cb2230d0be7276c103f5cc8d44479d756ff56","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"sha256:53512468739ec25c7d6444aa514178f45ca119204456c5dc3415b9828a3dc3a2","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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:c3d6afcf61b287779008e67dc08cb744448476b88ed3411382167024419789fa","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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:c9cb1ff8b123b3e861f291437d6fea0b4bbbdac61f56b043c69fb7659aefacf0","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"sha256:16f77bb58b79756f4025865e22154a40b728de80eb4d8393b6ca0136565a37f0","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"sha256:076788eda0fe9995b6d9c53cc19f5a9e3bbd7b361a3be9df3ac5cc14c3ce9cf1","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"sha256:39022b801b7dcf051fb5edb4dcdf4bf504b268766f3b9748511eb0f425df2ae2","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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:ec03e1212fafd55430eccae5ed7043d2b3be277a33439204aa4fcd4a092a1038","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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:d808fd8f67b597c7b6f2b0f4b1245ecbe7241a46334c63517eaff93f8501c19f","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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:e68de86466c311af313fbff960192dd76a00420c806021aeeb80f3dc9cb01ab0","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"sha256:98b871311976f88a372ea0478e2dba073abaf1c48d9054c1344833282591ebf6","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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:a3692cae7f88a812ba91f1e4be13f4c5b8b2c8cb834b4ba20fb95970336daf3f","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"sha256:46a39c5423a202e094ef15419a9d0b4e43fa2e9723b70e5d613cb31f55beef38","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"sha256:18df809b0e6a968dae3aca1f5382547a59a34ad3c9c228e56cb9a63569af74fa","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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:fcafa211119807fcb58d572254809c5ed8bf2b2e87182ebc196dc46542f73755","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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:d3492fced1c3456db35731ee812686703bf9ff31c7aa8b7467c7a64c21c80edf","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"sha256:6a3369f522debc9fe95504a349df13293941d34b92055beb0df95335edf32fd4","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"sha256:2161b1e37ff849c925b23adcd2613330f8fd7cca8b96cbcf8eeea054bcb695f1","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"sha256:4b0a63bdc83e0900d64d54e3288da9ef4e3f9687a6c3c3e1e809fc658a301c68","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"sha256:45dd69e5eda0ee71a23985e52b15e2fff98b993ad43061e7b2fbb36e0ec2f904","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"sha256:397193ed5434352b668e9766456685131a4f6c6ed95478d3444ef5c63f72dcbe","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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:a746bd96b144495cab954b3f204cb4b1927075230a5b3a0352ef1f2e57870b66","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"sha256:4245b98f521b875e4cb6bfd3a8480bf088bfd716c38b0e175e5d828ec34b84e6","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"sha256:17edfe86a951779a0827fcc487b66e0fb116a56671e047530d7d8a4431ee5379","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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:a5bc5c4386afd900333aaa7acd70aee250ba74a589028216f173afc44646e697","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"sha256:5c22a9dd7abecfaa41ebf4a98708cecc30168a4fa2d0ba382d79f96803017ab5","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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:d941327316b16ca3eb6f0f35d3a52b3f871d2e7f05f5d687575d036c2747b634","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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:d959c3c0598bc2d540fc17be06fa254be25b98bd4ce652e4e116784b87cd900c","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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:f5205c6ee26b4978e65c649e12f849a85699f810f91850843242d7b2a315e507","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"sha256:5750dbfb41ec7d12ffc7a8bfc1d46d36b05718aef9eb945330d1b0e838e7a459","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 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"thesis":"As of 23 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 2 inbound Pith citation observations for arXiv:2411.15178."}