{"as_of":"2026-08-07T20:23:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:aa14864a37a61a41acdcf8b09a1a88e73159cc0a0906b4035006b922f544e95b","coverage":[{"denominator":58,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":58,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-29T22:15:33.807145Z","state":"measured"},{"denominator":58,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":58,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2605.25786/citation-record","integrity":"/paper/2605.25786/integrity","json":"/paper/2605.25786/citation-record.json","paper":"/paper/2605.25786"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-29T22:15:33.807145Z","title":"Zico Kolter, and Vladlen Koltun","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:629f2d3cdee82becd3229c2fa10735dc807a936d6f859b8f8779311dcdaa52b5","observation_id":"fcbed4ce-9cf4-4895-accd-8a72dbc72786","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/1.9780898719505","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Briggs, V","venue":null,"work_id":"13858c8d-97c0-453f-a8ca-f837294e2bf3","year":2000},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:fb8990ab0d90242dc906baa612a58aed8e76d563828b0651a372af58229681c4","observation_id":"69684055-7452-4698-ba0b-6059eaf5cc71","resolution":{"observed_at":"2026-06-29T22:23:59.734846Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-05-23T07:23:22.303661+00:00","source":"crossref_status_cache"},{"observed_at":"2026-05-23T07:23:22.303661+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":1968},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:6d9612f4041ee7ae0b68c52b2aad835e73b74a5096898968e97bdd015424bf64","observation_id":"c9421ea8-db36-4ab5-96d6-7f18fb875e9a","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:e6e17a5de0715d8b5a51619989690c0e7970bef542488155b64d652865caafda","observation_id":"61fe9326-f526-4cd0-bdf4-b96c9bae20d1","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:98ca06d82daeaf638ed2e11b42dafa475ffdeae7fb8b94130d8972fdbe120d89","observation_id":"4c22b12e-0c28-45b8-b541-8f01050d1080","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:67feee0d6dc28f471d03b527c09b895f0a2276700401d9fe44085000df4077c7","observation_id":"c039d68d-1433-496d-8549-ace1011e79e0","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:b5ce2bc428379d7c5cffb432e16df6330419fb68c0070dd2aabf0368aebb507d","observation_id":"d021b3a3-b43e-4197-bc88-c016d6fc4654","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":1952},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:2576d1b1f82184352235ad39c4bdc566fe6543ea91aff605ed34f76710a15ad5","observation_id":"b54e1612-1499-4934-be2a-088986e7817f","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:68228704456d600f5546f97153c62387251e650afc02a7b85f50f155b6145eb8","observation_id":"dfff411c-ba8d-4c9d-a467-438db77b0951","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:bd7d65b0544daccc69abb22210e13fb9194270565998e1f4a7b8c15d4bb10975","observation_id":"be57a030-35f5-4130-88c6-4b5f1a6e969a","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:d259a10946d8cc00b8b7e13185c5833bf4fc9c62b7a279bdd00ca05388cf769c","observation_id":"83ee1944-45a0-44a4-927a-705c01fe71d9","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1912.00873","last_updated":"2019-11-27T19:51:39Z","snapshot_observed_at":"2026-07-06T08:41:25.156353Z","submitted_at":"2019-11-27T19:51:39Z","title":"Variational Physics-Informed Neural Networks For Solving Partial Differential Equations","version":1},"cited_work":{"arxiv_id":"1912.00873","doi":"10.48550/arxiv.1912.00873","metadata_source":"arxiv_reference","pith_arxiv_id":"1912.00873","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"V ariational physics-informed neural networks for solving partial di fferential equations","venue":"arXiv (Cornell University)","work_id":"fdac2bb8-473d-40ce-a8c9-4c19756594e4","year":1912},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"cited_paper":"/paper/1912.00873","citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:1f5ea3b1380a4f1facad71fc5a13e4ddd0f1b4889a68bfad723e15b7c3a616bb","observation_id":"9cd57287-90ae-4343-90ed-2eecb32dcea4","resolution":{"observed_at":"2026-06-29T22:24:00.818601Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2020.113547","doi":"10.1016/j.cma.2020.113547","metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Computer Methods in Applied Mechanics and Engineering , author =","venue":"Computer Methods in Applied Mechanics and Engineering","work_id":"b4525bdc-f61e-449c-8a5a-5f00fc571ccf","year":2021},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:b9b6114ffad91da7258890cff37ff8a8aab8f234e775f3603c315d087dbde886","observation_id":"fe6f48a9-525f-4396-9d32-49983e62fcdb","resolution":{"observed_at":"2026-06-29T22:23:59.744559Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-07-11T04:49:02.656098+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-11T04:49:02.656098+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:c495d675bb5ab56e496f99595c453e05f189781e193c80ca5d5ed1af3743183f","observation_id":"4db204bf-cbb5-4f50-bc52-ad2d586b5278","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:ecab2ee2bdcea78866c99057b7c67424d3248c475863e936cdec6e15bf39ef54","observation_id":"f4d4a736-988a-4073-a2a2-ffa266834f85","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:11d9a04906d2a2b28eb80c52555ba0679766494b3c91af1c07df2b1dd72ed3bd","observation_id":"93208715-1385-4c4a-8cc6-750693329954","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:6ba87e0a971b92117fccf7558ae3fc6eaac2b9fbc750c53e7deaae5ecdfe65df","observation_id":"dcc5255b-346e-44f5-abb7-d78df28f91eb","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:81a9592baf7998bdb058783fe10fdcb737c793f1b4e34f0a648703b531f3f769","observation_id":"5836e060-28bf-44d2-8256-817df0859a69","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:120c66823f0cdfa4c72db33da7975d38cc529abb14a13a460f320f6a44372c84","observation_id":"89f009a5-a31c-4a7d-81bd-a2fd6a1fec51","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:b36597cd92ca3897728470e38ef2d3c4eff6745f42b5bdfaf77e800883ccb7db","observation_id":"7c9e9990-e19b-49fb-aab1-e5448ed646ef","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1145/3690624","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Zhang, H","venue":null,"work_id":"50bdf4b1-b409-4a8d-ab4e-3755098ffd58","year":2025},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:75056d2c120e3228bc7fefaf7c464a79c2224d2082951f9a5b3cfcec2dc48070","observation_id":"7caabeab-bd39-46cb-9dd1-172374d31dec","resolution":{"observed_at":"2026-06-29T22:23:59.736480Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1145/3648506","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Physics-Informed Neural Operator for Learning Partial Differential Equations.ACM/IMS Journal of Data Science, 1(3):1–27","venue":"ACM / IMS Journal of Data Science","work_id":"44cb4ee2-1de7-4522-a7fd-a80cec1af2dc","year":2024},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:5ab3efea330de0c473af635fd7ed7e0dcbc6d2cc7aa2ebf3f7a9bdc8761d58f0","observation_id":"00cf66f2-c8a8-46c8-b953-efd103e74cbd","resolution":{"observed_at":"2026-06-29T22:23:59.739755Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-07-12T08:49:33.59807+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-12T08:49:33.59807+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:0c753ea33d776e38f7923620e76e96207ab4067f0525cfafc6567f703340e191","observation_id":"c58f86ab-93ae-4ba6-aa8a-f25f25bf2299","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T01:07:42.960769Z","title":"Masset, R","venue":null,"work_id":"238df2e4-a3e5-46f3-860e-3ae2b0094b97","year":2019},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:cccabe8a40fed71ae367e0b8a16041a93d5cc4edc66c1c5141803344579b53a1","observation_id":"f00b6db4-72e3-473f-bc57-19edd717c7b3","resolution":{"observed_at":"2026-06-29T22:23:59.735208Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:f96a48bb94174900483428b74d339ada661d5037e6a1604df06683d86d03f581","observation_id":"9da45726-5a5a-4e45-8598-e95ce5d39d37","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-3-319-16874-6","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Moukalled, L","venue":null,"work_id":"8cd7cc16-21ba-4dfd-a5a5-63f5833ae5dc","year":2016},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:2b3c3b892b560d50164b16210a8ce0afad59a774ffbb789ad5e7f7f45d4fafc3","observation_id":"064060bd-f1d8-4446-bb15-f356e42fdfb2","resolution":{"observed_at":"2026-06-29T22:23:59.729544Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-05-23T21:22:59.580232+00:00","source":"crossref_status_cache"},{"observed_at":"2026-05-23T21:22:59.580232+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:b761cc8c6a7777c5b1b4a2662668fc29720c42842eb976bbd2e5d1c643507a8d","observation_id":"7f571d7a-8993-4555-b471-5ffb118b2ec4","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":"1980.Numerical heat transfer and fluid flow","venue":null,"work_id":null,"year":1980},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:414660924ff5bd8e0867a3f1c2ea183a0a079711f2e3fe9aa225c9de509d80d5","observation_id":"af3b89f1-a993-44ed-816e-ce28b9dfc265","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:c5678238f5797ce04f6ce4e56ebab09d135d6a78cc4a19e4210e3e272d86bd00","observation_id":"1a480304-4656-482b-b3f4-c304160bf612","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":"InInternational Conference on Learning Representations","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:006e4c0b638e8d06e57742ec5c787723f106bdd81e714ea375ec9844c52b77c2","observation_id":"99f0f822-4e71-4354-bcda-f533f8f4b06e","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":"Qi, Li Yi, Hao Su, and Leonidas J","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:09f38325ed382a6f566fdc7cfb674bc494a8e340f2d536a1c9974724985ccd30","observation_id":"6b7982b7-b136-484b-a2ac-4cd656cf36d5","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:4135561aec6db9f0785cf5793f8d04709bd8503023eb50375c41353702dc2ffd","observation_id":"1d55dc86-ac24-4663-b2da-d5943ae0b349","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:ef4e93800dcffad6a8efb2502071df2482de91865a8453f2248facc4bfa3139d","observation_id":"53cae1d0-c649-4d7d-9a9b-4d6750675923","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jcp.2018.10.045","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T10:17:00.970707Z","title":"Raissi, P","venue":"Journal of Computational Physics","work_id":"16a1de8a-4145-44c7-a263-8f01bfe9ca2e","year":2019},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:6a4c8f715d9535f7ddafab153e03a0c8bc84ba3ec9d53f3c605fa86d50ae94cf","observation_id":"b0b9d93d-f816-4b8e-bf91-57d55e07fb44","resolution":{"observed_at":"2026-06-29T22:23:59.738749Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-01T09:38:23.838098+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-01T09:38:23.838098+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:6ec025d26a7ae0b4ca361a2bbb619ee498fea792f6a84fd17883b651d29673e8","observation_id":"e61afebe-3030-46e0-8605-410688abc337","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/1.9780898718003","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T01:04:09.603660Z","title":"Saad, Iterative Methods for Sparse Linear Systems, Society for Industrial and Applied Mathematics","venue":"Society for Industrial and Applied Mathematics eBooks","work_id":"5e107711-412b-4722-8240-e426a84e1694","year":2003},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:7b48058b10f3f43bbb9f9e58d6beb58ace6485952cc7865e5c1d3411fb112eb6","observation_id":"8e20feee-c5b7-47d3-87bd-ac9d2dfaa50e","resolution":{"observed_at":"2026-06-29T22:23:59.737149Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-03T20:08:05.950862+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-03T20:08:05.950862+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jcp.2018.08.029","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Sirignano, K","venue":"Journal of Computational Physics","work_id":"0ac51904-60f3-4c6f-91ef-b2b6fa83c2cf","year":2018},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:7305ae0a0692dbb79608fddee174f72ba7e6f589b0b50353a4ba4e6367e80143","observation_id":"f70d6037-0240-42b7-a190-1a79b71b662c","resolution":{"observed_at":"2026-06-29T22:23:59.723413Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-07-10T22:18:50.646323+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-10T22:18:50.646323+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:118b3a53000b717d8561063687702fbae2208f54ac2e73872c5b0ce4a002b47b","observation_id":"a735e14b-069d-4197-9f39-06b88d7051bc","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":"Oosterlee, and Anton Schüller","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:340148f25db2ff50436270c0645de3a53a9b35eb48794c5a7853b0527574da5b","observation_id":"eff62961-e258-4b13-9c2a-0f0d23790a9e","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1609/aaai.v40i2.37080","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Proceedings of the AAAI Conference on Artificial Intelligence","work_id":"79f2656a-fa7e-4e78-ad4c-9d8b43ea39ad","year":2026},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:fea945a58ab53c794679b401ffd01a267bf975d7d853e1459e9f413bdd3d665e","observation_id":"04e46041-0f96-400e-b7fe-4de53d51c301","resolution":{"observed_at":"2026-06-29T22:23:59.738009Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:0e4c09ab1ea1da2ca624a734197067574fc3364bc9651a3e44d01f2b96472a33","observation_id":"35ed451a-8b42-42cc-aac4-9b21d7aeb420","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1126/sciadv.abi8605","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-08T11:24:54.680484Z","title":"Learning the solution operator of parametric partial differential equations with physics-informed DeepONets","venue":"Science Advances","work_id":"0f87d1ac-648a-4fee-b653-32545121bed2","year":2021},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:f75593d2cdd4d3ca8494ca9827c3d537d7e13caa6645c68933beff181e740446","observation_id":"7032f3e2-7918-4f64-8108-07750da301fc","resolution":{"observed_at":"2026-06-29T22:23:59.731438Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-07-11T00:19:07.195894+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-11T00:19:07.195894+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:b11d9a31bfbce8c561e2709bdf1c2374571f96f17280c0b0ed4d4a97a6429fdd","observation_id":"2ec13f3d-852e-4eec-b930-4118fb035254","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:a4529b2b4231198ce2db43cf9a48cb026cc16662e1135ae3ba4bb4de893e2066","observation_id":"4f558e5f-d094-49ac-bb83-b9e87e61a679","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":"In International Conference on Machine Learning","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:a4dc963a09385e5c4db81bb4fc62d11e85b56d0eb9eb94ff90bfd45c6650b1eb","observation_id":"39f66514-2a1f-4d33-a67b-88ffe6cc7a59","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2022.114823","doi":"10.1016/j.cma.2022.114823","metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Gradient-enhanced physics- informed neural networks for forward and inverse PDE problems.Computer Methods in Applied Mechanics and Engineering, 393:114823, 2022","venue":"Computer Methods in Applied Mechanics and Engineering","work_id":"fd0e69d2-713e-4267-9c11-51b97f5cc9e0","year":2022},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:bdd92eeb5deaf6d356afc41ad83694cd5fb0150110bdb524ecf2d87046b07419","observation_id":"33e1074c-ec56-416c-b5ed-6b2ac42cceb0","resolution":{"observed_at":"2026-06-29T22:23:59.741704Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:191ac4eff6182b331362d206e9850c96808d4566766364fd3e07ff6bd50e609a","observation_id":"8e26da6b-5bff-4249-81f5-300fd1c442ed","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1038/s42256-024-00910-x","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Blending neural operators and relaxation methods in PDE numerical solvers","venue":"Nature Machine Intelligence","work_id":"aa48e378-61f0-47a6-8b4d-c3108be952e4","year":2024},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:f745157aa2648591713f2147c2b98cea55403ad2132527f4818c7bd350e69aa5","observation_id":"4f8b6a03-df55-48cf-8034-1e03310223d2","resolution":{"observed_at":"2026-06-29T22:23:59.727725Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:f4b2694c849ee47e0a0a26af9beb7576bb58f39bd834c330a8cc4f75002bc534","observation_id":"9905143e-5e02-43fd-b316-fc53110b83ac","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.10862","last_updated":"2025-08-09T08:53:51Z","snapshot_observed_at":"2026-08-07T04:13:41.928562Z","submitted_at":"2025-06-12T16:23:02Z","title":"OmniFluids: Physics Pre-trained Modeling of Fluid Dynamics","version":2},"cited_work":{"arxiv_id":"2506.10862","doi":"10.48550/arxiv.2506.10862","metadata_source":"arxiv_reference","pith_arxiv_id":"2506.10862","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Zhang, Q","venue":"arXiv (Cornell University)","work_id":"50182824-53c4-46ea-ac9b-d821938c7b41","year":2025},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"cited_paper":"/paper/2506.10862","citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:7d9eabad7419186dc45b5b063f6205517f72ace4c7fd689dd0f660a61b88beb0","observation_id":"c81cf41d-d3eb-43c3-835f-eb8e1598559b","resolution":{"observed_at":"2026-06-29T22:24:00.821301Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:60078e2902aef032ff1e6fb914c88439f221d36c88ddb5b0f216e5b600eda39b","observation_id":"86e45c45-0ac7-4947-8edd-13556934328e","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":"Zienkiewicz and R.L","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:1727c31739062500d59296f7b6133aed1ba490d1949c78624c1925f4abdd3821","observation_id":"2df98b7c-def6-45c9-8034-7f5a0c8be433","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":"hot spots","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:408eae4175d5298f5ab037cf7eae5627034b9002392ff860ea044b514718747e","observation_id":"316db972-a57b-4254-91d4-5bcfb5426431","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:f3142958ed86f392802bbaadda071ebf2c6ed41a1cd2ab637233c655856dcb52","observation_id":"1f22308d-27c4-46ee-b5b3-3b84d3a15cb1","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":"from {1,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:aa19523b848420b41235eb3f4f92b34ffa4674ad31b98fe4111acbf31bd88d0f","observation_id":"67a23e35-8dcb-40d1-9dc0-ffbea962dde0","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":"and we use isotropic widths 𝜎𝑘,𝑥 =𝜎 𝑘,𝑦 =𝑠 𝑘","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:163b8c62e3925a5251fa12d17ae7d779ea87c26170b7df72d2b6a8c7f468379d","observation_id":"f95185f5-d0d7-46e3-927a-1f2ec00ee657","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:b20145a9daa7edec8d75c96eb24ac2c9dd2c30922cf3c9c7ebdf8fcca30ec614","observation_id":"0edaab08-cb92-4ce5-85a1-fd9424d48fbc","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","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":"2026-06-29T22:15:33.807145Z","title":"Then the returned heat-source field is scaled: 𝑓(𝒙 𝑖 )=𝑓 0 (𝒙𝑖 ) · 1 ¯𝑓0 +𝜀","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-06-29T22:15:33.807145Z"},"links":{"citing_paper":"/paper/2605.25786"},"observation_digest":"sha256:46788da492ad35d3d6b8aa73a3156a964317d4815379ab9b7e57fea2748b831a","observation_id":"80fd0456-238c-4c60-9e38-4bb4bee8584f","resolution":{"observed_at":"2026-06-29T22:15:33.807145Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2605.25786","last_updated":"2026-05-25T12:33:52Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-03T19:16:51.554059Z","submitted_at":"2026-05-25T12:33:52Z","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision"},"reference_resolution":{"displayed":58,"state_counts":{"malformed_identifier":2,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":42,"verified_exact":13,"verified_fuzzy":0},"total_outbound_references":58},"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":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 7 August 2026, this Paper Citation Record lists 58 of 58 outbound references and 0 inbound Pith citation observations for arXiv:2605.25786."}