{"as_of":"2026-08-15T12:42:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:531aa4d7a463a9c4774ba9e2e4785e7f236639f8e91018310c476e6c80622324","coverage":[{"denominator":38,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":38,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T23:02:49.631514Z","state":"measured"},{"denominator":38,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":38,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-15T06:32:42.880941+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/2608.06660/citation-record","integrity":"/paper/2608.06660/integrity","json":"/paper/2608.06660/citation-record.json","paper":"/paper/2608.06660"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:02:50.055046Z","title":null,"venue":null,"work_id":"4814e693-231e-4ec5-b3f9-51e7c25024fd","year":2021},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.497481Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:4d16c4d816cc800f57f702eaf270726a78850c9a9c1b9a81dab76a9d305b5c55","observation_id":"8382c8df-2b28-4457-8b80-b1f70458e1c4","resolution":{"observed_at":"2026-08-10T23:02:50.058810Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:50.044517Z","title":null,"venue":null,"work_id":"a0942fb1-8b55-4d99-839e-d988f4da2b8d","year":2010},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.501574Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:72e89c23951fb5642113201739422d27fa9d260d152fb23c9c594c17fc1ee9da","observation_id":"fd4a3a9c-c9cd-4dc7-8510-91f687d9fff6","resolution":{"observed_at":"2026-08-10T23:02:50.048091Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:50.033482Z","title":"Numerical Mathematics (2nd ed.)","venue":null,"work_id":"178b41d0-c810-4509-ae9e-5d1ca0bd2e34","year":2007},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.505364Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:64a87b7a55115620bfdd64034a6d621bab7d6bcef1bebc91deae796b1d323d71","observation_id":"efcf94e9-4087-4a71-826c-e0c0016f4cff","resolution":{"observed_at":"2026-08-10T23:02:50.037188Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:50.022636Z","title":"C., Taylor, R","venue":null,"work_id":"0df9b782-6237-4b07-9b50-c0ceb01ba9e3","year":2013},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.508704Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:7a171f1ff02f78180523675715308d0f899a57ab11a572753a0881c3c0408015","observation_id":"e31a5014-eade-4bde-9174-403da2e0bace","resolution":{"observed_at":"2026-08-10T23:02:50.026278Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:50.012050Z","title":"H., & Peri, M","venue":null,"work_id":"37d76223-d569-4f8e-af88-a0c0bfb97c7b","year":2002},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.512460Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:843d212bab4164969fbcb1d84e47d90193e4585e0e58f5d1170c90a63a2de38b","observation_id":"0e1e110b-b09b-4c90-9828-bce1658bcce3","resolution":{"observed_at":"2026-08-10T23:02:50.015611Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:50.001050Z","title":"F., Soni, B","venue":null,"work_id":"ec326c09-9e43-4794-ba2e-6a322d508915","year":1999},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.515673Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:a27dd4a3f3148427035e3b01420a0dc52b095215a9cc66024b32b2be031de9b8","observation_id":"5c15678c-39c4-4929-8598-efb3e1f5695c","resolution":{"observed_at":"2026-08-10T23:02:50.005073Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.992063Z","title":null,"venue":null,"work_id":"c304dfc3-a3df-41fd-909e-0578612ffd51","year":2019},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.519530Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:1330212ee92ef2b9c4af6e1358b716defb26b91525518aa1b1762f89295daaf9","observation_id":"8597f63b-ebaa-4095-ac10-0ce72e53b29a","resolution":{"observed_at":"2026-08-10T23:02:49.995308Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.982894Z","title":"E., Kevrekidis, I","venue":null,"work_id":"6b37fa95-5084-49b2-83ec-f9a05e2568de","year":2021},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.522724Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:9b68fac84c0f80a08fcbba7d0c396e4552c55668376cdd30a300748c68706d59","observation_id":"ffd9d3af-b0f5-4dd2-98f2-d9645dfd0807","resolution":{"observed_at":"2026-08-10T23:02:49.986005Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.973382Z","title":"Understanding and mitigating gradient flow pathologies in physics-informed neural networks","venue":null,"work_id":"912af81d-4c5a-470c-a5f8-1d5f4c4e2ad0","year":2021},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.526121Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:bf8388653c3cf3296789b052aea6df817e1f61fcc325dcbd8be0635676d893a1","observation_id":"f30b682c-87fd-4713-ae45-9b7b1cc33268","resolution":{"observed_at":"2026-08-10T23:02:49.976589Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.963864Z","title":"S., Gholami, A., Zhe, S., Kirby, R","venue":null,"work_id":"474141b3-3bb8-4265-b064-8df56145a4c6","year":2021},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.529108Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:182348315a444507dafc387d601634146b104bfa38ceacb45b463f623c308dd2","observation_id":"85be662f-db27-4515-90d4-d1ac65d33c41","resolution":{"observed_at":"2026-08-10T23:02:49.967283Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.953950Z","title":"Respecting causality is all you need for train- ing physics-informed neural networks","venue":null,"work_id":"7eb7b31e-5767-45c4-b5aa-d2be39af3d33","year":2022},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.532037Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:dc556a8a06cb56e8e9332bd6a67f2e6470912a374b1f611c3fb72df1f4dcbc8f","observation_id":"14fc6739-99a3-4b7b-8c73-353bb49bf633","resolution":{"observed_at":"2026-08-10T23:02:49.957463Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.943388Z","title":"Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks","venue":null,"work_id":"80aa9eff-b674-4a7d-918b-d088fe106b58","year":2022},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.535037Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:c6f478b572f9f13abfc3d5d24ba81f1a904f72fff88b7d05d3b98e81b5712721","observation_id":"652da60c-56f2-4575-91a4-b9f12d2c0789","resolution":{"observed_at":"2026-08-10T23:02:49.947133Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.933212Z","title":"Finite Basis Physics-Informed Neural Networks (FBPINNs): A scalable domain decomposition approach for solving differential equations","venue":null,"work_id":"cc8aa709-57a9-4956-94f2-758cbc801003","year":2023},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.538197Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:2b9a9fa2c92ed247b89b425fa8c7e0da0c39b4891d384d2cf84ee234e9b8c37a","observation_id":"5e2f3d77-e0f8-4d97-9884-ca9e9f9c0b23","resolution":{"observed_at":"2026-08-10T23:02:49.937142Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.922662Z","title":"Y., & Tegmark, M","venue":null,"work_id":"de4ce0f4-ce0f-49e3-a6b7-d94b5aa2f1f8","year":2024},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.540938Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:3aeeb31c129620d7145c13ac1bbc6b585b442563ffd4c30432620aa0e64efbf7","observation_id":"3f8585e4-31e8-40cf-9450-63fdd0557ff0","resolution":{"observed_at":"2026-08-10T23:02:49.926633Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.912257Z","title":"S., Zhuang, X., Rabczuk, T., & Liu, Y","venue":null,"work_id":"3e4e940b-379f-4e36-8c0b-0c14ebd47911","year":2025},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.544037Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:f21167029302d3d1c1e51f6e7f6499f6dbbe771760df003e925f59660583cb4d","observation_id":"07dce702-e804-48bf-b76e-15c8197a4735","resolution":{"observed_at":"2026-08-10T23:02:49.915845Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.901596Z","title":"A., & Stinis, P","venue":null,"work_id":"37776a1e-2970-4d7a-999d-3944a1dafae9","year":2025},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.547067Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:667b9e5ce034c5519277c56723b497688c63467588dd7169d035cebd31795b5f","observation_id":"2f218296-0b70-4aff-8782-530836e7b255","resolution":{"observed_at":"2026-08-10T23:02:49.905515Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.889983Z","title":"A physics-informed deep learn- ing framework for solving forward and inverse problems based on KolmogorovArnold Networks","venue":null,"work_id":"aa988240-c0a9-4dbf-986b-3bbf2daafebd","year":2025},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.550396Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:d868953761fac9c2df8b9c30b3880db07cc8f897e99911d5e8af75512e8009d9","observation_id":"cfb1753e-b6e5-4ccf-bffe-b3ffadb79ed3","resolution":{"observed_at":"2026-08-10T23:02:49.894074Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.879255Z","title":"KAN-ODEs: KolmogorovArnold net- work ordinary differential equations for learning dynamical systems and hidden physics","venue":null,"work_id":"fd46f3f1-944a-4ed7-973a-ba0880630cfc","year":2024},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.553688Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:371f89206ca2166fe6f73547169d2b62799febcefb5fddbb6d95f0fc6f982b1c","observation_id":"5a337336-38e1-43e8-ad35-bb7d174d4944","resolution":{"observed_at":"2026-08-10T23:02:49.883038Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.868178Z","title":"Adaptive training of grid-dependent physics-informed kolmogorov-arnold networks","venue":null,"work_id":"66cffd92-12dd-4371-8186-82960435fc06","year":2024},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.556933Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:2798a82e1a7c601ee99439c54ac61463d20e0124448fcd3b73e2774282c07b3a","observation_id":"95617f78-4aff-4683-8910-e2a14e4ee9aa","resolution":{"observed_at":"2026-08-10T23:02:49.871475Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.858223Z","title":"Physics-informed kolmogorov-arnold networks for power system dynamics","venue":null,"work_id":"b44ec403-2ef4-4489-bc94-0c30b9a38ab7","year":2025},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.560767Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:9df565297d4748dde38df953b003254f8222396f1fe43302560fd3f66cd1c56c","observation_id":"4fb61ead-b7ba-4769-b415-6622c5bc6449","resolution":{"observed_at":"2026-08-10T23:02:49.861620Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.848087Z","title":"D., & Karniadakis, G","venue":null,"work_id":"e065bb6f-4702-4de2-9214-cb5ad28a5795","year":2020},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.565292Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:e0536d18b99234a6982311e5682597b30f198eebc32dcabb8b13b8890be77f48","observation_id":"18daa108-5d91-4434-b5f7-beccf2058750","resolution":{"observed_at":"2026-08-10T23:02:49.851231Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.837479Z","title":"PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irreg- ular Domain","venue":null,"work_id":"200c1df9-ef36-48ac-b515-3bda86045dab","year":2020},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.569264Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:fed426b0d7dca0fcb8fdd25631a7308f843c4dc189ec8a3279cc27d504c138ab","observation_id":"698439f6-da42-428b-a57c-597ea0f18fce","resolution":{"observed_at":"2026-08-10T23:02:49.841181Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.826633Z","title":"S., Son, S., Kim, Y., & Seok, J","venue":null,"work_id":"8222136d-21c2-46a6-bf8b-407fd13d8e89","year":2022},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.573023Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:592efe013958b5b71ed025fc5cfa2791ec726f86d2b51d3f63061f6d8a097adc","observation_id":"0c16d701-2aaf-4b55-86f7-515d37b9af0d","resolution":{"observed_at":"2026-08-10T23:02:49.829863Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.816455Z","title":"Pearlmutter, Alexey Andreyevich Radul, and Jeffrey Mark Siskind","venue":null,"work_id":"6af9f546-0c21-4dd0-8173-a8587d5c6b2c","year":2018},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.576717Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:73062f55f1eab7f46635e43c8126ca72cbbbca1d532f2795634251716a8c014a","observation_id":"3a8ff26d-0999-444a-a36d-3253bc8de289","resolution":{"observed_at":"2026-08-10T23:02:49.820235Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.805554Z","title":"A mathematical model for automatic differentia- tion in machine learning","venue":null,"work_id":"5f9ad928-2ebb-448c-9dd8-aab8be6cab91","year":2020},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.580406Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:d0417c12582512b59db1c3ef2317f17444e382d7efc5fdbf9d389b180f1e5477","observation_id":"1bdc8a6a-86ec-4c7a-88c6-42bfc1ffbb18","resolution":{"observed_at":"2026-08-10T23:02:49.809506Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.795104Z","title":"Auto- matic differentiation in ML: Where we are and where we should be going","venue":null,"work_id":"cb760300-3a0f-4a1c-a0c4-d3e742c350bc","year":2018},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.584198Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:02ca0fdfa0934a8e4913de890a1843a733a166285d373408034176fb48438540","observation_id":"d9bea659-2320-46c5-9bd6-a8588606d4a2","resolution":{"observed_at":"2026-08-10T23:02:49.798959Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.784430Z","title":"Nodal integral methods for heat and mass transfer in curvilinear coordinates","venue":null,"work_id":"95bfc04d-d0cb-4738-a3b2-e4bbb84907a8","year":2022},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.587902Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:b7e4841802af0337be2239233ed9bf398126447f5ac8c9eff41f49f62838daee","observation_id":"c5a6e074-4390-4589-a4e1-ed4c6714bab9","resolution":{"observed_at":"2026-08-10T23:02:49.788376Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.772924Z","title":"Pseudo-Spectral Methods for Linear Advection and Dispersive Problems","venue":null,"work_id":"171ecbff-5cd9-40f8-9a6f-e381e62f314f","year":2009},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.591557Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:9a562b084764de162392a1c4480454c52e1588454cb64f643efcf6754274940d","observation_id":"be56cecf-6d0d-439a-81be-95853dfb2dd7","resolution":{"observed_at":"2026-08-10T23:02:49.776780Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.761483Z","title":"A residual- based artificial viscosity finite difference method for scalar conservation laws","venue":null,"work_id":"2c252101-6d74-4b1c-8497-3060fe9fc8db","year":2021},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.595491Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:211248ee9f6b32d77247eddc2a3c3c5252bc340d6f658a618c3b47f354281a44","observation_id":"cedf73f4-d85a-43e6-97ba-30bd737c722d","resolution":{"observed_at":"2026-08-10T23:02:49.765445Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.750368Z","title":"Numerical study of 1D and 2D advection-diffusion-reaction equations using Lucas and Fibonacci polynomials","venue":null,"work_id":"efdf4431-e4a7-47d2-b9ff-63fc5070e49c","year":2021},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.600723Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:37edcc71888458395d677a46d42a158eeddaf866814c3c16569772c48f94a25d","observation_id":"ef0163b6-090f-461c-86c4-c8f095dfed06","resolution":{"observed_at":"2026-08-10T23:02:49.754498Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.739618Z","title":"Numerical Solution of TwoDimensional Nonlinear Unsteady AdvectionDiffusionReaction Equations with Variable Coefficients","venue":null,"work_id":"4e4bae02-d8f7-440b-954e-402875b7cb46","year":2024},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.604408Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:43324fbb591bd6f249d20ce72c2d5c6a70ad573f740bc0e21d04f01af7d716c9","observation_id":"a9683cf5-8df0-4dc6-9ffd-7423bfd3bf81","resolution":{"observed_at":"2026-08-10T23:02:49.743248Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.728573Z","title":"Nodal integral method for convection- diffusion transport using linear and higher order quadrilateral elements","venue":null,"work_id":"4f5e19f4-6456-4741-92d2-4d4e32f3ea12","year":2018},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.608032Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:ae3fcfac2c59d69a8ffa98b3b5c66cdd98344c8721543f7ac0e55caac2fd9e85","observation_id":"aa56c5a4-6db1-4eff-813a-fb986c0f5ab1","resolution":{"observed_at":"2026-08-10T23:02:49.732715Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.717511Z","title":"High-order accurate methods for unsteady vortical flows on curvilinear meshes","venue":null,"work_id":"a08b45d3-31e0-41e2-a831-acfea79447e6","year":null},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.611692Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:b0bb1cd35e3b10a1b68d92725c0e776f5c7a9c83653bda6c005ee6f342447df2","observation_id":"d7d0c15d-0591-4cbf-bfc7-1f7c1664ea75","resolution":{"observed_at":"2026-08-10T23:02:49.720908Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.707003Z","title":"On the use of higher-order finite-difference schemes on curvilinear and deforming meshes","venue":null,"work_id":"1490aa88-8fea-4817-9728-c23df61105be","year":2002},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.615196Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:fa33fc6458609e0000914806a5856057b8b0645239e440929efe9b8a1ab6a899","observation_id":"dd64e460-026c-44e2-baa4-2347c57710a6","resolution":{"observed_at":"2026-08-10T23:02:49.710643Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.696402Z","title":"A spectral difference lattice Boltzmann method for solution of inviscid compressible flows on structured grids","venue":null,"work_id":"c97faf9a-3404-4e96-8fb7-7d649b8087ee","year":2016},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.618732Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:eb63dbba289181c07a8af2cc35829c0ebe5dbb47aa92f69cdc0320e69d7a7fea","observation_id":"0143cba7-15e8-4e1d-9322-434355b7d357","resolution":{"observed_at":"2026-08-10T23:02:49.700116Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.685581Z","title":"Galerkin approach for estimating boundary data in Poisson equation on annular domain with application to heat transfer coefficient estimation in coiled tubes","venue":null,"work_id":"45175d21-79ba-40b0-911e-1f6a5ba99764","year":2019},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.622008Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:e2a4432cba0e477f7316e3662b651f84d67fe3d5ebadf89b3b890b8bb4fc3e82","observation_id":"9b4728bd-bba6-4265-83dd-3eeb2bd2819d","resolution":{"observed_at":"2026-08-10T23:02:49.689247Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.03347","last_updated":"2024-06-06T05:31:45Z","snapshot_observed_at":"2026-08-12T23:49:07.377358Z","submitted_at":"2024-06-06T05:31:45Z","title":"Chebyshev Spectral Neural Networks for Solving Partial Differential Equations","version":1},"cited_work":{"arxiv_id":"2407.03347","doi":null,"metadata_source":"pith","pith_arxiv_id":"2407.03347","snapshot_observed_at":"2026-08-10T23:02:49.662640Z","title":"Chebyshev Spectral Neural Networks for Solving Partial Differential Equations","venue":"math.NA","work_id":"0c8ac430-75a4-434f-9752-2caf3950ce17","year":2024},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.625699Z"},"links":{"cited_paper":"/paper/2407.03347","citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:d1eb64bb4b270831ace4358ae0a66966db3c187e27dbae0bb81418560b9205d4","observation_id":"42e6ba05-d038-46ec-b010-8e78646be9f1","resolution":{"observed_at":"2026-08-10T23:02:49.668250Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:02:49.675896Z","title":"Solution to the Problem of Convective Heat Transfer in a Toroidal Channel Using a Curvilinear Coordinate System","venue":null,"work_id":"9841c263-633b-426a-97bb-6cb167cb2ec9","year":2022},"citing_paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-10T23:02:49.631514Z"},"links":{"citing_paper":"/paper/2608.06660"},"observation_digest":"sha256:467230c7b13ffc2a1ec1de6d8174cc8fdd2cca163a56ee2ce6503f912e6a2af3","observation_id":"89a45dbf-5cf0-4328-9284-f17b0cb3b681","resolution":{"observed_at":"2026-08-10T23:02:49.679229Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2608.06660","last_updated":"2026-08-07T00:12:29Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-15T05:40:34.690007Z","submitted_at":"2026-08-07T00:12:29Z","title":"CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains"},"reference_resolution":{"displayed":38,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":1,"verified_fuzzy":34},"total_outbound_references":38},"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":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 15 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2608.06660."}