{"as_of":"2026-08-15T23:37:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:da69a7d3d55a96e4ca518c7bcb4aedb3aa74409b168e34f64390593a136f2ed2","coverage":[{"denominator":54,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":54,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T16:44:48.120963Z","state":"measured"},{"denominator":54,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":54,"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/2608.09483/citation-record","integrity":"/paper/2608.09483/integrity","json":"/paper/2608.09483/citation-record.json","paper":"/paper/2608.09483"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2025.11437","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:50.016832Z","title":null,"venue":null,"work_id":"917d19a8-de3f-40ac-9368-d0583f2cbd52","year":2025},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:47.835013Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:56b795ca10bc9d095813a47640fd79c1116965ad03d652515bafce8a02917b0a","observation_id":"b56856da-6b70-4218-bb26-7c6523c556f3","resolution":{"observed_at":"2026-08-11T16:44:50.022215Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"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":"2025.11438","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:49.955785Z","title":null,"venue":null,"work_id":"9f08792d-2e75-4bc1-9091-0dc9760b8d25","year":2025},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:47.839168Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:b9d11c6e6729ddb25605a97e05eea12461fbea9e63dd76690b2ed714a1ec3616","observation_id":"6bee5f21-b903-4108-9b28-d11b35ebfad6","resolution":{"observed_at":"2026-08-11T16:44:49.960869Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"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":"2023.11199","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:49.888493Z","title":"Rocha, S","venue":null,"work_id":"1135e54a-d499-4172-bc44-cfa87aa38e1d","year":2023},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:47.842766Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:90b92879a2032aa19fd54643446655007f4da1f2e7dc5f632430597e2320ce34","observation_id":"d7065738-87fa-4533-9a92-1268311ae33c","resolution":{"observed_at":"2026-08-11T16:44:49.892952Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:47.846320Z","title":"Würth, N","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:47.846320Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:95166b179e8dc162c3d4b21d68cd268dc53bfa44d2572f41b17ab660c3308595","observation_id":"c6bada1e-eb0d-4796-8b53-65065a1ab4ae","resolution":{"observed_at":"2026-08-11T16:44:47.846320Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:47.954528Z","title":"doi:10.1073/pnas.2530330123","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:47.954528Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:c54183d79c908bfb11d0fba3305f11aa8fb7be60f02e44b124153e673e888731","observation_id":"4ac8b1af-4980-4a81-9448-96a4d82023c6","resolution":{"observed_at":"2026-08-11T16:44:47.954528Z","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":"10.1137/25m1756818","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.268838Z","title":null,"venue":null,"work_id":"abae01df-5f99-4777-83be-1d1a8d1a3407","year":2026},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:47.958798Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:45fc082a786d1eeb926f60037dd6fdde3854178055dce780c7f72d0299c03913","observation_id":"ac073523-7385-498f-a7ef-f5ba5b3b3e0b","resolution":{"observed_at":"2026-08-11T16:44:48.272117Z","resolver_source":"doi","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:47.962882Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:47.962882Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:8777ddbf936223587a7bbd3b65d91e6e3b2c494289d32a77cf7ef1d28888aaa5","observation_id":"7b84aedc-103e-47ab-86a2-28e34727583d","resolution":{"observed_at":"2026-08-11T16:44:47.962882Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:47.965900Z","title":"Shang, C","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:47.965900Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:ce2e1391101cc67e966a402be90ef646d375b877ad579a3dc94540acd8c72615","observation_id":"1b403913-18b5-4638-b587-72e6b45f6f27","resolution":{"observed_at":"2026-08-11T16:44:47.965900Z","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":"10.1137/12086491x","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.254744Z","title":null,"venue":null,"work_id":"22fff1c3-2de8-4f9c-9935-0b4f06555775","year":2012},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:47.969884Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:9c0906e2b80170b35868b60ddfe42d18bd358077407ef6e228e18b26b2e414df","observation_id":"44853c13-2280-4f82-a742-ba6baf8c72db","resolution":{"observed_at":"2026-08-11T16:44:48.258338Z","resolver_source":"doi","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:47.973243Z","title":"Martínez-Lera, M","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:47.973243Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:2fed6bde77740154b662b4ec8883dd45b1e9cd5baa7f844fb4d8638657b966bf","observation_id":"db062de4-4719-4a47-8eaf-e9591b824c72","resolution":{"observed_at":"2026-08-11T16:44:47.973243Z","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":"2026.11472","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:49.639558Z","title":null,"venue":null,"work_id":"0145cde6-e448-460f-a666-b27e8b6d9b44","year":2026},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:47.976211Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:bc915c58cc6be1bbe183e7b506ab4caa614fb103b50cfff34eb57a8cd407a656","observation_id":"5962d968-54d2-4f0d-826f-98a5beeec6cd","resolution":{"observed_at":"2026-08-11T16:44:49.643712Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"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":"2022.11165","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:49.577781Z","title":null,"venue":null,"work_id":"5a3ef0ee-5b79-457c-b4d2-04449d44e5a8","year":2022},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:47.979826Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:48acc6307071811d73ac943b473d4019aa19072218199f90a1430b296e3c4e7e","observation_id":"a522baa4-105d-4aa9-a125-4df9d2f0586a","resolution":{"observed_at":"2026-08-11T16:44:49.582116Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:47.982764Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:47.982764Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:5b2f5ee1ecd9e4ed99d214acbd23676629d1f16c324b0f79b3b825556445ae9f","observation_id":"899fcd0c-b018-4eec-8f3d-f4f411ecd772","resolution":{"observed_at":"2026-08-11T16:44:47.982764Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:50.076966Z","title":"Hutzenthaler, A","venue":null,"work_id":"641576a9-0ee1-4950-a265-03e11d150afc","year":2022},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:47.986124Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:a73a1755cb678bf0b46e23ca01313f5570b00c66d2b330186675cf37ad322f77","observation_id":"7cc5ddb8-d8c5-4c72-970b-2924bc215434","resolution":{"observed_at":"2026-08-11T16:44:50.080794Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:47.989469Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:47.989469Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:5016a5d960327f09da3fb310509e405dcf3eba2ee46e392c573432a41d0caee2","observation_id":"cae41f4d-e8d8-4167-b269-0309c90eca8f","resolution":{"observed_at":"2026-08-11T16:44:47.989469Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:47.992506Z","title":"Raissi, P","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:47.992506Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:e5e37447ef90404ad5bef860efb7def0f1a72aac0ced44985aaa1229309e3ba9","observation_id":"d55fc9ad-4634-414c-a652-75eb4f9f8a04","resolution":{"observed_at":"2026-08-11T16:44:47.992506Z","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":"2026-08-11T16:44:47.995631Z","title":"Cuomo, V","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:47.995631Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:db885f608dfa48c19b617659d4980caa2ddc5728b7746b6f0ab33938459e8c1e","observation_id":"fbfcd23a-69cb-42b4-bddb-5eb73022ae1d","resolution":{"observed_at":"2026-08-11T16:44:47.995631Z","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":"2025.11390","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:49.454628Z","title":null,"venue":null,"work_id":"207d876d-c417-4a0b-bea5-d2c9fa7bf9e0","year":2025},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:47.998903Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:6ee96b9c57deb4fd46b6022b3fe43b5e5cdf9c20ee668239c330fca441279355","observation_id":"3ca9c82c-17f9-45d5-b8d2-cb1f0c64c2ca","resolution":{"observed_at":"2026-08-11T16:44:49.459422Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"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":"2025.11429","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:49.390815Z","title":"doi:10.1016/j.jcp.2025.114297","venue":null,"work_id":"f609f053-f12d-4d03-9226-d987357e37fe","year":2025},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.001906Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:87a6d4a1e6649a4d84754fb08273029b529b3da1f34d1f79816e61d06bc3ec97","observation_id":"8b788c24-66a2-4172-8da8-e3c5febb821f","resolution":{"observed_at":"2026-08-11T16:44:49.395995Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.005117Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.005117Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:e209164fe0b52ba38e455f252f0f0bb6b25c875e7179a220e8bea94d0a0bf2d0","observation_id":"9d20a4ee-5d5b-4260-a637-71496ad0fdda","resolution":{"observed_at":"2026-08-11T16:44:48.005117Z","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":"10.1007/978-3-030-36721-3_9","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T11:03:20.376878Z","title":"Calin, Universal Approximators, Springer International Publishing, Cham, 2020, pp","venue":"Springer series in the data sciences","work_id":"8c52db81-e482-47e5-94de-3cf8cb6eef98","year":2020},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.007959Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:aab3ea7d2b4fe73234eca08dfbc7e2f30e8ca5937a2590047ef9c587edbd6945","observation_id":"82c5eacb-74db-4d16-97f9-0f5dbcae8497","resolution":{"observed_at":"2026-08-11T16:44:48.232833Z","resolver_source":"doi","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.011175Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.011175Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:31254570197e44e0e6a9fc2b3b6566c4eac78b9e0f43a4a929c47dca1eb05bb0","observation_id":"120ce8c3-a116-4553-a239-124c9c85bb09","resolution":{"observed_at":"2026-08-11T16:44:48.011175Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.017249Z","title":"doi:10.1016/j.jcp.2023.112437","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.017249Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:bedc6e6828e6aa14e6d83a45182ce73585087f8353ae752b4db794a35bc659bb","observation_id":"557dafde-fa26-437f-aa51-275392063a1f","resolution":{"observed_at":"2026-08-11T16:44:48.017249Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.020791Z","title":"Sahli Costabal, S","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.020791Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:f106c44f33725ff4855103092692cabcc1800eb596bd671f2d10425ff88d761e","observation_id":"86c63fa3-ce40-4bb2-b6df-84ef7936d56e","resolution":{"observed_at":"2026-08-11T16:44:48.020791Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.024169Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.024169Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:6349573a115bf7c35d54a52d61be906d1b3e90e6016ba2a9001dc691dea6dcd3","observation_id":"d5d069b3-816e-4be5-a9da-bdf46f3f5faa","resolution":{"observed_at":"2026-08-11T16:44:48.024169Z","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":"2024.11291","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.953639Z","title":null,"venue":null,"work_id":"f51fb197-d522-4f13-97a2-e9985bb8ed98","year":2024},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.028037Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:2f0adcaa8d317fc8dbdded487b588ca5e08834ea8e17e2ae0213d27942948980","observation_id":"a7ddb5ca-1590-4126-9a59-0c3a0ea0aff9","resolution":{"observed_at":"2026-08-11T16:44:48.958910Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"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":"2026-08-11T16:44:50.067626Z","title":null,"venue":null,"work_id":"9e4b59ce-377c-4f4e-997e-fd348e8c66f8","year":2025},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.031663Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:226fd2840604865bafa3b7e295c2ea46b1a0553e888fa691ac4bd6712b83fc49","observation_id":"64d6fcc9-275e-4e9a-8a01-c65f979635a7","resolution":{"observed_at":"2026-08-11T16:44:50.071115Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.034483Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.034483Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:b7e73a840751a47f9044ccdd3d899b89cd23fc2c7fac6d11882f07d528a87b25","observation_id":"c29c6196-11b0-41d2-be5f-6781bd000715","resolution":{"observed_at":"2026-08-11T16:44:48.034483Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.037456Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.037456Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:c2021abbb0175e1e3bbb1a5831bb0c6e3af5af496aa04c8698aa32107af8bcc0","observation_id":"2fe11cde-b434-4e6d-9360-4a65e7c37532","resolution":{"observed_at":"2026-08-11T16:44:48.037456Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:50.057877Z","title":"26548–26560","venue":null,"work_id":"ff508149-dd6e-48d4-b3fa-4369579bef3f","year":2021},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.040360Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:fdeac746ec8e07329349ec6a5661a0d5840e0204f5608787eab55d827bbfcb30","observation_id":"eb8ec232-8e10-49d0-8c7e-2cd83384e915","resolution":{"observed_at":"2026-08-11T16:44:50.061489Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.043224Z","title":"doi:10.1137/20M1318043","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.043224Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:6b770f54dc2689af85a8949da3dd76705cc57e464b0019b7afdf96737fd61d2b","observation_id":"34bcc3bc-a7a4-4839-88a5-a885942d9ca9","resolution":{"observed_at":"2026-08-11T16:44:48.043224Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.046515Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.046515Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:9e91ae33cded447e0f83fbe900cc73945626bc6dbef7d90b50565e049ad0d5e0","observation_id":"8392b033-ec72-47f3-a997-e90232edceb0","resolution":{"observed_at":"2026-08-11T16:44:48.046515Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.049704Z","title":"Zhang, J","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.049704Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:8b3d6249da25069b4a7c00e8f2ee9366b7f12320ae582eae8599c891c9df034f","observation_id":"3292fbbf-5b68-4f8c-98bc-60180abe9421","resolution":{"observed_at":"2026-08-11T16:44:48.049704Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.052677Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.052677Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:0cfebe653bf12c267d502ab40874922918c56bcd230c1197af953a368e970232","observation_id":"3badb5ab-8aca-427a-84dc-6893770f946b","resolution":{"observed_at":"2026-08-11T16:44:48.052677Z","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":"2026.11507","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.636251Z","title":"doi:10.1016/j.jcp.2026.115071","venue":null,"work_id":"a2dc1f4c-3b1c-46fa-b7f6-39688cdc780f","year":2026},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.056194Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:4e0452ea788fb32fcb21a6eaf5970e9e2d2ec7bc8909d741ccdaaa81b145ad44","observation_id":"914149ff-7d8d-4d9d-86ec-25fc8130fea8","resolution":{"observed_at":"2026-08-11T16:44:48.641245Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"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":"2026-08-11T16:44:50.048137Z","title":null,"venue":null,"work_id":"8584e1ae-f5ac-49d7-ad33-cca6c3d8ba78","year":2023},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.059595Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:e1280a90576e39505e164467d8aa2d08dcf397f8daf0ce13c40e0e40171ae7e3","observation_id":"8eeb8a6e-0211-4a68-8a00-3248c8c26bb5","resolution":{"observed_at":"2026-08-11T16:44:50.051544Z","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":"2026-08-11T16:44:50.039150Z","title":null,"venue":null,"work_id":"a5bc9133-f239-4b90-9198-a4dd08cd889f","year":2025},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.062692Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:9747d0e133a13499bf1ea2dfe0e9ff76965c474de6d04ac812c07b7304c2a60a","observation_id":"a3e24b33-defa-4e33-a5e3-4694bb3959f1","resolution":{"observed_at":"2026-08-11T16:44:50.042056Z","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":{"arxiv_id":"2207.01751","last_updated":"2022-07-04T23:56:27Z","snapshot_observed_at":"2026-08-13T15:10:37.401435Z","submitted_at":"2022-07-04T23:56:27Z","title":"TT-PINN: A Tensor-Compressed Neural PDE Solver for Edge Computing","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2207.01751","snapshot_observed_at":"2026-08-11T16:44:48.065737Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.065737Z"},"links":{"cited_paper":"/paper/2207.01751","citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:f930f1cf650665d9f37d3f50efb933676fa2e35d55b2f1a56f7b579a953d9860","observation_id":"036abe7e-5aec-41e9-bcba-1dbf23f88d0c","resolution":{"observed_at":"2026-08-11T16:44:48.065737Z","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":"10.4208/jcm.2307-m2022-0233","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.212650Z","title":null,"venue":null,"work_id":"212bd140-d281-4a0f-9fe4-23f3ac889f06","year":2024},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.069660Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:59891f0f02258ff7466a4fa812ee6601b054dab6c9d1bd8169c1be5999fb6dc2","observation_id":"b61eb22d-0c0f-4686-b4f6-a298732a3bdd","resolution":{"observed_at":"2026-08-11T16:44:48.216126Z","resolver_source":"doi","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":"10.1007/s10915-024-02700-4","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.203840Z","title":null,"venue":null,"work_id":"0d065796-ae23-4946-9537-4988f59831e1","year":2024},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.073256Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:f3cc876cc4a8f149445057adb7ee37e63439b040e0debc1d7b41757a90aba8b4","observation_id":"d259af8f-b9e7-40f1-9f09-26a40efe7366","resolution":{"observed_at":"2026-08-11T16:44:48.206997Z","resolver_source":"doi","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":"10.1016/j.patrec.2026.06.027","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.192736Z","title":null,"venue":null,"work_id":"3b84ba50-8b16-4e93-8942-02e1430ef8f4","year":2026},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.076401Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:6331b7c6b23fb1bcb517dc4ed998fa279743cfc48c2da2ed0a08f480fe30f74e","observation_id":"5c3d62d7-2132-41ae-b585-c3dfaffed184","resolution":{"observed_at":"2026-08-11T16:44:48.196581Z","resolver_source":"doi","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.079477Z","title":"Mandl, S","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.079477Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:80873a7930f5707efbb9f9c7b88df5dc7a6f02a868386d8330e922e5d1c6a8b2","observation_id":"445ec391-c287-401a-82f7-52d2ed94df89","resolution":{"observed_at":"2026-08-11T16:44:48.079477Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.083174Z","title":null,"venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.083174Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:6affd1cd130757e343cbb0889956ea1e787ebdcda67ed6f5b0d84bb4dbffb39d","observation_id":"bc44de9f-85b2-44b7-97e4-2b2061aafc82","resolution":{"observed_at":"2026-08-11T16:44:48.083174Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1606.05535","last_updated":"2016-06-17T14:40:18Z","snapshot_observed_at":"2026-08-15T14:21:43.753243Z","submitted_at":"2016-06-17T14:40:18Z","title":"Tensor Ring Decomposition","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1606.05535","snapshot_observed_at":"2026-08-11T16:44:48.086367Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.086367Z"},"links":{"cited_paper":"/paper/1606.05535","citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:f193f21413124652f02c6265672a53af2d36ba0e74c4e7eaa3ce9cde8a0c5e99","observation_id":"3c901049-082f-47ac-b45a-55e9be2ba526","resolution":{"observed_at":"2026-08-11T16:44:48.086367Z","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.v35i12.17321","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.173066Z","title":"Zheng, T.-Z","venue":null,"work_id":"b9902bfa-1118-42b4-8f5b-3dc0f6446fbd","year":2021},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.089923Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:561f7fb55a07db261391c5177169195db3520caf0025b0e9e5cc37879de3cac9","observation_id":"05e59129-7fc3-48e7-9ee9-10d95b99f9f0","resolution":{"observed_at":"2026-08-11T16:44:48.176453Z","resolver_source":"doi","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":"10.1007/s10915-022-01841-8","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.163923Z","title":"doi:10.1007/s10915-022-01841-8","venue":null,"work_id":"62a19673-7a0b-4300-90d0-9083921849b4","year":2022},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.093742Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:e1f816a077126ec82a2881d7e4e57da82ac8636ac8df47ea074b4e7ef2285a9a","observation_id":"c6092905-6d76-400e-8a13-9ae6e0d979ab","resolution":{"observed_at":"2026-08-11T16:44:48.167149Z","resolver_source":"doi","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.097079Z","title":"22413–22422","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.097079Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:4c772ec6b96f83859822a272608ab8ad3a419c99d27876d94d8fa825c776f5de","observation_id":"15f302a9-a7ac-41d5-9175-55e54c2638f9","resolution":{"observed_at":"2026-08-11T16:44:48.097079Z","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":"2026.11495","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.481702Z","title":null,"venue":null,"work_id":"7e76dcc8-87d1-4174-ab5a-e469f974ea61","year":2026},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.100840Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:5bf18647686e7fd4121ead14ad76b31184d98d3ba3fac33f3ec8f186355e5c5f","observation_id":"07a4e9bd-36d6-412b-bd19-85eefef899f1","resolution":{"observed_at":"2026-08-11T16:44:48.486682Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.104425Z","title":"doi:10.1016/j.jcp.2022.111510","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.104425Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:ec8bfd34badd95bcd95130279ae3b6f32726a4eebf56d14bb52c4b8718eb0f5a","observation_id":"c05600d4-680b-4ee3-9f13-23bd02a8b4c5","resolution":{"observed_at":"2026-08-11T16:44:48.104425Z","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":"10.1137/23m1621356","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.153535Z","title":null,"venue":null,"work_id":"2182182c-c57c-4f28-bbf6-9da5bbef294b","year":2025},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.107720Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:56dca3c7ad4f1eca341c87aea10b951ddae02fac2097140e731a419f7f627645","observation_id":"353a88d1-83d3-4b56-9d6d-313c2cc3e72c","resolution":{"observed_at":"2026-08-11T16:44:48.157739Z","resolver_source":"doi","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.111318Z","title":"Arzani, J.-X","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.111318Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:ecd1045667dc3b1561b094495e73c77429b831d45c25592d14401b2d6765418d","observation_id":"81f922cc-0d63-4f4f-90bf-ba691a13c5ba","resolution":{"observed_at":"2026-08-11T16:44:48.111318Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.114789Z","title":"doi:10.1109/TPAMI.2023.3341688","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.114789Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:87d11a05274cc4ea0bc9bb52da7e0e02083648a83c9a23d041b0f9818e31ec7e","observation_id":"a716d6c3-de58-469e-b2a3-96bb58d79c96","resolution":{"observed_at":"2026-08-11T16:44:48.114789Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:50.028047Z","title":null,"venue":null,"work_id":"fc873f78-e498-46b4-8b63-bedc90548022","year":2015},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.118027Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:899ded8af0e108b2598c29ee9dfbf537766887e018f24fd2c93a11d3418ead3f","observation_id":"7736fc60-c133-4e59-b336-f058d85d20a1","resolution":{"observed_at":"2026-08-11T16:44:50.032341Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T16:44:48.120963Z","title":"Kochkov, J","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-11T16:44:48.120963Z"},"links":{"citing_paper":"/paper/2608.09483"},"observation_digest":"sha256:bd73ab84889329cc47e9363efd17765f48a73a1a1e06a299eeb3700083030f51","observation_id":"3d7f8101-4667-4889-96ba-864c4ead6506","resolution":{"observed_at":"2026-08-11T16:44:48.120963Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2608.09483","last_updated":"2026-08-10T11:48:43Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-14T20:24:15.663269Z","submitted_at":"2026-08-10T11:48:43Z","title":"Hierarchical rank-evolving representation for physics-informed neural networks"},"reference_resolution":{"displayed":54,"state_counts":{"malformed_identifier":2,"metadata_mismatch":10,"parse_uncertain":0,"unresolved":32,"verified_exact":9,"verified_fuzzy":1},"total_outbound_references":54},"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 54 of 54 outbound references and 0 inbound Pith citation observations for arXiv:2608.09483."}