{"as_of":"2026-08-08T09:12:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:48bd7bc03eb063d05fd6007bae05caa880cfc3f3e263ca4c20fac2dd42375d4e","coverage":[{"denominator":63,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":63,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T20:34:09.353275Z","state":"measured"},{"denominator":63,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":63,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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/2507.02524/citation-record","integrity":"/paper/2507.02524/integrity","json":"/paper/2507.02524/citation-record.json","paper":"/paper/2507.02524"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:34:10.676961Z","title":"Koric, D","venue":null,"work_id":"b9f845f3-db94-42d5-b928-147a95938e7a","year":2021},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:08.984592Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:1e804345fe43149a4fc4755301fdcbe26a99c4548f368fed6e96b2e17fab058f","observation_id":"2c903c88-b1a0-4742-90a4-35e407d46db1","resolution":{"observed_at":"2026-08-06T20:34:10.682622Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:10.660324Z","title":null,"venue":null,"work_id":"5da89e16-7fb1-4c08-b5cc-7ee808170bb2","year":2022},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:08.990348Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:6f1e03e7f7df5279b05eb56cc9a71b4bc66f44c16778fcbb86debb94288e2b4a","observation_id":"fa9612a4-c3a6-419f-a208-62a3cc867b3a","resolution":{"observed_at":"2026-08-06T20:34:10.665511Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2309.15421","last_updated":"2023-09-27T05:57:19Z","snapshot_observed_at":"2026-08-08T07:46:47.071731Z","submitted_at":"2023-09-27T05:57:19Z","title":"Deep Learning in Deterministic Computational Mechanics","version":1},"cited_work":{"arxiv_id":"2309.15421","doi":null,"metadata_source":"pith","pith_arxiv_id":"2309.15421","snapshot_observed_at":"2026-08-06T20:34:09.979105Z","title":"Deep Learning in Deterministic Computational Mechanics","venue":"cs.LG","work_id":"67e0689c-4d9b-4ee8-9845-1656ee6c0c52","year":2023},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:08.996250Z"},"links":{"cited_paper":"/paper/2309.15421","citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:201e0dfe4515e727d42b659b26d004df4a97ebe8a8c48d25fe80b1b3cdcec3ff","observation_id":"2e0dc50f-8286-4d13-9320-6ff691adebc0","resolution":{"observed_at":"2026-08-06T20:34:09.984558Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:10.644095Z","title":null,"venue":null,"work_id":"373a9920-04f0-4679-917e-25fab92aeb3c","year":2024},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.003234Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:2102bcdc767a49942adcc5e5a2db384b8aa1fa6f0823557c654008f816b61f9a","observation_id":"b174219d-2469-4544-ac2f-1568a28b6535","resolution":{"observed_at":"2026-08-06T20:34:10.650330Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:09.008157Z","title":"Bonatti, D","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.008157Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:09052a38df226525678ea1e610dfbb963397fa3d05f711a6459e23376dc4d193","observation_id":"dd22300a-50aa-45b0-b4f7-392554807e25","resolution":{"observed_at":"2026-08-06T20:34:09.008157Z","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":"2026-08-06T20:34:10.611840Z","title":"Kidger, J","venue":null,"work_id":"261e58d8-fdbd-47cf-9242-b009a146a3b2","year":2020},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.013016Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:97aecc809fe16b011264952293eea5713db22ff6005c1495b4d1b4d6f0ae3371","observation_id":"e165db73-994c-4f3a-bb6f-9141dafc2a3f","resolution":{"observed_at":"2026-08-06T20:34:10.621548Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:10.590232Z","title":null,"venue":null,"work_id":"800a037d-4e5b-4e62-88d8-5a621e4ccf19","year":2020},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.018567Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:680b4abcd2be0d0a6f2cd952c846f30f44496973ed75c7d101e0e47c29fb680f","observation_id":"fcdf9ddd-f44f-4555-b761-06878d4993df","resolution":{"observed_at":"2026-08-06T20:34:10.595556Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:10.573256Z","title":null,"venue":null,"work_id":"3a6614fc-451a-42b6-91d5-7736e22c4a5c","year":2023},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.023986Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:5b66c5b65c5ad4e3c268cd1c0558468a3c5818aaff377c929abcfd4f35753777","observation_id":"681086b2-410d-4c3a-b271-e663c85835d4","resolution":{"observed_at":"2026-08-06T20:34:10.578188Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:10.556923Z","title":null,"venue":null,"work_id":"35ae9fad-c1ce-49bf-912b-970cbe64c294","year":2023},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.029819Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:549a75dd9a692f3ded72b5283b99059a3b3bb09c8f48164b00bbac75e89840f4","observation_id":"2a8622f4-bfa6-4d98-b15f-d1efcd68da59","resolution":{"observed_at":"2026-08-06T20:34:10.562420Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:10.540768Z","title":"Pantidis, H","venue":null,"work_id":"92f10ae4-9719-43e6-9a1e-838aac066801","year":2024},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.034770Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:1b37db113aee22577c4dc96f153d1ba7e6e0bbc6a9170abdbfe82b126c5a5b42","observation_id":"91c13762-9b8d-4c6c-894b-d4a9a5ba3282","resolution":{"observed_at":"2026-08-06T20:34:10.546466Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:10.524094Z","title":null,"venue":null,"work_id":"966df6a6-33d9-458b-a750-bcd8d71fb4b1","year":2024},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.039637Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:a398f7582b6f5d93c23b24ee6e09e5669811b235ad5515a8c8e4d69c757934dc","observation_id":"1aace512-eb53-4c52-a158-93b9f803e42e","resolution":{"observed_at":"2026-08-06T20:34:10.529084Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:10.506125Z","title":null,"venue":null,"work_id":"bdcb7499-681d-4b5f-b81a-186519140484","year":null},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.044044Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:c0b5f64e0f522225ce607a93d7fc8d5eb9dcda39dd36037d81cb26361287dd49","observation_id":"f8186104-cdd0-47ef-a4d1-3bca3bdf156b","resolution":{"observed_at":"2026-08-06T20:34:10.512333Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:10.486588Z","title":"Anumasa, P","venue":null,"work_id":"7be9ce1a-46ca-4c85-94c4-43cd15e94fdf","year":2022},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.050556Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:89b6d1fa80323582f63cfe6788dc62f4a82fbbc6f2317869a562cfdf897ab0f0","observation_id":"f5f6caac-80d9-46bd-b0d9-8d981376ffdd","resolution":{"observed_at":"2026-08-06T20:34:10.492240Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:10.468750Z","title":null,"venue":null,"work_id":"b1306878-5526-4b99-b664-73951bc64073","year":2021},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.055154Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:14d247fc8259367d4f759cfbb368b6899f7af2914dbaec17475ce55b0f073bde","observation_id":"13bb2512-a974-4738-8d36-2b8cba26ad20","resolution":{"observed_at":"2026-08-06T20:34:10.474585Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2102.02248","last_updated":"2021-02-20T14:18:03Z","snapshot_observed_at":"2026-07-06T10:38:16.325587Z","submitted_at":"2021-02-03T19:33:51Z","title":"Reduced-order Model for Fluid Flows via Neural Ordinary Differential Equations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2102.02248","snapshot_observed_at":"2026-08-06T20:34:09.059764Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.059764Z"},"links":{"cited_paper":"/paper/2102.02248","citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:ee84a1718512df76707c598bfd54ece34235d13d30bf692ac9abd36213109e3a","observation_id":"63f9ff83-71ff-4add-833d-d47f77958c3d","resolution":{"observed_at":"2026-08-06T20:34:09.059764Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2104.13962","last_updated":"2021-04-22T19:20:47Z","snapshot_observed_at":"2026-07-06T11:04:30.929441Z","submitted_at":"2021-04-22T19:20:47Z","title":"Neural Ordinary Differential Equations for Data-Driven Reduced Order Modeling of Environmental Hydrodynamics","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2104.13962","snapshot_observed_at":"2026-08-06T20:34:09.065111Z","title":"Dutta, P","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.065111Z"},"links":{"cited_paper":"/paper/2104.13962","citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:e4e93c2f0b44e4ce0124ff37a4e833ebc1a01ccd3a4cd7c7b31101a492abc379","observation_id":"2061a3a6-40b4-46d1-a847-a27d3bcab982","resolution":{"observed_at":"2026-08-06T20:34:09.065111Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1911.05180","last_updated":"2019-11-12T22:54:54Z","snapshot_observed_at":"2026-07-06T08:36:33.016278Z","submitted_at":"2019-11-12T22:54:54Z","title":"Turbulence forecasting via Neural ODE","version":1},"cited_work":{"arxiv_id":"1911.05180","doi":null,"metadata_source":"pith","pith_arxiv_id":"1911.05180","snapshot_observed_at":"2026-08-06T20:34:09.907317Z","title":"Turbulence forecasting via Neural ODE","venue":"physics.comp-ph","work_id":"4664d932-5838-4018-8080-08ae8933e41c","year":2019},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.070286Z"},"links":{"cited_paper":"/paper/1911.05180","citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:0a100f466dad6dfeccd0d1c003948f02d0fe169559e638ab6fb8a4fdf609d2df","observation_id":"d8b2c85b-b778-48bc-9116-162dcbcdf279","resolution":{"observed_at":"2026-08-06T20:34:09.912891Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2202.02435","last_updated":"2022-02-04T23:32:29Z","snapshot_observed_at":"2026-07-06T12:34:39.580403Z","submitted_at":"2022-02-04T23:32:29Z","title":"On Neural Differential Equations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2202.02435","snapshot_observed_at":"2026-08-06T20:34:09.075360Z","title":"Kidger, On neural differential equations, arXiv preprint arXiv:2202.02435","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.075360Z"},"links":{"cited_paper":"/paper/2202.02435","citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:b353d13fb5234238c83e7f53975e042fb53062d8caee5fac10e7569030da438f","observation_id":"60304bcb-f0ec-47d5-902a-4588fecc8479","resolution":{"observed_at":"2026-08-06T20:34:09.075360Z","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":"2026-08-06T20:34:10.453320Z","title":"Morrill, C","venue":null,"work_id":"9cba3993-b779-4497-b85c-1252231fc7cc","year":2021},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.080418Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:356fc72c3e1652826450d7494b15baf98764bac6975ea7912e5ab8420b637517","observation_id":"ff9f2711-eca0-41a9-9310-8b79cd403cad","resolution":{"observed_at":"2026-08-06T20:34:10.458339Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2106.11028","last_updated":"2021-06-21T12:23:45Z","snapshot_observed_at":"2026-07-06T11:21:17.202999Z","submitted_at":"2021-06-21T12:23:45Z","title":"Neural Controlled Differential Equations for Online Prediction Tasks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2106.11028","snapshot_observed_at":"2026-08-06T20:34:09.085086Z","title":"Morrill, P","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.085086Z"},"links":{"cited_paper":"/paper/2106.11028","citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:98e8de6a30c9768cb773ca091fd0fd0e39735e3beb09bb2a4d4ac83b4b7b6949","observation_id":"82d59745-6a80-49dc-b58a-13d1275a4fe4","resolution":{"observed_at":"2026-08-06T20:34:09.085086Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2305.16791","last_updated":"2024-07-01T19:29:57Z","snapshot_observed_at":"2026-07-06T15:33:49.583359Z","submitted_at":"2023-05-26T10:02:32Z","title":"On the Generalization and Approximation Capacities of Neural Controlled Differential Equations","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2305.16791","snapshot_observed_at":"2026-08-06T20:34:09.092028Z","title":"Bleistein, A","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.092028Z"},"links":{"cited_paper":"/paper/2305.16791","citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:5b3d93f16b2a217c24741a67c1b5b55b61994d15872dceda3a19b2d4b9490e68","observation_id":"ddc2a4f1-7f21-40e7-963a-6ce8bc1703e2","resolution":{"observed_at":"2026-08-06T20:34:09.092028Z","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":"2026-08-06T20:34:10.437205Z","title":null,"venue":null,"work_id":"c6468ff3-fa61-445b-8f5b-769efd104747","year":2022},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.098337Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:12d22c84c81f10532a9218de1bb920d54a9c6ab4eae57e75778cedffc346ef05","observation_id":"cfef238f-e52d-47df-a3aa-42726ad4a656","resolution":{"observed_at":"2026-08-06T20:34:10.442383Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:10.421819Z","title":null,"venue":null,"work_id":"d8f082cf-a41a-41ef-9433-f571a3194483","year":2023},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.103937Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:2961431d77e742eed866510d593b0376c5ae82735c6dfd327f68ec1af84730ef","observation_id":"a1b8088c-0fea-4747-aa00-f09811f5c130","resolution":{"observed_at":"2026-08-06T20:34:10.426897Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:09.109251Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.109251Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:be2dcd93b39f8ef9d09c4459136420c1de1f50fd14a490c2d717283895d55e21","observation_id":"9402829b-94d3-455a-b74a-c6e3edee9fab","resolution":{"observed_at":"2026-08-06T20:34:09.109251Z","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":"2026-08-06T20:34:10.392548Z","title":null,"venue":null,"work_id":"e3337cab-b1d2-4770-9c2b-57a2e02cdef1","year":2021},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.114886Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:fa7f039b8574256f7d52bc8bf921d1de360e5881e8dfe43ad1b4a1cb5eceffc3","observation_id":"6c5088b5-f6ff-4efb-8f7c-7ca215b4bf7f","resolution":{"observed_at":"2026-08-06T20:34:10.398084Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:10.376859Z","title":null,"venue":null,"work_id":"03610045-745f-4cff-8e64-f5939aceb52e","year":2025},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.124310Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:e47c925eddd29463b9ec62909cf8b157b4318d9de214dd804c063aa8a1620b29","observation_id":"c84dc6a5-5aa9-4791-9de8-303c98cd5a5e","resolution":{"observed_at":"2026-08-06T20:34:10.382157Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:10.360542Z","title":null,"venue":null,"work_id":"1e3f73b8-78be-4e90-ab4b-f2099238f465","year":2022},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.131795Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:17649cf6de91943c7bf3ab5f219a654bac9461e790ccdc204ba27e84ddec1273","observation_id":"aad457a5-d8d2-4de4-9ee0-eb33594f5b19","resolution":{"observed_at":"2026-08-06T20:34:10.366120Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:10.345563Z","title":"Goswami, M","venue":null,"work_id":"851ae4aa-ede4-4830-9e7e-6112d8054a28","year":2022},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.137412Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:0790d5d4e685d1cc5a3fa099431784542a23884e425cb7c51fd2bb59ac01d65c","observation_id":"22643355-f1d9-4de4-b4b0-ee825e3f97fd","resolution":{"observed_at":"2026-08-06T20:34:10.350357Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:10.330669Z","title":null,"venue":null,"work_id":"c3039eaa-44b9-40f4-918d-7bed3d98fc11","year":2023},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.142899Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:79de0254ce58d5b40f02a4c51ca101a22cab087cd744547e27646fb0a891872b","observation_id":"02431e8b-f5ef-4f04-8a5a-93a14424324c","resolution":{"observed_at":"2026-08-06T20:34:10.335298Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:09.148158Z","title":"Kobayashi, J","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.148158Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:a8812c8b59a566f047a36fa1f1dbae55cc411f18dde5975bce986c429d1bb403","observation_id":"c23d7432-14ec-488b-aac7-1d80f38688b9","resolution":{"observed_at":"2026-08-06T20:34:09.148158Z","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":"2026-08-06T20:34:10.303599Z","title":null,"venue":null,"work_id":"5f4e8160-e8e2-4723-b7c8-d9c02aab829f","year":2021},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.153270Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:d8e64aa867c9288066f982d3d1303dea3fea5d12db25eb075ef879e35c929d90","observation_id":"75182cf3-d609-4eff-b798-bab522de0686","resolution":{"observed_at":"2026-08-06T20:34:10.309001Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:10.284126Z","title":"Goswami, A","venue":null,"work_id":"7a93d8e5-614d-418b-abb2-c1df8a9878bc","year":2023},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.158647Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:d22cc2693d94c076be74b8b6ec5b845376db5e4981671484060d247039ae0edc","observation_id":"4bd0f6d1-30cb-47a0-9634-e55419488698","resolution":{"observed_at":"2026-08-06T20:34:10.289203Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:09.163847Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.163847Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:d875d16c141382a91cd0a3b09438efccb05d588ea593e7bdf3c2cbd74e4fa574","observation_id":"a3ffdb67-21ad-40b0-879c-cfe95be53d88","resolution":{"observed_at":"2026-08-06T20:34:09.163847Z","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":"2026-08-06T20:34:10.258939Z","title":"Ingebrand, A","venue":null,"work_id":"9a1dae34-a247-4019-b12c-377406b0cd37","year":2025},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.169883Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:e54a8b78b80e453978705b70e39f8d0e74a279e63b969e3206fc123e96af0f8f","observation_id":"5df51d63-31b4-4843-85a0-88612b40b524","resolution":{"observed_at":"2026-08-06T20:34:10.263789Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.16118","last_updated":"2024-12-20T18:03:38Z","snapshot_observed_at":"2026-08-01T20:50:40.184368Z","submitted_at":"2024-12-20T18:03:38Z","title":"Convolutional Deep Operator Networks for Learning Nonlinear Focused Ultrasound Wave Propagation in Heterogeneous Spinal Cord Anatomy","version":1},"cited_work":{"arxiv_id":"2412.16118","doi":null,"metadata_source":"pith","pith_arxiv_id":"2412.16118","snapshot_observed_at":"2026-08-06T20:34:09.835543Z","title":"Convolutional Deep Operator Networks for Learning Nonlinear Focused Ultrasound Wave Propagation in Heterogeneous Spinal Cord Anatomy","venue":"physics.med-ph","work_id":"362851f5-058c-4b93-a149-5d185557e2ff","year":2024},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.175704Z"},"links":{"cited_paper":"/paper/2412.16118","citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:6cecf8a5da4e9d2d3c6624b8fc523398d2ba5576d2bf0ebb97b640c01c79e74c","observation_id":"f804671d-9556-4a83-bec6-4b1786bdc7ed","resolution":{"observed_at":"2026-08-06T20:34:09.841412Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:09.181990Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.181990Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:a60e0c129845664e200d80f36c73afdb4327fc1aa3ec27bea48b58e087ae3f6b","observation_id":"b234cdcb-8ebd-4710-9d14-9c25b4da1655","resolution":{"observed_at":"2026-08-06T20:34:09.181990Z","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":"2026-08-06T20:34:10.234026Z","title":null,"venue":null,"work_id":"223027c4-9bfa-4520-ae92-ae9b9c81fd13","year":2024},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.187495Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:6f96cae0d581119f737c0add0535f278997b99f561bb5b360619082da6b3e25f","observation_id":"0825d08f-6562-477d-8179-51af3b9b4013","resolution":{"observed_at":"2026-08-06T20:34:10.238571Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:10.218414Z","title":null,"venue":null,"work_id":"52933694-a105-4aab-a40e-7edf2d65c687","year":2024},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.193881Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:91e27761789e08de6581aaa7ddf55245236cbd435121a33f1c4d01bf27eb3c9c","observation_id":"2584fcfb-97b1-41af-b85c-94cd4751eb73","resolution":{"observed_at":"2026-08-06T20:34:10.223097Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:09.200549Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.200549Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:d19d7a743a24f45a06b3fadb6ca3c84715dc3bb4fa2e4efa1418a6900a3d51fe","observation_id":"5769bd10-3ecb-4d3f-bacc-d4fb015fbaba","resolution":{"observed_at":"2026-08-06T20:34:09.200549Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1912.10077","last_updated":"2020-02-25T03:12:57Z","snapshot_observed_at":"2026-07-06T08:46:09.705605Z","submitted_at":"2019-12-20T19:49:32Z","title":"Are Transformers universal approximators of sequence-to-sequence functions?","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1912.10077","snapshot_observed_at":"2026-08-06T20:34:09.205665Z","title":null,"venue":null,"work_id":null,"year":1912},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.205665Z"},"links":{"cited_paper":"/paper/1912.10077","citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:ce7f9e47a0eae9ed1060f7ebbe4e851b983d295edef3523cf442b48c7337c99d","observation_id":"e24742c2-24f2-4c94-9fb9-1d5775b6f79a","resolution":{"observed_at":"2026-08-06T20:34:09.205665Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2409.00841","last_updated":"2026-04-24T21:24:37Z","snapshot_observed_at":"2026-07-06T19:08:57.415038Z","submitted_at":"2024-09-01T21:10:36Z","title":"Universal Approximation of Operators with Transformers and Neural Integral Operators","version":3},"cited_work":{"arxiv_id":"2409.00841","doi":null,"metadata_source":"pith","pith_arxiv_id":"2409.00841","snapshot_observed_at":"2026-08-06T20:34:09.789316Z","title":"Universal Approximation of Operators with Transformers and Neural Integral Operators","venue":"cs.LG","work_id":"3932e3b9-7a90-4cb8-92a8-6a5e82906c1a","year":2024},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.214085Z"},"links":{"cited_paper":"/paper/2409.00841","citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:96e5af6c7f78a208e54ee65910d235e987267e86ab4f9e1a2bd6963dcb989f60","observation_id":"b239274c-d19b-4c31-a21e-185f1a048f42","resolution":{"observed_at":"2026-08-06T20:34:09.797418Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:09.219848Z","title":"Kovachki, Z","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.219848Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:7e6221ac22c9011b4afe1bfbec17e92983d8eea40be6bcd7a678b7a090f5ba8b","observation_id":"ad0db781-ea06-46c3-8555-d7e1e3d5212e","resolution":{"observed_at":"2026-08-06T20:34:09.219848Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2504.10932","last_updated":"2025-04-15T07:19:54Z","snapshot_observed_at":"2026-08-07T16:05:38.771225Z","submitted_at":"2025-04-15T07:19:54Z","title":"Multi-scale DeepOnet (Mscale-DeepOnet) for Mitigating Spectral Bias in Learning High Frequency Operators of Oscillatory Functions","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2504.10932","snapshot_observed_at":"2026-08-06T20:34:09.224896Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.224896Z"},"links":{"cited_paper":"/paper/2504.10932","citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:9470916d78a936150b0906f45cc1d993152c0b98c56e1e2184034b8ee5d66eed","observation_id":"ef5874a4-3c71-402e-b352-7d6963543de4","resolution":{"observed_at":"2026-08-06T20:34:09.224896Z","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":"2026-08-06T20:34:09.230142Z","title":"Tancik, P","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.230142Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:9cf134490bdd74dbf913f4ac49f4ccdbc8567cfb7c2a8e486f610af815919d3f","observation_id":"fdc1b93e-a515-4b6d-a815-14ca8f5070c4","resolution":{"observed_at":"2026-08-06T20:34:09.230142Z","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":"2026-08-06T20:34:10.172753Z","title":null,"venue":null,"work_id":"c718a45b-0c29-4b3b-8df1-f2d367f6ccdf","year":2024},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.236035Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:1b5a885273e1e7b83628baa2d3d5ddc3f1ec58448054b89ec50d47dee48c80b6","observation_id":"68bac212-8085-4a0b-9d82-7575c45610da","resolution":{"observed_at":"2026-08-06T20:34:10.177844Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:09.241971Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.241971Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:cdf038f036602ebb46854ea02b1a3d1b2b2ae7670edaf879d28b2dcd906694a1","observation_id":"30daeaef-d8bf-48c4-a489-191ac60d6c41","resolution":{"observed_at":"2026-08-06T20:34:09.241971Z","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":"2026-08-06T20:34:09.246866Z","title":"Nayak, S","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.246866Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:1706aa38bbf2722bcff9ae3dfb58e85f0c1d4457e9e1752dc24704f614fd446a","observation_id":"185a569e-88bf-47d6-b1fb-0ceb51e6fae6","resolution":{"observed_at":"2026-08-06T20:34:09.246866Z","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":"2026-08-06T20:34:09.252174Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.252174Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:cae05de65dc04ddb734e77358ae9b003da77c955cd568cd0fe0beb9d83c6017b","observation_id":"5b7ab877-497a-437d-b1b0-af00a468491c","resolution":{"observed_at":"2026-08-06T20:34:09.252174Z","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":"2026-08-06T20:34:09.258061Z","title":"Tretiakov, X","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.258061Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:e975633fbf20f73be1ddc509fd5c5ed02fd92f614ff6bc802c32d09d15c21341","observation_id":"71ec4440-8b80-4d2c-8fe3-1201329b75f5","resolution":{"observed_at":"2026-08-06T20:34:09.258061Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2205.11404","last_updated":"2022-05-23T15:47:47Z","snapshot_observed_at":"2026-08-05T18:26:04.000795Z","submitted_at":"2022-05-23T15:47:47Z","title":"Variable-Input Deep Operator Networks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2205.11404","snapshot_observed_at":"2026-08-06T20:34:09.265030Z","title":"Prasthofer, T","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.265030Z"},"links":{"cited_paper":"/paper/2205.11404","citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:a5760c032dc5ed54d687ea486e0d0f2763a50ba028ce31afb5f87ef1bbc116c2","observation_id":"b110b6fb-af01-4472-a2f5-1af681118509","resolution":{"observed_at":"2026-08-06T20:34:09.265030Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.08187","last_updated":"2024-02-13T03:14:32Z","snapshot_observed_at":"2026-07-06T17:29:17.367268Z","submitted_at":"2024-02-13T03:14:32Z","title":"Learning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular grids","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.08187","snapshot_observed_at":"2026-08-06T20:34:09.271975Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.271975Z"},"links":{"cited_paper":"/paper/2402.08187","citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:bc39884f52933fc1e7bf75a78a8038a87a0cbb761526a4b2a616786b951d8c82","observation_id":"21b96db6-73bd-470e-9b6b-7e9a9deea9f2","resolution":{"observed_at":"2026-08-06T20:34:09.271975Z","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":"2026-08-06T20:34:10.146958Z","title":"Bahmani, S","venue":null,"work_id":"f0d9bd71-5a17-43e4-a417-667d933903e9","year":2025},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.278256Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:21cbed5034a7bb350314407cbed341c4ae3f2049858e031ea19ed01ed2321d1f","observation_id":"ffbe5a24-f5a0-4cdc-aa43-b2ca1bc876ca","resolution":{"observed_at":"2026-08-06T20:34:10.152222Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:09.285172Z","title":"Graves, A","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.285172Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:d1ea0350477aba90b2cb244009eed53655704ce75267077ccc5ca7f4517d3afa","observation_id":"1d804a24-d2b5-4d51-aaa8-39a6e8253f24","resolution":{"observed_at":"2026-08-06T20:34:09.285172Z","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":"2026-08-06T20:34:10.115501Z","title":"Hochreiter, J","venue":null,"work_id":"d43a37b0-b8ba-41b0-be36-278991eb4477","year":1997},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.290892Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:fd6508dc2280586ce05d051a6b76569a7509f6d4ac13e4ba1597fd06a3f64ca6","observation_id":"6ab45c8d-fc99-464c-9b3e-2529323f8d00","resolution":{"observed_at":"2026-08-06T20:34:10.121702Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:10.099026Z","title":null,"venue":null,"work_id":"62e0f2b6-7317-495e-a993-a26fafff660b","year":2017},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.298156Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:9a64f3c280ba5ba060e1c375da4f5930adbf11fe88e76d11fa78d152da66c821","observation_id":"1131ee0d-c7dc-49a0-976d-e62644f51677","resolution":{"observed_at":"2026-08-06T20:34:10.104108Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:09.306570Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.306570Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:ffb4fa5f4433a53323b4e10d08927f7ac34c7e72882babd80196f70c2b4095e2","observation_id":"008bd51e-929d-4317-b1f9-fc72cc85cd7e","resolution":{"observed_at":"2026-08-06T20:34:09.306570Z","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":"2026-08-06T20:34:10.079328Z","title":"Dupont, A","venue":null,"work_id":"2dbdf8f3-752f-4662-a3b4-ba2413a83604","year":null},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.314948Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:211ac84b420cce07d2cd009046dc7a2088bd6b98864db030c7688692c76ed095","observation_id":"320ef78c-d5e6-4cdb-9eac-18878cba0037","resolution":{"observed_at":"2026-08-06T20:34:10.085031Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:10.064092Z","title":"Kobayashi, S","venue":null,"work_id":"e1cd5b2b-c0af-436c-bffa-cd2570814bb1","year":2024},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.322001Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:ac38585ae2ce252cc3da0b45964e7955e4454e1d42a6e1b626a1acfab8d20328","observation_id":"d774f805-7b78-40dd-9735-27f6c05d427d","resolution":{"observed_at":"2026-08-06T20:34:10.068997Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.11907","last_updated":"2025-03-16T03:43:14Z","snapshot_observed_at":"2026-08-04T05:24:43.502141Z","submitted_at":"2024-05-20T09:42:44Z","title":"Ensemble and Mixture-of-Experts DeepONets For Operator Learning","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.11907","snapshot_observed_at":"2026-08-06T20:34:09.327785Z","title":"Sharma, V","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.327785Z"},"links":{"cited_paper":"/paper/2405.11907","citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:9b89aa433122e2732f9f7488e2f73a1eddf1c1afa63cf077f023876675ee03b1","observation_id":"0d5f916d-f703-43b1-8cfb-aea6a93dc429","resolution":{"observed_at":"2026-08-06T20:34:09.327785Z","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":"2026-08-06T20:34:10.040256Z","title":"hey, that’s not an ode","venue":null,"work_id":"19c19625-b106-42d5-8667-711ac028f75d","year":2021},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.334899Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:60d636e48548d9d79076b30c4d393c1d54787a3518de788c99f98621353d3ff2","observation_id":"bdb1b7ca-7898-49fa-add0-26ccbf134544","resolution":{"observed_at":"2026-08-06T20:34:10.049677Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:10.017823Z","title":"Matsubara, Y","venue":null,"work_id":"a11e9f9a-411c-45f5-bfcf-d9c3aaf6c578","year":2021},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.340852Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:3aec07ea8cd1131c3ce7648d636ee0e3c7efe989b97696f7aa0ccdccea5bc866","observation_id":"a63450db-f16f-4a36-9806-452fb363093f","resolution":{"observed_at":"2026-08-06T20:34:10.026885Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T20:34:09.997379Z","title":"Zhuang, N","venue":null,"work_id":"c812f3e7-442a-4978-8d82-22628f08fd79","year":2020},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.347691Z"},"links":{"citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:12871a87fb82f702ae140990baa366f2b2c7a675b62cf95f1afce90c5699928f","observation_id":"6b5e726d-beaf-4cdc-96a3-2f6660b8c1cd","resolution":{"observed_at":"2026-08-06T20:34:10.002524Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1607.06450","last_updated":"2016-07-21T19:57:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2016-07-21T19:57:52Z","title":"Layer Normalization","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1607.06450","snapshot_observed_at":"2026-08-06T20:34:09.353275Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-06T20:34:09.353275Z"},"links":{"cited_paper":"/paper/1607.06450","citing_paper":"/paper/2507.02524"},"observation_digest":"sha256:764cbc326512b341d3a50d70974b5440fb84649a76defbe44fc61bd62b4308b9","observation_id":"1dd22819-bef1-45c0-86d6-a2d5add89eaa","resolution":{"observed_at":"2026-08-06T20:34:09.353275Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2507.02524","last_updated":"2025-07-03T10:44:57Z","latest_version":1,"primary_category":"cs.CE","snapshot_observed_at":"2026-08-06T23:07:17.263310Z","submitted_at":"2025-07-03T10:44:57Z","title":"Time Resolution Independent Operator Learning"},"reference_resolution":{"displayed":63,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":44,"verified_exact":4,"verified_fuzzy":15},"total_outbound_references":63},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 63 of 63 outbound references and 0 inbound Pith citation observations for arXiv:2507.02524."}