{"as_of":"2026-08-10T06:26:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:e943a6a65406f17a05529df03e25b626cc05a4c74f9fe98a36a98f64cf49aab5","coverage":[{"denominator":34,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":34,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T14:37:28.550390Z","state":"measured"},{"denominator":34,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":34,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+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/2507.18346/citation-record","integrity":"/paper/2507.18346/integrity","json":"/paper/2507.18346/citation-record.json","paper":"/paper/2507.18346"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:37:28.788489Z","title":"Arora, A","venue":null,"work_id":"f21c303c-9d60-430e-bce1-71f01ad7b11c","year":2023},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.469775Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:5970636ca47c5dbc66c7d900692303caa0a8e826c0897860b49122b1aa03c061","observation_id":"beb28d99-99a5-4793-a9a8-db212901e183","resolution":{"observed_at":"2026-08-06T14:37:28.791091Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.782123Z","title":null,"venue":null,"work_id":"0b3bb2c0-ea92-4c51-b271-ec98d9c2961e","year":2023},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.472938Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:a50f2e4c88b33e673750031e91c79e47aebc3711642e93c1c8f8b48831d73cec","observation_id":"ff76cd33-93da-4035-b01c-1b0d713beeb3","resolution":{"observed_at":"2026-08-06T14:37:28.784193Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.775286Z","title":null,"venue":null,"work_id":"bce09263-bdd3-49aa-bf97-24f082116a1a","year":2024},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.474995Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:cc7138458b091ae5ea2e052cefa35f3a255d2e2642dbc05f92a9e3e29d0b40a8","observation_id":"4846f4a8-bb7a-4b78-b04b-6fe6aa60f4ee","resolution":{"observed_at":"2026-08-06T14:37:28.777781Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.768572Z","title":"Bihlo and R","venue":null,"work_id":"b0edb69e-15ee-4c84-8fa9-f2fbecb1a38e","year":2022},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.477458Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:26b7e07d7d5b3f025464c795a80ca2602e3f29ce9564e3b4de2686a7e2edb258","observation_id":"b7214543-2f74-4baf-99d6-56c31c6e0f57","resolution":{"observed_at":"2026-08-06T14:37:28.771031Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.479452Z","title":"Bradbury, R","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.479452Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:77241ea75abfa9457d872d2375059be2d64024423ed6e8b43d0976dab666ee29","observation_id":"a7815e30-48b5-4edd-9019-d1de7fcbdac1","resolution":{"observed_at":"2026-08-06T14:37:28.479452Z","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":"2026-08-06T14:37:28.756828Z","title":"Brecht and A","venue":null,"work_id":"c26ff948-9a26-4c30-9f88-55345a16c3b1","year":2024},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.482345Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:a9d32dc192a8b6b4f8ff7bb008bbf083428d3fcf6fd7f1c77b09b46349e5908d","observation_id":"03be6481-3d4c-4bf5-912f-9be72bc17698","resolution":{"observed_at":"2026-08-06T14:37:28.758868Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.748703Z","title":"Brecht, E","venue":null,"work_id":"0724e6b2-7fd2-4fef-864f-51b44fd249ba","year":2025},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.484777Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:dfabb75db63ceae381090c41269460c16bc23cacb73cc57a9a44ae6548264589","observation_id":"99e8e826-8608-4e20-aefb-006115f62fee","resolution":{"observed_at":"2026-08-06T14:37:28.751788Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2309.07899","last_updated":"2024-06-24T17:54:58Z","snapshot_observed_at":"2026-08-09T10:22:20.812520Z","submitted_at":"2023-09-14T17:48:30Z","title":"Improving physics-informed DeepONets with hard constraints","version":2},"cited_work":{"arxiv_id":"2309.07899","doi":null,"metadata_source":"pith","pith_arxiv_id":"2309.07899","snapshot_observed_at":"2026-08-06T14:37:28.591381Z","title":"Improving physics-informed DeepONets with hard constraints","venue":"cs.LG","work_id":"88078103-9ce6-4f1b-9a93-a3698af12689","year":2023},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.487467Z"},"links":{"cited_paper":"/paper/2309.07899","citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:ee362ebcd487a80d6c0003740b5218a159ba52cb407f6c709c4014835401ed9e","observation_id":"66783dc7-2833-45bc-bfe8-d3a13238e6af","resolution":{"observed_at":"2026-08-06T14:37:28.594043Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.740915Z","title":"Cardoso-Bihlo and A","venue":null,"work_id":"f6f1f5fa-028b-450a-9084-32c8b6cf1415","year":2025},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.490799Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:91840456d7aebcf1edc3901622f689d8b161a3575e046c4f6b8f9940ced64612","observation_id":"27089574-6119-4eae-b8e9-ec347f2c19b5","resolution":{"observed_at":"2026-08-06T14:37:28.743385Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.734434Z","title":"Chen and H","venue":null,"work_id":"551016d7-5303-4c7d-b6af-0ff165d25797","year":1995},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.493995Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:e6e37d0aaa71917dfc67e251a08dbcd175e03e735b8e120b4b0663ac57a35bc2","observation_id":"1963f528-e952-4523-9092-69e53c9cc8c6","resolution":{"observed_at":"2026-08-06T14:37:28.736498Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.728170Z","title":"Cuomo, V","venue":null,"work_id":"115af208-689f-48fc-a3ec-56a894084e03","year":2022},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.496039Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:9e0f7c605586764ea15d227ea4aac85f2e40c94b505b72873cc71b789c3b3c65","observation_id":"8976f942-2c8c-4f1a-ba97-2ffaa5883e58","resolution":{"observed_at":"2026-08-06T14:37:28.730321Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.721964Z","title":null,"venue":null,"work_id":"4c3969a6-550b-406f-9952-fb287bab3776","year":2010},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.499271Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:41ada9a2967a54f7d89111eb733d84e9e470b4c648a3f6a67b7b754eacf5e0b5","observation_id":"11761f21-3e56-4aa9-9440-36c3c0ca46f8","resolution":{"observed_at":"2026-08-06T14:37:28.724136Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.713806Z","title":null,"venue":null,"work_id":"13a7031a-ee79-433b-ac89-2dad2ef337d5","year":2017},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.501816Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:fec47793d429758a5fa7b606476987e99225e59c90cc5c8d584e3d95aa98f586","observation_id":"5836b5e5-8d9f-48bb-add4-a7928359b746","resolution":{"observed_at":"2026-08-06T14:37:28.716500Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.706714Z","title":null,"venue":null,"work_id":"e94dee05-0df3-4a41-91f9-dbb5efcaec87","year":2022},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.503779Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:41ab2b7f2f7196fb860016e96adfeeec9149d52e4a4092dd19b7449a4b2809d6","observation_id":"2169cc43-46fa-4659-afa0-dd8c96beb0ea","resolution":{"observed_at":"2026-08-06T14:37:28.709952Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.700500Z","title":"Hairer, C","venue":null,"work_id":"b1245887-ec35-4db9-a425-c8e7b4964d3c","year":2006},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.505446Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:3ef4f79d4f60d9dee0d95bbd4a2b58e73a35d9d98134b30b2d15e88305d05df2","observation_id":"a2cfb0ca-2f8e-4411-8c95-eb95c62804dd","resolution":{"observed_at":"2026-08-06T14:37:28.702468Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.694444Z","title":null,"venue":null,"work_id":"d5ea2eee-5641-4b25-8e8d-ed80a1d71f14","year":2009},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.507993Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:de5c5c6fbaadc949909329fa87c1ceb1414e26dc3fbd7ee598272518a2e9e3da","observation_id":"375eb630-5780-4574-a34d-30c371df9a4a","resolution":{"observed_at":"2026-08-06T14:37:28.696429Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.510765Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.510765Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:d88ded1520920e78cb2105547a3bec4efe59a284dc28917487221fd83a4beab4","observation_id":"59670ea0-bf2d-459d-b3ad-6b9b50a800bb","resolution":{"observed_at":"2026-08-06T14:37:28.510765Z","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":"2026-08-06T14:37:28.685517Z","title":"Kochkov, J","venue":null,"work_id":"9c31a59b-b4ee-46cc-8230-c747fb729cdb","year":2024},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.512800Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:d9aac92505e978132b475c77e98efa91de3e635f11d6300f976916012d188709","observation_id":"07cfe36c-ad64-48b8-b66c-2dbb3e42794a","resolution":{"observed_at":"2026-08-06T14:37:28.687504Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.679748Z","title":null,"venue":null,"work_id":"080f9aab-4c02-4d50-9b60-4954ddd81f2a","year":2024},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.514753Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:b2493ae7b3a109bc620b9de6e8945e4638630496b7e689e4b6111d5c9adcecb0","observation_id":"101a77ad-178f-4e63-b3ca-3f8a9cb7a153","resolution":{"observed_at":"2026-08-06T14:37:28.682102Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.673165Z","title":"Krishnapriyan, A","venue":null,"work_id":"d3b4104a-ded9-4a64-aa09-1a33adcc9c1c","year":2021},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.516839Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:fab4275627bf3c76dc43bef650b494e2ff279bc64db85eec30017d88022b457a","observation_id":"4bac7f1e-6e4d-4188-afe4-afe54ba4aed8","resolution":{"observed_at":"2026-08-06T14:37:28.676012Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.668132Z","title":null,"venue":null,"work_id":"4a603068-3271-47b3-89ef-83262b5e0800","year":1998},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.519231Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:d8cceddf2d613c66fdc81cf5727381eb4eb5ee0fa8ef6df7411aec00458dbecf","observation_id":"61cd1408-b239-4c43-a7ba-046928b953aa","resolution":{"observed_at":"2026-08-06T14:37:28.669957Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2312.15949","last_updated":"2023-12-26T08:28:46Z","snapshot_observed_at":"2026-07-06T17:08:04.891015Z","submitted_at":"2023-12-26T08:28:46Z","title":"HyperDeepONet: learning operator with complex target function space using the limited resources via hypernetwork","version":1},"cited_work":{"arxiv_id":"2312.15949","doi":null,"metadata_source":"pith","pith_arxiv_id":"2312.15949","snapshot_observed_at":"2026-08-06T14:37:28.579084Z","title":"HyperDeepONet: learning operator with complex target function space using the limited resources via hypernetwork","venue":"cs.LG","work_id":"829a2507-efbf-44d0-b35a-d824b22f40d5","year":2023},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.521118Z"},"links":{"cited_paper":"/paper/2312.15949","citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:c0ad2283faa4ef554fa9d2198f7357f1d3af671429cd29d4d59bd4cc740fda4f","observation_id":"816d9203-4ef3-48a4-863c-442a3512848a","resolution":{"observed_at":"2026-08-06T14:37:28.583428Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.661891Z","title":null,"venue":null,"work_id":"a633b938-1324-483a-aae5-40605434b05c","year":2021},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.523181Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:883254527b51110e6a7e6f2da6fcccaca4896480063988ad00b6b90a313b3b23","observation_id":"b6986f49-5e37-438b-9126-34cff3d2f869","resolution":{"observed_at":"2026-08-06T14:37:28.664084Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.656566Z","title":null,"venue":null,"work_id":"cf804a84-0360-45ee-afc4-d6a94d08c177","year":2024},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.524914Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:8720253c80d8112543a92c58cab417f01170dbf7ba77402303a0a8a071467ac2","observation_id":"665e7d86-8154-4fe8-89b3-fafa030b6a3f","resolution":{"observed_at":"2026-08-06T14:37:28.658365Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.651160Z","title":null,"venue":null,"work_id":"9dd172f5-25aa-406e-b37d-8c4904a30493","year":2021},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.526824Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:e78db38bab5eb966fe3cb37ccf78ac739d889afb57459153c96ea1cbd622d267","observation_id":"64e4d689-093a-4034-a06f-20d0fee5ef62","resolution":{"observed_at":"2026-08-06T14:37:28.653019Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.645531Z","title":"McClenny and U","venue":null,"work_id":"4a51b2f5-5f75-436d-bed4-1dd9ecfe89c3","year":2023},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.528725Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:1f2111f2beaeae2d04684d1f6dd7d5a1b0de1550e6e961b34893f22c6fdf7d39","observation_id":"12566fce-a395-4b4f-9bb7-11de73765a8d","resolution":{"observed_at":"2026-08-06T14:37:28.647556Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.639685Z","title":null,"venue":null,"work_id":"63273013-a0a1-484a-b986-2f66ad19fd00","year":2000},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.530593Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:0b5d7fdc4882d08541e97281b6bedd12bc6688c3e1e6b2cd11da81ec4a7d2d48","observation_id":"4aaf6a4d-b215-433f-8504-3441fd29f6c2","resolution":{"observed_at":"2026-08-06T14:37:28.641654Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.633950Z","title":"Raissi, P","venue":null,"work_id":"138080eb-fb8b-4f62-b0b6-76d2d1b1e747","year":2019},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.533460Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:49d9b8af1d471cc7c9c5da805f094aa542e359900e33f949f111fc26d240952e","observation_id":"94fe8ac7-c32b-4380-805c-9f9a81f152c1","resolution":{"observed_at":"2026-08-06T14:37:28.635827Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.628071Z","title":"Seidman, G","venue":null,"work_id":"548be1bf-9755-4e90-bbbb-30edbfa298cf","year":2022},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.536396Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:73ed71c3ed1a76f3793730d1eb7546e391a49caeefbed0c6d882f6a88e73cdb5","observation_id":"96c52c32-4f80-446b-a35b-bd45b08f4b28","resolution":{"observed_at":"2026-08-06T14:37:28.630098Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.621252Z","title":"Venturi and T","venue":null,"work_id":"ca1cfc41-509b-4ae6-b864-0ca51b7a9d08","year":2023},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.539177Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:c597e7b60bf4b2516678e3d4441716062bf414ba316eb5a308eb9e68d6899c00","observation_id":"098bedf5-03bf-46c7-bb8d-bc64b9a6aa78","resolution":{"observed_at":"2026-08-06T14:37:28.623610Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.614548Z","title":"Wang and P","venue":null,"work_id":"e3b0224d-e030-46bf-b898-9f6c73ac5608","year":2023},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.543173Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:62c79d7192bf828824d95db39b9f8520ecbf4673d46eebe978841dfa128c0b41","observation_id":"799b6baa-d247-4c10-9e9b-1eb7a540ec0c","resolution":{"observed_at":"2026-08-06T14:37:28.616676Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2203.07404","last_updated":"2022-03-14T18:08:18Z","snapshot_observed_at":"2026-07-06T12:47:48.418460Z","submitted_at":"2022-03-14T18:08:18Z","title":"Respecting causality is all you need for training physics-informed neural networks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2203.07404","snapshot_observed_at":"2026-08-06T14:37:28.546121Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.546121Z"},"links":{"cited_paper":"/paper/2203.07404","citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:bed19443591639318d149b094d4158651a2876628eb893c123b5cbea3efb87d6","observation_id":"8b8ee16a-40a4-40f5-84fd-fc3a5a04768d","resolution":{"observed_at":"2026-08-06T14:37:28.546121Z","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":"2026-08-06T14:37:28.608043Z","title":null,"venue":null,"work_id":"c67963ea-2894-465f-b0f9-c184e01cb97a","year":2021},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.548249Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:0bae16678f16dcfdb6fe74d80354c8c16b9275db50af4dd22c78a7249d92aaeb","observation_id":"ecd29210-3929-4e50-b28b-18c375e676ec","resolution":{"observed_at":"2026-08-06T14:37:28.610277Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T14:37:28.598815Z","title":null,"venue":null,"work_id":"b83e0cba-7276-454d-8814-f95b852b2027","year":2022},"citing_paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T14:37:28.550390Z"},"links":{"citing_paper":"/paper/2507.18346"},"observation_digest":"sha256:d1cff63f5b6f024bf73a30b4410d6a36715d20a79a55c3066571149286689ac4","observation_id":"e04f5036-f473-4d69-b75a-3f08258246af","resolution":{"observed_at":"2026-08-06T14:37:28.602378Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.18346","last_updated":"2025-07-24T12:19:25Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-09T12:15:19.798839Z","submitted_at":"2025-07-24T12:19:25Z","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations"},"reference_resolution":{"displayed":34,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":17,"verified_exact":2,"verified_fuzzy":15},"total_outbound_references":34},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:2507.18346."}