{"as_of":"2026-08-09T05:06:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:73bad9b1d5a7023403c353435f07132f091d6279e803519c6f79965368fc5b91","coverage":[{"denominator":43,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":43,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T22:18:44.867001Z","state":"measured"},{"denominator":43,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":43,"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/2511.11228/citation-record","integrity":"/paper/2511.11228/integrity","json":"/paper/2511.11228/citation-record.json","paper":"/paper/2511.11228"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T22:18:39.510895Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:39.510895Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:eb788db06efa4bac436a229fc815c2e2a98a3bf9d4f34c127bc7057bb38bd042","observation_id":"0b6b5bf4-4f10-4dcb-8bbf-5a8ccbf875cb","resolution":{"observed_at":"2026-08-03T22:18:39.510895Z","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":"2026-08-03T22:18:39.603750Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:39.603750Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:b68515dc267b414266deee1350c041f012dc5e2f2ec17b5955c43030c3bb22ca","observation_id":"1cec581c-4196-4f35-aa84-7f85b89b954e","resolution":{"observed_at":"2026-08-03T22:18:39.603750Z","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":"2026-08-03T22:18:39.655124Z","title":"D., Karniadakis, G","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:39.655124Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:a5315184f125a5d2e92f88b63c51433a4d3d7591ff4c3eb339969af77e0289d8","observation_id":"d924415e-900a-4c98-8d00-d743496850f4","resolution":{"observed_at":"2026-08-03T22:18:39.655124Z","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":"2026-08-03T22:18:39.796935Z","title":"A., Ullmann, E., Peters, N","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:39.796935Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:aea7ad0c9671e45b493b52d63f607735dbe03077e0c1b2984fa864d1c3113f47","observation_id":"6c96b7cb-1b01-4e3e-a163-ffa221cfce65","resolution":{"observed_at":"2026-08-03T22:18:39.796935Z","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":"2026-08-03T22:18:39.935985Z","title":"P., Sun, Z","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:39.935985Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:3f30c5b59488d11a5ec37f407baee36f275ce76bfb9df887523125395f61ffd2","observation_id":"e9026c23-0e13-424a-a033-1e87ce317f0b","resolution":{"observed_at":"2026-08-03T22:18:39.935985Z","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":"2026-08-03T22:18:40.073486Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:40.073486Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:ce47a97f07107adf1ad4175570622104e21ae9f92d9c54e3511e14f9b9ebdc0e","observation_id":"49542349-c6be-4295-9b0e-0986a5b6912b","resolution":{"observed_at":"2026-08-03T22:18:40.073486Z","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":"2026-08-03T22:18:40.198623Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:40.198623Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:967173cc95f90ec969d30e2e3c5de96544bbf27305ba48c4b6b145aa19c74f06","observation_id":"4c07a83f-abf0-4942-a042-54989efebf65","resolution":{"observed_at":"2026-08-03T22:18:40.198623Z","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":"2026-08-03T22:18:40.340760Z","title":"X., Gu, Q","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:40.340760Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:efa5f81e6bc328ad452dcc04fc799e2e0c19455c4932f01403e14cfd0ee42c65","observation_id":"1344163a-8a1d-4c7b-8383-99a55fa7a875","resolution":{"observed_at":"2026-08-03T22:18:40.340760Z","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":"2026-08-03T22:18:40.457194Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:40.457194Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:bfca7f0400cb898deb2f674ab869fbc041a4a4532428e1cf6dd0366f9959b70b","observation_id":"622ea409-1b16-4f1d-927a-47a2584a7952","resolution":{"observed_at":"2026-08-03T22:18:40.457194Z","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":"2026-08-03T22:18:40.563314Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:40.563314Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:640505214974a0c1ff393305b1fff790be8b1058247097c936afdd5e1e062cdf","observation_id":"9883e79b-f669-4be3-bc16-0ec421b77612","resolution":{"observed_at":"2026-08-03T22:18:40.563314Z","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":"2026-08-03T22:18:40.681941Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:40.681941Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:d2ef7e80ef054fb6f9c9c2522f7469cdf656377a02c4593440a4e6135aa2f59d","observation_id":"587beb7f-6a18-4568-ae79-1f352675247d","resolution":{"observed_at":"2026-08-03T22:18:40.681941Z","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":"2026-08-03T22:18:40.793684Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:40.793684Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:17c384c2fd30b78bac484ff2bfc4e749299b80d3350d4b500f20eb2b68565600","observation_id":"f65c19ce-196f-4edb-a99f-1bc2613f5935","resolution":{"observed_at":"2026-08-03T22:18:40.793684Z","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":"2026-08-03T22:18:40.880458Z","title":"W., Abhayapala, T","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:40.880458Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:f70285f3c51495236e73510088d08fa2294eb38d451cbec0f7df32beec37b565","observation_id":"10e16ab3-39e2-46c6-8310-8f12ea0fd21f","resolution":{"observed_at":"2026-08-03T22:18:40.880458Z","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":"2026-08-03T22:18:41.009843Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:41.009843Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:dd3842ca5d5efb331d0a9d73581b35168ca5428a025395a71ee0611475236f5d","observation_id":"099b6797-ba1a-4943-8852-d82979733d60","resolution":{"observed_at":"2026-08-03T22:18:41.009843Z","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":"2026-08-03T22:18:41.104498Z","title":"C., Hagenbuchner, M., Monfardini, G","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:41.104498Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:640ac58dff86ec4836751096d46ac48227e870c06f493abae3e02991c63fa3a2","observation_id":"35ab62f6-4bbb-4ae1-bddc-6cf7563bbc0f","resolution":{"observed_at":"2026-08-03T22:18:41.104498Z","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":"2026-08-03T22:18:41.192488Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:41.192488Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:ba887ed7a923643bbfb1772da561a1015dc78da1d338e6de3cd44c02761388a8","observation_id":"b3acf9ce-2d2a-4dbe-a398-d4ba8d2dafbe","resolution":{"observed_at":"2026-08-03T22:18:41.192488Z","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":"2026-08-03T22:18:41.278762Z","title":null,"venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:41.278762Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:e624155f22d743a499dab9bba5d304435f72345382d6d5a81264c4ecb8b2422d","observation_id":"d626f7cb-628d-4a20-acbf-634753deb1e0","resolution":{"observed_at":"2026-08-03T22:18:41.278762Z","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":"2026-08-03T22:18:41.438675Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:41.438675Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:90573c66015c30028141b756d9e9a9f537d662cbd6da543664bfb1d7f7129b45","observation_id":"75e12ce2-521a-474c-a162-be9f8f30234b","resolution":{"observed_at":"2026-08-03T22:18:41.438675Z","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":"2026-08-03T22:18:41.539677Z","title":"J., Toscano, J","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:41.539677Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:9ee5df8ba444b724b96cb0281e5ab09fd23ca01151dc51882b0d4adb9ec65a49","observation_id":"1b41f4e6-9387-4c66-aa7c-6ba4394c1d89","resolution":{"observed_at":"2026-08-03T22:18:41.539677Z","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":"2026-08-03T22:18:41.683641Z","title":"A., Stinis, P","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:41.683641Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:71f66e0f65e9aef982e7941dccb4297ffced7304e225409f61d9a087ad937f47","observation_id":"91b34721-a9f9-4fab-b6e6-d2570f4ed5dd","resolution":{"observed_at":"2026-08-03T22:18:41.683641Z","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":"2026-08-03T22:18:41.845487Z","title":"A., Murphy, S","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:41.845487Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:d21f5a1455fc4f2c232f6386f122fae3cc1225b60444f199919b7e87d218b426","observation_id":"8c935172-47b7-4668-af97-2e2903d55a5c","resolution":{"observed_at":"2026-08-03T22:18:41.845487Z","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":"2026-08-03T22:18:42.015374Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:42.015374Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:f31885ce0e97256d3806df0ec84b676babfd7304f156a3c766d7797a1bb776db","observation_id":"6548ce6d-2fda-43e5-a959-f5c985b333a9","resolution":{"observed_at":"2026-08-03T22:18:42.015374Z","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":"2026-08-03T22:18:42.191666Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:42.191666Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:900bca931cdaaa3f9b622f0fe037fa40ab1a418eacaa38e2af02203bd9e7eddb","observation_id":"2199a009-353c-42ef-b62c-c59c08c8c3e8","resolution":{"observed_at":"2026-08-03T22:18:42.191666Z","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":"2026-08-03T22:18:42.350401Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:42.350401Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:1bc6f46ccf92b69a44a449ef68be663dbe404f4d8b6cd1c5ff737eff034c0deb","observation_id":"68edb80c-e570-46b4-bc6f-199aad43376c","resolution":{"observed_at":"2026-08-03T22:18:42.350401Z","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":"2026-08-03T22:18:42.513858Z","title":"E., Kevrekidis, I","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:42.513858Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:f1a4e866404205ea89542e89029b84e96a1931140ed396373d68c17c4183d07a","observation_id":"f2837f75-da98-48af-9d6b-22a54183d82f","resolution":{"observed_at":"2026-08-03T22:18:42.513858Z","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":"2026-08-03T22:18:42.700547Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:42.700547Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:c772b6203f4357ba29caa83f9e5e96b30c9ae32ce6a5ea885c8169f301d56cb4","observation_id":"437c3180-9b8d-4e0e-b904-b2d774da3ef9","resolution":{"observed_at":"2026-08-03T22:18:42.700547Z","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":"2026-08-03T22:18:42.812116Z","title":"A., Heniche, M., Glowinski, R","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:42.812116Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:5f5fb4ba6ec7e8bea3f7adc8374dc27451e50ddd5dc5d2c90b4d5ac154661fee","observation_id":"e411bf40-4711-4426-b6b0-405ff9c15216","resolution":{"observed_at":"2026-08-03T22:18:42.812116Z","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":"2026-08-03T22:18:42.904455Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:42.904455Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:439e7a3ab565615cb48cdfbee55ebccc05ff707ffcc1c8250d3c647dd25244b1","observation_id":"e29662fc-2ca8-4ceb-b3c3-152f17b96969","resolution":{"observed_at":"2026-08-03T22:18:42.904455Z","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":"2026-08-03T22:18:43.018738Z","title":"D., Karniadakis, G","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:43.018738Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:e34444a20e2da8f8d8d1d6e5727325493c7602cb18a5c547716d895d737d54f6","observation_id":"a987e0c6-f540-4263-8c2a-033fab1f02da","resolution":{"observed_at":"2026-08-03T22:18:43.018738Z","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":"2026-08-03T22:18:43.148118Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:43.148118Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:ff06a5913c8e8fe47e3f6655db5232e967e2dff6cdfb85e65c0df3f9f9d0808f","observation_id":"2aa79b5c-af95-47aa-83f7-fe8e009b85f7","resolution":{"observed_at":"2026-08-03T22:18:43.148118Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2401.07888","last_updated":"2024-06-06T08:50:53Z","snapshot_observed_at":"2026-08-08T16:19:41.536908Z","submitted_at":"2024-01-15T18:32:53Z","title":"Multifidelity domain decomposition-based physics-informed neural networks and operators for time-dependent problems","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2401.07888","snapshot_observed_at":"2026-08-03T22:18:43.256197Z","title":"A., Beecroft, D., Stinis, P","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:43.256197Z"},"links":{"cited_paper":"/paper/2401.07888","citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:0ef3d276d3766fc3d354844fc80dee22bc93040d8f29137a270d241ef855bfb5","observation_id":"bb9af202-4f9f-42ca-9907-59c68d78ada6","resolution":{"observed_at":"2026-08-03T22:18:43.256197Z","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":"2026-08-03T22:18:43.367326Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:43.367326Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:93d7348b186eea161266422208899070c75ae796ae6f7a2bc2e55c213c236057","observation_id":"887c0a57-127c-4db7-b142-0d5fdb6655c9","resolution":{"observed_at":"2026-08-03T22:18:43.367326Z","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":"2026-08-03T22:18:43.472724Z","title":null,"venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:43.472724Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:2f1e64849018803759584e62ff5bf2e9c5a65dfcee3364dc9623670dd9f75e03","observation_id":"d5234774-801f-4b5f-830b-9606ead4c2c6","resolution":{"observed_at":"2026-08-03T22:18:43.472724Z","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":"2026-08-03T22:18:43.623956Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:43.623956Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:5fc2b0da5dc705c45a3c1d10763a49309172de74c04f0c1f7dcad89cb4dda5c5","observation_id":"37f460d4-d391-4a29-b628-5b29eee7d202","resolution":{"observed_at":"2026-08-03T22:18:43.623956Z","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":"2026-08-03T22:18:43.786064Z","title":"S., Pato, M., Datia, N","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:43.786064Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:5add79982808a50ca27a1eb65c80494dfcc5019d790318529e728fc1e3606956","observation_id":"1a94232b-03ce-4719-b2cd-fd11d5ebcc08","resolution":{"observed_at":"2026-08-03T22:18:43.786064Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2406.01034","last_updated":"2025-08-14T10:41:49Z","snapshot_observed_at":"2026-08-05T02:05:56.574184Z","submitted_at":"2024-06-03T06:36:04Z","title":"Enhancing Graph Collaborative Filtering with FourierKAN Feature Transformation","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2406.01034","snapshot_observed_at":"2026-08-03T22:18:43.898045Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:43.898045Z"},"links":{"cited_paper":"/paper/2406.01034","citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:33d29657a531e3788c124d289602ba4468462157c9409afef766d7a469a96d7c","observation_id":"138eb7f9-1013-4d7f-9ae4-ecaa4ad01779","resolution":{"observed_at":"2026-08-03T22:18:43.898045Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2503.23289","last_updated":"2025-03-30T02:59:32Z","snapshot_observed_at":"2026-08-07T16:27:56.809476Z","submitted_at":"2025-03-30T02:59:32Z","title":"Enhancing Physics-Informed Neural Networks with a Hybrid Parallel Kolmogorov-Arnold and MLP Architecture","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.23289","snapshot_observed_at":"2026-08-03T22:18:44.049026Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:44.049026Z"},"links":{"cited_paper":"/paper/2503.23289","citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:256e7f4c2da4e7516c83ed55a0300fc46b85a601c4866a26a4184e11f1d7443b","observation_id":"5460264e-cdcb-484c-bffb-b0011a98aee9","resolution":{"observed_at":"2026-08-03T22:18:44.049026Z","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":"2026-08-03T22:18:44.153219Z","title":"A., Jacob, B., Murphy, S","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:44.153219Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:752ef2a77fa830737dcafd40914dcd60c74a584e6d6026acae82a6c3f788646a","observation_id":"0f378b23-5784-4837-a130-1d27036ebcf6","resolution":{"observed_at":"2026-08-03T22:18:44.153219Z","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":"2026-08-03T22:18:44.331979Z","title":"E., Likas, A., Fotiadis, D","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:44.331979Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:9e67ce4f41870d607522c49280cb230a95bcd3332058d900d696e10b552e4c0e","observation_id":"36de3c5e-b6c7-41df-83e1-35461170f545","resolution":{"observed_at":"2026-08-03T22:18:44.331979Z","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":"2026-08-03T22:18:44.472956Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:44.472956Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:1237ff20dca63425da9bf56e834456cc2270d2b5bda4248e7d95892233bc045a","observation_id":"17584ef2-5a33-40bb-9c65-2e2a29406e29","resolution":{"observed_at":"2026-08-03T22:18:44.472956Z","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":"2026-08-03T22:18:44.626799Z","title":"A., Agarwal, P., Elsayed, E","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:44.626799Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:136bbbe719141caaae6771289a52de9cb6bc582d2ba5e5c9fc72265c29852db4","observation_id":"9459ee0e-499c-4820-9613-ec65b16d7d57","resolution":{"observed_at":"2026-08-03T22:18:44.626799Z","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":"2026-08-03T22:18:44.690236Z","title":null,"venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:44.690236Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:15bcc8f5e4a92adc8d1222f26271262ec4a925dccea0993f047b2eefcc031f04","observation_id":"811bd72e-2969-48c8-ae76-fa4521915f20","resolution":{"observed_at":"2026-08-03T22:18:44.690236Z","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":"2026-08-03T22:18:44.867001Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition","version":3},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-03T22:18:44.867001Z"},"links":{"citing_paper":"/paper/2511.11228"},"observation_digest":"sha256:dc09048eb07414edc226740ffa45acb5c37559ef62f5165330c40d408206896f","observation_id":"92ce7d37-50d9-4d10-a613-082674daaa15","resolution":{"observed_at":"2026-08-03T22:18:44.867001Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2511.11228","last_updated":"2026-06-11T12:52:46Z","latest_version":3,"primary_category":"math.NA","snapshot_observed_at":"2026-08-08T23:22:08.267344Z","submitted_at":"2025-11-14T12:30:16Z","title":"The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition"},"reference_resolution":{"displayed":43,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":43,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":43},"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 9 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 0 inbound Pith citation observations for arXiv:2511.11228."}