{"as_of":"2026-08-08T12:31:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:83d40a9eeee6278128dc6c9b380bfbd90f5efcaad6cdf04511081afef96e4820","coverage":[{"denominator":40,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":40,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T12:28:03.381908Z","state":"measured"},{"denominator":40,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":40,"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/2505.24578/citation-record","integrity":"/paper/2505.24578/integrity","json":"/paper/2505.24578/citation-record.json","paper":"/paper/2505.24578"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:08.713896Z","title":"Piezoelec- tric materials for controlling electro-chemical processes,","venue":null,"work_id":"51070fe1-6b37-4b2f-b0ea-5fbb5da255c9","year":2020},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T12:27:59.713879Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:622b34975180616fa091d97e4104dee4a64594b441a9582f73e07a3aef47434a","observation_id":"5184fa11-0d68-4b9f-8b09-373914f31005","resolution":{"observed_at":"2026-08-07T12:28:08.762610Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:08.435678Z","title":"Piezoelectric materials for sus- tainable building structures: Fundamentals and applications,","venue":null,"work_id":"2d2615e6-22b2-4ec7-b42f-dbc7f12f1ceb","year":2019},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T12:27:59.833631Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:e797970bd26cd974086ef600ffb37755c976b08e74295210b8e6bea45b01f135","observation_id":"2eb68d29-a356-4949-9f62-98c8f30e0cc6","resolution":{"observed_at":"2026-08-07T12:28:08.562436Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:08.261337Z","title":"A review on applications of piezoelectric materials in aerospace industry,","venue":null,"work_id":"0a865a02-6239-4d41-a145-3b4e629c71b2","year":2020},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T12:27:59.912386Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:ef26721f98fa58396bf20acfd31524307a26b1656ed79a847ddf88764dfeeb24","observation_id":"902f7b37-a2d7-4429-bc84-b5168fe1f1c6","resolution":{"observed_at":"2026-08-07T12:28:08.312696Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:08.010609Z","title":"Applications of piezoelectric materials in biomedical engineering,","venue":null,"work_id":"33c40243-0ccb-4fc8-8a10-8076989307f2","year":2025},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:00.037114Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:ed18c0402b640251df1d57326d1183f98b645d4ab659a8769eede0d8e14bf274","observation_id":"0b9cef8e-e417-41fa-98d2-013cb6bfc23a","resolution":{"observed_at":"2026-08-07T12:28:08.098673Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:07.807526Z","title":"A review on piezoelectric materials and their appli- cations,","venue":null,"work_id":"0f118a8c-7743-46c3-91da-26fc128b823f","year":2023},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:00.151989Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:ff15c2b3bde78d70420ad9a8bbd877cb2b1f335ee1dad10a3cbef0ea5b68e48b","observation_id":"e32f6212-4c2d-4072-9245-467e2874a1f7","resolution":{"observed_at":"2026-08-07T12:28:07.908176Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:07.633553Z","title":"Hysteresis in piezoelectric and ferroelectric materials,","venue":null,"work_id":"5ed3275a-ad31-4f9b-8959-fc2cfb72c621","year":2006},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:00.234020Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:922cc329f13a963efe6d9257216fdbf7be167bcdb9cc61f47f4b35264f521c2e","observation_id":"096c7b4e-1b6f-422d-8aad-c3440957352f","resolution":{"observed_at":"2026-08-07T12:28:07.715644Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:07.487023Z","title":"Adaptive estimated inverse output-feedback quantized control for piezoelectric positioning stage,","venue":null,"work_id":"bf2a75e9-bbf8-492a-a161-827531bca39a","year":2018},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:00.356256Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:ae96fd2af564c2fe167789351312dacf9c36a9077a46b0b86b387f2ddf22ddf3","observation_id":"063aa39c-015a-4e76-b0fa-c3aeed78a7e1","resolution":{"observed_at":"2026-08-07T12:28:07.574498Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:07.282497Z","title":"Piezoelectric hysteresis analysis and loss separation,","venue":null,"work_id":"f647ae22-102b-44aa-b28c-9d33ef0505a9","year":2001},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:00.427312Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:4a61a57a564789a2d55689922d0b6fe0516d2ae9dd1f4a5469b848b0ef727dc1","observation_id":"717bc429-2f04-42f7-87df-106f3de9d65b","resolution":{"observed_at":"2026-08-07T12:28:07.359552Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:07.092394Z","title":"¨Uber die magnetische nachwirkung,","venue":null,"work_id":"e57bb3b7-df34-4d4e-8710-c1260da7f5f6","year":1935},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:00.507905Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:4745dcd4704426d82ce8eb94dd1c681e99c6b86ef68529700d0f289a29a5996b","observation_id":"564ebaf0-c3d1-479c-a186-feff3593b5e1","resolution":{"observed_at":"2026-08-07T12:28:07.167722Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:06.919596Z","title":null,"venue":null,"work_id":"950e03f9-1050-4a22-8b08-7ec0e6162a5d","year":2005},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:00.653996Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:965757ea33e8a4493826c2840fd2bc825c0b34c9364bbb8172b7cc1b46240054","observation_id":"9d9a6c23-5013-4fff-b48d-939114b3670f","resolution":{"observed_at":"2026-08-07T12:28:06.974721Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:06.788981Z","title":"Mag- netic hysteresis modeling with neural operators,","venue":null,"work_id":"42be93cf-b470-4f07-8868-c67cf370a6aa","year":2024},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:00.744888Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:8e0ace5fc4e41d0dda1069a2e790bdab17e9085c68b020c289b1b670250819fc","observation_id":"7e5b11ef-1327-4cbc-bc48-5a52ca17c10b","resolution":{"observed_at":"2026-08-07T12:28:06.852573Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:06.640768Z","title":"A survey on hysteresis modeling, identification and control,","venue":null,"work_id":"6b25a722-e65d-44fe-a092-278ba8c59292","year":2014},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:00.826352Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:72049617c40f8e01a3d1f993081b75904b23e3c6f9356cfbf1db4287dca6e221","observation_id":"8fa0a298-7c0a-4d77-84cf-5b616fda6721","resolution":{"observed_at":"2026-08-07T12:28:06.687315Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:00.908552Z","title":"Deep learning,","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:00.908552Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:994161ea1f99b9da1f55027e4bd53e4acc6b4abeac8ba8e91bee03a133b83b05","observation_id":"d1bd0924-5d3c-431a-bcb7-24c2814ddca5","resolution":{"observed_at":"2026-08-07T12:28:00.908552Z","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":"2026-08-07T12:28:01.005595Z","title":"Long short-term memory,","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:01.005595Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:9b6373d1626e900a4518ae8aa487a6f61d1a76f39b7079059ad48ab68502c82a","observation_id":"fca78b5a-c2d7-450b-9955-c02177baef27","resolution":{"observed_at":"2026-08-07T12:28:01.005595Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1406.1078","last_updated":"2014-09-03T00:25:02Z","snapshot_observed_at":"2026-07-06T03:45:28.546418Z","submitted_at":"2014-06-03T17:47:08Z","title":"Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1406.1078","snapshot_observed_at":"2026-08-07T12:28:01.090457Z","title":"Learning phrase representations using RNN encoder-decoder for statistical machine translation,","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:01.090457Z"},"links":{"cited_paper":"/paper/1406.1078","citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:a25fd7f9ab0b1ed753e555cf129a95466efc5697b4bc47bad6b5f6f9a4d73a32","observation_id":"ef48bfa1-3ec7-4b7f-a8a5-b4823787811d","resolution":{"observed_at":"2026-08-07T12:28:01.090457Z","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":"2026-08-07T12:28:06.500998Z","title":"Adaptive neural control for hysteretic nonlinear systems with hysteresis neural direct inverse compensator and its application,","venue":null,"work_id":"dd290fa8-f653-4c3a-b0fe-2952cead240a","year":2024},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:01.212560Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:fd1e3a72be9b2fe62c07aba9ac1f8f04ef1f76f5aecbcdb290a68ba6dd260c65","observation_id":"7b2ad8b3-40f6-4827-bdc4-82184cd41690","resolution":{"observed_at":"2026-08-07T12:28:06.554595Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:06.385588Z","title":"Generalizable models of magnetic hys- teresis via physics-aware recurrent neural networks,","venue":null,"work_id":"d1965369-fbe2-4c78-a126-10a5e1fc7464","year":2025},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:01.303228Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:4088c839c09a9156d3cbd89a3215b831976bfde44c36782fc64079c6fc303ddc","observation_id":"4673e52d-ffa8-4006-b6e5-c917dcf6a21f","resolution":{"observed_at":"2026-08-07T12:28:06.429741Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:06.258229Z","title":"Characterizing nonlinear piezoelectric dynamics through deep neural operator learning,","venue":null,"work_id":"39ff0fe1-94d7-4373-8ecc-961e6bf92fb0","year":2024},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:01.377806Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:bb828228887674696d8d47d50875ffcec21baa4697826fc3ac38840faf1edf23","observation_id":"325038ca-2b29-4c3c-86c6-014ec8438601","resolution":{"observed_at":"2026-08-07T12:28:06.293815Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:06.143361Z","title":"Neural operator: Learning maps be- tween function spaces with applications to PDEs,","venue":null,"work_id":"83afdcca-0170-4e04-a478-5c6c78269fd0","year":2023},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:01.464549Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:48bc0acc8803ae9c7004d1ee01187d3452f36ccfa81a2bd2dd8a4775429c92a9","observation_id":"6c68b774-6c92-4da0-b240-0865d991586a","resolution":{"observed_at":"2026-08-07T12:28:06.187205Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:06.047597Z","title":"Neural operators for accelerating scientific simu- lations and design,","venue":null,"work_id":"ca3cd579-e92c-494b-b99d-f8aba10b38c3","year":2024},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:01.562753Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:07a89b242c96c90a126150bc83d7b9a54f9e988b6f74c9cd3e7d66f770a01643","observation_id":"7efd7cd5-22c8-4ecc-ac6d-55b57361cf09","resolution":{"observed_at":"2026-08-07T12:28:06.081845Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:05.912895Z","title":"Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators,","venue":null,"work_id":"3bb12bb2-ef79-4a4e-a889-e79884158918","year":2021},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:01.653857Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:45af97602ce147b50a17b96abdac94107689c6c9158a7af50bec4bc3e71a0f87","observation_id":"3526865f-f15e-4444-b76e-ae0361d2994c","resolution":{"observed_at":"2026-08-07T12:28:05.978605Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:05.799882Z","title":"Fourier neural operator for parametric partial differential equations,","venue":null,"work_id":"69a92498-1936-445d-878e-32694c9e9ce9","year":2021},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:01.745937Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:39f11e4be89e5bf7757b6c61f2861ca02ffb0a1a73661df5475fb4bb962e3d94","observation_id":"042ede6a-b976-4b07-9837-4710cd1567f8","resolution":{"observed_at":"2026-08-07T12:28:05.835447Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:05.680823Z","title":"Convolutional neural operators for robust and accurate learning of PDEs,","venue":null,"work_id":"b0914ba4-e54c-4b6c-b25d-2bf57b69fcdb","year":2023},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:01.860245Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:3a2aa0bca0207fef492c713cdff6693b24363bf1cf4b954765227431119de707","observation_id":"85d04c2c-2f79-484b-94dc-0f823ed6ee9b","resolution":{"observed_at":"2026-08-07T12:28:05.745015Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:05.509590Z","title":"Discovery of sparse hysteresis models for piezoelectric materials,","venue":null,"work_id":"eb79fda9-398b-4ea7-a35d-6ea0822b1cea","year":2023},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:01.982009Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:2610289dbb84c38319cb8d0d3132d651bcc8fff4e78cae54144c7127096bb1d9","observation_id":"5f208512-a61d-48e8-a93f-28688c6a33fa","resolution":{"observed_at":"2026-08-07T12:28:05.600014Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:05.346257Z","title":"Identifi- cation of Bouc–Wen hysteretic systems based on a joint optimization approach,","venue":null,"work_id":"0c043f51-9f03-4725-bd56-041fc00d3455","year":2022},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:02.059652Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:f385216c58ec2b2ee3b6380345f633ad0f2445145bf57bb3b15946d727eed8d2","observation_id":"ff9c8b88-c6d1-41dc-aa1e-09e5369fe25b","resolution":{"observed_at":"2026-08-07T12:28:05.419719Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:05.177178Z","title":"Learning the solution operator of parametric partial differential equations with physics-informed deep- onets,","venue":null,"work_id":"ecc71e4f-db03-43a7-a65b-ea14c0aed03f","year":2021},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:02.156955Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:d3e20df9afd78e4379e2124ea6560a7a9523eadc6860c28307dd15cd025cc37d","observation_id":"57940fbb-1184-4912-8042-32d5e31f38b6","resolution":{"observed_at":"2026-08-07T12:28:05.250100Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.12556","last_updated":"2025-05-18T22:05:11Z","snapshot_observed_at":"2026-08-07T15:43:36.073606Z","submitted_at":"2025-05-18T22:05:11Z","title":"Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.12556","snapshot_observed_at":"2026-08-07T12:28:02.281195Z","title":"Beyond accu- racy: Ecol2 metric for sustainable neural PDE solvers,","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:02.281195Z"},"links":{"cited_paper":"/paper/2505.12556","citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:34df62d69a9604d127627d1eb30992c26117ae56a80634bd4271b35799389137","observation_id":"25903808-025d-48e8-9c46-71a80b912bf1","resolution":{"observed_at":"2026-08-07T12:28:02.281195Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2301.13331","last_updated":"2026-04-18T17:20:42Z","snapshot_observed_at":"2026-07-06T14:46:23.137171Z","submitted_at":"2023-01-30T23:29:33Z","title":"Neural Operator: Is data all you need to model the world? An insight into the paradigm of data-driven scientific ML","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2301.13331","snapshot_observed_at":"2026-08-07T12:28:02.348867Z","title":"Neural operator: Is data all you need to model the world? an insight into the impact of physics informed machine learning,","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:02.348867Z"},"links":{"cited_paper":"/paper/2301.13331","citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:39eff13e7afeb2a4cd6ba526506845cde19e595a4cf981213aa63d11fc33b452","observation_id":"353fda15-1c76-45d0-a133-e3f2668b0f1f","resolution":{"observed_at":"2026-08-07T12:28:02.348867Z","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":"2026-08-07T12:28:02.457513Z","title":"Discovering governing equations from data by sparse identification of nonlinear dynamical systems,","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:02.457513Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:12c1591e82258f1c329e7f681c35214996657857d86a4a5e487f2c887cfe2697","observation_id":"5e10eeae-0bb1-412c-82d4-6a0f7ca9f56d","resolution":{"observed_at":"2026-08-07T12:28:02.457513Z","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":"2026-08-07T12:28:04.978159Z","title":"Discovering symbolic models from deep learn- ing with inductive biases,","venue":null,"work_id":"1b50d7dd-7ac4-402a-9f29-228bfd294a58","year":2020},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:02.524154Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:fa8020b6399aa4dc4a2000f8152fdc49c6a6b326b2f95d7e1e0f990b7be14509","observation_id":"a5ae5da0-1059-44dc-b9a5-0c6e7e7bd463","resolution":{"observed_at":"2026-08-07T12:28:05.067920Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:04.832684Z","title":"Why are some hysteresis loops shaped like a butterfly?","venue":null,"work_id":"08578668-105d-491e-a54e-ae3deeb6a9c9","year":2011},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:02.605953Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:f894a69613fd9f4117109fa8f8ad43d0b7b47d0b2669a5fb4ba37f04694685a2","observation_id":"d2396091-a6d7-4fc5-b16a-95b94df256bc","resolution":{"observed_at":"2026-08-07T12:28:04.889657Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:04.638610Z","title":"Fourier neural operators for arbitrary resolution climate data downscaling,","venue":null,"work_id":"e544e69d-bb1f-449a-8a71-1aa677a42dea","year":2024},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:02.699493Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:db043601d47907380d2eedb76e54d4b7989c70e87d2e6941fe1924b8e0327c02","observation_id":"8651bb50-79f9-4f02-a961-1d2af40f0245","resolution":{"observed_at":"2026-08-07T12:28:04.726951Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:04.422984Z","title":"Sound propagation in realistic interactive 3D scenes with parameterized sources using deep neural operators,","venue":null,"work_id":"14b72473-bfe2-4ef4-8ec0-e40a6dcef03a","year":2024},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:02.791459Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:18b447c57487066aa731e13cefe9849e1f1184afee0091f1d1b9e1ef63f5126a","observation_id":"95195e29-bb77-44be-9e36-ababe6a64bbd","resolution":{"observed_at":"2026-08-07T12:28:04.524525Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:04.268697Z","title":"Data-driven discovery of partial differential equations,","venue":null,"work_id":"a19c8caa-ec69-4f28-840e-299176228bdc","year":2017},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:02.878882Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:550c8d7269b7e8da674280419d7d128dd5f535e40929048ae1a49415767b4901","observation_id":"a885edc2-0514-4a65-b3bf-0abcb60cd03e","resolution":{"observed_at":"2026-08-07T12:28:04.331866Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:02.968259Z","title":"Regression shrinkage and selection via the lasso,","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:02.968259Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:93a5c4b7663d66ba1a1e0dd1b14e1a4e486aa8b862d440f28c10571c9996a12d","observation_id":"18757d58-0bf9-4b32-93aa-2dd12ece08ac","resolution":{"observed_at":"2026-08-07T12:28:02.968259Z","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":"2026-08-07T12:28:04.112273Z","title":"Ensemble- SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control,","venue":null,"work_id":"feca5328-71c6-4b6c-b1e2-ff1f6475b40f","year":2022},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:03.044628Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:8a4d68acbf5379abf6ed6e636c41f478222351adcf0bd54d3ccb43b1c2ab374c","observation_id":"32603b99-8a87-45c9-97b4-b908940595b1","resolution":{"observed_at":"2026-08-07T12:28:04.159535Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:03.972565Z","title":"Derivative-based SINDy (DSINDy): Address- ing the challenge of discovering governing equations from noisy data,","venue":null,"work_id":"0d3c1817-c9bf-414e-8789-dffbb890d33d","year":2023},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:03.129490Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:e4a6785eb8a269ad821e05d028501e92aaab47230d2ac9aa454c0b22828e77f8","observation_id":"bdcf4906-9d04-41f2-996d-6e10e6dc193c","resolution":{"observed_at":"2026-08-07T12:28:04.042841Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2504.04863","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:28:03.678322Z","title":"Dynamic hysteresis model of grain-oriented ferromagnetic material using neural operators,","venue":null,"work_id":"a8597c11-a275-4ccd-b29b-966b459707dd","year":2025},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:03.188809Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:980e4eafbd38b53478b7685be5ba416ed3d134074574fef77001ca3363b2cbc0","observation_id":"f2b8a9d9-1749-4223-87f8-6b34217106cb","resolution":{"observed_at":"2026-08-07T12:28:03.783118Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1412.6980","last_updated":"2017-01-30T01:27:54Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2014-12-22T13:54:29Z","title":"Adam: A Method for Stochastic Optimization","version":9},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1412.6980","snapshot_observed_at":"2026-08-07T12:28:03.260521Z","title":"Adam: A method for stochastic optimization,","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:03.260521Z"},"links":{"cited_paper":"/paper/1412.6980","citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:5cd642031665c80be2cab04666e409b701e9e03f47af4828c5b57dfc5270dd5e","observation_id":"243abd67-6335-495b-a451-46d4e01c46d5","resolution":{"observed_at":"2026-08-07T12:28:03.260521Z","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":"2026-08-07T12:28:03.381908Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-07T12:28:03.381908Z"},"links":{"citing_paper":"/paper/2505.24578"},"observation_digest":"sha256:2e866095db53c5d11183653be02272c9397702a0c573cc212beb4b395ecd2574","observation_id":"e4af9125-74b8-4d4f-a197-6592c5008168","resolution":{"observed_at":"2026-08-07T12:28:03.381908Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2505.24578","last_updated":"2025-05-30T13:28:11Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-07T15:26:20.071166Z","submitted_at":"2025-05-30T13:28:11Z","title":"Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems"},"reference_resolution":{"displayed":40,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":10,"verified_exact":1,"verified_fuzzy":29},"total_outbound_references":40},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 0 inbound Pith citation observations for arXiv:2505.24578."}