{"as_of":"2026-08-12T06:33:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:770d86eb8367351032557174996ab167a130a6429d498dc0edbfb29a915d554c","coverage":[{"denominator":32,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":32,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-30T08:23:17.867346Z","state":"measured"},{"denominator":32,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":32,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+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/2606.29083/citation-record","integrity":"/paper/2606.29083/integrity","json":"/paper/2606.29083/citation-record.json","paper":"/paper/2606.29083"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T21:17:43.924572Z","title":"Benjamin Erichson, Vanessa Lin, and Michael Mahoney","venue":null,"work_id":"caf16949-a6e1-4dd8-ab04-5eadee72a04b","year":2020},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:2fd2f687505040b0cbc8e1ad422e20b6ced0788613661132e2a99d0ebb6828af","observation_id":"581f1920-9120-409c-b2c1-e1b06977571a","resolution":{"observed_at":"2026-07-10T21:17:43.938649Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:17:44.051187Z","title":"Bollt, Felix Dietrich, Ioannis G","venue":null,"work_id":"87e52bff-886d-4642-b16a-beb21efe156c","year":2017},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:2eaa040c7bea15562e69fff473ecdc64c6905074736fee54796edfac1d9e8e43","observation_id":"a0a5430a-421d-4ad0-a042-902a2b6275f1","resolution":{"observed_at":"2026-07-10T21:17:44.065503Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:17:43.956035Z","title":"Brunton, Bingni W","venue":null,"work_id":"7ff3d50c-033e-44d6-8584-8ed69d4beed6","year":2016},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:ca0439e2c61caa8aa1112b119c12098d709dc103746409b9c2de93f36bdd1445","observation_id":"9b8758cd-4f5d-4593-aec7-b1656a5d0290","resolution":{"observed_at":"2026-07-10T21:17:43.969345Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:17:43.940604Z","title":"Brunton, Marko Budi ˇsi´c, Eurika Kaiser, and J","venue":null,"work_id":"8d524aab-b9f6-43c6-9609-5444c5a8b07f","year":2022},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:9e17692f9272635f8af783b3b2f5f07edd75f39b4d243d20d130fde4dc6e305e","observation_id":"327895dd-8801-482b-b9cb-d7dff81de361","resolution":{"observed_at":"2026-07-10T21:17:43.954105Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:17:43.848090Z","title":"Brunton, Bernd R","venue":null,"work_id":"fa05d26d-89cb-457b-b579-e9df9d425d42","year":2020},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:c699bdfb0177be6f26a9944b190ad6d4bb6e6a12c6156fca3d897201f1d77893","observation_id":"21ec8687-6dff-41ab-91b6-b0e104495d14","resolution":{"observed_at":"2026-07-10T21:17:43.861202Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:17:43.909418Z","title":"Colbrook","venue":null,"work_id":"a4f796a3-bd47-49cf-b037-3a4f23dd3bed","year":2024},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:2b41e649a4bddb7f5f6d73c520d1143bb8da29deeff6240418661b7ab40fb406","observation_id":"2a4d7fd9-cd87-459d-a4a4-237497aae38f","resolution":{"observed_at":"2026-07-10T21:17:43.922500Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:17:44.034553Z","title":"Colbrook.Infinite-Dimensional Spectral Computations: Foundations, Algorithms, and Modern Applications","venue":null,"work_id":"247fd3dd-b7b6-403a-ae9d-1726d5912732","year":2026},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:18cd9724e12745d65fd6a929755da2222223ed7d7b55043c0097acec7fffed4d","observation_id":"055ed6a9-a805-463a-86bc-f2e36734d431","resolution":{"observed_at":"2026-07-10T21:17:44.048980Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:17:43.879082Z","title":"Colbrook, Lorna J","venue":null,"work_id":"89201d40-15bd-4d63-bff8-5ad4fad7f9bd","year":2023},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:86578f9a51bab8ac14eed8b0a21d72973e7d0fc70a9433f948c540fa2ddc9026","observation_id":"ebc5684d-6ff2-4d33-a346-2ce55f44deb2","resolution":{"observed_at":"2026-07-10T21:17:43.892409Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:17:43.817387Z","title":"An introductory guide to Koopman learning","venue":null,"work_id":"ab4f60fc-4b7a-4bda-a077-5fe9c1db19dc","year":2026},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:465bc343aea59597485994125d7c814e7bdc26375d3bea1fe8fbdaee1e4722f5","observation_id":"4ec5575a-9b4b-4689-9d55-909a5ffec907","resolution":{"observed_at":"2026-07-10T21:17:43.831056Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:17:44.003624Z","title":"Colbrook, Qin Li, Ryan V","venue":null,"work_id":"6429d63f-a5f4-46fe-bc74-ab446be1647f","year":2037},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:8f59d3b2d3c9c0ecdd6cb103cdf857063bc8943a2cd1de4d76b8fe45aa2dc9f0","observation_id":"6f339ef8-07ab-44da-85ed-bba40164a706","resolution":{"observed_at":"2026-07-10T21:17:44.016379Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:17:44.018678Z","title":"Colbrook, Igor Mezi ´c, and Alexei Stepanenko","venue":null,"work_id":"1bdcf18c-9bf0-47b5-9e5e-ac904c91b2c1","year":null},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:a7d5d86fa5ecd7273e193d4c303ca08331d1a942c5ecb0c87dc7222ebe785f1d","observation_id":"89d40220-74ed-42ba-9ece-d80d9b8f24da","resolution":{"observed_at":"2026-07-10T21:17:44.032502Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:17:43.971489Z","title":"Colbrook and Alex Townsend","venue":null,"work_id":"8d4cb1e4-746d-4785-bc14-792bf0c4b0bb","year":2024},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:9038d0a39a640dde9b964a7f1a145f2463d72cb76ffa918f4c7e67f6afe2d616","observation_id":"e72b8d6a-91c4-471f-b3c8-d4561057f21a","resolution":{"observed_at":"2026-07-10T21:17:43.985532Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:17:43.894559Z","title":"Froyland, D","venue":null,"work_id":"17e17153-fd52-4d85-a141-0d256423b293","year":2021},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:e9509f378a990c4105af80b161e15f66e39cb26ca40d5c26c4e4f20edcec1849","observation_id":"08c88511-dafb-498e-a6f3-a0364fd88b83","resolution":{"observed_at":"2026-07-10T21:17:43.907388Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:17:44.067544Z","title":"Deep sparse rectifier neural networks","venue":null,"work_id":"ae955fbb-4ab9-40c0-826b-320c1b9b6448","year":2011},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:29f0dd5528c34806c2d75705f3e5c2c226a997d7a97febe0415d6e852a0d4e61","observation_id":"2b2be61a-3238-4c5f-803f-3bdcae22872a","resolution":{"observed_at":"2026-07-10T21:17:44.083529Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:17:43.833134Z","title":"Haggerty, Michael J","venue":null,"work_id":"3713e118-5dfd-4935-a1e0-8b1e5d89a8ab","year":2023},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:a515b388b254ed3aba5ca5a5ea3034ed0128e7a0d36ebcd6dd044dbac8090f4d","observation_id":"84cc0b3f-f8a8-49b5-be65-0c6e4d187f68","resolution":{"observed_at":"2026-07-10T21:17:43.845968Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:17:43.863472Z","title":"Haykin.Neural Networks: A Comprehensive Foundation","venue":null,"work_id":"37325c99-02d1-48de-baf0-046e4bd30770","year":1999},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:a87c658fd3bbd79230ec15c5ccd135dae8f53a1aa281a533ccd021c36c2a454e","observation_id":"abd5b5d7-dab6-408c-afff-62ca9a287d6b","resolution":{"observed_at":"2026-07-10T21:17:43.877214Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:17:44.085668Z","title":null,"venue":null,"work_id":"a2dc1a61-daca-49e1-a6f8-283379669a56","year":1931},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:cfb11bf06f7e9d8b8e09cdb3519f5dd064df05b5f409a3c20b3a5ee45af6c860","observation_id":"10a4addf-4b3e-4251-819b-0c777509251c","resolution":{"observed_at":"2026-07-10T21:17:44.099203Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:17:44.101280Z","title":"Koopman and J","venue":null,"work_id":"2a7e6a71-84bf-46a4-ac0b-cf1467b1263a","year":1932},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:0e29f075283fb32c0de860a3394efabc2006f068ad9147914448d8bca41b0079","observation_id":"ed4b4933-a2a2-4304-a21e-03fadff59249","resolution":{"observed_at":"2026-07-10T21:17:44.114930Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:17:43.987629Z","title":"Reskoopnet: learning Koopman representations for complex dynamics with spectral residuals","venue":null,"work_id":"b9bd5ff6-5fff-4ec3-bd09-ca355bc35757","year":2025},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:752f26088397329b2091175c87859a5eb3595fa23e86650b5bdc0c2838f459bd","observation_id":"c5dc3c34-831a-4ea8-9570-66a1cfaf61cd","resolution":{"observed_at":"2026-07-10T21:17:44.001779Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2606.09369","last_updated":"2026-06-08T11:45:45Z","snapshot_observed_at":"2026-07-06T23:48:44.159537Z","submitted_at":"2026-06-08T11:45:45Z","title":"Residual Pseudospectra Reveal a Physics-Informed Koopman Backbone for Tropical Pacific Variability and ENSO Prediction","version":1},"cited_work":{"arxiv_id":"2606.09369","doi":null,"metadata_source":"pith","pith_arxiv_id":"2606.09369","snapshot_observed_at":"2026-06-30T08:24:26.327253Z","title":"Residual Pseudospectra Reveal a Physics-Informed Koopman Backbone for Tropical Pacific Variability and ENSO Prediction","venue":"math.NA","work_id":"5faa82db-5bef-4a93-a443-7b3590dcddfd","year":2026},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"cited_paper":"/paper/2606.09369","citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:9d4c93d34e6d9791db4da8bb3489175a33eefd545230f08c5491e4458119d75c","observation_id":"34895c5e-8481-4428-87bb-950ec1709860","resolution":{"observed_at":"2026-06-30T08:24:26.328721Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:07:43.130526Z","title":"Nathan Kutz, and Steven L","venue":null,"work_id":"09ad44b7-ceea-4e07-ba9b-dab36583b982","year":2018},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:b20bcec248e2d2b26097f231463c8d06e2cefc6fa564764fdb84f3fbcc50bef3","observation_id":"a3a3cdf1-1d32-4079-a51f-7fee9254464b","resolution":{"observed_at":"2026-07-10T21:07:43.144484Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:07:43.111577Z","title":"Spectral properties of dynamical systems, model reduction and decompositions.Nonlinear Dynamics, 41(1):309–325, 2005","venue":null,"work_id":"152651be-120d-4e19-9429-1d0c37019850","year":2005},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:7801e4fe0718429e74368bcd6be21fbe63f3513303b46240a0d0c297a6147771","observation_id":"c84048f5-8899-4313-ae2a-ea60bf7a2cde","resolution":{"observed_at":"2026-07-10T21:07:43.126452Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:07:43.147697Z","title":"Analysis of fluid flows via spectral properties of the Koopman operator.Annual Review of Fluid Mechanics, 45(1):357–378, 2013","venue":null,"work_id":"1fb3f7b4-0b93-4d49-9010-6d123a9cc2ea","year":2013},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:a353de10f992a2426c22e503336156f445b25a2c59d043078f08223699baa881","observation_id":"a1cc1f6e-8741-4c38-b44c-773cd53c14f8","resolution":{"observed_at":"2026-07-10T21:07:43.162509Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:07:43.095058Z","title":"Orvieto et al","venue":null,"work_id":"b51ca631-5a61-447a-b287-7d725b92b499","year":2023},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:b505a620280b8d67ed1aa5760ed31054a46151798c78a961b5eb979df23d89cc","observation_id":"719b5c0a-5a43-487e-8cb8-ef81a524ea48","resolution":{"observed_at":"2026-07-10T21:07:43.108707Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:17:43.786166Z","title":"Otto and Clarence W","venue":null,"work_id":"7b1f9ae8-28c5-4e12-ae82-4bb0e974bbd6","year":2019},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:4e23ced60de69f1e4d0d6e880671f0dfb5a9653f19b2a495442b9633e9b8a400","observation_id":"5271d54e-0540-4ee1-b988-2c51ec777e56","resolution":{"observed_at":"2026-07-10T21:17:43.799201Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:17:43.801230Z","title":"Physics-informed probabilistic learning of linear embeddings of nonlinear dynamics with guaranteed stability.SIAM Journal on Applied Dynamical Systems, 19(1):480–509, 2020","venue":null,"work_id":"00ad8e94-ffea-40c3-9ae9-b11320281d1c","year":2020},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:cfd1920557f0af7a04b5642fd429e5a3313ed60e2813d5a00bc5fe32637c5c57","observation_id":"5dfbf0be-f6f7-45a8-a1f6-7b743729777b","resolution":{"observed_at":"2026-07-10T21:17:43.815427Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:07:42.871171Z","title":"Proctor and P","venue":null,"work_id":"bf9b5df5-7968-4128-9e90-8049fafd148d","year":2015},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:a6d5538fcafc19dd6515cf88676a72ba695246ba88db581b9509173f515597af","observation_id":"a6438155-d763-47dd-9317-5d06a4ddc80a","resolution":{"observed_at":"2026-07-10T21:07:42.884181Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:07:43.079971Z","title":"Rowley, Igor Mezi ´c, Shervin Bagheri, Philipp Schlatter, and Dan S","venue":null,"work_id":"c031790c-9b12-4bc8-bf6e-c464df0922f0","year":2009},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:71c6a96d8a4b9cfa166761354be3e8b2c985dd0fe5d65b094fc5362c114cc25e","observation_id":"0601ea38-8e34-4a13-8e41-efe51c52862d","resolution":{"observed_at":"2026-07-10T21:07:43.093186Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2602.04720","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T08:24:26.330070Z","title":"On data-driven unbiased predictors using the Koopman operator.arXiv preprint arXiv:2602.04720, 2026","venue":null,"work_id":"e03831dc-c430-4436-8862-04095cfba374","year":2026},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:93fab9f568c11abc03a1c05f210be5c193b4b5d45ec74ffe82ee3733090cf872","observation_id":"f55f99ba-bdd2-47d7-8f26-f39d46e29ee7","resolution":{"observed_at":"2026-06-30T08:24:26.331693Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:07:42.821449Z","title":"Learning Koopman invariant subspaces for dynamic mode decomposition","venue":null,"work_id":"b1b32eb7-1685-430a-bf1a-7f126d26b55b","year":2017},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:2fdce43f3e10c6eaabae0a53968584ad403b46e6015d223b72853237351221d3","observation_id":"7960c457-4dab-43b1-b925-5a2303cff64a","resolution":{"observed_at":"2026-07-10T21:07:42.834945Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:07:42.837960Z","title":"Williams, Ioannis G","venue":null,"work_id":"ef7c246a-9f1f-4044-9e99-44a7d82d6faa","year":2015},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:3339d9a35a8da677cb41ef09bca149dabccfc2584d30e3d26441510242a5167e","observation_id":"d6864f3a-63ec-4692-aee1-2c9caa73eeba","resolution":{"observed_at":"2026-07-10T21:07:42.850666Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-07-10T21:07:42.854288Z","title":"Learning deep neural network representations for Koopman operators of nonlinear dynamical systems","venue":null,"work_id":"f5e67dd7-1a63-4a9d-bb49-25657bba5360","year":2019},"citing_paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-06-30T08:23:17.867346Z"},"links":{"citing_paper":"/paper/2606.29083"},"observation_digest":"sha256:0bef34e2829b9ce4d48e486e90fbf50c6d8c61908041278a234614fed993a1bb","observation_id":"f31e92e7-3630-4b20-9ddf-4f71080dad72","resolution":{"observed_at":"2026-07-10T21:07:42.868382Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2606.29083","last_updated":"2026-06-27T20:53:18Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-07-07T00:03:07.870153Z","submitted_at":"2026-06-27T20:53:18Z","title":"Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation"},"reference_resolution":{"displayed":32,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":1,"verified_exact":2,"verified_fuzzy":29},"total_outbound_references":32},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2606.29083."}