{"as_of":"2026-08-09T02:07:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:2408263477e955fa9af51b53866a46e1ef2318de88d028c03b7b4fc42b6ed3a8","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":"2026-08-02T12:18:27.537415Z","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/2607.22576/citation-record","integrity":"/paper/2607.22576/integrity","json":"/paper/2607.22576/citation-record.json","paper":"/paper/2607.22576"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T12:18:22.115405Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:22.115405Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:7dc44a0266270592916097643994cbcc06d93333360bee24266e08807b57ceec","observation_id":"65a83d72-61ae-4919-9ad1-4e10389f8ecd","resolution":{"observed_at":"2026-08-02T12:18:22.115405Z","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":"2026-08-02T12:18:22.212725Z","title":"Berljafa and S","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:22.212725Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:44d45aa342067d77e7dede27bb9cea8e3e380084aea3bd592de774bb59ec3a4b","observation_id":"45f8533d-5cc8-4037-a855-e66f9b930326","resolution":{"observed_at":"2026-08-02T12:18:22.212725Z","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":"2026-08-02T12:18:22.393435Z","title":null,"venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:22.393435Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:1e355a4bbc7cf723efe482d6659723d199102a065ea2d5856ab08c49d5553837","observation_id":"b51f1d63-1f45-4aa1-a4fc-e02e33964f87","resolution":{"observed_at":"2026-08-02T12:18:22.393435Z","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":"2026-08-02T12:18:22.588306Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:22.588306Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:d90504b128c84465a399f31a1561c82bf08611995ae12cffee784057c470dfbd","observation_id":"3a9312e9-1dea-4cae-9693-331290ad6623","resolution":{"observed_at":"2026-08-02T12:18:22.588306Z","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":"2026-08-02T12:18:22.692226Z","title":"Deschrijver, M","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:22.692226Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:c4064c0a1300c0f0b421a45f01a4978b878be3863e8cca0fabeee100236450fa","observation_id":"af7e9d4e-4f05-4a0c-b69f-4ec258cfcdb6","resolution":{"observed_at":"2026-08-02T12:18:22.692226Z","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":"2026-08-02T12:18:22.863804Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:22.863804Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:2470303ef93b96446caf83dc6c4b795fd261b5eb8f76aa5c66d45169d2e40130","observation_id":"67d4c8b8-7fa0-4b22-be8a-4e89bb7a2f77","resolution":{"observed_at":"2026-08-02T12:18:22.863804Z","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":"2026-08-02T12:18:22.963593Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:22.963593Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:3ee29fb5f6ae17ff7875b4ee90500a815aae848e1f08ecb8ba78098212bda520","observation_id":"cb63d51d-14b3-480c-82c2-c20912daafb5","resolution":{"observed_at":"2026-08-02T12:18:22.963593Z","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":"2026-08-02T12:18:23.121794Z","title":"Gustavsen, Improving the pole relocating properties of vect or fitting, IEEE Trans","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:23.121794Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:d5b9023a3ea3a5a2b3e31f30a784d0e5af185e62ad5d1569b35de14ce42b0591","observation_id":"6f00e1f9-016a-49af-b079-34b6a8f173a6","resolution":{"observed_at":"2026-08-02T12:18:23.121794Z","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":"2026-08-02T12:18:23.262300Z","title":"Gustavsen, Matrix Fitting Toolbox, 2009, Https://www.sintef .no/en/software/vector- fitting/downloads/matrix-fitting-toolbox/","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:23.262300Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:cd8e9865dd7c5c9211f7eb30c66123fec30f942a955eacb41ed39bb5c3b3e62d","observation_id":"c96c6fb8-b6d8-4d2d-82bf-d14655c1cfae","resolution":{"observed_at":"2026-08-02T12:18:23.262300Z","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":"2026-08-02T12:18:23.394842Z","title":"Gustavsen and A","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:23.394842Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:3476af55569c23a93c82287e28d0768238e40cc55bbe0aa28235352c71f6db81","observation_id":"8e9c239b-f1f3-4668-821d-186e1342c4fd","resolution":{"observed_at":"2026-08-02T12:18:23.394842Z","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":"2026-08-02T12:18:23.604803Z","title":null,"venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:23.604803Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:6437aaa2788a6241876b48f082e144040a1a87f035bf4ad88700b08e22ba2374","observation_id":"c9cef30f-353b-4201-a1b6-276982905d8b","resolution":{"observed_at":"2026-08-02T12:18:23.604803Z","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":"2026-08-02T12:18:23.809442Z","title":"G¨ uttel and F","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:23.809442Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:ec57f406a3595c738905d6f05b73c54a4d1695bb603f5f00f9b0010ceb4933a1","observation_id":"ab6c4b3a-a6ae-449a-9c57-5cc27314df11","resolution":{"observed_at":"2026-08-02T12:18:23.809442Z","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":"2026-08-02T12:18:23.910718Z","title":"G¨ uttel, G","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:23.910718Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:94ef663a36548dd66e0a585667f916b14d54167b7f8e2be07872cec651bdb119","observation_id":"140fd614-dcd0-494a-94cc-f339469cbaa6","resolution":{"observed_at":"2026-08-02T12:18:23.910718Z","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":"2026-08-02T12:18:24.036795Z","title":null,"venue":null,"work_id":null,"year":1948},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:24.036795Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:1af98117bbaafab72c008c8c26568c9118f595eea339e72e3acae5b2d32b1a81","observation_id":"d6c346ef-d288-457c-88af-a7b007af3344","resolution":{"observed_at":"2026-08-02T12:18:24.036795Z","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":"2026-08-02T12:18:24.175358Z","title":"Lietaert, K","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:24.175358Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:002bf86c5b6a7ea745d30a1b7e591baa520948aad5a06f316aab7e6ccae9820e","observation_id":"bf5226b8-2368-4c55-89e9-e14174cc7bdf","resolution":{"observed_at":"2026-08-02T12:18:24.175358Z","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":"2026-08-02T12:18:24.389295Z","title":"Meinardus, Approximation of Functions: Theory and Numerical Methods","venue":null,"work_id":null,"year":1967},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:24.389295Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:acb57e6ca5184cc0e01059bc8c5f891b0684b8e4cc2a2ac91fce883ccb7b6b98","observation_id":"4ca53ada-c82b-48c6-957f-a087126a01b8","resolution":{"observed_at":"2026-08-02T12:18:24.389295Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2312.03565","last_updated":"2023-12-06T15:57:12Z","snapshot_observed_at":"2026-07-06T16:57:46.724781Z","submitted_at":"2023-12-06T15:57:12Z","title":"The first five years of the AAA algorithm","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.03565","snapshot_observed_at":"2026-08-02T12:18:24.587820Z","title":"Nakatsukasa, O","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:24.587820Z"},"links":{"cited_paper":"/paper/2312.03565","citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:0d843f8494d6a71f4371bc7cadd7d0c4ad139e1904b657b7a204a41ffc164100","observation_id":"d619a247-61aa-4c49-90b9-dbe22df85d23","resolution":{"observed_at":"2026-08-02T12:18:24.587820Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2510.16237","last_updated":"2025-10-17T22:00:37Z","snapshot_observed_at":"2026-08-04T09:20:51.136867Z","submitted_at":"2025-10-17T22:00:37Z","title":"Applications of AAA rational approximation","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2510.16237","snapshot_observed_at":"2026-08-02T12:18:24.754837Z","title":"Nakatsukasa and L","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:24.754837Z"},"links":{"cited_paper":"/paper/2510.16237","citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:e9f75bcadd6c2187c350496933379f01300b2e945c1be4345dafef9c8ddc4274","observation_id":"e41dafd3-27d7-4db4-baf7-207b21b8e184","resolution":{"observed_at":"2026-08-02T12:18:24.754837Z","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":"2026-08-02T12:18:24.859390Z","title":null,"venue":null,"work_id":null,"year":1969},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:24.859390Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:ce8236fdbb1359fb4b4bd0272a38247d95bfea00222282a28c1013d8dfd26a2f","observation_id":"896c43f2-019d-4da3-9d8f-6469fcc59db6","resolution":{"observed_at":"2026-08-02T12:18:24.859390Z","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":"2026-08-02T12:18:24.975345Z","title":null,"venue":null,"work_id":null,"year":1961},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:24.975345Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:a99fc668252d4c3b45b3510a4fc907862da14e9acbea697a7f78978f885fe7ab","observation_id":"5bf2f2d9-3a28-4e5f-8e68-12eac9c3e76b","resolution":{"observed_at":"2026-08-02T12:18:24.975345Z","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":"2026-08-02T12:18:25.158645Z","title":"Ruttan, A characterization of best complex rational appro ximants in a fundamental case, Constr","venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:25.158645Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:12903f63d34bd57096e26ec051ccff2c8f9a01d56fa8cda4335914e5da5e9b22","observation_id":"bbf3aa38-717c-4d4e-94bc-5f771642d319","resolution":{"observed_at":"2026-08-02T12:18:25.158645Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1901.01188","last_updated":"2020-06-09T15:58:07Z","snapshot_observed_at":"2026-07-06T07:24:56.165977Z","submitted_at":"2019-01-04T16:03:04Z","title":"A rational approximation method for the nonlinear eigenvalue problem","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1901.01188","snapshot_observed_at":"2026-08-02T12:18:25.292043Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:25.292043Z"},"links":{"cited_paper":"/paper/1901.01188","citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:0c9712e9a56eb277f68842d91ada733c35be85226d3399bd4abc7a48a35fef1e","observation_id":"4d1d2c45-4de7-4502-9332-4f96f5bac67e","resolution":{"observed_at":"2026-08-02T12:18:25.292043Z","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":"2026-08-02T12:18:25.441030Z","title":null,"venue":null,"work_id":null,"year":1971},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:25.441030Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:a9915c8924648019eb48e02606ef337b3e3175945f769202be6b2f9bcef85c1f","observation_id":"0ec5f3e3-efb8-4b31-a7a4-cbc1df170035","resolution":{"observed_at":"2026-08-02T12:18:25.441030Z","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":"2026-08-02T12:18:25.623277Z","title":"Singer, Best approximation in normed linear spaces by elements of li near subspaces, Springer- Verlag, Berlin-Heidelberg-New York, 1970","venue":null,"work_id":null,"year":1970},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:25.623277Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:da0629e609e1da26c31041520e530f470149a3d49248f4fa1826cee4080de1ee","observation_id":"54b77ccb-1dfa-4d8b-95f4-df0d3e91ef49","resolution":{"observed_at":"2026-08-02T12:18:25.623277Z","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":"10.1007/0-387-28395-1","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Singer, Duality for Nonconvex Approximation and Optimization , Springer-Verlag, New York, NY, 2006, URL https://doi.org/10.1007/0-387-28395-1","venue":"CMS books in mathematics","work_id":"21297250-28f4-494b-a540-052f5934c7b7","year":2006},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:25.738171Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:58706f2800e39e2ce3d7c59048e03161f1b686cdb5abc2d625aef3f0b556c190","observation_id":"6037ad7a-34c4-4b50-b42c-512e133eb98e","resolution":{"observed_at":"2026-08-02T12:18:31.525664Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T12:18:25.883024Z","title":"Thiran and M.-P","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:25.883024Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:9f0fe49bb40d069c21a0b9fdfabed40ae384ffba217936d583f2e98c48834cdf","observation_id":"9b057f94-2513-47a0-afc3-4489436f392d","resolution":{"observed_at":"2026-08-02T12:18:25.883024Z","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":"2026-08-02T12:18:26.039161Z","title":"Traina, Cauchy Method Modeling: Applied to Computer-Aided Tuning o f Microwave Filters and Duplexers , VDM Verlag Dr","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:26.039161Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:cbc167d9c711e739bb30464d04beed302287ce0335976ba26b71ddcac1a234d5","observation_id":"f93a0e3e-9636-4cb2-8665-54da09da4ce9","resolution":{"observed_at":"2026-08-02T12:18:26.039161Z","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":"2026-08-02T12:18:26.194791Z","title":"Traina, G","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:26.194791Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:b5f7f1552c0fd98c152cc762334d28825da83141bd4a9510483d4da8f78f5875","observation_id":"37cfc760-40fb-41cc-a958-88b8fbba3a81","resolution":{"observed_at":"2026-08-02T12:18:26.194791Z","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":"2026-08-02T12:18:26.285902Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:26.285902Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:ff617d9b1d37045276d7b60edab4828a1b30cfe48eab8d81a35f6106e8b7304f","observation_id":"79e7f548-4190-4045-9fcc-7456d170cd3c","resolution":{"observed_at":"2026-08-02T12:18:26.285902Z","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":"2026-08-02T12:18:26.377987Z","title":null,"venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:26.377987Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:754b0fc8e996e040cc1cd68f240215946857e3e0de306696c76002500849ca10","observation_id":"fdb18a24-0073-4f31-9724-0cf82cc384ab","resolution":{"observed_at":"2026-08-02T12:18:26.377987Z","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":"2026-08-02T12:18:26.493724Z","title":null,"venue":null,"work_id":null,"year":1931},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:26.493724Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:6757013ba4334303cd29b01ec57f18dde90a4287918fc61fcdb296f4b66e4c06","observation_id":"00e93b17-ad36-4d28-a9c3-3518c0c19174","resolution":{"observed_at":"2026-08-02T12:18:26.493724Z","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":"2026-08-02T12:18:26.628682Z","title":null,"venue":null,"work_id":null,"year":1969},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:26.628682Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:98e3425b192d6268795b93004016b8741a7de210092c3894f2e8278d3a405461","observation_id":"d6e9a64c-ad2c-4a05-b56b-ce2bcd4f45d4","resolution":{"observed_at":"2026-08-02T12:18:26.628682Z","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":"2026-08-02T12:18:26.759344Z","title":"Williams, Characterization and computation of rational Cheby shev approximations in the complex plane, SIAM J","venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:26.759344Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:549ba47bcd85defa0ece1d728227f7d8ee11ae5026e7fc2b3244a97d97302e4a","observation_id":"69298047-ed93-476b-8dba-11545acccc1d","resolution":{"observed_at":"2026-08-02T12:18:26.759344Z","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":"2026-08-02T12:18:26.884945Z","title":"Zhang, J","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:26.884945Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:a7e79331818d3446bb42632f5cba02f8e921a0b3f4d9c84ec8215cd578f23d66","observation_id":"d87a2543-d16d-4a11-8a72-9d56effd552b","resolution":{"observed_at":"2026-08-02T12:18:26.884945Z","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":"2026-08-02T12:18:26.986939Z","title":"Zhang and S","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:26.986939Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:695a64f0d8fb510f07e7ada4997424b922290fe968231ea5c85a9e87a2d4f7c1","observation_id":"207b821b-5235-4968-8f0e-252bee35d989","resolution":{"observed_at":"2026-08-02T12:18:26.986939Z","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":"2026-08-02T12:18:27.081161Z","title":"Zhang, L","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:27.081161Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:42275bfa6d393f73d82e96d2e9fbc0a4aaceb9734f1681f470dd6f7dbff3dd67","observation_id":"8754cf44-0bb0-4f55-8b2d-f15fe7434049","resolution":{"observed_at":"2026-08-02T12:18:27.081161Z","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":"2026-08-02T12:18:27.192487Z","title":"Zhang, Optimality conditions for rational minimax approxima tions: Bridging Ruttan’s criteria to dual-based methods, 2026, URL https://arxiv.org/abs/2602.07862v1","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:27.192487Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:9cc897216076b14503051384970608c80b5bd8506a02b4a243f9c45e246ccb40","observation_id":"58d46414-8cd2-4244-9b32-6b93da34ab3e","resolution":{"observed_at":"2026-08-02T12:18:27.192487Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.10665","last_updated":"2026-05-18T12:59:45Z","snapshot_observed_at":"2026-08-06T09:13:29.983966Z","submitted_at":"2025-02-15T04:19:47Z","title":"Interpolation constrained rational minimax approximation with barycentric representation","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.10665","snapshot_observed_at":"2026-08-02T12:18:27.302406Z","title":"Zhang and Y","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:27.302406Z"},"links":{"cited_paper":"/paper/2502.10665","citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:3a1d1fd089e7424a3d72c95f00f1f5e322a3b8f72ce4ab817fd6607b42e08531","observation_id":"d6f57a97-4543-42f5-a829-1ea696912924","resolution":{"observed_at":"2026-08-02T12:18:27.302406Z","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":"10.1007/s11075-025-02058-0","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Zhang, Y.-N","venue":"Numerical Algorithms","work_id":"901ef47b-1bac-4a34-9b10-f51932f554de","year":2025},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:27.462704Z"},"links":{"citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:bb51129e343c5d82598fd9e1d93a0f21d20fd6430e6043bdc7720d57d76da0df","observation_id":"b53f67cc-96ad-4ec1-ba92-a82e972574f6","resolution":{"observed_at":"2026-08-02T12:23:26.683607Z","resolver_source":"doi","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":"2508.06378","last_updated":"2025-09-11T12:01:14Z","snapshot_observed_at":"2026-08-06T19:18:15.572483Z","submitted_at":"2025-08-08T15:09:24Z","title":"Rational minimax approximation of matrix-valued functions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2508.06378","snapshot_observed_at":"2026-08-02T12:18:27.537415Z","title":"Zhang, Y.-N","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-02T12:18:27.537415Z"},"links":{"cited_paper":"/paper/2508.06378","citing_paper":"/paper/2607.22576"},"observation_digest":"sha256:ab306ab5da2dc8c40a022dcb5e4026264d631f521e976e6af99eb55b5f70a174","observation_id":"5f79a4a7-b9c6-40cd-9a1d-9f55920721b0","resolution":{"observed_at":"2026-08-02T12:18:27.537415Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.22576","last_updated":"2026-06-06T10:02:40Z","latest_version":1,"primary_category":"math.OC","snapshot_observed_at":"2026-08-08T21:35:12.385695Z","submitted_at":"2026-06-06T10:02:40Z","title":"Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms"},"reference_resolution":{"displayed":40,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":38,"verified_exact":2,"verified_fuzzy":0},"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 9 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 0 inbound Pith citation observations for arXiv:2607.22576."}