{"as_of":"2026-08-10T19:39:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:99cf043912147198f6c224ba84549d7ceac9b5aea7382d86216661f960dab41a","coverage":[{"denominator":46,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":46,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T22:54:04.737483Z","state":"measured"},{"denominator":47,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":47,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-02T12:18:27.537415Z","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":[{"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"}}],"links":{"evidence":"/evidence","html":"/paper/2508.06378/citation-record","integrity":"/paper/2508.06378/integrity","json":"/paper/2508.06378/citation-record.json","paper":"/paper/2508.06378"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T22:54:04.549526Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_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},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.549526Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:44c8583944ad35852dca0020af479e944acf21f03e7f3446a833b99e200d382e","observation_id":"1287ed38-b4e4-4c6f-b310-d1b366f03126","resolution":{"observed_at":"2026-08-05T22:54:04.549526Z","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":"2026-08-05T22:54:07.365112Z","title":"Barrodale and J","venue":null,"work_id":"d2736dde-14be-417a-90a2-0a17e2dcf911","year":1970},"citing_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},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.554824Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:c5bc01662a94eb206f59fcbabf3134df36c67891e125a7d8e96373e23301559d","observation_id":"65048547-831e-40fc-9049-c2144b217f36","resolution":{"observed_at":"2026-08-05T22:54:07.437848Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-05T22:54:04.559243Z","title":"Berljafa and S","venue":null,"work_id":null,"year":2015},"citing_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},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.559243Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:0c1a5b59b5ef0698331bd664e9f9ce8f75af1298ab1255c8833e17e12693e7fa","observation_id":"2c3fffb4-52fe-4c53-9fcf-b18443351803","resolution":{"observed_at":"2026-08-05T22:54:04.559243Z","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":"2026-08-05T22:54:04.563837Z","title":"Berljafa and S","venue":null,"work_id":null,"year":2017},"citing_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},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.563837Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:637ca2f49746dfd2304843b7579e9bded48cdb2dc7a8dc382a493c40b5b53c38","observation_id":"5fde9192-ae21-4f16-bd4c-423bf12dc1ae","resolution":{"observed_at":"2026-08-05T22:54:04.563837Z","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":"2026-08-05T22:54:07.288148Z","title":"Boyd and L","venue":null,"work_id":"09c9281b-c843-4800-a574-03502a210b0f","year":2004},"citing_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},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.569121Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:09f4cff105650869f8e7d6b3dbc5ad24d6c8a655fb76416d81f305a9f2367ddc","observation_id":"b5716615-f82c-4dec-bb8d-41dfd1d051ad","resolution":{"observed_at":"2026-08-05T22:54:07.312039Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-05T22:54:07.132895Z","title":null,"venue":null,"work_id":"e5a12223-8971-48d1-81cf-84e2837eb3ef","year":2021},"citing_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},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.574069Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:7cf2548c30222dfbc94604d4e559ad7bd64140af817236969854f0103844918a","observation_id":"2df73848-00bc-4d28-9f46-1db6a0288cf6","resolution":{"observed_at":"2026-08-05T22:54:07.215149Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-05T22:54:04.579135Z","title":null,"venue":null,"work_id":null,"year":1972},"citing_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},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.579135Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:7cddad760e07fbda86300de2e21c98a83216c5dad6b403ccdb2b038d29868f85","observation_id":"bca400c7-fb3d-431f-b2c3-94aa56e461ea","resolution":{"observed_at":"2026-08-05T22:54:04.579135Z","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":"2026-08-05T22:54:06.983711Z","title":"Deschrijver, M","venue":null,"work_id":"a20faced-2215-4c7c-892e-10d78035c19d","year":2008},"citing_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},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.583297Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:68ae1116299cadcc25216e6bab8d50bc342c1ff418a52833c70a5883ffd59b62","observation_id":"bcf251cc-1107-4db0-bcfd-82e0d884a001","resolution":{"observed_at":"2026-08-05T22:54:07.044563Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-05T22:54:06.801039Z","title":"Drmaˇ c, S","venue":null,"work_id":"93667ab9-15fb-41f3-9968-c379f9c64ef2","year":2015},"citing_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},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.587571Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:b901ef686853d3f70cf6e59c8c14c952c56e43b8670df92dda88d29cd0accc0d","observation_id":"73266614-e51a-44c1-9c37-a09fb12d4917","resolution":{"observed_at":"2026-08-05T22:54:06.893358Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-05T22:54:06.663821Z","title":"Ellacott and J","venue":null,"work_id":"cf4e33a4-0d90-4983-9a25-52ee2d15d269","year":1976},"citing_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},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.591763Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:87fcc4652d00b12cfd6f9dfe6ce6c3571016c13447cf6993aa625e2cbdb4fb6c","observation_id":"480848f8-5dab-4ffb-97d5-27b8a070290f","resolution":{"observed_at":"2026-08-05T22:54:06.724495Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-05T22:54:04.595847Z","title":null,"venue":null,"work_id":null,"year":1978},"citing_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},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.595847Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:cc9273b22b98849c3b2a5c99b64a87aeb881c89ad19d99d2e1d5b0c5e8fcb1cd","observation_id":"412a7a50-0397-45e7-b5aa-ff48d6db356e","resolution":{"observed_at":"2026-08-05T22:54:04.595847Z","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":"2026-08-05T22:54:04.600082Z","title":"Filip, Y","venue":null,"work_id":null,"year":2018},"citing_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},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.600082Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:2e66e6e4d0ecb32da9982de078ece8378a4cd0e99ed0a4cfa199d8ed3dd609c6","observation_id":"a86382b4-27f9-4490-acd2-5334511d501b","resolution":{"observed_at":"2026-08-05T22:54:04.600082Z","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":"2026-08-05T22:54:06.448463Z","title":null,"venue":null,"work_id":"1ff2359c-cd02-4e1a-9d4d-e8fb223149b1","year":2013},"citing_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},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.603914Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:f72fe17541b424880d0fbd5f8e868a0e2ee42040332040a28bb4e8293a88461d","observation_id":"9376ecac-c8f1-480c-842f-14dc1a2bca43","resolution":{"observed_at":"2026-08-05T22:54:06.511823Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/20","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T22:54:04.798315Z","title":null,"venue":null,"work_id":"f76b992b-43c4-4372-a3c0-4801f3d3c1ac","year":2021},"citing_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},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.607702Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:14b3bce7a636def4cbd50d0dd2959186c51db9d4ab22993c337dd0ea34991082","observation_id":"b664af79-f509-4614-83cb-ca8abcc9d9e2","resolution":{"observed_at":"2026-08-05T22:54:04.803443Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-05T22:54:06.283753Z","title":null,"venue":null,"work_id":"df1d8af8-5dfa-484b-9b56-04e76e81c4cb","year":2022},"citing_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},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.611724Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:0c549d36e352ac237e318c1c44992271808f5bc937d63cf6272cd6d2fc4622a0","observation_id":"cc6ae2e0-5587-4e6a-9857-d42748db2e7b","resolution":{"observed_at":"2026-08-05T22:54:06.338811Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-05T22:54:06.187784Z","title":"Gustavsen, Improving the pole relocating properties of vec tor fitting, IEEE Trans","venue":null,"work_id":"ff0490bc-7c80-416d-ae2b-4096acfa261b","year":2006},"citing_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},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.615696Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:3169f38525311041c029ed297b59d4a4bb241b881c1660a3293b2650ad687e4b","observation_id":"24cabac4-d891-4869-aa34-08e4d4f0123b","resolution":{"observed_at":"2026-08-05T22:54:06.226273Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-05T22:54:05.991179Z","title":"Gustavsen, Matrix Fitting Toolbox, 2009, Https://www.sinte f.no/en/software/vector- fitting/downloads/matrix-fitting-toolbox/","venue":null,"work_id":"250e1e43-eded-4c39-9cff-42894086d4f2","year":2009},"citing_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},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.619760Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:f2354f9243fe15059dd941b9f6af272c2946554c648fdf12394f5bda18ddbe09","observation_id":"2f272d08-d919-434b-b5ad-f4e32d2ec12a","resolution":{"observed_at":"2026-08-05T22:54:06.061722Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-05T22:54:04.623614Z","title":"Gustavsen and A","venue":null,"work_id":null,"year":1999},"citing_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},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.623614Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:dde1700341b890b208a0f66f1dbc8f0fc9468f4145c0273b469c961c915cd978","observation_id":"a430b02c-4180-4637-ae0a-baac91fbc92e","resolution":{"observed_at":"2026-08-05T22:54:04.623614Z","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":"2026-08-05T22:54:04.627772Z","title":null,"venue":null,"work_id":null,"year":1983},"citing_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},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.627772Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:30b37417d94624f0185faa6d4a2369cc261dd872913b458be9a5501a8c3d60c3","observation_id":"5f2dd16b-63da-420a-ae71-5955d26e098f","resolution":{"observed_at":"2026-08-05T22:54:04.627772Z","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":"2026-08-05T22:54:05.808555Z","title":"G¨ uttel and F","venue":null,"work_id":"cc65d188-cb08-4a54-9c36-1c9df1ad84db","year":2017},"citing_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},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.631848Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:16f3b268c5fc1a4aec1bdb6251e6e91455140431ec7d577c872380dd76652d50","observation_id":"96036aab-2083-4a6f-9cd3-fd501fb0387d","resolution":{"observed_at":"2026-08-05T22:54:05.889194Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-05T22:54:04.635904Z","title":"G¨ uttel, G","venue":null,"work_id":null,"year":2022},"citing_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},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.635904Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:8f8aaa0c2d27c86ac2dcbf5cc94ad904c22ce03189b46c497150cb1fc8c5f615","observation_id":"5bd03600-5107-41a4-ad4a-4c73456b5e95","resolution":{"observed_at":"2026-08-05T22:54:04.635904Z","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":"2026-08-05T22:54:05.686832Z","title":null,"venue":null,"work_id":"531694be-86d3-421c-9619-9b3b83f73415","year":2019},"citing_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},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.639986Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:72c01a0d68123483eb97ff7b767fab5a668a03b25f9459b3ad1d40a1470ba3c8","observation_id":"7a67194e-efc2-43c4-b28e-111031708f74","resolution":{"observed_at":"2026-08-05T22:54:05.731405Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2009.10803","last_updated":"2020-09-22T20:38:56Z","snapshot_observed_at":"2026-08-10T18:22:23.261285Z","submitted_at":"2020-09-22T20:38:56Z","title":"Multivariate Rational Approximation Using a Stabilized Sanathanan-Koerner Iteration","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2009.10803","snapshot_observed_at":"2026-08-05T22:54:04.644173Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_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},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.644173Z"},"links":{"cited_paper":"/paper/2009.10803","citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:663308459964391fc3d43e9deb322c5b8b81701854540317561e044dc30cfc7c","observation_id":"198ff45b-4ffb-4a12-b2ca-3ad500016d01","resolution":{"observed_at":"2026-08-05T22:54:04.644173Z","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":"2026-08-05T22:54:05.480248Z","title":null,"venue":null,"work_id":"c4de3461-faf5-4bbd-8792-7b716e8b4bc1","year":1961},"citing_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},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.648730Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:3e16f668d90b754ecb1b942af71f7839da08572516a38f0a7dd7a43757b9f32a","observation_id":"be74d4e0-61ba-4812-819a-984aa67bea70","resolution":{"observed_at":"2026-08-05T22:54:05.596669Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-05T22:54:05.280181Z","title":"Liang, R.-C","venue":null,"work_id":"aefbdb24-ba55-44b4-aeee-2a06d46a6630","year":2013},"citing_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},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.652662Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:abae422e9d1c1e499626e78ed960b7ed3cfff39b5eb0e2dc6b6e125104cc28cf","observation_id":"b7f8879a-0cb1-4b4c-9533-a8c68a53fdba","resolution":{"observed_at":"2026-08-05T22:54:05.366922Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-05T22:54:04.656585Z","title":"Lietaert, K","venue":null,"work_id":null,"year":2022},"citing_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},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.656585Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:bbf47d823c7ea8f5300ee2341dd5a0735c4beb62b813bc3e82eb01bc25989d4e","observation_id":"74ec13d7-99ba-4df3-a8a7-a78e0b4733e9","resolution":{"observed_at":"2026-08-05T22:54:04.656585Z","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":"2026-08-05T22:54:05.168223Z","title":null,"venue":null,"work_id":"ca15bc34-2fa6-4067-8f50-1539dfcc839e","year":2007},"citing_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},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.660638Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:476fcca9ba85b14377343ab4015f21a7c6a2153cd707545bced4e62f1b81223c","observation_id":"f0025734-f12b-446e-9747-ac9fb9fb1fb9","resolution":{"observed_at":"2026-08-05T22:54:05.189461Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-05T22:54:04.664701Z","title":"Nakatsukasa, O","venue":null,"work_id":null,"year":2018},"citing_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},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.664701Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:8eeade53d054d50113b977a95ca7dc3a76f1eafcb3cd744db327111de3b78c44","observation_id":"e1fb7751-9246-4dc3-8fa8-acde797ec73e","resolution":{"observed_at":"2026-08-05T22:54:04.664701Z","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":"2026-08-05T22:54:04.668555Z","title":"Nakatsukasa and L","venue":null,"work_id":null,"year":2020},"citing_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},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.668555Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:2908bad2ff06e05ba7c4fdf6d37535b6cfe3d4ab33a10a08525a2b02ae836df1","observation_id":"4f55c13e-571e-47f3-8382-98850e796c30","resolution":{"observed_at":"2026-08-05T22:54:04.668555Z","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":"2026-08-05T22:54:04.672360Z","title":"Nocedal and S","venue":null,"work_id":null,"year":2006},"citing_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},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.672360Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:6bafd3f8d3908e9be71865ddcc0f56af4bb2208025dd108d94d9895290ecc9e1","observation_id":"097fa2ad-71d6-4a88-9043-88dd73f238a0","resolution":{"observed_at":"2026-08-05T22:54:04.672360Z","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":"2026-08-05T22:54:05.091508Z","title":null,"venue":null,"work_id":"4f897041-f73d-443f-bdb2-8e69f965bb69","year":1969},"citing_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},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.676140Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:daf73b628263f8e22c87aaea51decc99e6af7a7fc360d56aeb46e9d29440953f","observation_id":"0ef36270-5fc4-41c4-b0c3-caf64231b24a","resolution":{"observed_at":"2026-08-05T22:54:05.111568Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-05T22:54:04.680150Z","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":"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},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.680150Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:41b956f2d35748eff485c51e544facea50cf7f73c83f9a03b4b47df8e3c3d15d","observation_id":"9a39cb24-4676-466f-a570-c3758365bfe0","resolution":{"observed_at":"2026-08-05T22:54:04.680150Z","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":"2026-08-10T08:44:50.555029Z","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":"2026-08-05T22:54:04.684075Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_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},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.684075Z"},"links":{"cited_paper":"/paper/1901.01188","citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:02377e9bc54226c8af71115e6ce355dc2f7f49136317d8e54bb528d5eae08cf5","observation_id":"b23ff6d2-96f9-4e6c-a705-58ce3d633b66","resolution":{"observed_at":"2026-08-05T22:54:04.684075Z","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":"2026-08-05T22:54:04.688395Z","title":null,"venue":null,"work_id":null,"year":1977},"citing_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},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.688395Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:939ac421a250367e10f258259bd640cf503e8680d301503a0b809098bf8d01cc","observation_id":"b9d13924-a65f-4f63-9252-fc786a866956","resolution":{"observed_at":"2026-08-05T22:54:04.688395Z","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":"2026-08-05T22:54:04.692294Z","title":"Thiran and M.-P","venue":null,"work_id":null,"year":1993},"citing_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},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.692294Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:792528938b6718ffb42669315b625c3560202b0e2b59c26ea4a6fe14b14fbd5a","observation_id":"f7d87c45-bf21-4eaa-9d4d-046a242e644b","resolution":{"observed_at":"2026-08-05T22:54:04.692294Z","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":"2026-08-05T22:54:05.017486Z","title":"Traina, Cauchy Method Modeling: Applied to Computer-Aided Tuning o f Microwave Filters and Duplexers , VDM Verlag Dr","venue":null,"work_id":"0ce0a858-57ea-4ce7-b4d2-d9ec513860f0","year":2010},"citing_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},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.696854Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:d83b105d8542e98fdb5ebae714c7c503a0deb0696bc49ded699ad64b0c8c7d05","observation_id":"f6efd117-1eeb-4f3d-9c9a-13304a6d3e57","resolution":{"observed_at":"2026-08-05T22:54:05.035189Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-05T22:54:04.976210Z","title":"Traina, G","venue":null,"work_id":"a5d4b9d8-8817-4880-9589-119589731c1a","year":2007},"citing_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},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.700978Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:cb1f8bf094aa18e685aef4d0bb2b78371ce7a5ff0eefaf7f0f3cd032e052f7fa","observation_id":"bfd3f538-9f93-4045-bdad-fd2f64a44c78","resolution":{"observed_at":"2026-08-05T22:54:04.994230Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-05T22:54:04.705107Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_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},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.705107Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:ed6284193640339479fc1773536b968c9bebcad8aae8d866e7f76fdc8cc8ab4c","observation_id":"10b9b5be-f9f2-45de-a0f6-e6dd894c68dc","resolution":{"observed_at":"2026-08-05T22:54:04.705107Z","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":"2026-08-05T22:54:04.708862Z","title":"Williams, Numerical Chebyshev approximation in the complex plan e, SIAM J","venue":null,"work_id":null,"year":1972},"citing_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},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.708862Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:0777e061923262dd02d4b4cc323f9d083e3e3f3b3a560951133ca863bdfb635a","observation_id":"ddd41021-7a78-4eb4-b74e-d86da6957d2a","resolution":{"observed_at":"2026-08-05T22:54:04.708862Z","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":"2026-08-05T22:54:04.712808Z","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":"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},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.712808Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:e3ef141aedd01cb84670b4c7c147705b568459e8357c014ca40c29988f051386","observation_id":"f0c72347-037b-43fa-9b69-d4d670617dee","resolution":{"observed_at":"2026-08-05T22:54:04.712808Z","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":"2026-08-05T22:54:04.716834Z","title":null,"venue":null,"work_id":null,"year":1980},"citing_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},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.716834Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:72bc45d1db37538579fb4f4c1ed027d10c1410992d954d7d4a5548417a78fd62","observation_id":"52ba01de-219d-4aea-ad92-39f3bde391ed","resolution":{"observed_at":"2026-08-05T22:54:04.716834Z","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":"2026-08-05T22:54:04.906635Z","title":"Yang, L.-H","venue":null,"work_id":"fa5fda21-c05f-4f8a-8eee-135aabeb0f63","year":2024},"citing_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},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.720612Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:0db2b567eaa58ade2f889aad59458d34d7eb09595620d51a29768c1a173a4d70","observation_id":"9d4fdcc5-e803-4230-a7bf-cdd63e859917","resolution":{"observed_at":"2026-08-05T22:54:04.915021Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2401.00778","last_updated":"2025-08-07T09:41:27Z","snapshot_observed_at":"2026-07-06T17:10:32.750276Z","submitted_at":"2024-01-01T14:56:01Z","title":"A convergence analysis of Lawson's iteration for computing polynomial and rational minimax approximations","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2401.00778","snapshot_observed_at":"2026-08-05T22:54:04.724427Z","title":"Zhang and S","venue":null,"work_id":null,"year":null},"citing_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},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.724427Z"},"links":{"cited_paper":"/paper/2401.00778","citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:6026d46df3ef21107fcfa0608b033fa63f989c046bce78d362a1afd91050a199","observation_id":"8b411c83-95a2-4bb5-9d57-ccd30ffceb4a","resolution":{"observed_at":"2026-08-05T22:54:04.724427Z","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":"2026-08-05T22:54:04.891511Z","title":"Zhang, Y","venue":null,"work_id":"fe6ca4f4-3be8-4ad3-aec1-763efd1525f8","year":2024},"citing_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},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.728886Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:4953af50d187bdd23e8c173128733471b86c7e7a1b527c18a936c29893c5f392","observation_id":"0b6051c6-4adb-4f8e-8015-257ba8e5ba50","resolution":{"observed_at":"2026-08-05T22:54:04.896448Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-05T22:54:04.733417Z","title":"Zhang, L","venue":null,"work_id":null,"year":2025},"citing_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},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.733417Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:aadf292dc83e320609a92aa85311b340fce6f16b3153049cd6f75d679f119561","observation_id":"139e953b-236e-497f-94a7-1c7754298015","resolution":{"observed_at":"2026-08-05T22:54:04.733417Z","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":"2026-08-05T22:54:04.737483Z","title":"Zhang, Y.-N","venue":null,"work_id":null,"year":null},"citing_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},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-05T22:54:04.737483Z"},"links":{"citing_paper":"/paper/2508.06378"},"observation_digest":"sha256:eeca855a31df2ebe95d4ad55f46835e4db9f3545afe2e5f0ff8d9ef656279c90","observation_id":"c8b45b7e-88d5-41b5-b93c-4f205c628742","resolution":{"observed_at":"2026-08-05T22:54:04.737483Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2508.06378","last_updated":"2025-09-11T12:01:14Z","latest_version":2,"primary_category":"math.NA","snapshot_observed_at":"2026-08-06T19:18:15.572483Z","submitted_at":"2025-08-08T15:09:24Z","title":"Rational minimax approximation of matrix-valued functions"},"reference_resolution":{"displayed":46,"state_counts":{"malformed_identifier":2,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":32,"verified_exact":0,"verified_fuzzy":12},"total_outbound_references":46},"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":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 46 of 46 outbound references and 1 inbound Pith citation observation for arXiv:2508.06378."}