{"as_of":"2026-08-23T17:54:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:58bd2cefae6bbf2ca83d95a91d341d29500c71d9d607f87c5a0ad8dd7b40a812","coverage":[{"denominator":54,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":54,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T00:09:34.617295Z","state":"measured"},{"denominator":56,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":56,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-23T06:30:58.430688+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T20:36:32.740774Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-07-02T08:56:49.343478Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.03057","snapshot_observed_at":"2026-08-15T20:36:32.740774Z","title":"ArXiv e-print 2505.03057 (2025) https://doi.org/10.48550/arXiv.2505.03057","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.12529","last_updated":"2026-07-01T08:46:54Z","snapshot_observed_at":"2026-08-16T05:33:30.738864Z","submitted_at":"2025-05-18T19:41:44Z","title":"$\\mathcal{H}_\\infty$ model order reduction for quadratic output systems","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-15T20:36:32.740774Z"},"links":{"cited_paper":"/paper/2505.03057","citing_paper":"/paper/2505.12529"},"observation_digest":"sha256:1390a9eb472d41d2a70ab7767b414b0e0502fed9fe0fdd8c3c6cb427deb1252c","observation_id":"b6ffa6ca-7c49-49f5-b8ea-0410786425ed","resolution":{"observed_at":"2026-08-15T20:36:32.740774Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"cited_work":{"arxiv_id":"2505.03057","doi":null,"metadata_source":"pith","pith_arxiv_id":"2505.03057","snapshot_observed_at":"2026-07-02T08:56:49.343478Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","venue":"math.NA","work_id":"28dc929a-6c7e-487c-b798-b6cc7d3debef","year":2025},"citing_paper":{"arxiv_id":"2607.00552","last_updated":"2026-07-01T07:43:25Z","snapshot_observed_at":"2026-08-12T07:47:33.591381Z","submitted_at":"2026-07-01T07:43:25Z","title":"L2-L2-gain bounds for quadratic output systems","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-02T08:48:39.360541Z"},"links":{"cited_paper":"/paper/2505.03057","citing_paper":"/paper/2607.00552"},"observation_digest":"sha256:335f48d237b81662605ce32656ad75841dfb46c98cffc88278e645b42ac62f00","observation_id":"7f385f2e-1e8d-4676-9bdd-f72e2b90b04f","resolution":{"observed_at":"2026-07-02T08:56:49.344782Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2505.03057/citation-record","integrity":"/paper/2505.03057/integrity","json":"/paper/2505.03057/citation-record.json","paper":"/paper/2505.03057"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:09:34.220847Z","title":"Antoulas","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.220847Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:33ac070f57a443742c9fe03db8ae159a1844b6a5d412da74a5eb7ef6f6e55f8c","observation_id":"e9f401a0-8c85-4cb7-8265-2b5407403eba","resolution":{"observed_at":"2026-08-16T00:09:34.220847Z","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":"2026-08-16T00:09:34.228655Z","title":"Antoulas, Christopher A","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.228655Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:0aab8508520a6cac5040bfde694d56dba32241abccdffaf7fed4745ea44a4964","observation_id":"152a5ab1-f136-4d5b-899a-210bd2f77578","resolution":{"observed_at":"2026-08-16T00:09:34.228655Z","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":"2026-08-16T00:09:36.107852Z","title":null,"venue":null,"work_id":"f79c1846-3dfb-41c4-85b4-4bd1e166e2da","year":null},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.235625Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:25621265cd29201cf5bcc2313a3d3d6f9645051fd3c3df9e55e17cd13375191a","observation_id":"24ce2992-ac01-415f-9c2e-23f27a4b0507","resolution":{"observed_at":"2026-08-16T00:09:36.113022Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2409.19730","last_updated":"2025-02-08T15:21:58Z","snapshot_observed_at":"2026-08-16T13:14:22.423261Z","submitted_at":"2024-09-29T15:11:28Z","title":"Energy-Based Approximation of Linear Systems with Polynomial Outputs","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.19730","snapshot_observed_at":"2026-08-16T00:09:34.253243Z","title":"Energy-based approx imation of linear systems with polyno- mial outputs","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.253243Z"},"links":{"cited_paper":"/paper/2409.19730","citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:76309aab4dce5b94633f2fa0d6a25cb88976fcb8f2f2e37d88c4786d4a643d09","observation_id":"ca47f160-9df9-495e-bef5-788ae83dc4dd","resolution":{"observed_at":"2026-08-16T00:09:34.253243Z","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":"2026-08-16T00:09:34.259851Z","title":"Model order r eduction for linear and nonlinear systems: a system-theoretic perspective","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.259851Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:832ef41452aa2324fa1260439855fd3435cc1e6134d0cb45bf95456b93244f00","observation_id":"538a732c-7ce5-4830-94b1-d03a9be136dc","resolution":{"observed_at":"2026-08-16T00:09:34.259851Z","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":"10.1016/j.laa.2011.07.015","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:09:35.094851Z","title":"Inexact solves in interpo- latory model reduction","venue":null,"work_id":"280fc86b-19e4-404c-865e-55fcbcde553f","year":2012},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.268029Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:b3277a97bef05a165e56afc896e5a13d64f36069e138c89509039fdf8c4484d8","observation_id":"c574fc0f-dff6-45e0-84ec-f1023c355627","resolution":{"observed_at":"2026-08-16T00:09:35.100799Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T00:09:34.277253Z","title":"Interpolation-based H2-model reduction of bilinear con- trol systems","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.277253Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:d7fc17591e68a57eddcb4539efa951980374381a3f0c89aa86b0929edbc82a3c","observation_id":"5e577e9b-065c-4765-9d57-829d1a4a570a","resolution":{"observed_at":"2026-08-16T00:09:34.277253Z","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":"2026-08-16T00:09:34.283830Z","title":"H2-quasi-optimal model order reduction for quadratic-bilinear control systems","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.283830Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:ae0f6a523dc431274d0fd248b20350c0b6e256f1509eff4ed1c3302264b8894d","observation_id":"998df13d-a83a-4814-ace0-3876a347a757","resolution":{"observed_at":"2026-08-16T00:09:34.283830Z","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":"2026-08-16T00:09:34.291715Z","title":"Gramians, energy functionals, and bal- anced truncation for linear dynamical systems with quadrat ic outputs","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.291715Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:db176837491dde7cbd4ce474663a4b51dd15b4c8704c89c43c1b2a424df2af23","observation_id":"1c7088eb-628c-4cd0-a5de-c3948c1e39e8","resolution":{"observed_at":"2026-08-16T00:09:34.291715Z","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":"2026-08-16T00:09:34.299209Z","title":"Sorensen","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.299209Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:026706545c93f4ce3d773e2c0cdb278bddc3f8c540762c49fd61dfb6914d2fec","observation_id":"1e5f8d46-c70f-4067-a8be-8e35a1f49d95","resolution":{"observed_at":"2026-08-16T00:09:34.299209Z","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":"2026-08-16T00:09:34.306250Z","title":"Model Reduc- tion and Approximation: Theory and Algorithms","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.306250Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:075c4898e0405145f700536a87f964a4d3683a55b8439c604f7304e9ad78902f","observation_id":"323589ee-e709-4edc-aef3-e6770a0e6238","resolution":{"observed_at":"2026-08-16T00:09:34.306250Z","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":"10.1515/9781400882243","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:09:35.032737Z","title":"Fourier Transforms","venue":null,"work_id":"0b026b6f-d614-419e-8d4a-dba7083e8768","year":1949},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.311531Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:b746edf620e64d71f91f9469ee43b8a2ee4f0c635560bd39f9724c5f1fd06e0a","observation_id":"2e170f7a-28a6-4998-8ed3-6a7a2c9d89a9","resolution":{"observed_at":"2026-08-16T00:09:35.039861Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"1978.10845","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:09:35.792344Z","title":"Kronecker products and matrix calculus in system theory","venue":null,"work_id":"66afe1fb-b429-439f-8e48-a0c00c40f4fe","year":1978},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.318448Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:297f0882aa295bbc703968a845d191c38013bcfffda375db50cd91edf894b975","observation_id":"9cd291d3-35b4-44f0-8e41-65df9fe207e2","resolution":{"observed_at":"2026-08-16T00:09:35.806293Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T00:09:36.088913Z","title":"Krylov subspace model order reduction of l inear dynamical systems with quadratic output","venue":null,"work_id":"96f6a9a0-04e7-41f0-8aca-646e53dfe722","year":null},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.325241Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:75297308bce2aadd3a057fd2df450e259caef53262a9dd414f4b4def7876ecfd","observation_id":"f1da41e0-1bd3-437b-81c0-f28892c9e286","resolution":{"observed_at":"2026-08-16T00:09:36.094427Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.cam.2008.12.029","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-21T11:03:19.436173Z","title":"h2-norm optimal model reduction for large scale discrete dynamical MIMO systems","venue":"Journal of Computational and Applied Mathematics","work_id":"8a78f209-469f-4f87-b5a6-37efca3a1be0","year":2010},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.336688Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:74d4643ae9a41458ebb9477289982fdfc5f0bc930e8d7e3fc0190f83a91abad0","observation_id":"d12a19d7-cfab-4c87-a49e-e9c7c54478a5","resolution":{"observed_at":"2026-08-16T00:09:35.001079Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-3-030-95157-3_7","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-17T11:03:46.409680Z","title":"Interpolation-based model order reduction for quadratic-bilinear systems and H2 optimal approximation","venue":null,"work_id":"2690564f-59a2-4c47-8e0d-88c3198e9bdf","year":2022},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.342509Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:a20a853f8d4f80759391001ad85d4e7d0954f46da5e0e234a08c678049a3553e","observation_id":"64683e8d-ee69-444c-a630-930bdc2fd22a","resolution":{"observed_at":"2026-08-16T00:09:34.987573Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T00:09:34.349541Z","title":"Diaz, Matthias Heinkenschloss, Ion Victo r Gosea, and Athanasios C","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.349541Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:3229ced01bfe9121ae41f5e7bdab2eb54cf61d6f79346ad11db1db0e56e2b10d","observation_id":"b4a4db95-4016-40e0-91ea-ce6e47b42051","resolution":{"observed_at":"2026-08-16T00:09:34.349541Z","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":"2026-08-16T00:09:34.354976Z","title":"Realization independent sin- gle time-delay dynamical model interpolation and H2-optimal approximation","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.354976Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:24a50de9cb0e71846f22e8b9997a7cd63bd6b2849b6b73f37e43e6b3eaa852bd","observation_id":"46eaba3b-5d74-4c1f-9f4c-bbd858f211bd","resolution":{"observed_at":"2026-08-16T00:09:34.354976Z","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":"2026-08-16T00:09:34.363607Z","title":"Multipoint Volterra series interpolation and H2 optimal model reduction of bilinear systems","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.363607Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:405236cf2cbc581f9646431f46f4e3be3f9bcf5d3544dc528de5999373a4ce3b","observation_id":"39d724b3-3351-4098-ba0c-1d877b63f78d","resolution":{"observed_at":"2026-08-16T00:09:34.363607Z","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":"2026-08-16T00:09:36.070850Z","title":"Interpolation Methods for the Model Reduction of Bilinear Sy stems","venue":null,"work_id":"67c17338-0f0b-445a-ad07-d68339d2fe6b","year":2012},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.375478Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:affe14acbe2f45cdfb0da65d6ca85bf2a2db246a5f0aec7fef61f69048357c76","observation_id":"398dbecb-72ad-4ac2-a92b-981bda1f3f3d","resolution":{"observed_at":"2026-08-16T00:09:36.078410Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T00:09:36.056029Z","title":"Complex Analysis","venue":null,"work_id":"29b9a0f6-68db-4227-983e-79431312415c","year":null},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.385822Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:477ee90be2d2434d26363f3ba99a6d77fda8a8ab7cb584b2200af9e1bc8a13e0","observation_id":"73c52bf8-00f0-45f6-a33f-b41085e87dbd","resolution":{"observed_at":"2026-08-16T00:09:36.060953Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T00:09:34.395258Z","title":"Antoulas","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.395258Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:b3cd2203037454e19abd84d562b6abbe3e02cc88b3b17396f244537484c82039","observation_id":"7e06d857-f8b3-4661-a863-09c027b9e41a","resolution":{"observed_at":"2026-08-16T00:09:34.395258Z","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":"2026-08-16T00:09:36.037319Z","title":"Data-driven mode ling of linear dynamical systems with quadratic output in the AAA framework","venue":null,"work_id":"9e94b1b7-f8dd-4bc0-ad86-19e8e533fcc3","year":null},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.400899Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:f81e70d1330118acfb9d6f776bbc9c43c610cc8573b9b94e276d8b511e10c856","observation_id":"d6ed63d8-d7f4-4cfd-adf9-752400dd6ab6","resolution":{"observed_at":"2026-08-16T00:09:36.046268Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/06066612","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:09:34.915933Z","title":"Antoulas, and Christop her Beattie","venue":null,"work_id":"b8df123b-9e04-44bb-afbe-7da747d119e4","year":2008},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.412492Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:3ffaabc68f877e4ea1eb2f47d959fbb841c9119c4a41d9d3d336a027e5fea855","observation_id":"beec5530-6afb-482d-9eb1-ab1fbcfdac86","resolution":{"observed_at":"2026-08-16T00:09:34.922655Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2309.05778","last_updated":"2025-03-11T12:09:44Z","snapshot_observed_at":"2026-08-17T17:52:47.370779Z","submitted_at":"2023-09-11T19:14:11Z","title":"Energy matching in reduced passive and port-Hamiltonian systems","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2309.05778","snapshot_observed_at":"2026-08-16T00:09:34.418285Z","title":"Energy matching in reduced passive and port-Hamiltonian systems","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.418285Z"},"links":{"cited_paper":"/paper/2309.05778","citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:dd6d36234c85f099405227bbe2d5c33b7c8e041331e6f8209b595483a99ef34c","observation_id":"2d4a5950-faeb-4d9f-8cca-524eca6d0bcc","resolution":{"observed_at":"2026-08-16T00:09:34.418285Z","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":"2026-08-16T00:09:34.424875Z","title":"The commutation matri x: some properties and applica- tions","venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.424875Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:b64660da0ea03fd76216a8500439b86720c60f5fc7872b17ae38209182dbdd25","observation_id":"6006a6e0-cf6b-4b7f-94a6-f4110e968985","resolution":{"observed_at":"2026-08-16T00:09:34.424875Z","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":"2026-08-16T00:09:34.429312Z","title":"Control of port-Ha miltonian diﬀerential-algebraic sys- tems and applications","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.429312Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:e37c31a512d3051cd936679dfc09edfad29064e5c15d073f453a1a0058ca81e7","observation_id":"f7821516-9373-4fcb-a353-1bea7cb782ae","resolution":{"observed_at":"2026-08-16T00:09:34.429312Z","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":"1967.10986","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:09:35.438537Z","title":"Approximation of linear c onstant systems","venue":null,"work_id":"74d4caa6-4e7c-4718-9680-e50ae65fc78e","year":1967},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.434228Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:f4d6be0067de4de8c914304713d4d754b25450377d508972cc994a49e80fb0f6","observation_id":"00a48e1b-d0c6-4131-99a1-7edf45dd72be","resolution":{"observed_at":"2026-08-16T00:09:35.447457Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.14716","last_updated":"2024-02-22T17:17:12Z","snapshot_observed_at":"2026-08-18T03:57:24.342232Z","submitted_at":"2024-02-22T17:17:12Z","title":"Balanced Truncation of Descriptor Systems with a Quadratic Output","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.14716","snapshot_observed_at":"2026-08-16T00:09:34.440311Z","title":"Balanced truncation of descriptor systems with a quadratic output","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.440311Z"},"links":{"cited_paper":"/paper/2402.14716","citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:760047146fe7be0d25f149b09ac7086b8cfe0ec9e83b7bdee8dcf2b6cad8f8d1","observation_id":"1c99ad0c-695b-4f6e-904b-b142fad47a94","resolution":{"observed_at":"2026-08-16T00:09:34.440311Z","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":"2026-08-16T00:09:34.447403Z","title":"Energy-based model order reduction for l inear stochastic Galerkin systems of second order","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.447403Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:c01906c89086e7a2b26aec0ec818cdb2a10c17d5473b6c6eeaf29764769bcd4b","observation_id":"95332899-2510-4224-ba69-6139f9842ee5","resolution":{"observed_at":"2026-08-16T00:09:34.447403Z","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":"2026-08-16T00:09:34.459540Z","title":"Balanced truncation for model order reduction of linear dy- namical systems with quadratic outputs","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.459540Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:0b44f27c6ea6d3fa6e70e3966ea6c6dd9ad0cee7acc514275d9f13c97fe1d3a4","observation_id":"afdf10ae-3277-4b23-8892-9d89b83306c0","resolution":{"observed_at":"2026-08-16T00:09:34.459540Z","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":"2026-08-16T00:09:36.020634Z","title":"H2-optimal model reduction of linear quadratic-output systems by multivariate ration al interpolation","venue":null,"work_id":"67c1caf8-f23d-4b55-a5b4-939344e2819d","year":null},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.470643Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:35ba851c838fb0cb24681ea0e401f8e96d4d9c6b4917b8a18a0b515d25bd5d42","observation_id":"8ac2a9d4-4ba5-4bdb-bd40-514ecb0dbdee","resolution":{"observed_at":"2026-08-16T00:09:36.025601Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.05951","last_updated":"2026-06-02T17:24:10Z","snapshot_observed_at":"2026-08-21T17:13:57.147863Z","submitted_at":"2024-05-09T17:44:25Z","title":"$H_2$ optimal model reduction of linear systems with multiple quadratic outputs","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.05951","snapshot_observed_at":"2026-08-16T00:09:34.486878Z","title":"H2 optimal model reduction of linear systems with multiple quadratic output s","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.486878Z"},"links":{"cited_paper":"/paper/2405.05951","citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:fa491ea9e936cb8d3cfa16a1d30f24427aa1fcff16f14ff01c260fd8260dcc10","observation_id":"dbcc77df-0ae4-4a05-b2ec-7c96959d3973","resolution":{"observed_at":"2026-08-16T00:09:34.486878Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.08894","last_updated":"2025-04-18T20:53:40Z","snapshot_observed_at":"2026-08-16T14:10:03.080281Z","submitted_at":"2024-03-13T18:35:51Z","title":"Interpolatory model reduction of dynamical systems with root mean squared error","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.08894","snapshot_observed_at":"2026-08-16T00:09:34.493386Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.493386Z"},"links":{"cited_paper":"/paper/2403.08894","citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:a298863444cbb3c3ebee774c69c550d2ecdb32a405d543d2a8716aaef479a462","observation_id":"9d62b17e-3e9b-4a57-b7b9-10f3ecb92d00","resolution":{"observed_at":"2026-08-16T00:09:34.493386Z","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":"2026-08-16T00:09:36.007371Z","title":"Nonlinear System Theory","venue":null,"work_id":"c75ee261-21e1-41ba-afb8-7d7405a58551","year":1981},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.500185Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:58efc3d3ddd0a8e4afc1f3b84bcf102f32058de775577fa12270e07b9e107f62","observation_id":"c5bb5fa6-bea2-4c1c-9083-239b98f706b3","resolution":{"observed_at":"2026-08-16T00:09:36.011870Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.11445","last_updated":"2024-03-05T06:43:19Z","snapshot_observed_at":"2026-08-16T14:17:40.662073Z","submitted_at":"2024-02-18T03:54:21Z","title":"Balanced Truncation of Linear Systems with Quadratic Outputs in Limited Time and Frequency Intervals","version":2},"cited_work":{"arxiv_id":"2402.11445","doi":null,"metadata_source":"pith","pith_arxiv_id":"2402.11445","snapshot_observed_at":"2026-08-16T00:09:35.290413Z","title":"Balanced Truncation of Linear Systems with Quadratic Outputs in Limited Time and Frequency Intervals","venue":"eess.SY","work_id":"9a4812eb-7d1f-4818-92ec-391faf366308","year":2024},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.507529Z"},"links":{"cited_paper":"/paper/2402.11445","citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:46394d2eaa228eda7434a2343f56956e7efec4c34658893c44a2685dea9e1fbe","observation_id":"73c5509e-e208-4188-b3aa-535125fc8596","resolution":{"observed_at":"2026-08-16T00:09:35.297287Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.5281/zenodo.15319961","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:09:34.864430Z","title":null,"venue":null,"work_id":"c7f7fcd7-be1b-4a8e-9a3b-de2beb19b125","year":null},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.477818Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:a712894dc4d7bf3723830b98854307d0208c7f93a2661704f5bce13f5bc54f4e","observation_id":"ad455744-6dd1-4253-9e67-ff1bf73b9af9","resolution":{"observed_at":"2026-08-16T00:09:34.872285Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T00:09:34.527628Z","title":"Model reduction for dynamical systems with quadratic output","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.527628Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:8d598bd644419377b9cfc9de82804d0e1e1c91cbf3c93d7aa60c5ef42d50573f","observation_id":"0e847010-f93f-41ca-b60f-bc9c5b2c5b8a","resolution":{"observed_at":"2026-08-16T00:09:34.527628Z","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":"2026-08-16T00:09:34.535515Z","title":"Port-Hamiltonian systems: an int roductory survey","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.535515Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:8cb265abf55bf84641cfd123a9d1031a610e30f8daf193a94a9553a05e987a45","observation_id":"0604f52e-87e4-4bb5-ab34-9a558e90ae46","resolution":{"observed_at":"2026-08-16T00:09:34.535515Z","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":"10.1016/j.aml.2007.09.015","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-21T11:03:19.436173Z","title":"H2-optimal model re- duction of MIMO systems","venue":"Applied Mathematics Letters","work_id":"482a756f-6a4a-43d9-af58-da1a767bfda1","year":2008},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.542927Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:89536d90f3abeb3c3d1e3bc648acc4151762d00315126049594e5c59769cf0b2","observation_id":"3c9f8f25-8da0-49de-bf41-5d0e0ff45c63","resolution":{"observed_at":"2026-08-16T00:09:34.783306Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/080731591","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:09:34.746160Z","title":"Gallivan, and P.-A","venue":null,"work_id":"7759725e-7103-4f7a-aa9a-34dfc400082c","year":2010},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.559489Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:aad27101b035c0806762a5fed9a6fdeb6b878fc5aad860eefecd5d5131ff691f","observation_id":"917a1dc6-903c-4b75-abd8-4554e2332b81","resolution":{"observed_at":"2026-08-16T00:09:34.753322Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T00:09:35.988386Z","title":"Model reduction b y balanced truncation of linear systems with a quadratic output","venue":null,"work_id":"2d457fee-daf8-48a1-b08f-b51f6bca1a77","year":null},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.514676Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:b4582991f93e9d38583dd78f92932441f4c6ed6268d2d41775eb666f3d1cf157","observation_id":"23fd78a6-ba08-46fd-9c96-fada10c2f9d1","resolution":{"observed_at":"2026-08-16T00:09:35.994243Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"1970.0227","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:09:35.263616Z","title":null,"venue":null,"work_id":"0ac0444f-18d7-4d12-b523-c757cb2c0450","year":1970},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.577267Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:f8bfbf1e87e5e970dadc9265a4f646fd86920cb4a55a8e6bd946d99238031675","observation_id":"b1c70c5f-0dca-4b0d-898f-4dcab6f72141","resolution":{"observed_at":"2026-08-16T00:09:35.273678Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.matcom.2025.03.021","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:09:34.704203Z","title":"H2 optimal model reduction of linear dy- namical systems with quadratic output by the Riemannian BFG S method","venue":null,"work_id":"5e69bcda-f842-423d-8782-f0c19e147f78","year":2025},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.586327Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:b4e4e644cb34c0cc429d7acb2e5a254d3cd6b909e6a9687e95b9ddcd002cda31","observation_id":"df768bad-098e-450d-a903-b1e89ae239c6","resolution":{"observed_at":"2026-08-16T00:09:34.712924Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T00:09:34.593474Z","title":"Using Krylov-Pad´ e model o rder reduction for accelerating design optimization of structures and vibrations in the fre quency domain","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.593474Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:6dca95c3fbbb828ba97e3994b9472ee30490e44e3c58bfaf88ffe4570b3bad7f","observation_id":"2c83998e-f777-4ad2-a373-e7619b62046f","resolution":{"observed_at":"2026-08-16T00:09:34.593474Z","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":"2026-08-16T00:09:34.600909Z","title":"Accelerating optimizatio n of parametric linear sys- tems by model order reduction","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.600909Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:ae26b562607600451698dd32e7290898c00a75d786a6bb786c885d125bd7295a","observation_id":"966cc853-d8ac-4186-92af-307fe8228272","resolution":{"observed_at":"2026-08-16T00:09:34.600909Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2408.07939","last_updated":"2025-04-18T22:59:58Z","snapshot_observed_at":"2026-08-18T05:22:01.709762Z","submitted_at":"2024-08-15T05:27:02Z","title":"$\\mathcal{H}_2$-optimal Model Reduction of Linear Quadratic Output Systems in Finite Frequency Range","version":2},"cited_work":{"arxiv_id":"2408.07939","doi":null,"metadata_source":"pith","pith_arxiv_id":"2408.07939","snapshot_observed_at":"2026-08-16T00:09:35.176602Z","title":"$\\mathcal{H}_2$-optimal Model Reduction of Linear Quadratic Output Systems in Finite Frequency Range","venue":"eess.SY","work_id":"49ea67a4-a69c-495a-b247-20f82c9b33f6","year":2024},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.610156Z"},"links":{"cited_paper":"/paper/2408.07939","citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:935541f2c01804627485d8ce7b53dd6ce05e7d3755a2b0c115c7e6334f46733c","observation_id":"c8fd4d1e-8a8e-47dc-847f-6c0ca1f07154","resolution":{"observed_at":"2026-08-16T00:09:35.183976Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.25673/38617","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:09:34.725404Z","title":null,"venue":null,"work_id":"ac019b5a-aedc-4aeb-b957-eefaafe370b3","year":2021},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.570663Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:18d07676a195db87f21292596e9e675b55228fa4d8a93cbd2b4b7aa056c3abc0","observation_id":"25edee39-2412-48c6-84c5-dec72da18d4c","resolution":{"observed_at":"2026-08-16T00:09:34.731378Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2408.05965","last_updated":"2024-08-12T07:36:54Z","snapshot_observed_at":"2026-08-16T13:27:05.730894Z","submitted_at":"2024-08-12T07:36:54Z","title":"Time-limited H2-optimal Model Order Reduction of Linear Systems with Quadratic Outputs","version":1},"cited_work":{"arxiv_id":"2408.05965","doi":null,"metadata_source":"pith","pith_arxiv_id":"2408.05965","snapshot_observed_at":"2026-08-16T00:09:35.151073Z","title":"Time-limited H2-optimal Model Order Reduction of Linear Systems with Quadratic Outputs","venue":"eess.SY","work_id":"abc4f06b-f24e-491d-85a7-c6cbe16f1db3","year":2024},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.617295Z"},"links":{"cited_paper":"/paper/2408.05965","citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:cf231f52e42b2b4f54b2d43561d43d16be26393c35e55cba030c29d756f33695","observation_id":"cf879a77-1801-4d89-9850-868c467213ae","resolution":{"observed_at":"2026-08-16T00:09:35.157862Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T00:09:34.390494Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":2003,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.390494Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:8bf3d5e0a4afeb933de2f6b4523063ca9d28268d19ff39b393175ceaa6bcfb23","observation_id":"707dfb20-5716-4a8e-a245-77c93fd3b7fc","resolution":{"observed_at":"2026-08-16T00:09:34.390494Z","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":"2026-08-16T00:09:34.406008Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":2022,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.406008Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:57f372d189c65794be4efe48b5ee1d2e1891942c3541cdd6579654bfd141405a","observation_id":"10f35230-1447-4761-b544-4fcc50ef568f","resolution":{"observed_at":"2026-08-16T00:09:34.406008Z","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":"2026-08-16T00:09:34.245250Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":2023,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.245250Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:6d22a6ca476521cc59039a5b7195d01e481b30e39a10927dbcbbacaca4583610","observation_id":"e773c233-e0cf-4900-b32e-de26db98c5db","resolution":{"observed_at":"2026-08-16T00:09:34.245250Z","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":"10.1177/01423312241257298","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:09:35.011497Z","title":null,"venue":null,"work_id":"80d5ee17-ffe0-4f18-b520-d2dffc3311a5","year":null},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":2025,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.330128Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:4f3a7af3b21ca96e0b5c6154753253d750317e1073adee0f0384aa5fa72d24d3","observation_id":"2a90d98e-24c1-4a73-a394-8aa2244144b8","resolution":{"observed_at":"2026-08-16T00:09:35.019711Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1063/1.3498345","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:09:34.832805Z","title":"doi:10.1063/1.3498345","venue":null,"work_id":"f6c8a97c-52c6-4710-8138-e22b5ba80f12","year":2010},"citing_paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation","version":2},"reference_index":2036,"source":"pdf_text","source_observed_at":"2026-08-16T00:09:34.519954Z"},"links":{"citing_paper":"/paper/2505.03057"},"observation_digest":"sha256:575554639145e04609d8803254f4891fc5f717476c3307953055ac09b3609e87","observation_id":"9f65f475-e2b1-45e4-8daf-21a5367b663f","resolution":{"observed_at":"2026-08-16T00:09:34.843761Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.03057","last_updated":"2026-06-02T18:06:52Z","latest_version":2,"primary_category":"math.NA","snapshot_observed_at":"2026-08-15T23:58:32.309725Z","submitted_at":"2025-05-05T22:39:27Z","title":"$\\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation"},"reference_resolution":{"displayed":54,"state_counts":{"malformed_identifier":1,"metadata_mismatch":2,"parse_uncertain":0,"unresolved":29,"verified_exact":15,"verified_fuzzy":7},"total_outbound_references":54},"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":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"thesis":"As of 23 August 2026, this Paper Citation Record lists 54 of 54 outbound references and 2 inbound Pith citation observations for arXiv:2505.03057."}