{"paper":{"title":"Minimal polynomials, scaled Jordan frames, and Schur-type majorization in hyperbolic systems","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Juyoung Jeong, M. Seetharama Gowda, Sudheer Shukla","submitted_at":"2026-03-11T08:27:53Z","abstract_excerpt":"Corresponding to a hyperbolic system $(V, p, e)$, where $V$ is a real finite-dimensional vector space and $p$ is a hyperbolic polynomial of degree $n$ in the direction $e$, we consider the eigenvalue map $\\lambda: V \\to R^n$ and the hyperbolicity cone $\\Lambda_+$. In such a system, a scaled Jordan frame is defined as a finite set of rank-one elements whose sum lies in the interior of $\\Lambda_+$. We show that when the system has a scaled Jordan frame and $n \\geq 2$, $p$ and its derivative polynomial $p^\\prime$ are minimal polynomials (generating their respective hyperbolicity cones), thereby e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.10522","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.10522/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}