{"paper":{"title":"Some remarks on structured Keyfitz-Kranzer systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Katarzyna Saxton, Ralph Saxton","submitted_at":"2026-07-30T21:56:34Z","abstract_excerpt":"Several applications for systems of conservation laws of the form $U_t + (\\Phi (U) U)_x =0$, $U: R_t\\times R_x\\rightarrow R^n$ , $n\\geq 2$, with $\\Phi (U) = \\phi (r, \\Theta): R^n\\rightarrow R$, $r = |U|$, and $\\Theta = U/|U|\\in S^{n-1}$, are obtained by imposing structural conditions to provide a classification framework for solutions dependent on the form of $\\phi(U)$. By prescribing the evolution of a particular eigenvalue, we can categorize classes of such functions, $\\phi$, for which this evolution is met, into depending on either a scalar field $z=rK(\\Theta)$, where $K: S^{n-1}\\rightarrow"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28860","kind":"arxiv","version":1},"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/2607.28860/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"}