{"paper":{"title":"Finiteness of Nonscattering Wavenumbers for Herglotz Incident Waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jingni Xiao","submitted_at":"2026-02-22T18:47:39Z","abstract_excerpt":"This paper continues the study initiated in \\cite{VogXia25} on nonscattering phenomena for inhomogeneous media. We investigate star-shaped domains in $\\mathbb{R}^2$ and establish finiteness results for nonscattering wavenumbers associated with Herglotz incident waves of fixed density. First, for ellipses we establish finiteness for all constant contrasts $q\\neq 1$, removing the geometric restrictions required in previous work. Second, for admissible star-shaped domains with $q\\in(0,1)$, we introduce a flexible interval-wise geometric framework that unifies and generalizes earlier finiteness re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.19302","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/2602.19302/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"}