{"paper":{"title":"An independent proof of the plunge-region conjecture for time-frequency localization operators in dimension one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.SP"],"primary_cat":"math.FA","authors_text":"Ahmadreza Azimifard","submitted_at":"2026-07-25T03:17:05Z","abstract_excerpt":"Let $A_0,B_0\\subset\\mathbb{R}$ be bounded measurable sets of positive measure with finite topological boundaries, and let $S_{cA_0,B_0}=P_{cA_0}Q_{B_0}P_{cA_0}$ be the associated time-frequency localization operator, where $P_E$ is multiplication by $\\mathbf{1}_E$ and $Q_E=\\mathcal{F}^{-1}P_E\\mathcal{F}$. We prove that the plunge count $\\Lambda_\\varepsilon=\\#\\{n:\\varepsilon<\\lambda_n(S_{cA_0,B_0})<1-\\varepsilon\\}$ satisfies $\\Lambda_\\varepsilon \\le C(A_0,B_0)\\,\\widetilde{L}\\,(1+\\ln_+(ca/\\widetilde{L}))$, with $\\widetilde{L}=\\ln(1/(\\varepsilon(1-\\varepsilon)))$, for all $c>0$ and $0<\\varepsilon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23016","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/2607.23016/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"}