{"paper":{"title":"Core equality of real sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Paolo Leonetti","submitted_at":"2024-01-02T10:23:02Z","abstract_excerpt":"Given an ideal $\\mathcal{I}$ on $\\omega$ and a bounded real sequence $\\textbf{x}$, we denote by $\\text{core}_{\\textbf{x}}(\\mathcal{I})$ the smallest interval $[a,b]$ such that $\\{n \\in \\omega: x_n \\notin [a-\\varepsilon,b+\\varepsilon]\\} \\in \\mathcal{I}$ for all $\\varepsilon>0$ (which corresponds to the interval $[\\,\\liminf \\textbf{x}, \\limsup \\textbf{x}\\,]$ if $\\mathcal{I}$ is the ideal $\\text{Fin}$ of finite subsets of $\\omega$).\n  First, we characterize all the infinite real matrices $A$ such that $$ \\text{core}_{A\\textbf{x}}(\\mathcal{J})=\\text{core}_{\\textbf{x}}(\\mathcal{I}) $$ for all bound"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.01136","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/2401.01136/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"}