{"paper":{"title":"A remark on dimensionality reduction in discrete subgroups","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Rodolfo Viera","submitted_at":"2025-01-02T18:15:08Z","abstract_excerpt":"In this short note, we prove a version of the Johnson-Lindenstrauss flattening Lemma for point sets taking values in discrete subgroups. More precisely, given $d,\\lambda_0,N_0\\in\\mathbb{N}$ and $\\epsilon\\in \\left(0,\\frac{1}{2}\\right)$ suitably chosen, we show there exists a natural number $k=k(d,\\epsilon)=O\\left(\\frac{1}{\\epsilon^2}\\log d\\right)$, such that for every sufficiently large scaling factor $\\lambda\\in\\mathbb{N}$ and any point set $\\mathcal{D}\\subset\\frac{\\lambda}{\\lambda_0}\\mathbb{Z}^d\\cap B(0,\\lambda N_0)$ with cardinality $d$, there exists an embedding $F:\\mathcal{D}\\to\\frac{1}{\\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.01396","kind":"arxiv","version":3},"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/2501.01396/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"}