{"paper":{"title":"A lower bound on dimension reduction for trees in \\ell_1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.MG","authors_text":"James R. Lee, Mohammad Moharrami","submitted_at":"2013-02-26T19:13:55Z","abstract_excerpt":"There is a constant c > 0 such that for every $\\epsilon \\in (0,1)$ and $n \\geq 1/\\epsilon^2$, the following holds. Any mapping from the $n$-point star metric into $\\ell_1^d$ with bi-Lipschitz distortion $1+\\epsilon$ requires dimension $$d \\geq {c\\log n\\over \\epsilon^2\\log (1/\\epsilon)}.$$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6542","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":""},"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"}