{"paper":{"title":"On the volume of non-central sections of a cube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.MG","authors_text":"Hermann K\\\"onig, Mark Rudelson","submitted_at":"2019-08-25T16:25:42Z","abstract_excerpt":"Let $Q_n$ be the cube of side length one centered at the origin in $\\mathbb{R}^n$, and let $F$ be an affine $(n-d)$-dimensional subspace of $\\mathbb{R}^n$ having distance to the origin less than or equal to $\\frac 1 2$, where $0<d<n$. We show that the $(n-d)$-dimensional volume of the section $Q_n \\cap F$ is bounded below by a value $c(d)$ depending only on the codimension $d$ but not on the ambient dimension $n$ or a particular subspace $F$. In the case of hyperplanes, $d=1$, we show that $c(1) = \\frac{1}{17}$ is a possible choice. We also consider a complex analogue of this problem for a hyp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.09358","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/1908.09358/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"}