{"paper":{"title":"A stability result for the cube edge isoperimetric inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Eoin Long, Peter Keevash","submitted_at":"2017-03-29T16:29:46Z","abstract_excerpt":"We prove the following stability version of the edge isoperimetric inequality for the cube: any subset of the cube with average boundary degree within $K$ of the minimum possible is $\\varepsilon $-close to a union of $L$ disjoint cubes, where $L \\leq L(K,\\varepsilon )$ is independent of the dimension. This extends a stability result of Ellis, and can viewed as a dimension-free version of Friedgut's junta theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10122","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":""},"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"}