{"paper":{"title":"Improved Upper Bounds for Slicing the Hypercube","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.AI","authors_text":"Blake Bruell, Christopher D. Rosin, Daniel Reichman, Duncan Soiffer, G\\'abor N. S\\'ark\\\"ozy, Mason DiCicco, Nathaniel Itty, Ryan Offstein","submitted_at":"2026-02-06T17:52:13Z","abstract_excerpt":"A collection of hyperplanes $\\mathcal{H}$ slices all edges of the $n$-dimensional hypercube $Q_n$ with vertex set $\\{-1,1\\}^n$ if, for every edge $e$ in the hypercube, there exists a hyperplane in $\\mathcal{H}$ intersecting $e$ in its interior. Let $S(n)$ be the minimum number of hyperplanes needed to slice $Q_n$. We prove that $S(n) \\leq \\lceil \\frac{4n}{5} \\rceil$, except when $n$ is an odd multiple of $5$, in which case $S(n) \\leq \\frac{4n}{5} +1$. This improves upon the previously known upper bound of $S(n) \\leq \\lceil\\frac{5n}{6} \\rceil$ due to Paterson reported in 1971. We also obtain ne"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.16807","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/2602.16807/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"}