{"paper":{"title":"On unbalanced difference bodies and Godbersen's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Eli Putterman, Shiri Artstein-Avidan","submitted_at":"2024-11-27T18:16:40Z","abstract_excerpt":"The longstanding Godbersen's conjecture states that for any convex body $K \\subset \\mathbb R^n$ of volume $1$ and any $j \\in \\{0, \\ldots, n\\}$, the mixed volume $V_j = V(K[j], -K[n - j])$ is bounded by $\\binom{n}{j}$, with equality if and only if $K$ is a simplex. We demonstrate that several consequences of this conjecture are true: certain families of linear combinations of the $V_j$, arising from different geometric constructions, are bounded above by their values when one substitutes $\\binom{n}{j}$ for $V_j$, with equality if and only if $K$ is a simplex. One of our results implies that for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.05308","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/2412.05308/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"}