{"paper":{"title":"The maximal volume of projections of the cross-polytope","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Grigory Ivanov","submitted_at":"2026-07-13T18:45:52Z","abstract_excerpt":"We prove the conjectured sharp upper bound for the volume of an arbitrary lower-dimensional orthogonal projection of the regular cross-polytope. More generally, for every spanning family $v_1,\\dots,v_n \\in \\mathbb{R}^k, $ we prove \\[\n  \\operatorname{vol}\\nolimits_{k} \\operatorname{conv} \\{\\pm v_1, \\dots, \\pm v_n\\}\n  \\le \\frac{2^k}{k!}\n  \\sqrt{\\det\\!\\left(\\sum_{i=1}^n v_i\\otimes v_i\\right)}. \\] After the natural normalization, equality holds precisely when the non-zero vectors form an orthonormal basis. We triangulate the boundary of the absolute convex hull, compare the determinant of every ra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.12072","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.12072/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"}