{"paper":{"title":"Hyperplane mass equipartition problem and the shielding functions of Ramos","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Rade T. \\v{Z}ivaljevi\\'c, Sini\\v{s}a T. Vre\\'cica","submitted_at":"2015-08-06T22:04:30Z","abstract_excerpt":"We give a proof of the result of Edgar Ramos which claims that two finite, continuous Borel measures $\\mu_1$ and $\\mu_2$ defined on $\\mathbb{R}^5$ admit an equipartition by a collection of three hyperplanes. Our proof illuminates one of the central methods developed and used in our earlier papers and may serve as a good `test case' for addressing (and resolving) the `issues' raised in the paper \"Topology of the Gr\\\"unbaum-Hadwiger-Ramos hyperplane mass partition problem\", arXiv:1502.02975 [math.AT]. We also offer a degree-theoretic interpretation of the `parity calculation method' developed by"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01552","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":""},"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"}