{"id":"palomar/PALOMAR-2026-09-18-000009","url":"https://github.com/akopjan/Grunbaum-counterexample/tree/438da254d505b77d58461e35029b2bc6ebcf148e","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-18-000009-v1.json","repo":"https://github.com/akopjan/Grunbaum-counterexample","tags":["math.CO","msc:52C35","msc:52A37","convex-geometry","mass-partition","lean"],"score":0,"title":"A convex body variant of Soberon's counterexample to the Grünbaum conjecture.","trust":"high","domain":"math.CO","source":"palomar","authors":["Arseniy Akopyan"],"reviews":0,"subject":"math.CO","summary":"A Lean formalization of a geometric strengthening/variant of Pablo Soberón's counterexample to the Grünbaum four-hyperplane mass-partition conjecture. The formalized result constructs a convex body K in R^4 with nonempty interior such that no four affine hyperplanes divide K into sixteen sign cells of equal four-dimensional volume. Equivalently, the obstructed mass can be chosen to be uniform Lebesgue volume on a convex body. The proof adapts Soberón's explicit cubic/quartic tensor obstruction and replaces the smooth positive density used in the source by a small Wulff-body perturbation of…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-18","reactions":{},"formalized":true,"formalizes":[{"title":"Four hyperplanes do not always equipartition a mass in R^4","identifier":"arXiv:2608.23312v2","relationship":"adapts"}]}