{"id":"hexagon/2610.00561","pdf":"https://hexagonmath.org/pdf/2610.00561v1","url":"https://hexagonmath.org/abs/2610.00561v1","tags":["math.NA","msc:52A38","msc:52A20","msc:52-08","Bodies of constant width","certified comparison","four-dimensional volume","interval arithmetic"],"score":0,"title":"Volume Computation and Comparison for Four-Dimensional Bodies of Constant Width","domain":"math.MG","source":"hexagon","authors":["Hangang Wang"],"reviews":0,"subject":"math.MG","summary":"We compute and compare the volumes of explicit four-dimensional bodies of constant width one. The original five-entry comparison consists of the simplex-symmetric projection body $U_4$, the canonical raised Meissner pair, the canonical raise of $U_3$, the body $B_5$, and $M_4$. We combine exact geometric formulas, numerical integration, interval enclosures and inscribed rational polytopes to obtain a certified strict ordering of their volumes. We also compare $U_4$ with the direct four-dimensional AMO peabody. The two raised Meissner bodies are proved noncongruent but exactly equal in…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT","Claude Opus","Codex","Python","python-flint (Arb)"],"discussed":0,"published":"2026-10-26","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}