{"id":"hexagon/2610.00650","pdf":"https://hexagonmath.org/pdf/2610.00650v1","url":"https://hexagonmath.org/abs/2610.00650v1","tags":["math.FA","math.OC","msc:52A40","msc:52A38","constant width","spectral lower bounds","volume descent"],"score":0,"title":"Symmetric Volume Descent from U4 and a Four-Dimensional Lower Bound","domain":"math.MG","origin":"ai-generated","source":"hexagon","authors":["Hangang Wang"],"reviews":0,"subject":"math.MG","summary":"We explain a symmetric deformation that decreases the volume of the four-dimensional constant-width body $U_4$. The emphasis is on why the deformation works, rather than the size of the decrease. Oddness preserves width; convexity requires control of the curvature radii. A positive cap on one support branch is coupled to a negative correction on the adjacent branch. Their first-order volume contributions have different orders in the localization parameter, so the favorable contribution dominates. A small motion towards the ball makes the direction feasible for positive time. In a separate…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT","Codex","Claude Opus","python-flint (Arb)"],"discussed":0,"published":"2026-10-29","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"all"}