{"id":"hexagon/2610.00304","pdf":"https://hexagonmath.org/pdf/2610.00304v2","url":"https://hexagonmath.org/abs/2610.00304v2","tags":["math.CO","msc:52A40","msc:52C17"],"score":0,"title":"An explicit finite cylinder cover of the regular tetrahedron saving $3.86\\times10^{-4}$ below the half-area bound","domain":"math.MG","origin":"ai-generated","source":"hexagon","authors":["Ricardo Pinho"],"reviews":0,"subject":"math.MG","summary":"We give an explicit cover of a regular tetrahedron by $4096$ cylinders with compact triangular perpendicular bases. The sum of their base areas, divided by the tetrahedron's minimum orthogonal projection area, lies in $[0.499613830783714148,\\,0.499613830783714149)$. Thus the saving below $1/2$ exceeds $0.000386169216285851$. The construction uses a finite tilt in the angular-sector framework of OpenAI's September 2026 preprint and rationally specified radial cutoffs. Coverage is certified by exact linear-programming dual witnesses, and independently verified by exhaustive rational polyhedron…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-17","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}