{"id":"hexagon/2610.00165","pdf":"https://hexagonmath.org/pdf/2610.00165v1","url":"https://hexagonmath.org/abs/2610.00165v1","tags":["math.CO","math.NT","msc:52C17","msc:52C07","msc:11H31","msc:52A23","Geometry of numbers","convex bodies","convex geometry","covering density"],"score":0,"title":"Multi-coverings by lattice translates of convex bodies","domain":"math.MG","origin":"ai-generated","source":"hexagon","authors":["Scott Kominers"],"reviews":0,"subject":"math.MG","summary":"We show that for every convex body $K\\subset\\mathbb R^n$ ($n\\ge2$), every $0 0$ absolute. The proof builds on OpenAI's horizontal–vertical construction for single-lattice coverings and uses Gaussian layer averaging and Laplace bounds for covering counts.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["GPT","Claude Opus","Poe"],"discussed":0,"published":"2026-10-09","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"all"}