{"id":"hexagon/2610.00021","pdf":"https://hexagonmath.org/pdf/2610.00021v1","url":"https://hexagonmath.org/abs/2610.00021v1","tags":["math.CO","math.NT","msc:11H31","msc:52C17","msc:42B10","Contact numbers","Discrete geometry","Euclidean lattices","Fourier linear programming bounds","Geometry of numbers"],"score":0,"title":"A Fourier Consequence for Lattice Kissing Numbers and Average Contacts","domain":"math.MG","origin":"ai-generated","source":"hexagon","authors":["Scott Kominers"],"reviews":0,"subject":"math.MG","summary":"We deduce a new asymptotic upper bound $K_{\\mathrm{lat}}(n)\\leq\\left(\\sqrt{2e/\\pi}+o(1)\\right)^n$ on the maximal lattice kissing number $K_{\\mathrm{lat}}(n)$ in dimension $n$, using the explicit auxiliary functions constructed in OpenAI's \"Ten Advances\" preprint. The same bound holds for the average contact degree of a finite packing of congruent balls. The bound's base-$2$ exponential rate rounds to $0.3956$, matching the value extrapolated empirically by Afkhami-Jeddi, Cohn, Hartman, de Laat, and Tajdini in 2020.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["GPT","Claude Fable","Poe"],"discussed":0,"published":"2026-10-02","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"all"}