{"id":"hexagon/2610.00330","pdf":"https://hexagonmath.org/pdf/2610.00330v1","url":"https://hexagonmath.org/abs/2610.00330v1","tags":["msc:52C17","Sphere packing"],"score":0,"title":"A construction of the sphere-packing magic functions in dimensions 8 and 24","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Thomas Hales"],"reviews":0,"subject":"math.NT","summary":"We develop an alternative route to the solutions of the sphere-packing problem in dimensions 8 and 24, through the auxiliary functions in the Cohn--Elkies Fourier bound. In each dimension we construct a radial Schwartz function with the prescribed lattice zeros by solving a countable system of linear equations in absolutely summable coefficients. We prove existence and uniqueness after normalization, without using the known magic functions or Fourier interpolation. Through a Cauchy boundary problem, solutions of the homogeneous equations are identified with global sections of a rank-six…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-18","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}