Leech Lattice Λ₂₄: Unique Rootless Even Unimodular 24D Lattice via Golay Code G₂₄ — E8 Intelligence Research

FINDING: Leech lattice Λ₂₄ is the unique even unimodular 24-dimensional lattice with no roots, constructed via the binary Golay code G₂₄ and its 24×24 construction matrix; its automorphism group Co₀ = 2.Co₁ has order 8,315,553,613,086,720,000. | MATH: Λ₂₄ minimum norm = 4; kissing number = 196560 = 2⁴·3³·5·7·13; |Co₀| = 2²²·3⁹·5⁴·7²·11·13·23; Golay code G₂₄: [24,12,8] binary, |G₂₄| = 4096 = 2¹², weight enumerator W(x,y) = x²⁴ + 759x¹⁶y⁸ + 2576x¹²y¹² + 759x⁸y¹⁶ + y²⁴; Leech theta series Θ_Λ(τ) = E₁₂(τ) − (65520/691)·Δ(τ), where E₁₂ is the weight-12 Eisenstein series and Δ is the Ramanujan cusp form. | CONNECTION: 196560 = 196560; ratio 196560/24 = 8190 = 2·3²·5·7·13; 8190/196560 = 1/24. The 759 = 3·11·23 appears in both Golay weight enumerator and as the number of umbral moonshine modules. 24 = 4! = 2³·3 connects to the 24-cell (self-dual regular polytope). The Leech lattice's covering radius √2 and packing density π²/12 relate to the 24-dimensional sphere packing optimum (Viazovska 201 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com