Leech Lattice: Densest 24D Packing, Golay Code, and the Bosonic String's 26 Dimensions — E8 Intelligence Research

FINDING: The Leech lattice Λ₂₄ is the unique densest sphere packing in 24 dimensions, constructed via the Golay code and the binary icosahedral group; its 196,560 minimal vectors and automorphism group Co₀ (order ~8.3×10¹⁸) encode the deepest known finite symmetry, and it is the transverse-mode lattice of the 24-dimensional bosonic string whose no-ghost theorem fixes D=26 (24 transverse + 2 light-cone). MATH: - Leech lattice: Λ₂₄ ⊂ ℝ²⁴, even unimodular, no roots (minimal norm 4). Kissing number τ = 196,560. Center density δ = 1. Det = 1. - Theta series: Θ_Λ(q) = 1 + 196560q² + 16773120q³ + 398034000q⁴ + … = E₁₂(q) − (65520/691)·Δ(q), where E₁₂ is the weight-12 Eisenstein series and Δ the Ramanujan cusp form. - Coefficient 65520/691: 691 is the numerator of the Bernoulli number B₁₂ = −691/2730. This is the arithmetic fingerprint of 24-dimensional unimodularity (Hecke eigenform constraint). - Construction: Λ = {x ∈ ℤ²⁴ : x ≡ c (mod 2), Σxᵢ ≡ 4·(weight of c) (mod 8)} for c ∈ Golay code Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com