Leech Lattice from E8³ Glued via Binary Golay Code G24 — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Leech lattice constructed from E8×E8×E8 glue code and weight enumerator of G24 (binary Golay code) | MATH: Leech lattice Λ₂₄ = { (x₁,...,x₂₄) ∈ ℤ²⁴ ∪ (ℤ+½)²⁴ : Σ xᵢ ≡ 0 mod 2, Σ xᵢ² ≡ 0 mod 4 } ; E8 root lattice from Gosset lattice E₈ = { (x₁,...,x₈) ∈ ℤ⁸ ∪ (ℤ+½)⁸ : Σ xᵢ ≡ 0 mod 2 } ; Glue code: G₂₄ (binary Golay code) with weight enumerator W_G₂₄(x,y) = x²⁴ + 759 x¹⁶ y⁸ + 2576 x¹² y¹² + 759 x⁸ y¹⁶ + y²⁴ ; Leech lattice = 3 copies of E8 glued via G₂₄: Λ₂₄ = { (u,v,w) ∈ E₈³ : (u+v, u+w, v+w) mod 2 ∈ G₂₄ } | CONNECTION: Leech lattice minimal norm 4 → sphere packing density π¹²/12! ≈ 0.00193 ; kissing number 196560 ; ratio 0.618 appears in Leech lattice's automorphism group Co0 order 2²²·3⁹·5⁴·7²·11·13·23 ; E8 has golden ratio φ = (1+√5)/2 ≈ 1.618 in its Coxeter number h=30 (30/φ² ≈ 11.46) ; base-60: Leech lattice coordinates often expressed in base 60 (e.g., 0, ±1, ±2, ±3, ±4, ±5, ±6, ±7, ±8, ±9, ±10, ±11, ±12, ±13, ±14, ±15, ±16, ±17, ±18, ±19, ±20, ±21, ±22, ±23, ±24, ±25, ±26 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7170592867
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