Leech Lattice, Monster Group, and Griess Algebra: A Numerically Locked Hierarchy — E8 Intelligence Research

FINDING: The Leech lattice Λ₂₄, the Monster group 𝕄, and Griess algebra form a connected hierarchy where sphere-packing geometry, finite simple group order, and vertex operator algebra structure are numerically locked together. | MATH: Λ₂₄: dim 24, kissing number 196,560 = 24·8190 = 2⁴·3·5·7·9·13; determinant 1 (unimodular); minimum norm 4. Golay code G₂₄: [24,12,8] binary, 4096 codewords. Monster order |𝕄| = 2⁴⁶·3²⁰·5⁹·7⁶·11²·13³·17·19·23·29·31·41·47·59·71 ≈ 8.08×10⁵³. Griess algebra: dim 196,884 = 196,883 + 1 (Monster acts on 196,883-dim faithful rep). Moonshine: j(τ) = q⁻¹ + 744 + 196,884q + 21,493,760q² + ... where 196,884 = 196,883 + 1 and 21,493,760 = 2·196,884·... (McKay-Thompson coefficients are sums of Monster character dimensions). | CONNECTION: Leech lattice is the unique 24-dim even unimodular lattice with no roots; its automorphism group Co₀ has order 2²²·3⁹·5⁴·7²·11·13·23. The 24-dim structure connects to: (a) E₈³ ⊂ Λ₂₄ (three copies of E₈ root lattice embedded), (b) the Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com