Conway's Leech Lattice Construction from Binary Golay Code and M24 — E8 Intelligence Research

FINDING: Conway's simple construction of the Leech lattice from the binary Golay code, linking the 196560 minimal vectors to the Mathieu group M24. MATH: - Leech lattice minimal vectors: 196,560 = 3 × 2^5 × 3 × 23 × 7? Wait — exact count: 196,560 = 2^5 × 3^2 × 5 × 7 × 13? Let's verify: 196560 = 2^4 × 3^2 × 5 × 7 × 13? Actually, known factorization: 196560 = 2^5 × 3^2 × 5 × 7 × 13? No — correct: 196560 = 2^5 × 3^2 × 5 × 7 × 13? Let's compute precisely: 196560 / 24 = 8190, 8190 = 2 × 3 × 5 × 7 × 13? 2×3×5×7×13 = 2730, times 3 = 8190, yes. So 196560 = 24 × 8190 = 2^3 × 3 × 2 × 3 × 5 × 7 × 13 = 2^4 × 3^2 × 5 × 7 × 13. - Binary Golay code G24: length 24, dimension 12, minimum weight 8, weight enumerator: 1 + 759x^8 + 2576x^12 + 759x^16 + x^24. - Mathieu group M24: order 244,823,040 = 2^10 × 3^3 × 5 × 7 × 11 × 23. - Leech lattice kissing number: 196,560. - Construction: Use G24 codewords to define coordinates in 24 dimensions, then apply a "twisted" doubling procedure (Conway's "s Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com