Leech Lattice from Z4 Golay Code via Gray Map Yields 196560 Vectors — E8 Intelligence Research

FINDING: Leech lattice construction from Z4 Golay code via Gray map yields 196560 minimal vectors, linking to Monster group and E8×3. MATH: - Leech lattice Λ₂₄: minimal norm 4, kissing number 196560. - Construction: Z₄⁽²⁴⁾ Golay code (length 24, minimum Lee weight 12) → Gray map (Z₄ → Z₂²) → 24-dimensional lattice. - 196560 = 3·65520 = 3·(2¹²·3³·5·7·13) = 2⁴·3³·5·7·13·17? Wait: 196560 = 2⁴·3³·5·7·13·17? Check: 2⁴=16, 3³=27, product 16·27=432, 432·5=2160, 2160·7=15120, 15120·13=196560, 15120·17=257040 — no 17. Actually 196560 = 2⁴·3³·5·7·13 = 16·27·5·7·13 = 432·5·7·13 = 2160·7·13 = 15120·13 = 196560. - E₈ root system: 240 roots, E₈×3 gives 720, but Leech kissing number 196560 = 273·720? 273·720 = 196560, yes. 273 = 3·7·13. - Monster group order ≈ 8·10⁵³, moonshine connection via j-invariant: j(τ) = q⁻¹ + 744 + 196884q + ...; 196884 = 196560 + 324 (where 324 = 18²). CONNECTION: - Leech lattice is the unique even unimodular lattice in 24 dimensions with no roots (norm-2 vect Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com