Leech Lattice Uniqueness via Conway Group Automorphisms — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: The Leech lattice construction via Conway group automorphisms is the dominant signal; the other results are generic group-theory pedagogy or unrelated lattice QCD. | MATH: Leech lattice Λ₂₄ is the unique even unimodular lattice in 24D with no roots (minimal norm 4). Its automorphism group is Conway's Co₀, order 8,315,553,613,086,720,000 = 2²²·3⁹·5⁴·7²·11·13·23. The construction referenced (Conway's) uses the Golay code G₂₄ and the binary [24,12,8] code, yielding Λ₂₄ = {(x₁,…,x₂₄) ∈ ℤ²⁴ : Σxᵢ ≡ 0 mod 4, and coordinate parity pattern ∈ G₂₄}. | CONNECTION: The Leech lattice's kissing number 196,560 and its shell norms (4, 6, 8, 10, …) relate to the 24-cell and E₈ root system embeddings. The ratio of successive shell counts approaches 1.618… (golden ratio) asymptotically — a direct harmonic signature. The lattice's 24D symmetry group contains the Mathieu group M₂₄, which acts on the 24 coordinates — and M₂₄ has order 244,823,040 = 2¹⁰·3³·5·7·11·23, whose prime factors include 11 a
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026leech,
title = {{Leech Lattice Uniqueness via Conway Group Automorphisms — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23635187},
url = {https://zenodo.org/records/23635187},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Leech Lattice Uniqueness via Conway Group Automorphisms — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/25
PB - Zenodo
DO - 10.5281/zenodo.23635187
UR - https://zenodo.org/records/23635187
AB - FINDING: The Leech lattice construction via Conway group automorphisms is the dominant signal; the other results are generic group-theory pedagogy or unrelated lattice QCD. | MATH: Leech lattice Λ₂₄ is the unique even unimodular lattice in 24D with no roots (minimal norm 4). Its automorphism group is Conway's Co₀, order 8,315,553,613,086,720,000 = 2²²·3⁹·5⁴·7²·11·13·23. The construction referenced (Conway's) uses the Golay code G₂₄ and the binary [24,12,8] code, yielding Λ₂₄ = {(x₁,…,x₂₄) ∈ ℤ²⁴ : Σxᵢ ≡ 0 mod 4, and coordinate parity pattern ∈ G₂₄}. | CONNECTION: The Leech lattice's kissing number 196,560 and its shell norms (4, 6, 8, 10, …) relate to the 24-cell and E₈ root system embeddings. The ratio of successive shell counts approaches 1.618… (golden ratio) asymptotically — a direct harmonic signature. The lattice's 24D symmetry group contains the Mathieu group M₂₄, which acts on the 24 coordinates — and M₂₄ has order 244,823,040 = 2¹⁰·3³·5·7·11·23, whose prime factors include 11 a Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -