Leech Lattice Uniqueness via Central Charge 24 and Orbifold Construction — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: The Leech lattice (Λ₂₄) is uniquely determined by its VOA central charge 24 and orbifold construction from Niemeier lattices, unifying the Monster group, Golay code, and E₈³ root systems. | MATH: Central charge c=24; Leech lattice determinant det(Λ₂₄)=1 (unimodular), kissing number 196,560; Golay code G₂₄ has 4,096 codewords, weight enumerator x24+759x16y8+2576x12y12+759x8y16+y24; Conway group Co₀ order 222·39·54·72·11·13·23; Monster order 246·320·59·76·112·133·17·19·23·29·31·41·47·59·71; E₈ root system rank 8, 240 roots, E₈³ ⊂ Λ₂₄. | CONNECTION: Λ₂₄ is even unimodular — its theta series ΘΛ24(q)=1+196560q2+16773120q3+… has coefficients tied to Eisenstein series E43 and E62, with ratio 196560/16773120 ≈ 0.0117 (no direct golden ratio). However, the orbifold construction uses fixed-point-free automorphisms of order
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 Central Charge 24 and Orbifold Construction — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23553574},
url = {https://zenodo.org/records/23553574},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Leech Lattice Uniqueness via Central Charge 24 and Orbifold Construction — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/22
PB - Zenodo
DO - 10.5281/zenodo.23553574
UR - https://zenodo.org/records/23553574
AB - FINDING: The Leech lattice (Λ₂₄) is uniquely determined by its VOA central charge 24 and orbifold construction from Niemeier lattices, unifying the Monster group, Golay code, and E₈³ root systems. | MATH: Central charge c=24; Leech lattice determinant det(Λ₂₄)=1 (unimodular), kissing number 196,560; Golay code G₂₄ has 4,096 codewords, weight enumerator x^24+759x^16y^8+2576x^12y^12+759x^8y^16+y^24; Conway group Co₀ order 2^22·3^9·5^4·7^2·11·13·23; Monster order 2^46·3^20·5^9·7^6·11^2·13^3·17·19·23·29·31·41·47·59·71; E₈ root system rank 8, 240 roots, E₈³ ⊂ Λ₂₄. | CONNECTION: Λ₂₄ is even unimodular — its theta series Θ_Λ_24(q)=1+196560q^2+16773120q^3+… has coefficients tied to Eisenstein series E_4^3 and E_6^2, with ratio 196560/16773120 ≈ 0.0117 (no direct golden ratio). However, the orbifold construction uses fixed-point-free automorphisms of order Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -