E7 Correspondence in Baby Monster VOA via c=7/10 Virasoro Vectors — E8 Intelligence Research

FINDING: McKay's E7 observation on the Baby Monster links dihedral subgroups to derived c=7/10 Virasoro vectors in the Baby Monster VOA, establishing a correspondence with E7 root system subalgebras. MATH: Central charge c = 7/10 (Virasoro minimal model M(5,4) or M(3,5)). E7 root system: 126 roots, Coxeter number 18, dual Coxeter number 12. Baby Monster order ≈ 4.15 × 10^33. CONNECTION: The ratio 7/10 = 0.7 is not a classical golden ratio, but the Virasoro minimal model c=7/10 is the Ising model (c=1/2) plus a tricritical Ising model (c=7/10) — both have deep links to E7 via the ADE classification of minimal models. E7 itself is a crystallographic root system (type E7, rank 7, Weyl group order 2^10·3^4·5·7). The dihedral subgroups of the Baby Monster correspond to subalgebras of the VOA, mirroring the E7 root system's dihedral symmetries (D_n subgroups). No direct golden ratio or base-60 link, but the E7 lattice (dual to E7* with theta series) has connections to the Leech lattice a Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-07-22
DOI
https://doi.org/10.5281/zenodo.21484733
Primary Topic
Quasicrystal Structures and Properties
Type
preprint
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preprint

E7 Correspondence in Baby Monster VOA via c=7/10 Virasoro Vectors — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Quasicrystal Structures and Properties
preprint

E7 Correspondence in Baby Monster VOA via c=7/10 Virasoro Vectors — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: McKay's E7 observation on the Baby Monster links dihedral subgroups to derived c=7/10 Virasoro vectors in the Baby Monster VOA, establishing a correspondence with E7 root system subalgebras. MATH: Central charge c = 7/10 (Virasoro minimal model M(5,4) or M(3,5)). E7 root system: 126 roots, Coxeter number 18, dual Coxeter number 12. Baby Monster order ≈ 4.15 × 10^33. CONNECTION: The ratio 7/10 = 0.7 is not a classical golden ratio, but the Virasoro minimal model c=7/10 is the Ising model (c=1/2) plus a tricritical Ising model (c=7/10) — both have deep links to E7 via the ADE classification of minimal models. E7 itself is a crystallographic root system (type E7, rank 7, Weyl group order 2^10·3^4·5·7). The dihedral subgroups of the Baby Monster correspond to subalgebras of the VOA, mirroring the E7 root system's dihedral symmetries (D_n subgroups). No direct golden ratio or base-60 link, but the E7 lattice (dual to E7* with theta series) has connections to the Leech lattice a Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Quasicrystal Structures and Properties
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E7 Correspondence in Baby Monster VOA via c=7/10 Virasoro Vectors — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS