THE MONSTER GROUP FROM FIRST PRINCIPLES (REVISED) Complete Derivation from Q² = Q + I
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2025
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| _version_ | 1866901089157120000 |
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| author | Hughes, Martin |
| author_facet | Hughes, Martin |
| contents | <p>We prove that the minimal faithful representation dimension of the Monster sporadic group, 196883 = 47 × 59 × 71, is uniquely determined by icosahedral geometry originating from the Fibonacci matrix equation Q² = Q + I. We establish the novel identities |Roots(E8)| = V × F = 240 and dim(E8) = F₆ × M₅ = 8 × 31 = 248, where V = 12, F = 20 are icosahedral counts derived from the discriminant Δ = 5. The Leech lattice kissing number satisfies 196560 = 240 × (L₂ × F₇ × F₈), where the factor 819 encodes the Collatz multiplier times the Bott Fibonacci times half the bosonic string dimension. All critical string theory dimensions emerge as 2F_k for k ∈ {5, 6, 7, 8}. Of the 26 sporadic simple groups, 21 have dimensions with 100% Q-derived expressions (p < 10⁻¹⁶ under conservative null hypothesis). The Monster appears as the arithmetic progression L₈ × (L₈ + V) × (L₈ + 2V), where the Coxeter coefficients 8, 10, 12 correspond to Bott periodicity, double discriminant, and icosahedral vertices respectively, completing the icosahedral hierarchy.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17982042 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | THE MONSTER GROUP FROM FIRST PRINCIPLES (REVISED) Complete Derivation from Q² = Q + I Hughes, Martin Monster group Fibonacci matrix golden ratio E8 leech lattice sporadic groups string theory McKay correspondence <p>We prove that the minimal faithful representation dimension of the Monster sporadic group, 196883 = 47 × 59 × 71, is uniquely determined by icosahedral geometry originating from the Fibonacci matrix equation Q² = Q + I. We establish the novel identities |Roots(E8)| = V × F = 240 and dim(E8) = F₆ × M₅ = 8 × 31 = 248, where V = 12, F = 20 are icosahedral counts derived from the discriminant Δ = 5. The Leech lattice kissing number satisfies 196560 = 240 × (L₂ × F₇ × F₈), where the factor 819 encodes the Collatz multiplier times the Bott Fibonacci times half the bosonic string dimension. All critical string theory dimensions emerge as 2F_k for k ∈ {5, 6, 7, 8}. Of the 26 sporadic simple groups, 21 have dimensions with 100% Q-derived expressions (p < 10⁻¹⁶ under conservative null hypothesis). The Monster appears as the arithmetic progression L₈ × (L₈ + V) × (L₈ + 2V), where the Coxeter coefficients 8, 10, 12 correspond to Bott periodicity, double discriminant, and icosahedral vertices respectively, completing the icosahedral hierarchy.</p> |
| title | THE MONSTER GROUP FROM FIRST PRINCIPLES (REVISED) Complete Derivation from Q² = Q + I |
| topic | Monster group Fibonacci matrix golden ratio E8 leech lattice sporadic groups string theory McKay correspondence |
| url | https://doi.org/10.5281/zenodo.17982042 |