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| Format: | Recurso digital |
| Idioma: | anglès |
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Zenodo
2026
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| Accés en línia: | https://doi.org/10.5281/zenodo.20136725 |
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| _version_ | 1866901665624358912 |
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| author | Eva, Moss |
| author_facet | Eva, Moss |
| contents | <p><strong>This paper establishes that the Chinese Remainder decomposition Z/60Z ≅ Z/3Z × Z/4Z × Z/5Z coincides with the successive coset decomposition along the unique maximal subgroup chain {e} ⊂ Z₃ ⊂ A₄ ⊂ A₅ of the icosahedral group. </strong></p> <p>The indices 3, 4, 5 serve simultaneously as CRT moduli and as geometric symmetry layers: triangular, tetrahedral, and pentagonal. This identification yields a canonical base-60 coordinate on A₅ via CRT reconstruction, extending to a Z/2Z × Z/60Z coordinate on the binary icosahedral group 2I through its double cover. The coordinate map is not a group homomorphism; its failure is measured by a 2-cocycle σ: A₅ × A₅ → Z/60Z encoding the non-abelian multiplication of A₅ within the abelian numeration system.</p> <p>Applied to the icosian ring, the construction provides an intrinsic base-60 numeration of E₈ in which lattice addition and unit multiplication are coupled through σ. As a consequence, the E₈ → 2I branching coefficients decompose along the same three CRT factors, resolving the last open entry in a previously established correspondence between Poincaré Dodecahedral Space and exceptional geometry.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20136725 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Subgroup Ladder is the Chinese Remainder Theorem: Base 60 as the Canonical Coordinate of 2I Eva, Moss icosahedral group Chinese Remainder Theorem base 60 <p><strong>This paper establishes that the Chinese Remainder decomposition Z/60Z ≅ Z/3Z × Z/4Z × Z/5Z coincides with the successive coset decomposition along the unique maximal subgroup chain {e} ⊂ Z₃ ⊂ A₄ ⊂ A₅ of the icosahedral group. </strong></p> <p>The indices 3, 4, 5 serve simultaneously as CRT moduli and as geometric symmetry layers: triangular, tetrahedral, and pentagonal. This identification yields a canonical base-60 coordinate on A₅ via CRT reconstruction, extending to a Z/2Z × Z/60Z coordinate on the binary icosahedral group 2I through its double cover. The coordinate map is not a group homomorphism; its failure is measured by a 2-cocycle σ: A₅ × A₅ → Z/60Z encoding the non-abelian multiplication of A₅ within the abelian numeration system.</p> <p>Applied to the icosian ring, the construction provides an intrinsic base-60 numeration of E₈ in which lattice addition and unit multiplication are coupled through σ. As a consequence, the E₈ → 2I branching coefficients decompose along the same three CRT factors, resolving the last open entry in a previously established correspondence between Poincaré Dodecahedral Space and exceptional geometry.</p> |
| title | The Subgroup Ladder is the Chinese Remainder Theorem: Base 60 as the Canonical Coordinate of 2I |
| topic | icosahedral group Chinese Remainder Theorem base 60 |
| url | https://doi.org/10.5281/zenodo.20136725 |