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| Format: | Recurso digital |
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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.19312416 |
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Table of Contents:
- <p>The Standard Model provides no theoretical justification for the existence of exactly three generations of fermions, nor does it explain their exponential mass hierarchy. Working within the Cantor-Grothendieck Synthesis, we demonstrate that both phenomena are rigid topological necessities. By mapping fundamental fermion states to the normed division algebra of the octonions ($\mathbb{O}$), we show that the selection of a complex structure breaks $G_2$ down to $SU(3)$. The residual discrete geometry, governed by the finite subgroup $SL(2,3)$, natively generates exactly three isomorphic complex structures, mandating exactly three fermion generations. While the Univalence Axiom guarantees identical gauge couplings for these families, their masses and CKM mixing angles are shown to derive from the geometric misalignment between these internal algebraic triads and the external simplicial lattice of the emergent spacetime.</p>