Three Generations from Topological Braiding: A G-MaTT Derivation of Fermion Families

Abstract We derive the origin of the three fermion generations in Generalized Mass as Twisted Time (G-MaTT) from the topological braiding structure of the primordial mass-time torsional potential $\mathcal{M}_\mu$. In G-MaTT, particles are stable knots in the emergent field $\hat{M}_\mu$, sourced by synchronized branches of $\mathcal{M}_\mu$. We show that the number of generations arises from the braid group representation over the configuration space $\chi$: for $n=3$ strands, the braid group $\mathcal{B}_3$ has three distinct irreducible representations — corresponding to generation I (light), II (medium), and III (heavy). Fermion masses scale as $m_n \propto w_k^2$, where $w_k$ is the winding number of the $k$-th branch, yielding the observed hierarchy. The CKM and PMNS matrices emerge from cross-braiding interference, and coupling constants from braid entropy. This derivation eliminates the need for ad hoc Higgs mechanisms or extra dimensions — generations are a geometric consequence of pre-mass topology.