Geometric Origin of Fermion Masses and Emergent Flavor Mixing in the QAMG Framework

We develop a purely geometric mechanism for fermion mass generation and flavormixing within the framework of Quaternion Angular–Momentum Gravity (QAMG),without introducing any fundamental scalar fields or arbitrary Yukawa parameters.In this approach, fermions arise as topologically protected zero modes of a Diracoperator twisted by an antisymmetric two–form geometry, and their masses andmixings are determined by global geometric constraints rather than local modelassumptions.We show that the global angular–momentum neutrality (GAN) constraint actsas a genuine vacuum selection principle: it discretizes admissible vacua into topological branches and locks a unified effective mass scale through zero–mode consistency.As a result, fermion masses originate from geometric Yukawa kernels constructedfrom two–form invariants and internal projection operators, whose allowed structurespace is finite–dimensional.Within this framework, the number of fermion generations is identified witha topological index associated with two–form defects, and quantum consistencyconditions single out three generations as the unique minimal nontrivial solution.Furthermore, the observed wide fermion mass hierarchy and the contrasting structures of the CKM and PMNS matrices emerge naturally from the geometric nonorthogonality of internal projection operators, without introducing new light degreesof freedom.These results elevate fermion masses, flavor mixing, and generation structurefrom empirical inputs to consequences of global geometry and topology, providinga unified and predictive geometric origin for the fermion sector.