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

We develop a purely geometric mechanism for fermion mass generation and flavor
mixing 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 Dirac
operator twisted by an antisymmetric two–form geometry, and their masses and
mixings are determined by global geometric constraints rather than local model
assumptions.
We show that the global angular–momentum neutrality (GAN) constraint acts
as a genuine vacuum selection principle: it discretizes admissible vacua into topolog
ical branches and locks a unified effective mass scale through zero–mode consistency.
As a result, fermion masses originate from geometric Yukawa kernels constructed
from two–form invariants and internal projection operators, whose allowed structure
space is finite–dimensional.
Within this framework, the number of fermion generations is identified with
a topological index associated with two–form defects, and quantum consistency
conditions single out three generations as the unique minimal nontrivial solution.
Furthermore, the observed wide fermion mass hierarchy and the contrasting struc
tures of the CKM and PMNS matrices emerge naturally from the geometric non
orthogonality of internal projection operators, without introducing new light degrees
of freedom.
These results elevate fermion masses, flavor mixing, and generation structure
from empirical inputs to consequences of global geometry and topology, providing
a unified and predictive geometric origin for the fermion sector.