Fermion Chirality from Non-Bipartite Topology: Resolving the Doubling Problem via Lattice Saturation

We present a rigorous resolution to the Nielsen-Ninomiya “No-Go” theorem by deriv-

ing fermion chirality from the non-bipartite topology of a saturated cuboctahedral vacuum

(K = 12). Standard hypercubic discretizations of the Dirac equation inevitably produce

spurious mirror fermions due to the bipartite symmetry of the grid. We demonstrate that a

Face-Centered Cubic (FCC) lattice, formed of simplicial tetrahedra, introduces topological

frustration that breaks this symmetry. By explicitly constructing the discrete Dirac operator

and specifying the Γj matrices as spin projections along the 12 bond directions, we evaluate

the dispersion relation across the first Brillouin zone. We show that while the physical mode

at the Γ-point is massless, doubler modes at the L and X points are lifted to the Planck

cutoff. To validate this geometric framework, we derive the bare Higgs coupling λ ≈0.125

from the ratio of surface-to-volume configurations, predicting a mass of 123.11 GeV.

Keywords: Fermion Doubling, Nielsen-Ninomiya Theorem, Lattice Field Theory, Higgs Mass, Grav-

itational Echoes, Selection-Stitch Model