  A formalism is presented to construct a non-perturbative Grand Unified Theory
when gravitational Planck-scale phenomena are included. The fundamental object
on the Planck scale is the three-torus T^3 from which the known properties of
superstrings, such as the geometric action and duality, follow directly. The
low energy theory is 11-dimensional and compactification to a Lorentzian
four-manifold is an automatic feature of the unified model. In particular, the
simply-connected K3 Calabi-Yau manifold follows naturally from the model and
provides a direct link with M-theory. The high energy theory is formulated on a
T^3 lattice with handles which exhibits the necessary symmetry groups for the
standard model, and yields a consistent amplitude for the cosmic microwave
background fluctuations. The equation of motion for the supersymmetric, unified
theory is derived and leads to the Higgs field. This formulation predicts a
remnant, scalar topological defect of mass < 9 m_Planck/46 from the Planck
epoch, which is a candidate for dark matter. Finally, it is shown that if the
universe is quantum-mechanical, its spatial dimension is equal to three and the
laws of nature are Lorentz invariant when gravity can be neglected.
