Simplicial Lattice Field Theory (Vol I): The Lorentzian Metric from D4 Lattice Frustration

We construct a discrete vacuum from the D4 root lattice with unit cell the 24-cell. Topological frustration breaks O(4) to O(1,3), producing the Lorentzian signature. The frustration angle arctan(2) is derived from the virial theorem. SO(8) triality provides exactly three fermion sectors. Two free parameters (lattice spacing a and tension τ) fix all dimensional scales.