Relational Geometric Mechanics VI: General Relativity — The Einstein Field Equations from the Self-Consistent Amplitude Lattice

Paper VI of the Relational Geometric Mechanics series. Completes the general relativistic correspondence begun in Paper III. Starting from the gravitational amplitude lattice sum, the continuum limit is taken, the foam metric response is defined, and self-consistency is imposed. Lovelock's theorem establishes that the Einstein field equations are the only stable covariant second-order closure in four dimensions. The electroweak unification structure is developed, including the Weinberg angle as the projection angle between the U(1) and SU(2) phase directions in the broken-symmetry QF vacuum, and the mass relation m_W = m_Z cosθ_W derived from the projection structure.