Manifestly Covariant Formulation of the Quantum Viscoelastic Lattice: Unifying Einstein-Cartan Gravity and Non-Abelian Gauge Fields

We present a manifestly covariant, four-dimensional extension of the Quantum Viscoelastic Lattice (QVL) model, modeling the spacetime vacuum as a 4D micropolar Cosserat continuum. We demonstrate that General Relativity and non-Abelian Yang-Mills gauge structures emerge analytically from the translational and rotational degrees of freedom of this lattice. Rather than treating the gravitational Lagrangian as a purely formal mathematical construct, we physically interpret the governing action as the couple-stress energy of the structured vacuum, identifying the quadraticr curvature term with the flexo-torsional elastic energy of the Cosserat nodes. Utilizing the Palatini variational principle, we avoid higher-derivative Ostrogradsky instabilities and rigorously extract both Einstein-Cartan gravity and covariant Yang-Mills equations from this single elastic framework.By incorporating the explicit Dirac action for fermionic defects, we demonstrate that minimal coupling is a strict kinematic necessity of parallel transport. Furthermore, we explore the topological consequences of this framework: a macroscopic lattice director field reduces the local Lorentz symmetry to spatial rotations SO(3), generating the geometric precursor to the electroweak gauge sector.The Aharonov-Bohm phase is rigorously derived as geometric Cartan holonomy, and the fundamental quantization of magnetic flux is shown to emerge naturally from the discrete Planck-scale periodicity of the underlying Cosserat lattice.