PART VI Unified Vacuum Lattice Mechanics and Manifold Tensor Framework: Multi-Component Alloys & High-Entropy Systems

Abstract

Part VI of the Unified Vacuum Lattice Mechanics and Manifold Tensor Framework presents a fully closed, mathematically auditable extension that generalizes elemental and binary constitutive models to complex multi-component alloys, high-entropy alloys (HEAs), and compositionally disordered lattice states. Rather than relying on unconstrained empirical fitting parameters or post-hoc disorder adjustments, the framework evaluates complex compositions strictly downstream of frozen, independently established elemental inputs by incorporating state variables such as the composition-weighted Wigner–Seitz radius, volumetric variance, and the scalar elastic invariant. By enforcing a transparent, one-directional computational chain without feedback loops, this section details the complete mathematical mapping and computational evaluation sequence while directly connecting bulk elastic states to acoustic Christoffel symbols and effective spacetime metric and curvature tensor quantities.