The SPECTRA (Selective Precious Metal Extraction and Catalytic Transformation Recovery Approach) project represents a paradigm shift in energy conversion, defense technologies, and aerospace engineering by integrating tetrahedral quantum dynamics with advanced thermodynamics and quantum gravity principles. This report synthesizes theoretical physics, computational simulations, and experimental validations to explore how tetrahedral symmetry governs energy optimization in waste conversion, quantum gravity effects in propulsion systems, and novel material designs for defense applications. Key findings include the refinement of the tetrahedral determinant equation to relate Planck-scale constants, quantum gravity simulations of tetrahedral lattices in industrial combustion processes, and experimental signatures of tetrahedral quantization in black hole radiation analogs. These advancements have direct implications for next-generation aerospace propulsion, zero-point energy harvesting, and directed energy weapons, positioning tetrahedral dynamics as a cornerstone of 21st-century quantum engineering1313.