Formal Verification and Stress-Testing of the Al-Mizan Al-Mutakamil Master Equation for Computational Cosmology and Relational State Dynamics

Before any foundational physical theory or operator framework can be adopted by the scientific community, it must undergo rigorous validation against established physical and mathematical benchmarks. This paper presents the formal mathematical formulation of the unified Al-Mizan Al-Mutakamil Equation and submits it to six critical scientific stress tests: Dimensional Analysis, Mathematical Consistency, the Correspondence Principle, Falsifiability, Empirical Verification, and Independent Reproducibility. We demonstrate that the framework is strictly non-dimensionalized, globally singularity-free on k \in \mathbb{N}^+, converges to standard unitary quantum dynamics and the Lindblad/FLRW limits as k \to \infty, and makes testable predictions for discrete quantum simulation platforms at a 5\sigma statistical confidence standard.