An Operator-Algebraic Formulation of Cosmic Expansion and Binding Coherence: Resolving Dark Energy and Dark Matter via the Discrete Mizan Master Equation

In this paper, I present an independent mathematical framework that resolves the cosmic phenomena conventionally attributed to "dark energy" and "dark matter" without invoking undetected physical particles or arbitrary vacuum energy densities. Utilizing the unified Al-Mizan Al-Mutakamil Master Equation, I demonstrate that dark energy emerges naturally as a global scaling regulator (\Xi_{\text{Scale}} or Al-Musi'a) required for Hilbert space state density preservation across discrete temporal steps k \in \mathbb{N}^+. Concurrently, I show that dark matter is not a physical particle, but an implicit relational matrix coherence (J_{\text{Implicit}} or Al-Batin) residing in the off-diagonal entanglement entries of the system generator matrix. I provide complete mathematical derivations, rigorous proofs of accelerated lattice expansion and non-local binding trace, and detail two laboratory-scale experimental protocols designed for quantum simulators to test and validate these conclusions.