Qubit Dispersion Control and Physical Hardware Verification: Real-Time Implementation of Discrete Matrix (M) Operations via Termux and Edge Computing

[Abstract / Description]To address the persistent challenge of qubit dispersion in quantum computing architectures, this study rejects the continuous manifold paradigm in favor of a discrete crystalline pixel-lattice framework. Implementing the Master Matrix M and the Biranks operator cascade within a mobile POSIX C edge computing environment (Termux), we empirically demonstrate the absolute elimination of numerical accumulation errors (Error: 0.000000000) and verify exact bit-level synchronization (TRUE State) directly on physical hardware registers. This work establishes a rigorous discrete algebraic foundation for modern theoretical physics and quantum computation models.