Discrete Wave Mechanics: Deriving the Schr¨odinger Equation and the Mass Limit of Quantum Superposition from Vacuum Lattice Sintering

Standard Quantum Mechanics treats the complex wavefunction and its first-order time evolution as fundamental postulates. Expanding on the Selection-Stitch Model (SSM) [1], we propose that these properties are emergent consequences of a discrete, crystallized vacuum. We define a “particle” as a stable K = 13 topological defect within a K = 12 Face-Centered Cubic (FCC) lat- tice. We model the vacuum as a **Micropolar (Cosserat) Continuum**, where nodes possess both translational and rotational degrees of freedom. We introduce a novel **Chiral Velocity Coupling** into the lattice Lagrangian, arising from the broken mirror symmetry of the defect. We explicitly derive the equations of motion via the Euler-Lagrange formalism, demonstrating that this coupling generates the complex unit i. We calculate the Noether current associated with the global U (1) sym- metry, proving that the topological coupling ensures a positive-definite conserved charge. Finally, we provide a step-by-step derivation of the non-relativistic limit, recovering the exact Schr¨odinger equation and unifying the deterministic discrete vacuum programs of ’t Hooft and Kleinert [3, 4].