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 evo-

lution as fundamental postulates. Expanding on the Selection-Stitch Model (SSM), 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) lattice. We model this vacuum as a Chiral Micropolar Continuum, where

nodes possess both translational and rotational degrees of freedom. We explicitly derive the

isotropic Laplacian from the 12 nearest-neighbor forces and introduce a novel Chiral Veloc-

ity Coupling arising from the Berry connection of the defect’s topology. We demonstrate

that this coupling naturally generates the complex unit i, the global U(1) symmetry, and

the exact Schr¨odinger equation in the non-relativistic limit. Finally, using the geometrically

renormalized lattice spacing (a ≈0.77lP ) derived in previous work, we predict a specific

mass limit for quantum coherence at mmax ≈28µg. This distinguishing prediction identifies

the physical mechanism for the transition from quantum superposition to classical gravity

as a geometric resolution limit of the vacuum.