The Double-Slit Experiment on a Discrete Holographic Lattice: Interference, Decoherence, and the Emergence of Classical Probability.

We show that exact unitary propagation of an electron wavepacket on a fi- nite 4.8.8 lattice reproduces single-slit and double-slit diffraction patterns in close quantitative agreement with experiment, with no continuum approxima- tion. When environmental coupling is introduced at the slit, interference is destroyed and Born rule statistics emerge from decoherence alone. Using the deterministic kinematics of the circlette lattice, we demonstrate that wave- function collapse need not be postulated. The transition from quantum inter- ference to classical probability distributions emerges naturally from unitary evolution through the deterministic tracing-out of environmental degrees of freedom. The lattice addresses the apparent measurement problem through finite bandwidth and orthogonal geometry, requiring no conscious observer. This is the third paper in a series developing the Holographic Circlette frame- work, but remains mathematically self-contained.