UDCT v4.3: Internal Encoding of Path Information through Geometric Memory in the Double-Slit Experiment

We present a detailed numerical investigation of the internal encoding of path information in the double-slit experiment within the Unified Dimensional Cohesion Theory (UDCT 4.3) framework. Using the Auxiliary Variable Method, we evolve a geometric memory field concurrently with the wavefunction in a strictly unitary manner. In one-dimensional simulations, we systematically vary the memory coupling strength γ across the range [0, 100] with fixed relaxation time τ = 0.12 and perform quantitative analysis of interference visibility and peak broadening. Visibility is computed using peak detection with prominence thresholding on the final probability density. In two-dimensional simulations with a physically realistic double-slit barrier, we demonstrate that the geometric memory field develops a clear spatial asymmetry between the two slits. This asymmetry is quantified and shown to encode which-path information internally without any external measurement. We compare our wavefunction-based approach with previous trajectory-based formulations (v4.2) and discuss the advantages and limitations of each. Our results provide concrete evidence that geometric memory can serve as a physically grounded internal mechanism for path distinguishability in quantum systems.