UDCT v4.5: Dynamical Emergence of Born Rule Statistics from the DSBB Stability Landscape (Paper + Reproducibility Code)

This record provides the full paper and reproducibility package for UDCT v4.5, which investigates the dynamical emergence of Born Rule statistics within the Double-Slit Born-Backreaction (DSBB) framework — originally introduced in v4.4 as Dynamic Self-Regulating Bidirectional Back-Reaction. In this work, we introduce a measurement-induced deformation of the Stability Landscape through the Detector Freezing mechanism. By constructing a Free Energy Functional combining DSBB feedback energy with a Shannon entropy term, we demonstrate that the system relaxes toward a biased bimodal probability distribution. A perturbative analysis yields an explicit zeroth-order solution that reproduces the main features of full two-dimensional simulations with a minimum L2 relative error of only 2.41%. This result suggests that Born Rule-like statistics can emerge dynamically from the interplay between unitary evolution and geometric back-reaction, rather than being introduced as an independent postulate. Future directions include developing a more rigorous first-principles derivation from functional Fokker-Planck dynamics and extending the scalar feedback field to a chiral restoring tensor in four-dimensional spacetime. The reproducibility package contains the full paper and a self-contained Python script that allows anyone to exactly reproduce the main quantitative results reported in the paper (including the 2.41% L2 error and optimized parameters). Researchers are encouraged to download the code and run Mode A, which reproduces the paper’s benchmark results using the original dataset. □ Related Work This work builds upon the DSBB framework originally introduced in: Paik, W. S. (2026). UDCT v4.4: DSBB Double-Slit Framework and Stability Landscape Dynamics. Zenodo. https://doi.org/10.5281/zenodo.20793605