UDCT v4.7: Parametric Robustness of the Emergent Born Rule in the DSBB Stability Landscape

UDCT v4.7: Parametric Robustness of the Emergent Born Rule in the DSBB Stability Landscape This paper presents a comprehensive One-Factor-at-a-Time (OFAT) robustness verification of the dynamically emergent Born Rule within the Double-Slit Born-Backreaction (DSBB) framework of the Unified Dynamic Cohesion Theory (UDCT v4.7). Building on the geometric derivation established in UDCT v4.5, we subject the DSBB system to twelve independent parametric perturbations across four key parameters: wavepacket width σ (±10%), detector freezing time t_freeze (±0.1), coupling strength λ (±20%), and effective temperature k_eff (±20%). Results show that the L2 relative error between the full 2D microscopic simulation and the theoretical zeroth-order solution remains tightly bounded within ±0.44% of the baseline value (2.41%), while preserving 100% bimodal structural integrity in all cases. These findings provide strong quantitative evidence that the emergent Born-like probability distribution functions as a robust geometric attractor inherent to the DSBB Stability Landscape. A major goal of this work is full reproducibility. The accompanying reproducibility package implements a dual-mode execution system (Mode A: Paper Reproduction Mode; Mode B: Full Scratch Mode) together with a self-healing environment designed to be accessible even to undergraduate students. This work establishes a high-precision, reproducible benchmark for future investigations into the geometric origin of quantum probability.