Supplementary Information for the Entropy-Induced Collapse (EIC) Model: Part I Dynamic Thresholds and Probabilistic Collapse Description

This supplementary information document accompanies Part I of the Entropy-Induced Collapse (EIC) model, presenting detailed theoretical expansions and mathematical formulations that underpin the dynamic entropy threshold framework for wavefunction collapse. It rigorously develops the non-Markovian kernel representation of collapse probability, large deviation principles governing false-collapse events, and the modulation effects of quantum error correction (QEC) on the collapse threshold. Furthermore, it analyzes the coupled stochastic differential equations governing environmental entropy and threshold evolution, and introduces a multi-stage collapse process incorporating intermediate convergence states. This supplement enhances the foundational framework by explicitly clarifying inevitable theoretical consequences that were previously implicit, thereby strengthening reproducibility and interpretability. Designed for researchers and experimentalists in quantum foundations and quantum information, this document bridges abstract theory and practical experimental considerations, serving as a critical resource for testing and refining the EIC model.