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Streamlines the process of constructing high-dimensional probability distributions that meet precise numerical properties such as KL divergence, entropy, and other information-theoretic metrics. By prioritizing mathematical analysis before implementation, the skill guides users through choosing efficient parameterization strategies—like power law or multi-tier models—to navigate large vocabulary spaces. It provides a robust framework for modular implementation, optimization refinement, and independent verification, ensuring solutions are both statistically accurate and computationally feasible.