Contextual Entropy Reduction in Mixture Models: A Conditional Theorem, Proof, and Worked Example

This record contains the manuscript 'Contextual Entropy Reduction in Mixture Models: A Conditional Theorem, Proof, and Worked Example.' The paper proves that hierarchical context reduces predictive entropy in finite mixture models in expectation: E[H(Q_psi)] = H(X|Psi) <= H(X) = H(Q), with strict inequality exactly when I(X;Psi) > 0. The manuscript provides an explicit theorem statement with named assumptions, strictness and equality diagnostics, a softmax parameterization for hierarchical context, a quantitative analysis of approximation error under assumption violation, and a reproducible finite-alphabet worked example with verification code. Claims are intentionally limited to this conditional entropy theorem and its assumptions.