Minimum Viable Evidence and Value-optimal Evidence: Decision-theoretic Sufficiency, Strategic Evidence Games, Machine-learning Alternatives, and Categorical Structure

This paper develops minimum viable evidence (MVE) as a decision-theoretic framework for determining when evidence is sufficient to justify action under uncertainty, loss, cost, bias, and strategic manipulation. It extends the framework through value-optimal evidence acquisition, signed MVE test statistics, Type I/II MVE error control, anytime-valid e-processes, game-theoretic adversarial auditing, and machine-learning alternatives such as PAC-Bayes certificates, conformal risk-control gates, selective prediction, active learning, and safe reinforcement learning. The result is a unified statistical architecture for moving from abstract evidential sufficiency to operational, auditable, and strategically robust decision systems in high-stakes scientific, regulatory, and AI-mediated environments.