Proposed by Kevin Funchal, the Theory of the Minimum Necessary advances the hypothesis that a universal principle underlies complex systems: observable consequences are governed not by the full apparent complexity of reality, but by the smallest structures capable of preserving them. Through the introduction of the Mentz Value and related mathematical constructs, this work establishes the foundational formalism of the theory and explores its implications across logical, dynamical, cognitive, and physical domains. While the broader consequences and applications of the theory remain under active and rigorous investigation, its core definitions, equations, and falsifiability criteria have been formally established and frozen as the foundational layer from which future developments must derive. This preprint presents the initial mathematical formulation, computational evidence, and explicit conditions under which the theory may be tested, refined, or refuted as research progresses.