We present a rigorous formalization of the Bateson One-Way Function, a novel approach tocryptographic irreversibility rooted in semantic ambiguity rather than number theory. We definethe function based on a formal grammar comprising messages, interpretive frames, and outputs.Irreversibility arises from ”frame suppression,” where the context of interpretation is lost duringevaluation. We define the Frame Recovery Problem (FRP) and prove its NP-completeness via a directreduction from 3-SAT. We establish the function’s information-theoretic irreversibility by provinga loss of mutual information between the input and the frame, and quantify this loss using theconcept of Symbolic Degeneracy (∆G). Empirical analysis confirms high output entropy, solidifyingthe Bateson function’s potential as a candidate one-way function.