The Bateson Equilibrium: A Formal Model of Undecidability Fixpoints in Recursive Type Arithmetic

We formally reconstruct the Bateson Equilibrium framework within a revised Recursive Type Arithmetic (RTA), providing a rigorous model for the persistence of undecidable propositions as stability fixpoints. By replacing the system's prior heuristic entropy function with a formal symbolic degeneracy measure, $\Delta_G(\phi)$, grounded in rewrite theory, we define the Bateson Game as a coherence-preserving symbolic system. We prove a formal undecidability fixpoint theorem and characterize strategic ambiguity as a syntactically admissible and model-theoretically stable resolution state. The result reframes classical logical independence as a structural feature of symbolic representation within a formal system, not as a defect of completeness.