The Zhu-Liang Truth Function Theorem: A Proof That Truth Necessarily Is a Function

Based on the Zhu-Liang Truth Function Theorem (Version 3.1), this paper introduces the Calamity Recursor Axiom System and provides rigorous mathematical constructions for the Calamity Axiom (A5), including the definition of the calamity object, the proof of the existence of the quotient category, a detailed demonstration of the exactness of the recursor category, and an isomorphic proof of the automorphism group of the calamity object. These works extend the functional form of truth from a static functor to a dynamic calamity recursor, revealing the mechanism of contradiction resolution in the metabolic process of truth. All proofs in this paper are complete and do not rely on external references.