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

Based on previous versions 3.0–3.6 of the Zhu-Liang Truth Function Theorem, this paper introduces a new foundational approach: starting from the meta‑logic of **the negation of the negation**, we directly derive the **Truth Metric Theorem**, and from it the Truth Function Theorem and the recursor axioms A1–A4. This new approach is more fundamental and clearer than the original path based on meta‑facts, grounding the entire theory in the internal logic of recursive evolution. We retain the meta‑fact path as historical background and auxiliary explanation; the two paths eventually converge in the unified Zhu‑Liang Calamity‑Crossing Recurron Paradigm. This paper systematically integrates the Entropy Reduction Corollary and the dynamic ontological content of truth (temporality, holism, expressibility, non‑isolatable rigidity), reinterpreting these core ideas from the metric theorem. The paper provides a rigorous mathematical construction of the Calamity‑Crossing Axiom A5, proving the exactness of the recursor category, the existence of the tribulation object, and the isomorphism of its automorphism group. These works elevate truth from a static function to a dynamic calamity‑crossing recursor, revealing the mechanism by which truth resolves contradictions in its metabolic process. All proofs are complete and do not depend on external references.