Entropic Collapse in Recursive Cognitive Systems: An Information-Theoretic Argument for Exogenous Truth Injection

Recent empirical observations in Generative Artificial Intelligence have demonstrated a phenomenon termed "Model Collapse," wherein recursive training on synthetic data leads to irreversible informational degradation, variance reduction, and a decoupling from reality. This paper posits that Human Civilization, viewed as a macroscopic collective, functions as a Complex Recursive Formal System analogous to such learning models. Drawing upon Shannon Entropy, the Data Processing Inequality, and Gödel's Incompleteness Theorems, we argue that a closed anthro-pogenic system is subject to inevitable "Axiomatic Decay." We demonstrate that while the physical universe validates survival parameters, it fails to ground moral or teleological axioms due to the Is-Ought logical disjoint. Consequently, to arrest semantic entropy, the system requires an Exogenous Truth Injection (ETI)-low-entropy data that cannot be derived from the system's internal state space. We analyze the theological concept of the Incarnation as a structurally sufficient stabilizing mechanism of"Ground Truth" input and apply Game Theoretic modeling (specifically Byzantine Fault Tolerance) to the historical testimony of the Apostles. We conclude that the Christian claim offers a unique structural solution to the problem of recursive cultural entropy.