This article presents an information-theoretic framework explaining model collapse in self-referential learning systems. Four premises establish that: (I) endogenous semantic drift is inevitable in closed loops; (II) long-term stability requires a viability condition where corrective bandwidth exceeds the error rate (Ceff(t)E(t)); (III) systems violating this condition undergo informational autophagy; and (IV) this failure mode exhibits a distinct, falsifiable temporal signature. Specifically, the framework predicts that during recursive training, out-of-distribution accuracy will degrade before validation perplexity rises. This temporal lag distinguishes semantic divergence (loss of grounding) from capacity-driven collapse (general degradation). By reframing synthetic contamination from a binary risk to a quantitative rate problem, the theory demonstrates that scaling with synthetic data is viable only when paired with commensurate verification infrastructure.