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We show that decoder-only large language models exhibit a depth-wise transition from context-processing to prediction-forming phases of computation accompanied by a reorganization of representational geometry. Using a unified framework combining geometric analysis with mechanistic intervention, we demonstrate that late-layer representations implement a structured geometric code that enables selective causal control over token prediction. Specifically, angular organization of the representation geometry parametrizes prediction distributional similarity, while representation norms encode context-specific information that does not determine prediction. Together, these results provide a mechanistic-geometric account of the dynamics of transforming context into predictions in LLMs.