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Cross-entropy loss falls monotonically while the correct token never overtakes the competitor. We study five transformer architectures of two families over a fivefold parameter range, on ten contexts where the correct completion and nearest competitor overlap substantially. We construct an order parameter combining the predicted distribution with the geometric overlap between token embeddings. The density-matrix formulation is natural because the prediction distribution lives over a non-orthogonal embedding basis. It decomposes additively into a signal, tracking commitment to the correct token over its nearest competitor, and a background drag, set by how the embedding bulk leaks probability into the score. This isolates two failure modes. In kinematic failure the signal stays small and the model never commits. 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