A retrieval‑augmented language model draws answers from two sources—the retrieved context and its own knowledge. When the context is incomplete or wrong, the two sources disagree. Existing approaches resolve the disagreement with a rule fixed at design time: always follow the context, amplify it proportionally to how much it moves the model, or trust the model’s memory. Each rule is guaranteed to fail in some deployment. In a decision‑theoretic model of the two sources, the score of any fixed rule grows linearly with the share of reliable contexts, while the optimal achievable score is convex, so any non‑optimal rule is outperformed. Moreover, the symmetric divergence used by signal‑adaptive decoding carries no information about which source is correct. Therefore, resolving a conflict requires two inputs that current methods do not keep: separate evidence for each source and a prior on how often the context is right. We evaluate these claims on GRACE, a benchmark that intervenes on the knowledge‑graph context of a fixed question, measuring separately what the model knows, what the context says, and the ground truth. Every baseline from four families excels on either right or wrong contexts, never on both. We then construct the two inputs: the model states its knowledge as notes, a small policy assigns each note a calibrated confidence, a reader answers in two voices, and a selector commits or abstains under a prior $\pi$ applied as an exact prior shift. With $\pi$ set to the true share of correct contexts, the system surpasses the best baseline at every mixture of GRACE contexts, improving by up to 26 points. Overall scores are 45.3 (Qwen3.5-35B-A3B) and 35.0 (Llama-3.1-8B) versus 29.4 and 27.5 for the best baseline. On the preregistered ClashEval it beats same‑backbone CK‑PLUG and TCR by 12 and 26 points. As theory predicts, gains disappear when the model lacks the necessary knowledge.
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