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However, embedding advertisements within unstructured LLM outputs introduces a critical trilemma: balancing advertiser payoffs, platform revenue, and user experience. Existing methods, such as prompt injection or rigid position slots, disrupt semantic coherence and lack a parametric framework for independent control, rendering rigorous mechanism design intractable. To bridge this gap, we introduce Neuron Auctions, a novel paradigm that shifts the auction object from the surface text space to the LLM's internal representations. Leveraging mechanistic interpretability, we identify brand-specific feed-forward network (FFN) neurons and demonstrate that competing brands activate within approximately orthogonal subspaces. 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