Retrieval-Augmented Generation (RAG) systems remain susceptible to hallucinations despite grounding in retrieved evidence. Current detection methods rely on semantic similarity and natural language inference (NLI), but their fundamental limitations have not been rigorously characterized. We apply conformal prediction to hallucination detection, providing finite-sample coverage guarantees that enable precise quantification of detection capabilities. Using calibration sets of approximately 600 examples, we achieve 94% coverage with 0% false positive rate on synthetic hallucinations (Natural Questions). However, on three real hallucination benchmarks spanning multiple LLMs (GPT-4, ChatGPT, GPT-3, Llama-2, Mistral), embedding-based methods - including state-of-the-art OpenAI text-embedding-3-large and cross-encoder models - exhibit unacceptable false positive rates: 100% on HaluEval, 88% on RAGTruth, and 50% on WikiBio. Crucially, GPT-4 as an LLM judge achieves only 7% FPR (95% CI: [3.4%, 13.7%]) on the same data, proving the task is solvable through reasoning. We term this the "semantic illusion": semantically plausible hallucinations preserve similarity to source documents while introducing factual errors invisible to embeddings. This limitation persists across embedding architectures, LLM generators, and task types, suggesting embedding-based detection is insufficient for production RAG deployment.

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