We propose a lightweight, modular framework for hallucination detection in Retrieval-Augmented Generation (RAG) systems, addressing the critical challenge where logical dependencies span across fragmented retrieval results. To address the inherent limitations of compact models in processing long-context information and performing multi-hop reasoning, our approach systematically analyzes the logical relationships among retrieved documents within the vector space. By capturing these geometric patterns through a novel feature extraction framework, the proposed classifier significantly enhances context-aware hallucination detection without requiring complex architectures or pre-training on datasets. Meanwhile, to evaluate multi-document reasoning, we release HotPotQA-derived, a hallucination dataset preserving separate retrieved texts. Experimental results on HotPotQA-derived and several open-source datasets demonstrate that our framework can achieve results comparable to or even surpassing those of large language models (LLMs) on the task of hallucination detection.