Multi-hop question answering needs evidence that is scattered across many sentences and ordered along a reasoning chain. Existing RAG systems struggle with this setting because flat chunk retrieval can miss bridge facts, binary graph structures lose n-ary information, and unordered top-K contexts leave evidence composition to the answer model. We introduce HyperPathsRAG, a hypergraph-based RAG framework that aligns query decomposition with the corpus index. It decomposes questions into n-ary sub-questions aligned with hypergraph facts, jointly matches all sub-questions to retrieve reasoning paths, scores paths by chain completeness, and presents the retrieved evidence in reasoning order. We evaluate in the candidate-passage setting on the 1k-question hard subsets of HotpotQA, 2Wiki, and MuSiQue, with three answering LLMs. HyperPathsRAG attains the best average Exact Match on every backbone (up to 42.2 EM / 56.2 F1 with Llama-3.3-70B-Instruct), and the best average F1 on two of three backbones; ablations attribute the bulk of the gain to the hypergraph index and the multi-target retriever. Our code is available at https://anonymous.4open.science/r/HyperPathsRAG-AE05/.