Multi-hop question answering often fails when retrieval treats evidence as isolated matches to the original question, since the facts needed to answer a complex question are usually connected through intermediate entities, relations, and constraints. We propose HyperProve, a retrieval-augmented QA framework that addresses this challenge by coupling question decomposition with answer-conditioned expansion over a hypergraph of atomic facts. HyperProve does not use atomic facts, hypergraphs, or iterative retrieval in isolation; instead, it carries intermediate answers and supporting hyperedges as retrieval state, then uses that state to bias the next local hypergraph expansion. This design enables HyperProve to construct coherent evidence chains for final answer generation while making the retrieval process stateful and fact-centered. Across multi-hop QA benchmarks, HyperProve achieves the best overall performance in our evaluation, outperforming the strongest baselines by an average relative improvement of 6.2% in answer accuracy and 4.9% in F1.

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