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Knowledge graphs (KGs) enable reasoning tasks such as link prediction, question answering, and knowledge discovery. However, real-world KGs are often incomplete, making link prediction both essential and challenging. Existing methods, including embedding-based and path-based approaches, rely on Euclidean embeddings, which struggle to capture hierarchical structures. GNN-based methods aggregate information through message passing in Euclidean space, but they struggle to effectively encode the recursive tree-like structures that emerge in multi-hop reasoning. To address these challenges, we propose a hyperbolic GNN framework that embeds recursive learning trees in hyperbolic space and generates query-specific embeddings. By incorporating hierarchical message passing, our method naturally aligns with reasoning paths and dynamically adapts to queries, improving prediction accuracy. Unlike static embedding-based approaches, our model computes context-aware embeddings tailored to each query. Experiments on multiple benchmark datasets show that our approach consistently outperforms state-of-the-art methods, demonstrating its effectiveness in KG reasoning.