arXiv:2506.07446v1 Announce Type: new Abstract: Fact verification plays a vital role in combating misinformation by assessing the veracity of claims through evidence retrieval and reasoning. However, traditional methods struggle with complex claims requiring multi-hop reasoning over fragmented evidence, as they often rely on static decomposition strategies and surface-level semantic retrieval, which fail to capture the nuanced structure and intent of the claim. This results in accumulated reasoning errors, noisy evidence contamination, and limited adaptability to diverse claims, ultimately undermining verification accuracy in complex scenarios. To address this, we propose Atomic Fact Extraction and Verification (AFEV), a novel framework that iteratively decomposes complex claims into atomic facts, enabling fine-grained retrieval and adaptive reasoning. AFEV dynamically refines claim understanding and reduces error propagation through iterative fact extraction, reranks evidence to filter noise, and leverages context-specific demonstrations to guide the reasoning process. Extensive experiments on five benchmark datasets demonstrate that AFEV achieves state-of-the-art performance in both accuracy and interpretability.