Large language models (LLMs) are impressive text generators, but they can struggle with factual accuracy, especially in longer pieces. Researchers are constantly looking for ways to improve their truthfulness, and a new study explores how adding context can significantly boost the fact-checking process. Traditionally, fact-checking AI-generated text involves breaking down statements into individual claims and verifying them against a reliable source (like Wikipedia). However, isolating these claims can strip away crucial context, leading to inaccurate assessments. Imagine trying to verify the statement "He directed the film" without knowing who "he" refers to! This new research introduces a method called DnDScore, which cleverly combines *decontextualization* and *decomposition*. Decontextualization adds essential information back into atomic claims, clarifying ambiguities. For example, "He directed the film" becomes "Quentin Tarantino directed Pulp Fiction." This enriched information makes verification more reliable. The researchers found that by verifying these decontextualized claims, accuracy improves considerably. But simply plugging decontextualized claims into existing fact-checking systems isn't enough. They can be too complex and include redundant information. DnDScore tackles this by providing the original subclaim *and* its decontextualized version to the verifier, highlighting the specific aspect to verify. This nuanced approach not only clarifies meaning but also prevents the verification process from getting bogged down in unnecessary details. The results show that DnDScore significantly outperforms traditional methods, boosting fact-checking accuracy. This research points to a crucial insight: context is king in the realm of AI fact-checking. While decomposition breaks down complex statements into manageable chunks, decontextualization intelligently weaves back essential information, enabling AI systems to better understand and verify the truth. This has important implications for developing more reliable and trustworthy AI writing tools in the future, tackling one of the biggest challenges in LLM development — ensuring the information generated is not only engaging but also accurate.