Static benchmarks often conflate memorization with reasoning, failing to capture the dynamic nature of world knowledge. We present LiveSearchBench, a scalable pipeline that automatically constructs snapshot-grounded benchmarks from knowledge graph differentials, in which every answer is unique and SPARQL-verifiable against a target snapshot. Unlike prior template-based approaches, our method leverages topology-aware synthesis to generate multi-constraint compositional questions with unique answers guaranteed via SPARQL validation. Evaluating 1,000 questions across three difficulty levels on both open-weight and frontier models, we expose a pronounced Recency Gap on facts that post-date a model’s training cutoff, particularly for compositional queries; retrieval dependence is thus an empirical property we measure, not a formal guarantee we claim. Through Oracle and Wikidata-as-corpus analyses, we disentangle dual failure modes: retrieval coverage limitations for single-hop questions and reasoning failures for compositional queries even with ground-truth evidence. LiveSearchBench provides both a rigorous construction methodology and a continuously updatable testbed for evaluating evidence integration under evolving knowledge.