Community Notes enable scalable, community-based fact-checking, but automated generation faces a coverage--quality trade-off. Note-dependent methods (e.g., summarization-based Supernotes) cannot operate without prior crowd input, while web-search LLMs achieve broad coverage but often retrieve evidence misaligned with what raters need. We introduce GitSearch (Gap-Informed Targeted Search), which treats missing, ambiguous, or disputed information as first-class retrieval targets. It infers information gaps from a post and optional incomplete notes, searches specifically to resolve them, and synthesizes an evidence-grounded Community Note. To evaluate this, we introduce PolBench, a new dataset of 78,698 U.S. political tweets with Community Notes. Keeping single-call search inference budget fixed, GitSearch improves human-rated helpfulness by 0.43 over unconditioned web search and wins 59% of pairwise comparisons. It generates notes for 99% of test cases, including the 46% where summarization methods fail. Human evaluators prefer GitSearch to human-written helpful notes in 69% of comparisons, primarily due to better context coverage. These findings show that how search is organized matters more than information access alone.

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