Personalization has long relied on customer data to infer what an individual is likely to value. We call this customer evidence: the customer's historical behavior and preferences. Generative AI extends personalization by allowing providers to supply changing situational information at the moment a response is produced, without encoding every condition in advance. We define this provider-side context as information about what is possible, permitted, or advisable now. This flexibility creates a new problem: once context becomes easy to supply, more is not necessarily better. We develop a theory of context sufficiency in which the relevance of context to the customer's current intent matters more than its volume. The theory identifies four states, insufficiency, sufficiency, saturation, and interference, and introduces the Context-Sufficiency Frontier to locate the minimal relevant set. In a full-factorial experiment with a generative recommender at a large home-furnishing retailer, relevant context improved appropriateness, while irrelevant context reduced it and destabilized retrieval. The framework shifts personalization from supplying more context toward identifying what the current interaction actually requires and enforcing constraints throughout the service process.