Small changes to how a buyer phrases a question -- "best CRM" vs "top CRM" vs "best CRM for a SaaS startup" -- produce substantially different brand recommendations from AI assistants. Across ~6,000 paraphrase runs and ~6,000 same-prompt rerun controls on OpenAI and Anthropic models, the recommendation-set similarity (Jaccard) between two paraphrases of the same underlying buying intent is 0.288 for cosmetic rewordings (clustered 95% CI [0.215, 0.361]) and 0.135 for constraint-adding rewordings ([0.098, 0.175], pooling region/language and specificity-ladder axes) -- both far below the 0.50-0.61 same-prompt rerun baseline. The prompt string, not the underlying buyer intent, is the dominant input to which brands surface. Increasing reasoning effort does not narrow the gap (bounded by +/-0.05). This is a direct challenge to an increasingly popular AEO/GEO practice. Tracking a brand's "AI visibility" by counting brand mentions over a fixed set of prompts produces a metric whose dominant source of variance is which paraphrase the tracker happens to issue, not the model's behavior toward the brand: the same buyer intent in two natural paraphrases produces recommendation sets that overlap 14-29% in Jaccard versus 50-61% for same-prompt reruns. Sampling more paraphrases per intent reduces the artifact in principle, and efficient multi-prompt evaluation methods exist in the academic literature, but the natural buyer-phrasing space is much larger than the benchmark-scale prompt sets those methods have been validated on, and far beyond what any commercial tracker issues per brand-intent combination. Prompt-by-prompt mention tracking is therefore structurally unstable as a unit of measurement; meaningful improvement likely requires a different unit rather than a larger prompt set.