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.

翻译：买家提问方式的细微变化——例如"最佳CRM"与"顶级CRM"或"适合SaaS初创企业的最佳CRM"——会使AI助手生成截然不同的品牌推荐。在OpenAI和Anthropic模型上进行的约6,000次释义运行和约6,000次相同提示重跑对照中，相同潜在购买意图的两个释义之间的推荐集相似度（Jaccard系数）为：措辞美化类为0.288（聚类95%置信区间[0.215, 0.361]），约束添加类为0.135（聚类95%置信区间[0.098, 0.175]，合并区域/语言与特异性层级轴）——两者均远低于相同提示重跑基线（0.50-0.61）。提示字符串（而非潜在购买意图）是决定品牌显现的主要输入。增加推理努力程度未能缩小差距（变化范围限于±0.05）。这直接挑战了日益流行的AEO/GEO实践。通过固定提示集上的品牌提及次数追踪"AI可见性"会产生一种指标，其主导方差来源是追踪器恰好发出的特定释义，而非模型针对该品牌的行为：相同购买意图的两个自然释义产生的推荐集Jaccard重叠率为14-29%，而相同提示重跑则为50-61%。从原理上看，对每个意图采样更多释义可减少此类人为偏差，学术界也存在高效的多提示评估方法，但自然买家释义空间远大于这些方法已验证过的基准规模提示集，且远超任何商业追踪器针对每个品牌-意图组合所发出的提示数量。因此，逐提示的提及追踪作为测量单位存在结构性不稳定；有意义的改进可能需要采用不同的单位而非更大的提示集。