A cross-sectional audit of 50+ mid-market e-commerce brands across the four leading large language models (ChatGPT, Claude, Gemini, Perplexity), conducted in three sprints between 17 April and 4 May 2026. The study reports approximately 200 audit rows across 6 product categories, 9 e-commerce platforms, and 11 countries, and tests three claims common in current Generative Engine Optimization (GEO) advice. Headline findings. Schema completeness explains approximately 9 percentage points of Share of Voice (SOV) variance in our sample (n=21). Native-language audits lift SOV by an average of 36 percentage points when English baseline SOV is at or below 50 percent, but reduce SOV by 7 percentage points when the English baseline is at or above 75 percent (n=14). Country-category pairs with strong cultural authority (Italy/coffee, Japan/audio, Switzerland/watches, France/fragrance, Germany/tools) achieve a mean English SOV of 90 percent, against 12.5 percent for non-authority pairs, a 77.5 percentage point gap (n=9). Contribution. We propose a unifying account, the mention-density model: AI citation rate is governed by a brand's mention density across two distinct corpora the LLM uses, a frozen training corpus and a live retrieval corpus. Schema is a retrieval-time feature, not a training-time feature; the levers most often promoted by GEO tooling target the smaller of the two layers. The paper also includes an extension audit of 10 UK footwear brands (400 prompts, 14 May 2026) and a 34-brand standing corpus (mean SOV 16.5 percent) that reproduce the same pattern in a single category.