Who Owns the AI Recommendation? A Multi-Industry Empirical Map of Brand Category Ownership Across Large Language Models

arXiv:2606.23057v2 Announce Type: replace-cross Abstract: This exploratory study measures brand inclusion across five industries, 50 brands and 250 queries, each put five times to GPT-5.2, Gemini 3 Flash and Perplexity sonar-pro in February and September 2026 (3,614 and 3,750 scored answers). Category Inclusion Rate, Recommendation Share, Competitive Vacuum Index and Co-Mention Asymmetry have stated denominators. February inclusion rates sit close together across an industry's sampled brands (mean Gini 0.30), while at least one brand is named in 80% or more of answers to 204 of 250 queries. Vacuums occur in 7.6% of queries; provisional open-vocabulary model readings suggest most reflect the sampled brand list. The partially pre-specified September replication shows strong cross-date Recommendation Share correlation (Spearman 0.994), unchanged vacuum prevalence and agreement of 60.8% against February's 57.2%. The descriptive size association persists. Fixed margins do not account for all co-mention structure: 31 ordered pairs depart from the September null. Agreement exceeds the query-independent null, and both parametric-pair advantage intervals are positive. All ten clustering seeds yield zero emergent clusters. Matcher validation remains provisional pending author checks. The statistics describe system output and identify no causal mechanism.