Repeated Queries Exhaust an LLM's Brand Recommendations but Not Its Sources

Abstract: Whether repeated identical buying questions exhaust a LLM's brand recommendations depends on retrieval. Across 300 question-engine cells (50 questions, six engines, 15 runs each, open extraction over 1,470 adjudicated organizations), the five engines answering without web search were still adding never-seen brands at run 15 in 86-92% of cells, with median repertoires of 15-31 organizations; the one retrieval-enabled engine closed its list (median 8 organizations, 64% of cells still adding), matching four earlier deep cells where web-search runs saturated by run ten. Cited-domain accumulation keeps rising at every horizon tested: four deep cells were still adding domains at run 24 with 59-84% of the Chao2 lower-bound estimate observed, and 44% of the retrieval engine's breadth cells were still adding domains at run 15. A single run shows 62-77% of the five-run brand set, and across engines the median question draws 38 organizations, of which a median of 15 appear in exactly one engine. Estimators are exact rarefaction and Chao2 richness; a parallel fixed-roster extraction reproduces flat curves on identical responses, so roster-bounded tracking manufactures plateaus that open extraction removes.