Fan-out Query Length as an Inverse Predictor of Citation Rate in Perplexity: A 5-Day Pre-Registered Measurement of AI Search Behaviour on Proprietary-Concept Queries

This pre-registered study tested whether AI-search citation rate increases monotonically with query length. The hypothesis (H1) predicted that longer fan-out queries (10–12 words) would be cited more reliably than short root queries (2–4 words) on a fixed set of three stably-cited proprietary-concept pages, measured on Perplexity (sonar-pro API) over five consecutive days (225 binary citation measurements, Semantic fan-out category only, length-isolated). The result inverts the hypothesis. Citation rate decreases as query length increases: 2–4 words 61.3% (46/75), 6–8 words 36.0% (27/75), 10–12 words 16.0% (12/75). The 45.3pp spread between the shortest and longest tiers exceeds the pre-registered 22.0pp interpretability threshold (Welch's t = 6.398, p < 0.0001, Cohen's d = 1.045) and holds across all three pages and all five days with no day-over-day drift (chi-square = 0.118, df = 4, p = 0.9983). Pre-registered falsification criterion 2 (inverted result) is confirmed. A secondary finding: /extractability/ recorded a complete citation floor (0/25) at the 10–12 word tier across all five days. The implication is that Perplexity retrieval rewards keyword density over compositional matching for proprietary-concept queries, with short queries anchoring within the proprietary namespace and longer queries drifting into a generic competitive set.