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arXiv · 2609.23162

From Prompt to Recommendation: A Fitted Stage Model of Brand Visibility in AI Search

Benjamin Tannenbaum
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Abstract

We analyze 34,960 unbranded prompt-engine observations from 75 anonymized Aiso projects, covering 2,854 distinct monitored prompts and repeated GPT and Gemini runs from June-September 2026. When neither the target brand nor its own domain appears in the observable live retrieval path, target mention rates are 2.8% for GPT and 3.8% for Gemini. With an own-domain citation but no branded fan-out, they rise to 49.0% and 58.4%. When both own-domain exposure and a branded fan-out occur, mention rates reach 91.4% and 100%. The relationship persists within the same project, prompt, and engine across repeated runs: among prompt cells that vary in own-domain exposure while holding branded fan-out absent, exposure is associated with a mean mention-rate increase of 40.2 percentage points on GPT and 49.0 points on Gemini. Prior visibility is independently persistent. A previous non-mention plus no current own-domain exposure yields next-run mention rates of 1.6% and 1.9%; previous mention plus current exposure yields 80.5% and 83.7%. We fit a chronological diagnostic model using prior-run history and contemporaneous retrieval indicators: $ \operatorname{logit}P(M_t=1)=α_e+β_e\operatorname{logit}(\widetilde P_{t-1})+γ_e E_t+δ_e F_t+θ_e^\top X. $ On the latest 30% holdout, the full model achieves AUC 0.963 on GPT and 0.942 on Gemini, compared with 0.937/0.917 for prior history alone and 0.880/0.840 for live signals alone. A manually curated prompt sensitivity gives nearly identical AUCs (0.960 and 0.943). A separate 199-prompt page-corpus validation finds that prompt-page match predicts Gemini exposure (AUC 0.641) more clearly than GPT exposure (0.545), placing relevance upstream of a larger engine-mediated exposure effect. The equation is predictive and observational, not a causal description of proprietary engine internals.

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Benjamin Tannenbaum. 2026-09-19. From Prompt to Recommendation: A Fitted Stage Model of Brand Visibility in AI Search. https://arxiv.org/abs/2609.23162

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