As Generative Information Engines (GIEs) increasingly replace traditional search engines as the primary interface for information retrieval, the mechanisms that govern visibility and decision-making are fundamentally shifting. Unlike ranking-based systems, generative models synthesize information into structured outputs, where entities are not only surfaced but described and evaluated. This transition necessitates new frameworks to measure how entities are represented within AI-generated responses. In this paper, we introduce the Artificial Intelligence Reputation Score (AIRS), a quantitative metric designed to capture both the sentiment and authority of entity representation within generative systems. AIRS provides a standardized methodology for evaluating AI-mediated reputation through prompt-based sampling and structured scoring across sentiment and authority dimensions. We demonstrate that in generative environments, representation—not visibility alone—serves as the primary driver of outcomes, with significant implications for commerce, capital allocation, and broader decision-making processes.