The exponential growth of generative artificial intelligence has fundamentally changed how users access information, shifting discovery from ranked search results to a synthesis of multiple credible sources as answers. Traditional metrics such as search engine rankings and click-through rates no longer adequately capture visibility in this new age. This paper introduces the Artificial Intelligence Visibility Index (AIVI), a conceptual and analytical framework designed to quantify how entities, such as brands, organizations, or topics, are represented within generative information engines like ChatGPT, Gemini, and Claude. AIVI integrates multi-dimensional metrics including mention frequency and positional prominence to produce a visibility score. By turning AI visibility into a quantitative construct, public figures and companies can evaluate their presence in AI-generated outputs, identify optimization opportunities competitively position themselves in a new attention economy.