Spanish title: Gestión de la reputación en la era de los buscadores con IA: una aplicación exploratoria de la Teoría de la Autoridad Algorítmica. This preprint presents the first formal citable research version of the study “Reputation Management in the Era of AI-Powered Search: An Exploratory Application of Algorithmic Authority Theory”. An earlier preliminary version of this work was presented at the I Congreso Internacional IACOM Astorga (2025) as a conference communication without DOI. The present manuscript constitutes a substantially revised and methodologically strengthened version, including expanded research design, clarified scope boundaries, moderated inferential claims, and strengthened analytical framing. The study applies the Theory of Algorithmic Authority (TAA-AI) to examine how AI-powered conversational systems construct, distribute, and condition digital authority in response generation environments within contemporary communication ecosystems.