Entropy of Identity in LLM-Mediated Environments: A Framework for Measuring and Stabilizing Algorithmic Identity Representation

Large Language Models increasingly determine how individuals are represented in digital environments. Unlike search engines that retrieve documents, LLMs reconstruct identity from incomplete, distributed data — introducing systematic distortion we term identity entropy: the divergence between a person's verifiable digital presence and their AI-generated representation. We formalize this divergence, introduce the Entity Life Cycle (ELC) framework as a practical stabilization architecture, and illustrate it through a documented case of an independent artist resolving competitive namespace interference without institutional resources. This work positions identity management as an engineering problem, not a visibility problem.