AI Visibility Aggregation Threshold Theorem

This paper formalizes the AI Visibility Aggregation Threshold Theorem, establishing that stable entity representation within large language model (LLM) training requires structured corpus aggregation exceeding a minimum survival threshold. Drawing on documented multi-platform ingestion observations, the study identifies a measurable discontinuity: an entity lacking representation under minimal corpus conditions achieved consistent multi-model recall following structured corpus expansion under low-authority constraints. The theorem situates this threshold behavior within previously documented shallow-pass selection mechanisms, budget-constrained ingestion, and structured signal compression dynamics. It defines…