The Ontological Dominance Papers: Entity Authority in AI Citation Systems

Large language models increasingly mediate business-to-business discovery: when a buyer asks an AI system to identify or compare providers in a category, the system's answer is shaped by signals embedded during training and retrieval, not by product quality alone. This paper introduces a governing framework — Byrum's Law — for reasoning about how an entity's citation probability in AI systems evolves under competitive pressure. We propose a decomposition of AI-directed signals into two classes: frequency signals, which are subject to competitive erosion, and categorical authority signals, which the underlying training geometry renders structurally resistant to it. The logical structure of this distinction is presented in Section 6. We introduce two accompanying instruments — the Entity Authority Score (EAS), a 100-point diagnostic of an entity's machine-readable authority position, and Citation Probability at Query (CPQ), an outcome metric linking signal investment to citation likelihood — and extend the framework to adversarial dynamics and attribute-level brand representation. We close with a direct statement of the framework's empirical standing: its core claims are deductions from established mathematical traditions applied to a new domain, and are best treated as a rigorously derived working hypothesis pending independent, large-sample confirmation in deployed commercial AI systems.