The Tyranny Coefficient: A Formal Model of Provenance, Legitimacy, and Authority Appearance and Provenance

This paper develops a formal framework for analyzing the relationship between appearance, provenance, legitimacy, and authority. Beginning from the claim in Plato's Republic that appearance tyrannizes over truth, the paper argues that tyranny may be understood not merely as a political condition but as an epistemic condition. A distinction is developed between fictional provenance and real provenance, and a provenance-legitimacy-authority model is proposed. Using marginal analysis, a derivative-based Tyranny Coefficient is introduced to measure the degree to which institutional outcomes respond to projected representations rather than underlying source conditions. The result is a formal framework for investigating opacity, legitimacy formation, and provenance recovery within epistemic systems.