Bandwidth Mismatch and the Decoherence of Sovereign Questions: A Formal Model of χ-Dynamics Across Social, Institutional, and Cognitive Systems

This work introduces a formal information-theoretic model explaining why high-density,temporally extended questions are systematically classified as anomalous, unscientific,or dangerous during their early stages, even when later empirically validated. The model attributes this phenomenon not to cognitive or moral failure, but to astructural mismatch between sovereign-level inquiry and the finite bandwidth andsynchronization constraints of consensus-based social, institutional, and cognitivesystems. By formalizing sovereign question density, consensus bandwidth, and synchronizationpressure, the paper derives a χ-index that quantifies anomalization intensity and provesits exponential divergence over time, independently of the truth value of the underlyingquestion. The framework applies across scientific institutions, bureaucratic governance, andhigh-velocity information environments, with implications for distributed knowledgesystems and AGI-aligned inquiry.