Persistent misinformation poses serious challenges to risk communication, public understanding, and coordinated risk management decision-making. While past models-such as opinion dynamics, informational cascades, and the Social Amplification of Risk Framework-help explain how misinformation spreads, they do not explain when and why locally reasonable-seeming beliefs fail to cohere into a shared, accurate global understanding of risks. This paper models how beliefs are communicated, filtered, and interpreted across social and institutional networks. We draw on tools from sheaf theory-a mathematical framework for integrating local information into global structures-to diagnose and quantify situations where consistent beliefs at the local level cannot be coherently reconciled across the system. We discuss how these tools can support targeted interventions, such as trust-based bridge agents, semantic alignment, and control strategies that improve belief integration. Examples and simulations demonstrate how both classical and novel problems-such as information silos and echo chambers, fragile consensus stemming from information cascades, and agreement on words without agreement on meanings-can be reframed and addressed as design flaws in the processes used to communicate and update individual beliefs. From this perspective, risk communication should be treated not just as a matter of accurate content, but as a system design problem in which coherence, interoperability, and resilience must be deliberately engineered. We propose that tools from sheaf theory can help meet this challenge by supporting risk communication that is more likely to produce shared, accurate beliefs-and thereby enable better informed and better coordinated risk management decision-making.
Louis Anthony Cox (Sun,) studied this question.