The Theory of the Unit of Dynamic Energy (UDE): A Formal Framework for Quantifying Instability

The Theory of the Unit of Dynamic Energy (UDE) presents a unified mathematical–physical model for quantifying instability in diverse systems. It introduces the concept of the Vilelon (Vl) as a universal unit that measures how close a system is to collapse, bridging phenomena from black hole formation to structural failure, computational overload, and phase transitions. By defining UDE as the ratio between an instability load and a distance-to-collapse metric, the work establishes a predictive tool capable of describing, comparing, and potentially controlling instability across scientific domains.