A Concrete Metric for Boundary Pressure $F_B$

This paper introduces a measurable formulation for boundary pressure ($F_B$) within the Theory of Non-Derivable Admissibility (TNA) framework. We define $F_B$ as a quantifiable metric derived from three observable components: reliability degradation ($R$), prediction uncertainty ($U$), and structural instability ($D$). The proposed integral and discrete models allow for the localization of structural tension at the system's boundary ($\partial\Omega$), providing a domain-independent tool to identify expansion triggers ($\Omega \rightarrow \Omega^+$). By instantiating this metric in physics, machine learning, and cognition, we demonstrate its utility in predicting system adaptation or failure. This formalization transforms the qualitative concept of boundary pressure into a rigorous analytical parameter for assessing the structural health and evolutionary potential of complex systems.