Interpretation of Structural Circularity in the TNA Framework

This work provides a structural mapping from formal logic to dynamic systems within the Theory of Non-Derivable Admissibility (TNA) framework. We reinterpret the inherent circularity of formal theories—traditionally viewed as a limitation—as a fundamental and necessary property for system persistence and generative expansion. By establishing a correspondence between formal non-self-sufficiency and boundary-driven dynamics, we demonstrate that internal validation creates recursive dependencies that generate indeterminacy at the system's boundary. This indeterminacy results in boundary pressure ($F_B$), acting as a generative engine that drives the system to extend its domain and introduce new structures. Ultimately, what appears as a static constraint in formal logic is revealed to be the essential mechanism for non-terminating evolution in generative systems.