Reset Dynamics: $\Gamma$-Constrained Realizability and the Structural Inevitability of Non-Composability

Abstract: > This paper introduces Reset Dynamics (RD), a foundational meta-structural framework within the Unified Open Structural Systems Framework (UOSSF). We challenge the universal axiom of composability by internalizing finite actuation budgets ($\Gamma$). Key Contributions: Defines the Instability Functional $P(S)$ based on historical complexity and recursive depth. Proves the Structural Inevitability of Non-Composability in multi-axial constrained systems. Establishes the Reset Operator ($\hat{R}$) as the canonical minimal repair mechanism. Derives foundational constants ($0, 1, \infty$) as emergent operational states of the Reset cycle. This is Paper 1 of a three-part series, bridging the gap between abstract category theory and realizable physical execution.