A Neutrosophic Topological Approach to Scientific Decision Architectures: Structural Stability, Convergence, and Information Dynamics

This paper establishes a rigorous mathematical foundation for modeling scientific research design as a dynamic, decision-centric system. We introduce the Scientific Decision Architecture for Complex Systems (SDA-CS), formalizing research configurations as trajectories within a complete neutrosophic metric space D. By employing the Banach Fixed-Point Theorem, we prove that the research evolution operator Ψ acts as a contraction mapping, ensuring convergence toward a unique, stable methodological state Vd∗ even under conditions of high initial indeterminacy. The framework integrates neutrosophic logic to explicitly characterize indeterminacy (I), and local stability is analyzed through the spectral radius of the methodological Jacobian matrix JΨ. Furthermore, we examine the system through information theory, demonstrating that the SDA-CS architecture acts as an entropy-reduction mechanism that promotes information gain by pruning inconsistent decision paths. These theoretical results provide a cybernetic basis for ensuring reproducibility and structural robustness in complex scientific investigations.