Rotational Multidimensional Regulatory Model (NOAH6): Formal Mathematical Structure and Experimental Validation Framework

Abstract Background: A biological organism can be described as a multi-layer regulatory system in which stability arises from the coordinated dynamics of interconnected physiological axes. Most existing intervention models are based on continuous modulation of individual signaling pathways, which often leads to adaptation and regulatory compensation. Objective: Formally define a rotational multi-domain regulatory model derived from the NOAH6 hierarchical framework and specify an experimental design that enables its empirical verification and potential falsification. Methods: The system is modeled as a nonlinear controlled dynamical system of the form Ẋ = (A-D) X + Bu (t) + f (X), where the matrices represent internal physiological coupling, homeostatic damping, and intervention influence, while the control signal represents a time-discretized rotation of active regulatory domains. The properties of stability, controllability, and observability of the system were analyzed, and an objective function was defined to determine the optimal rotation interval. Results (theoretical): The model satisfies formal stability criteria under the spectral condition of negative real parts of the eigenvalues of the Jacobian matrix, remains controllable under sequential activation of domains, and is observable under the condition of full rank of the measurement mapping. The optimal time rotation interval follows from minimizing the deviation of the system from equilibrium. Conclusion: The proposed model represents a mathematically closed, experimentally testable, and falsifiable regulatory framework. Its key prediction is the existence of a temporal causal sequence of regulatory layers that can be verified by longitudinal biomarker analysis.