SYNAPSE-GEAR: A Stochastic Control Framework for Neuromotor-Cognitive Coupling

Title: SYNAPSE-GEAR: A Stochastic Control Framework for Neuromotor-Cognitive Coupling and Noise Regulation in High-Precision Systems. Summary: This paper introduces the SYNAPSE-GEAR (Gated-Executive Adaptive Regulator) framework, a theoretical model designed to analyze the interplay between neuromotor control and cognitive noise regulation. By employing stochastic differential equations (SDEs) and Hamilton-Jacobi-Bellman (HJB) optimality conditions, the model investigates the regulatory role of the Thalamic Reticular Nucleus (TRN) in filtering information flow between the Dorsolateral Prefrontal Cortex (DLPFC) and motor outputs. The framework provides a formal mathematical derivation for the suppression of cognitive interference during high-precision tasks, identifying critical thresholds for neuromotor stability. The results suggest that the "GEAR" mechanism operates as an adaptive information filter, optimizing the signal-to-noise ratio in complex neural architectures. This work establishes a foundation for future applications in autonomous AI alignment and neuromorphic computing. Keywords: Neuromotor Control, Stochastic Processes, Cognitive Noise, Information Theory, Thalamic Regulation.