NeuroSynthet-X (NSX-9): A Unified Mathematical and Pharmacological Framework for the Cumulative Restoration of Neural Homeostasis

This manuscript presents NeuroSynthet-X (NSX-9), a novel synthetic pharmaco-therapeutic agent designed to address the multifaceted pathologies of neuropsychiatric disorders through a synergistic mechanism involving sigma-1 receptor (Sig1R) agonism and histone deacetylase (HDAC) inhibition. By integrating advanced mathematical modeling---encompassing stochastic differential equations (SDEs), the free-energy principle, and Fokker-Planck dynamics---NSX-9 is positioned as a precision intervention for restoring neural homeostasis. The framework elucidates how NSX-9 modulates epigenetic landscapes and synaptic plasticity, offering cumulative therapeutic benefits beyond conventional mono-therapies. Simulations demonstrate superior efficacy in mitigating stress-induced dysregulation, with implications for depression, addiction, and cognitive impairments. This self-contained document is optimized for compilation on the free version of Overleaf, with embedded bibliography and standard packages.