A Rigorous Poset Framework for DSM Disorders via Neural Substructures and Functional Affordances

We propose a mathematical framework using category theory and partially ordered sets (posets) to analyze psychiatric disorders from the DSM-5 based on their neural substructures and functional impacts, termed _affordances_ (e.g., memory, emotional regulation). We define a monotone mapping between neural substructures and their functional affordances, proving that disorders with the greatest functional impact correspond to maximal elements in the affordance poset. This approach provides a systematic ranking of disorders by their neurofunctional severity, offering a tool to prioritize treatment strategies.