SDM and D-SDM: On-Screen Mathematical Foundation

This theoretical research extends the Scretching Diagnostic Matrix (SDM) into a 15-coordinate mathematical framework integrating the original 12 diagnostic dimensions with three additional symptom coordinates representing psychosis, bipolar-spectrum manifestations, and dissociation. The study develops and examines state-dependent Jacobian equations, numerical examples, multidimensional symptom interactions, network representations, and a six-dimensional extension for modeling complex psychopathology and potential comorbidity. Algebraic refinements improve mathematical consistency while preserving the original theoretical formulation. Building upon earlier Scretching publications, the expanded framework proposes a quantitative approach to investigating symptom overlap, diagnostic differentiation, and interacting psychiatric conditions. Numerical verification, methodological limitations, and proposed empirical tests are presented. The 15-coordinate extension remains theoretical and requires independent clinical validation before diagnostic application.