SDM and D-SDM: On-Screen Mathematical Foundation
- 1Scretching Quantum Press LLC
Abstract
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.
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BibTeX
@misc{scretching2026dsdm,
title = {{SDM and D-SDM: On-Screen Mathematical Foundation}},
author = {Daniel Scretching},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23600689},
url = {https://zenodo.org/records/23600689},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - SDM and D-SDM: On-Screen Mathematical Foundation
AU - Daniel Scretching
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23600689
UR - https://zenodo.org/records/23600689
AB - 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.
ER -