{
  "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.",
  "abstract_shown": true,
  "affiliations": [
    "Scretching Quantum Press LLC"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Daniel Scretching",
      "orcid": "0009-0008-9586-2717"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5dsmm49k8gpjj.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23600689",
  "fulltext_url": null,
  "id": "5dsmm49k8gpjj",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23600689",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23600689/files/01_Onscreen_SDM_DSDM_Mathematical_Foundation_CITED%20zenodo.23600689.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5dsmm49k8gpjj.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:21:04Z",
      "native_id": "23600689",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23600689"
    }
  ],
  "subjects": [],
  "title": "SDM and D-SDM: On-Screen Mathematical Foundation",
  "title_text": "SDM and D-SDM: On-Screen Mathematical Foundation",
  "type": "preprint",
  "updated_at": "2026-11-06T12:21:04Z",
  "url": "https://research.draconitic.com/paper/5dsmm49k8gpjj",
  "venue": "Zenodo",
  "versions": []
}