Non-Executable Tensorial Structures for Organizations – A Formal Scientific Schema in YAML

Non-Executable Tensorial Structures for Organizations – A Formal Scientific Schema in YAML Description:This work presents a generalized scientific YAML schema for representing organizationalstructures as high-dimensional tensor spaces. Each department, unit, and process withinan institution is expressed as a state or operator within a metric tensor field, enablingmathematical reasoning over complex institutional relations without any executable code. The YAML file encodes traversal and semantic hierarchy purely through indentation andsymbolic relationships. It functions as a non-executable, auditable documentation modelfor institutional dynamics, interpretable as a static, high-dimensional embedding field. This representation treats an organization as a metric space \( (X, d) \) of configurations,where each entity is mapped into a tensorial embedding \( φ: Attributes → ℝ^n \). Processesare described as non-operational transformations \( T: X → X \), maintaining invariants ofconsistency, dimensional coherence, and policy constraints. Unlike conventional organizational modeling (BPMN, ArchiMate, or RDF/OWL ontologies),this approach integrates formal mathematical properties (tensor rank, contraction, metric)with governance constraints (access, ethics, reproducibility) into a single declarativestructure. The result is a "Formal Organizational Twin": a model that can be audited,replicated, and verified, but never executed. Applications include:- Formal AI governance documentation- Institutional modeling in research and education- Synthetic testbeds for audit-driven organizational theory All variables, embeddings, and metrics are synthetic and non-personal. The schemaconforms to civil-science ethics and non-harm principles, following the ruahAI LicenseCatalog 2025 (Unified Edition). Author:Winfried Brückner (ruahAI)Independent Researcher, GermanyORCID: https://orcid.org/0009-0009-0008-5263 License:CC BY-ND 4.0 — Attribution, No Derivatives, Non-executable scientific use only.