## 3 Methods  
We describe a category-theoretic framework and methods for architecting and executing the CMGVC, which consists of four processes: (a) Conceptual Modeling: the transformation of concepts to models; (b) Model Transforming: converting models into generic, language-agnostic artifacts; (c) Stakeholder-Informing View Rendering: transforming generic representations into visualizations or representations; and (d) Reasoning, the cognitive process of rationalizing, understanding, perceiving, deciding, and revising the concept. This process is specified using an OPM model and illustrated in Figure 5.  
The framework defines mappings between the conceptual and computational phases of the CMGVC: the concept phase (Section 3.1), the model phase (Section 3.2), the generic representation phase (Section 3.3), the view phase (Section 3.4), and the iteration (Section 3.5). While the CMGVC is universal, we focus on conceptual system architectures as an instance of C, on the OPM modeling language (M), on graph data structures as a global representation (G), and on stakeholder-informing matrices as views (V). This specialization is also shown in Figure 5.  
Figure 5: The CMGVC, as a cognitive–computational cycle of Conceptual Modeling, Model Transforming, Stakeholder-informing View Rendering, and Reasoning. The System, OPM Model, GDS, and SIM are specializations of the respective generic artifacts: Concept, Model, Generic Representation, and View.  
We present a series of propositions regarding the possibility, validity, and superiority of creating views from models through a robust mechanism. Our main assertion in Proposition 1 is that a transform from any model M to any view V through an intermediate GDS representation G is superior to a set of direct transformations from all models M\({}_{1}\),..., M\({}_{\text{M}}\), to all views V\({}_{1}\),..., V\({}_{\text{V}}\).  
Proposition 1: _GDS-based transform is superior to direct transforms. A graph-mediated transform M\(\rightarrow\)G\(\rightarrow\)V is superior to direct model-to-view transforms M\(\rightarrow\)V: MGV \(\succcurlyeq\) MV._  
Proposition 2 asserts that a transform from any model M to any view V through an intermediate GDS representation G is also superior to a transform from all models \(M_{1}\),..., \(M_{M}\) through an ML-bound generic representation GR to all views \(V_{1}\),..., \(V_{V}\).  
Proposition 2: _GDS-based transform is superior to language-specific transform. A graph-mediated transformation M\(\rightarrow\)G\(\rightarrow\)V is superior to an ML-bound mediating representation-based transformation MRV: MGV \(\succcurlyeq\) MRV._  
MGV is a composition of M\(\rightarrow\)G and G\(\rightarrow\)V. Proposition 3 asserts that a transform M\(\rightarrow\)G exists. Proposition 4 asserts that a transform G\(\rightarrow\)V exists.  
Proposition 3: _A model-to-GDS transform exists. Let ML be a modeling language and M a model in ML. There exists a formal, valid, and feasible model-to-graph transform MG:ML\(\rightarrow\)GDS._  
Proposition 4: _A GDS-to-view transform exists. Let V be a view and G a set of GDS tuples. There exists a formal, valid, and feasible graph-to-view transform GV: GDS\(\rightarrow\)V._  
Specifically focusing on SIMs, Proposition 5 asserts that SIMs are valid views of GDS.  
Proposition 5: _A GDS-to-SIM transform exists. Let SIM be a stakeholder-informing view and G a set of GDS tuples. There exists a formal, valid, and feasible graph-to-SIM transform GV: GDS\(\rightarrow\)SIM._