## 1 Introduction  
Recent thrust in the systems engineering (SE) community has been toward the use of models to perform SE activities [1]. This change comes from a desired conversion away from document-based SE (DBSE) to model-based SE (MBSE) to leverage potential improvements such as traceability through authoritative sources of truth [2]. However, a recent survey presented several obstacles to the adoption of MBSE in practice [3], alluding, among others, to conceptual misalignment. In fact, models from the leading MBSE language, the Systems Modeling Language (SysML), have been shown to have multiple interpretations [4]. We argue that these barriers may be symptoms of a lack of a theoretical foundation for MBSE. While current practices of MBSE provide digital representations of the system model through descriptively linking elements within and related to the system, they lack a formal underlying foundation, such as could be provided through mathematical theory [5]. This is in contrast to more traditional engineering disciplines, such as mechanical engineering or electrical engineering, where modeling tools leverage formal mathematical foundations (e.g., finite element analysis and computational fluid dynamics). We contend that such foundations are necessary to enable a science-informed approach to MBSE. Several efforts in that direction were initiated several decades ago, including [PERSON]'s General Systems Theory [6], [PERSON]'s Cybernetics [7], [PERSON] and [PERSON]'s general [8] and abstract systems [9] theories, [PERSON]'s computational systems theory [10], and [PERSON]'s Mathematical Theory of Systems Engineering [11]; after which no other contribution at such scale has been completed. The SE community did not ground its practice upon such foundation at the time and is reclaiming now a new wave of research to unveil the theoretical foundations of SE [12; 13; 14; 15; 16; 17]. This vision aligns with that of the International Council on Systems Engineering (INCOSE), which has called for SE to \"be grounded in more rigorous foundations of mathematics\" [1]. From a historical perspective, coining the term MBSE has been credited to [PERSON] [18; 19] through his mathematical framework for system design that he comprehensively referred to as the Tricotyledon Theory of System Design (T3 SD) [20]; a tricotyledon refers to a triad of leaf-shaped spaces. In [PERSON]'s words, he created T3 SD \"to provide the system theoretic foundations necessary to the study and practice of systems engineering\" and \"to explicate mathematical system theory as the basis for the development of models and designs of large-scale, complex systems consisting of personnel, machines, and software\" [20]. Conceptually, T3 SD defines a mathematically guided process of engineering systems through reliance on formal mappings between designs that have increasing technology dependence. The term \"tricotyledon\" originates in the distinctive three cotyledon leaf configurations of the Buildability space, the Functionality space, and the Implementationity space. The subset of buildable designs that formally map to the subset of functional designs constitutes the space of implementable designs. For simplicity, a visualization of the conceptualization of [PERSON]'s T3 SD is shown in Figure 1.  
[PERSON] defined three levels of system designs in T3 SD: the _functional system design_ (FSD), the _buildable system design_ (BSD), and the _implementable system design_ (ISD). The map  
Figure 1: The conceptualization of [PERSON]’s T3 SD (i.e., mathematical theory of MBSE). The functionality space is defined by required input/output and ordered according to preferred performance. The buildability space is defined by required technology and ordered according to preferred cost. The implementability space is defined by the formal mapping between buildability and functionality subsets and ordered according to preferred tradeoff between performance and cost; from which the design for the real system is selected.