The existence of such an optimal linearization is now supported by the implementation of a merging algorithm, which has further paved the way for a more straightforward proof. This proof establishes the optimality of $\operatorname{opt}(G)$.

The integration of these mathematical concepts not only simplifies the existing framework but also enhances our understanding of the underlying structures. The merging algorithm, pivotal in this development, serves as a crucial tool in demonstrating the feasibility of achieving an optimal linearization. Consequently, the newfound simplicity in proving the optimality of $\operatorname{opt}(G)$ signifies a leap forward in the study of this domain.