The tropical generation conjecture for Lagrangian cobordism of bielliptic surfaces

Let $\mathcal K$ denote the symplectic bielliptic surface, and let $\operatorname{Cob}^{trop}(\mathcal K)$ be the subgroup of the Lagrangian cobordism group $\operatorname{Cob}(\mathcal K)$ generated by tropical Lagrangians. Tropical generation conjecture. The inclusion

$$\operatorname{Cob}^{trop}(\mathcal K) \hookrightarrow \operatorname{Cob}(\mathcal K)$$

is an isomorphism. This would show that every Lagrangian cobordism class on a symplectic bielliptic surface is represented by the tropical Lagrangians considered in the paper; the preceding theorem establishes the analogous isomorphism from the tropical subgroup to the relevant Grothendieck group, but does not establish that the full cobordism group is generated tropically.