Unobstructedness and B-realizability conjecture for tropical curves

Let $V\twoheadrightarrow \text{?}$ be a tropical curve in $\mathbb R^n$, and let $L_V$ be a geometric Lagrangian lift of $V$. The lift is unobstructed when its obstruction term vanishes in the relevant Floer-theoretic deformation theory, and $V$ is $B$-realizable when it lifts to an analytic subset of $(\Lambda^*)^n$.

Unobstructedness and B-realizability conjecture. The geometric Lagrangian lift $L_V$ is unobstructed if and only if $V$ is $B$-realizable.

The conjecture proposes an equivalence between the symplectic unobstructedness of a tropical curve's Lagrangian lift and its algebraic realizability. The paper proves unobstructedness for genus-zero tropical curves and realizability for tropical curves in tropical abelian surfaces, but the stated equivalence is not established in general.