Adjunction conjecture for Chern classes of tropical manifolds

Let $X$ be a pure-dimensional compact tropical manifold, and let $D$ be a tropical submanifold of codimension $1$. Let $\iota\colon D\to X$ be the inclusion, let $c^{\mathrm{sm}}(X)=\sum_{k=0}^{n}c_k^{\mathrm{sm}}(X)$ denote the total Chern class defined from the Chern–Schwartz–MacPherson cycles, and let $[D]_{\mathrm{PD}}$ denote the Poincaré dual of $D$.

Tropical Chern-class adjunction conjecture. For every $k\in\mathbb{Z}_{\geq 0}$,

$$\iota^*c^{\mathrm{sm}}(X)=c^{\mathrm{sm}}(D)\bigl(1+\iota^*[D]_{\mathrm{PD}}\bigr),$$ $$\iota^*c_k^{\mathrm{sm}}(X)=c_k^{\mathrm{sm}}(D)+c_{k-1}^{\mathrm{sm}}(D)\,\iota^*[D]_{\mathrm{PD}}\in H^{k,k}(D;\mathbb{Z}).$$

This is the tropical analogue of the classical adjunction formula for total Chern classes of a smooth divisor. The source presents it as an expectation and gives no general proof, so it remains open.