Huh–Sturmfels conjectural inductive formula for maximum likelihood degree

Let $X$ be an irreducible algebraic subvariety of $({\mathbb C}^*)^n$ contained in

$$H=\{p_1+\cdots+p_n=1\},$$

and let $\bar X$ be its closure in $({\mathbb C}^*)^{n-1}\times{\mathbb C}$. Suppose that $\bar X\cap\{p_n=0\}$ is nonempty, reduced, and irreducible. The quantity $\operatorname{MLdeg}(\bar X\cap\{p_n=0\})$ is its maximum likelihood degree as a subvariety of $({\mathbb C}^*)^{n-1}\times\{p_n=0\}$, and $\operatorname{MLdeg}(X|_{\lambda_n=0})$ counts the points of $X_{\operatorname{reg}}$ where

$$\frac{\lambda_1dp_1}{p_1}+\cdots+\frac{\lambda_{n-1}dp_{n-1}}{p_{n-1}}$$

degenerates for generic $(\lambda_1,\ldots,\lambda_{n-1})\in{\mathbb C}^{n-1}$. Huh–Sturmfels' conjectural inductive formula.

$$\operatorname{MLdeg}(X)=\operatorname{MLdeg}(\bar X\cap\{p_n=0\})+\operatorname{MLdeg}(X|_{\lambda_n=0}).$$

The formula is intended to give an inductive computation of the maximum likelihood degree by passing to the boundary $p_n=0$ and restricting the likelihood parameters; the source does not specify its resolution status.