Matsubara-Heo–Telen dual-degree conjecture for reciprocal linear spaces

Let $L\subseteq\mathbb{P}^n$ be a linear subspace of dimension $d$ not contained in any coordinate hyperplane, let $L^{-1}$ be its reciprocal linear space, and let $M=\operatorname{M}(L)$ be the matroid represented by $L$. Write $\beta(M)$ for the beta invariant of $M$, and denote the projective dual of $L^{-1}$ by $(L^{-1})^\vee$. Matsubara-Heo–Telen's dual-degree conjecture. If the matroid $M$ is connected, then $(L^{-1})^\vee$ is a hypersurface of degree

$$2^d\beta(M).$$

This conjecture predicts the degree of the dual hypersurface in the connected case, complementing the associated dual-defectivity claim; the source gives no evidence that it has been resolved.