The sectional-degree formula for the Euclidean distance degree

Let $X \subseteq \mathbb{C}^n$ be an irreducible affine variety, and let $\overline{X} \subset \mathbb{P}^n$ be its projective closure. Let $Q_{\infty}$ denote the quadric at infinity, and let $s_i(X)$ denote the $i$th sectional degree of $X$. The sectional-degree conjecture. If $\overline{X}$ intersects $Q_{\infty}$ transversely, then the Euclidean distance degree of $X$ is

$$\operatorname{EDdegree}(X)=s_0(X)+\cdots+s_{n-1}(X).$$

The conjecture proposes an affine analogue of the relation between Euclidean distance degree and polar degrees. The preceding results establish the corresponding mixed-volume formula under additional hypotheses, but the stated formula is presented as a conjecture for varieties whose projective closure intersects the quadric at infinity transversely.