The ED-degree stabilization conjecture for hypersurface Segre products

Let $V_1$ and $V_2$ be complex vector spaces, let $Q_1\subset\mathbb{P}(V_1)$ be the isotropic quadric, and let $X\subset\mathbb{P}(V_1)$ be a projective hypersurface such that $X\cap Q_1$ is reduced. For a general subspace $L_j\subset\mathbb{P}(V_1)$ of codimension $j$, consider the Segre product $X\times\mathbb{P}(V_2)$.

ED-degree stabilization conjecture.

$$\operatorname{EDdegree}_F(X\times\mathbb{P}(V_2))=\sum_{j=0}^{n_1-1}\operatorname{EDdegree}_F(X\cap L_j).$$

Here $n_1$ is the projective dimension parameter used for $\mathbb{P}(V_1)$. This is presented as a conjectural generalization suggested by experiments in Macaulay2; the asserted formula remains open.