The multiplicative Euclidean distance degree formula for parameterized hypersurface classes

Let $X_{m,n}^d$ be a variety parameterizing a set of hypersurfaces with the same Euclidean distance degree, let $H$ be a point of $X_{m,n}^d$, and let $k$ be the number of parameters in the parametrization of the hypersurface class. The multiplicative EDD formula. The conjecture states

$$EDdegree(X_{m,n}^d)=EDdegree(H)^{m-k}EDdegree(X_{k,n}^d).$$

The formula is proposed for classes whose members have the same Euclidean distance degree, but the supplied context gives no proof or resolution. Its general status therefore remains open.