The multiplicative formula for the Euclidean distance degree of hypersurface classes

Let $\mathcal H_{m,n}$ be the variety parametrizing the relevant hypersurface class, let $C_{m,n}$ denote the corresponding parameter variety, and let $\pi$ be a generically finite map of degree $\omega$. Write $\beta$ for the factor appearing in the relation between the two parameterizations. The Euclidean distance degree formula. If $mr>k$, then

$$EDdegree(\mathcal H_{m,n})=\frac{1}{\omega}\beta EDdegree(C_{m,n}).$$

The formula is motivated by numerical observations and is proved in two special cases in the paper. Its general validity remains open.