Mardešić's conjecture on metrizable factors of products of compact spaces

Let $d,s\geq 1$. Suppose that $L_1,\ldots,L_d$ are linearly ordered compact spaces and there is a continuous surjection

$$L_1\times\cdots\times L_d\to K_1\times\cdots\times K_{d+s},$$

where $K_1,\ldots,K_{d+s}$ are infinite compact spaces. Mardešić's conjecture. There are at least $s+1$ metrizable factors among the spaces $K_j$.

Mardešić proved this when the target factors are separable; the conjecture asks whether the separability assumption can be removed. The paper establishes the corresponding result in the case of one additional factor, and thus resolves the original problem in that case.