Taranenko's even-dimensional decomposition conjecture for 1-polystochastic matrices

Let $\Omega_1(d,n)$ be the set of $1$-polystochastic $d$-dimensional matrices of order $n$, and let a $(d-1)$-permutation matrix be an element of the corresponding set of $(d-1)$-permutation matrices. Taranenko's decomposition conjecture. Every $1$-polystochastic matrix of even dimension can be represented as a non-negative linear combination of $(d-1)$-permutation matrices. The source reports no known counterexamples in even dimensions, so the conjecture remains open.