The TM-MDS conjecture on generic nonsingularity

Let $M$ be an $m\times n$ binary matrix satisfying the MDS condition. Let $N=\{\alpha_1,\dots,\alpha_n\}$ be independent indeterminates, let $V=V(N)$ be a generic $m\times n$ Vandermonde matrix with parameters $\alpha_1,\dots,\alpha_n$, and let $T=T(M,N)$ be a generic $m\times m$ transformation matrix such that $TV$ fits $M$. A matrix is generically singular when its determinant, viewed as a multivariate polynomial in $\alpha_1,\dots,\alpha_n$, is identically zero. TM-MDS conjecture. If $M$ satisfies the MDS condition, then $T(M,N)$ is not generically singular. The conjecture is equivalent to the GM-MDS conjecture through generalized Reed--Solomon constructions, but was open in the source.