Anstee–Sali conjecture on forbidden configuration growth

Let $F$ be a $k\times \ell$ matrix with $F\ne \begin{bmatrix}0\\ 1\end{bmatrix}$. Let $I_k$ be the $k\times k$ identity matrix, $I_k^c$ its (0,1)-complement, and $T_k$ the $k\times k$ upper triangular matrix whose $i$th column has 1's in rows $1,2,\ldots,i$. For matrices $A_1,\ldots,A_p$, let $A_1\times\cdots\times A_p$ be their product configuration formed by stacking one column from each factor in every possible combination. Define $\operatorname*{forb}(m,F)$ as the maximum number of columns in an $m$-rowed simple matrix avoiding $F$. Let $X(F)$ be the largest $p$ for which there are choices $A_1,A_2,\ldots,A_p\in\{I_{m/p},I^c_{m/p},T_{m/p}\}$ such that $F\nprec A_1\times A_2\times\cdots\times A_p$. Anstee–Sali conjecture. Then

$$\operatorname*{forb}(m,F)=\Theta(m^{X(F)}).$$

This conjecture predicts the precise polynomial order of the extremal function for every forbidden matrix other than the excluded two-row column. It is a central proposed framework for forbidden configuration problems, but the supplied source does not state whether it has been resolved in full.