Regularity characterization conjecture for correctable patterns in tensor-product topologies

Consider the topology $T_{m\times n}(a,b,0)$ and an erasure pattern $E\subseteq [m]\times[n]$. For all $U\subseteq [m]$ and $V\subseteq [n]$, write $|U|=u$ and $|V|=v$. The pattern $E$ is regular if

$$|E\cap (U\times V)|\leq va+ub-ab.$$

Regularity characterization conjecture. An erasure pattern $E$ is correctable for $T_{m\times n}(a,b,0)$ if and only if it is regular.

Regularity is known to be necessary for correctability, while the source states that sufficiency is proved in the setting where $a=1$; the general characterization remains open.