The determinantal-ring conjecture on n-sem dualizing modules

Let $X$ be an $m \times n$ matrix of indeterminates over a field $\mathsf{k}$, and let $R=R_t(X)$ be the determinantal ring associated to the ideal of $t\times t$ minors, where $t\leqslant\min(m,n)$. Let $\operatorname{Cl}(R)$ denote the divisor class group, and let $\mathfrak{S}_0^i(R)$ denote the isomorphism classes of exactly $i$-semidualizing modules.

The determinantal-ring conjecture. If $0\neq[M]\in\operatorname{Cl}(R)$, then $M$ is exactly $(m+n-2t+1)$-semidualizing. Hence

$$\mathfrak{S}_0^{m+n-2t+1}(R)=\operatorname{Cl}(R).$$

In particular, if $t=2$ and $d=\dim R=m+n-1$, then

$$\mathfrak{S}_0^{d-2}(R)=\operatorname{Cl}(R).$$

This extends the paper's results on semidualizing modules over determinantal rings and predicts that all nonzero divisor-class-group elements arise at the indicated semidualizing level. The supplied text does not establish the general assertion or provide a resolution status beyond identifying it as a conjecture.