The square determinantal-ring F-threshold conjecture

Let $R=S/I_t(X)$ be the determinantal ring associated with an $n\times n$ matrix of indeterminates, and let $c^{\mathfrak{m}}(\mathfrak{m})$ denote the F-threshold of its homogeneous maximal ideal. Square determinantal-ring F-threshold conjecture. If $n=m=t$, then

$$c^{\mathfrak{m}}(\mathfrak{m})=n(n-1).$$

The formula is proved in the paper when $n=3,4$, while the conjecture concerns the remaining square maximal-minor cases.