De Loera's determinantal refinement of Kahn's conjecture

Let $M_{d,d}$ be the generic $d\times d$ matrix over a field $k$, and let $I$ be the ideal of $d\times d$ permanents of the $d\times2d$ matrix $(M_{d,d}\mid M_{d,d})$. De Loera's refinement of Kahn's conjecture. One has

$$(\det M_{d,d})^d\in I.$$

This is presented as a refinement of Kahn's conjecture and, according to the surrounding text, it implies Kahn's result set-theoretically. The supplied text gives no resolution status.