Equality of degrees conjecture for Kazhdan–Lusztig and inverse Kazhdan–Lusztig polynomials

Let $M$ be a matroid, and let $P_M(t)$ and $Q_M(t)$ denote its Kazhdan–Lusztig and inverse Kazhdan–Lusztig polynomials, respectively. Degree equality conjecture. For any matroid $M$,

$$\deg P_M(t)=\deg Q_M(t).$$

This conjecture is motivated by a known equality of the top coefficients for matroids of odd rank, where it is equivalent to equality of the maximal possible degree; the source notes that the corresponding coefficient statement fails in even rank. The proposed equality for all matroids remains open.