Nakajima's geometric formula conjecture for the t-analogue of q-characters

Let $M=M_P$ be a standard module, let $Q/R$ be an $l$-weight of $M$, and let $M(Q/R)$ be the corresponding $l$-weight space. Define a filtration on $M(Q/R)$ by

$$0=M^{-1}(Q/R)\subset M^0(Q/R)\subset M^1(Q/R)\subset\cdots,$$

where

$$M^n(Q/R)=\bigcap_k\operatorname{Ker}\left(\psi_k^\pm(z)-\Psi_k^\pm(z)\operatorname{id}\right)^{n+1}.$$

Let $d(Q/R,P)$ be the integer determined explicitly from $Q/R$ and $P$ by the dimension formula, and let $m_{Q/R}$ be the monomial in $Y_{k,a}^{\pm}$ corresponding to the $l$-weight space $M(Q/R)$. Nakajima's geometric formula conjecture. The geometrically defined $t$-analogue of the $q$-character satisfies

$$\chi_{q,t}(M_P)=\sum_{Q/R}\sum_n t^{2n-d(Q/R,P)}\mathop{\text{\rm dim}}\nolimits\left(M^n(Q/R)/M^{n-1}(Q/R)\right)m_{Q/R}.$$

This conjectural formula proposes an algebraic description of the geometric $t$-analogue of the $q$-character using the filtration on each $l$-weight space. The source presents it as an alternative definition and does not provide evidence of a resolution here.