Mozgovoy's motivic ADHM formula for twisted Higgs-bundle moduli

Let $X$ be a smooth complex projective curve of genus $g\geq 2$, let $L$ be a line bundle on $X$ with $\deg(L)=2g-2+p$ for $p>0$, and let $r$ and $d$ be coprime positive integers. Write $\mathcal{M}_L(X,r,d)$ for the moduli space of semistable $L$-twisted Higgs bundles on $X$ of rank $r$ and degree $d$. For each integer $n\geq 1$, define

$$\mathcal{H}_n(t)=\sum_{\lambda\in\mathcal{P}(n)}\prod_{s\in d(\lambda)}(-t^{a(s)-l(s)}\mathbb{L}^{a(s)})^p t^{(1-g)(2l(s)+1)}Z_X(t^{h(s)}\mathbb{L}^{a(s)}),$$

where $\mathcal{P}(n)$ is the set of ordered partitions of $n$, $d(\lambda)$ is the set of boxes of the partition, $a(s)$ and $l(s)$ are its arm and leg lengths, and $h(s)=a(s)+l(s)+1$. Define $H_r(t)$ by

$$\sum_{r\geq 1}H_r(t)T^r=(1-t)(1-\mathbb{L}t)\sum_{j\geq 1}\sum_{k\geq 1}\frac{(-1)^{k+1}\mu(j)}{jk}\left(\sum_{n\geq 1}\psi_j[\mathcal{H}_n(t)]T^{jn}\right)^k.$$

Mozgovoy's motivic ADHM conjecture. For every $r\geq 1$, $H_r(t)$ is a polynomial in $t$ and

$$[\mathcal{M}_L(X,r,d)]=M_{g,r,p}^{\operatorname{ADHM}}:=(-1)^{pr}\mathbb{L}^{r^2(g-1)+p\frac{r(r+1)}{2}}H_r(1).$$

This formula is a conjectural solution to the motivic ADHM recursion and predicts the motive of the moduli space of coprime-rank-and-degree twisted Higgs bundles. The source attributes the conjecture to Mozgovoy; no resolution status is supplied.