Uniform rationality conjecture for totally negative quiver jet-counts

Let $Q$ be a quiver and let $\mathbf{d}\in\mathbb{Z}_{\geq0}^{Q_{0}}\setminus\{0\}$ such that $(Q,\mathbf{d})$ has property (P). Let $\mu_{Q,\mathbf{d}}$ be the corresponding moment map. Uniform rationality conjecture. There exists a rational fraction $W\in\mathbb{Q}(T)$ such that, for almost all primes $p$ and every finite field $\mathbb{F}_{q}$ of characteristic $p$,

$$W(q)=\lim_{n\to+\infty}q^{-n\dim\mu_{Q,\mathbf{d}}^{-1}(0)}\#\mu_{Q,\mathbf{d}}^{-1}(0)(\mathbb{F}_{q}[t]/(t^{n})).$$

The preceding result establishes convergence for totally negative quivers, while the conjecture asks for a single rational function governing the limit uniformly over finite fields; the source notes that this is known when $\mathbf{d}=\underline{1}$.