Asymptotic product formula conjecture for refined BPS invariants of local $\mathbb{P}^2$

Consider the generating series

$$F_{d,\mathrm{BPS}}(q,t)=\sum_{i,j}n_d^{i,j}q^it^j.$$

Set

$$H(q,t)={\mathsf{S}}^\bullet\left(\frac{q^2+t^2+q^2t^2}{1-qt}\right)=\prod_{i\geq 0}\frac{1}{(1-(qt)^iq^2)(1-(qt)^iq^2t^2)(1-(qt)^it^2)},$$

where $\mathsf{S}^\bullet$ denotes the plethystic exponential, and let $[H(q,t)]^{i,j}$ denote the coefficient of $q^it^j$ in the expansion at $q,t\to 0$. Asymptotic product formula conjecture. For $i+j\leq 2d-4$, one has

$$n_d^{i,j}=[H(q,t)]^{i,j}.$$

This predicts that the refined BPS invariants defined via the perverse filtration agree, in the indicated range, with the coefficients of a universal plethystic product. The source presents this as a conjectural asymptotic formula arising from the Okounkov--Nekrasov proposal and a combinatorial algorithm; its resolution status is not specified.