Equivariant DT descendent series Frankenstein algebra conjecture

Let $X$ be a nonsingular projective toric 3-fold equipped with an action of the 3-dimensional torus $\mathsf{T}$. Let $H_{\mathsf{T}}(\bullet)=\mathbb{C}[s_1,s_2,s_3]$, and let $\mathfrak{Fr}$ be the algebra generated by the series

$$F_{2k+1}(-q)=\sum_{n=0}^{\infty}(-q)^n\sum_{d\mid n}d^{2k},\qquad k\geq 1,$$

and their iterated $q\frac{d}{dq}$ derivatives.

Equivariant DT descendent algebra conjecture. For $\gamma_i\in H^*_{\mathsf{T}}(X,\mathbb{C})$ and $\beta\in H_2(X,\mathbb{Z})$,

$$\big\langle \operatorname{ch}_{k_1}(\gamma_1)\dots \operatorname{ch}_{k_l}(\gamma_l)\big\rangle^{\mathsf{DT},\mathsf{T}}_\beta\in H^*_{\mathsf{T}}(\bullet)\otimes\mathbb{Q}(q)\otimes\mathfrak{Fr}.$$

The conjecture proposes an algebraic description of equivariant DT descendent series based on computer experiments. The source identifies the analytic behavior of these series as a major unresolved question.