8 problems

Kashaev–Luo–Vartanov partition-function conjecture. The partition function of the Kashaev–Luo–Vartanov model is conjectured to satisfy

Faddeev's conjecture. The constant part of the inversion factor on the right-hand side, namely $\exp\left(-\frac{\mathsf i\pi}{12}(\lambda^2+\lambda^{-2})\right)$, is related to th…

Let $t\in\mathbb{C}^{\times}$ satisfy $\operatorname{Im}(t)>0$. Let $\mathcal{X}_{\beta^{\vee}}(t,\lambda)$ be the specified convergent expression for the conformal limit of the tw…

Modular-product q-series conjecture. After setting $y_1=y_2=1$ in the charge-refined identity, the following identity holds:

Charge-refined q-series conjecture. The following identity holds:

Let $P$, $Q$, and $V$ be as in Lem.. The octagon equation of the non-compact quantum dilogarithm. … This identity is presented as the equation corresponding to Fock–Goncharov's…

Let $P$, $Q$, and $V$ be as in Lem.. The hexagon equation of the non-compact quantum dilogarithm. … This identity is presented as the equation corresponding to Fock–Goncharov's…

Let $P$, $Q$, and $V$ be as in Lemma cited in the source. The octagon equation. … This identity is the operator relation corresponding to Fock–Goncharov's $G_2$-type identity; the…