JNS conjecture on eight tau functions for q-Painlevé VI

Let $\tau(\boldsymbol{\theta};\sigma,s|t)$ be the tau function defined from the five-dimensional Nekrasov partition function, and let $\boldsymbol{\theta}^{\uparrow}_k,\boldsymbol{\theta}^{\downarrow}_k$ be the eight parameter choices indexed by $k\in\{0,t,1,\infty\}$. JNS conjecture. The eight tau functions

$$\begin{aligned} &\tau^{\uparrow}_{\infty}=\tau(\boldsymbol{\theta}^{\uparrow}_{\infty};\sigma,s|t),\qquad \tau^{\downarrow}_{\infty}=\tau(\boldsymbol{\theta}^{\downarrow}_{\infty};\sigma,s|t),\\ &\tau^{\uparrow}_{0}=\tau(\boldsymbol{\theta}^{\uparrow}_{0};\sigma+1/2,s|t),\qquad \tau^{\downarrow}_{0}=\tau(\boldsymbol{\theta}^{\downarrow}_{0};\sigma-1/2,s|t),\\ &\tau^{\downarrow}_{1}=\tau(\boldsymbol{\theta}^{\downarrow}_{1};\sigma,s|q^{-1/2}t),\qquad \tau^{\uparrow}_{1}=\tau(\boldsymbol{\theta}^{\uparrow}_{1};\sigma,s|q^{-1/2}t),\\ &\tau^{\downarrow}_{t}=\tau(\boldsymbol{\theta}^{\downarrow}_{t};\sigma+1/2,s|q^{-1/2}t),\qquad \tau^{\uparrow}_{t}=\tau(\boldsymbol{\theta}^{\uparrow}_{t};\sigma-1/2,s|q^{-1/2}t) \end{aligned}$$

satisfy the $q$-Painlevé VI equation in tau form. This conjecture proposes a two-parameter family of general solutions, up to $q$-periodicity, for the second-order $q$-Painlevé VI equation; the supplied text gives no resolution status.