AGT conjecture for genus-one Liouville conformal blocks

Let $\boldsymbol a_i=(a_i,-a_i)$ for $1\leq i\leq N$. The Liouville conformal block is

$$\mathcal{B}(c,\tilde{k},\tilde{h},\tilde{q})=\operatorname{Tr} q^d V^{h_N}_{k_1,k_N}(x_N)\cdots V^{h_2}_{k_3,k_2}(x_2)V^{h_1}_{k_2,k_1}(x_1),$$

with $q=x_1=q_1\cdots q_N$ and $x_i x_{i+1}^{-1}=q_{i+1}$. Define

$$\Delta_{m,n}=\frac{m(t_1+t_2-n)}{t_1t_2}.$$

AGT conjecture. One has

$$Z(t_1,t_2,\tilde{\boldsymbol a},\tilde{m},\tilde{q})=Z'(t_1,t_2,\tilde{m},\tilde{q})\mathcal{B}(c,\tilde{k},\tilde{h},\tilde{q}),$$

under the substitution

$$c=1+6\frac{(t_1+t_2)^2}{t_1t_2},\qquad k_i=\frac{(t_1+t_2)^2-4a_i^2}{4t_1t_2},\qquad h_i=\Delta_{m_i,m_i},$$

where

$$Z'=(q;q)_\infty^{2\Delta_{m_1,m_1}+\cdots+2\Delta_{m_N,m_N}-1}\prod_{i<j}(x_i x_j^{-1};q)_\infty^{2\Delta_{m_i,m_j}}(x_i^{-1}x_jq;q)_\infty^{2\Delta_{m_j,m_i}},$$

and $(x;q)_\infty=\prod_{i\geq0}(1-xq^i)$. This is the proposed relation between Nekrasov partition functions and Liouville conformal blocks for a genus-one Riemann surface with $N$ punctures; the parser supplies no evidence resolving it.