Singularity-free conjecture for torus one-point conformal blocks

Let $H^{(N)}_{\Delta}$ denote the contribution at order $N$ to the torus one-point conformal block, expressed in terms of the central charge $c$. Singularity-free conjecture. At each order $H^{(N)}_{\Delta}$, the poles in the central charge $c$ cancel between terms, and therefore a singularity-free expression exists. Explicit calculations establish this cancellation through orders $3$ and $4$; the conjecture asserts that it holds at every order.