The rank-$n$ conformal-block conjecture for multi-leg PT vertices

Let $n$ be the rank of the gauge-origami construction, and let the conformal blocks

$$and$$

be the blocks defined in the source. The corresponding multi-leg Pandharipande–Thomas (PT) vertices impose boundary conditions in multiple directions of $\mathbb{C}^3$ and $\mathbb{C}^4$. Rank-$n$ multi-leg PT vertex conjecture. The conformal blocks

$$and$$

are the rank-$n$ multi-leg PT vertex of $\mathbb{C}^3$ and $\mathbb{C}^4$. From the geometric viewpoint, the relevant conformal block is identified with the fully generic origami vertex function in $\mathbb{C}^4$; the general identification with the rank-$n$ multi-leg PT vertices remains conjectural.