The two-colored Jones-Wenzl projector existence conjecture

Let $(W,S)$ be a two-colored realization over a field $\Bbbk$, with colors $s$ and $t$, and let $JW_{n_s}$ and $JW_{n_t}$ denote the corresponding Jones-Wenzl projectors. Write ${n \brack k}_s$ and ${n \brack k}_t$ for the two-colored quantum binomial coefficients associated with the colors $s$ and $t$. Jones-Wenzl projector existence conjecture. The Jones-Wenzl projectors $JW_{n_s}$ and $JW_{n_t}$ exist over $\Bbbk$ if and only if ${n \brack k}_s$ and ${n \brack k}_t$ are invertible in $\Bbbk$ for all $1\leq k\leq n$. This conjecture revises an earlier claim that the criterion was a theorem; the ordinary uncolored analogue is known, but the two-colored case is left open.