Okada's $(q,t)$-hook formula conjecture for connected $d$-complete posets

Let $P$ be a connected $d$-complete poset with maximum element $v_0$, rank function $r:P\to\mathbb{N}$, top tree $T$, and $d$-complete coloring $c:P\to T$. Let $\widehat P=P\sqcup\{\widehat1\}$ be obtained by adjoining a maximum element $\widehat1$ covering $v_0$, with extended coloring $\widehat c:\widehat P\to T\sqcup\{\widehat1\}$. For a $P$-partition $\pi\in\mathrsfs{A}(P)$, let $\widehat\pi$ extend $\pi$ by $\widehat\pi(\widehat1)=0$, and define $W_P(\pi;q,t)$ by

$$W_{P}(\pi;q,t) =\frac{\displaystyle \prod_{{x,y\in\widehat P}\atop{x<y,\ \widehat c(x)\sim \widehat c(y)}} f(\pi(x)-\pi(y);d(x,y)) }{\displaystyle \prod_{{x,y\in P}\atop{x<y,\ c(x)=c(y)}} f(\pi(x)-\pi(y);e(x, y)) f(\pi(x)-\pi(y);e(x, y)-1) },$$

where $d(x,y)=(r(y)-r(x)-1)/2$ and $e(x,y)=(r(y)-r(x))/2$. Here $\widehat c(x)\sim\widehat c(y)$ means that the colors are adjacent in the top tree. Okada's $(q,t)$-hook formula conjecture. Using these notations,

$$\sum_{\pi\in{\mathrsfs{A}}(P)} W_{P}(\pi;q,t)z^{\pi} =F\left(z[H_{p}];q,t\right).$$

This conjecture proposes a generating-function identity for weighted $P$-partitions of connected $d$-complete posets, extending the role of hook formulas in the theory of $P$-partitions. The supplied text gives no evidence of resolution, so its status remains open.