Qi Chen's Gram determinant conjecture for the Möbius band

Let $R=\mathbb{Z}[A^{\pm1},w,x,y,z]$. For $n\geq1$, let $D_n^{\mathit{Mb}}(d,w,x,y,z)$ be the Gram determinant of type $\mathit{Mb}$. Let $T_k$ and $S_k$ denote the Chebyshev polynomials used in the source, and let $D_{n,i}$ encode the contribution from diagrams with $i$ curves passing through the crosscap. Qi Chen's conjecture. For $n\geq1$,

$$D^{\mathit{Mb}}_n(d,w,x,y,z)=\prod_{k=1}^n\left(T_k(d)+(-1)^kz\right)^{\binom{2n}{n-k}} \prod_{\substack{k=1\\ k\text{ odd}}}^n\left(\left(T_k(d)-(-1)^kz\right)T_k(w)-2xy\right)^{\binom{2n}{n-k}}$$ $$\cdot\prod_{\substack{k=1\\ k\text{ even}}}^n\left(\left(T_k(d)-(-1)^kz\right)T_k(w)-2(2-z)\right)^{\binom{2n}{n-k}}\prod_{i=1}^nD_{n,i},$$

where

$$D_{n,i}=\prod_{k=1+i}^n\left((d^2-4)(S_{k-1}(d))^{2\binom{2n}{n-k}}\right),$$

and $i$ represents the number of curves passing through the crosscap. The displayed formula is given as a future-direction conjecture and is described as a restatement associated with Qi Chen.