Product formula conjecture for Kazhdan–Lusztig R-polynomials

Let $n\geq 2$, and let $e\leq \sigma_1\leq \sigma_2\leq \Omega_n$. For the Kazhdan–Lusztig $R$-polynomial $\widetilde{R}_{\sigma_1,\sigma_2}(q)$, write $F_j(q)$ for the $q$-Fibonacci polynomials used in the paper. Product formula conjecture. There exist integers $k$, $g(\sigma_1,\sigma_2)$, and $h_i(\sigma_1,\sigma_2)$, depending on $\sigma_1$ and $\sigma_2$, such that

$$\widetilde{R}_{\sigma_1,\sigma_2}(q)=q^{g(\sigma_1,\sigma_2)}\prod_{i=1}^{k}F_{h_i(\sigma_1,\sigma_2)}(q^{-2}).$$

The conjecture proposes that every polynomial in this interval factors, up to a power of $q$, into $q$-Fibonacci polynomials. It had been verified for $n\leq 9$ in the source, while the general case remains open.