BBDVW conjectural recurrence for Kazhdan–Lusztig polynomials

Let $[u,v]\subset S_n$ be a Bruhat interval, let $I$ be a hypercube decomposition of $[u,v]$, and let $\ell(u,v)$ denote the length of the interval. The polynomials $N_{u,v,I}$ and $Q_{u,v,I}$ are the polynomials defined from Kazhdan–Lusztig polynomials of smaller subintervals in the BBDVW construction. BBDVW conjecture. For any hypercube decomposition $I$ of $[u,v]\subset S_n$,

$$q^{\ell(u,v)}P_{u,v}(q^{-1})-P_{u,v}(q)=N_{u,v,I}+Q_{u,v,I}.$$

This is a conjectural recurrence intended to use only the poset structure of the interval, and would provide a major step toward the combinatorial invariance conjecture. The source describes the formula as conjectural; its resolution is not specified here.