Crucial–Lundqvist–Nevo lattice-path conjecture for two generic forms in an exterior algebra

Let $V$ be a $k$-vector space of dimension $n$, and let $\Lambda(V)$ be its exterior algebra. Let $f$ and $g$ be generic forms in $\Lambda(V)$. For each $s$, let $a(n,s)$ be the number of lattice paths inside the rectangle $(n+2-2s)\times(n+2)$ from the bottom-left corner to the top-right corner, using steps

$$(x,y)\longmapsto(x+1,y+1)\quad\text{or}\quad(x,y)\longmapsto(x-1,y+1).$$

Crucial–Lundqvist–Nevo conjecture. The Hilbert series of $\Lambda(V)/(f,g)$ is

$$1+a(n,1)t+a(n,2)t^2+\cdots+a(n,s)t^s+\cdots.$$

The conjecture gives a combinatorial description of the Hilbert series for quotients of an exterior algebra by two generic forms. The source provides no resolution status.