The spanning conjecture for graded pieces of the arrangement quotient

Let $Q$ be a generic central hyperplane arrangement of degree $k$ in $n$ variables, let $R_n$ be the graded ring used in the paper, let $E$ denote the Euler operator, and let $U$ be the relevant graded vector space quotient. Write $(R_n/(E+(Q-1)))_r$ and $U_r$ for their degree-$r$ pieces. For $k eleq r eleq 2k-n-2$, consider the expressions in the paper's generating family indexed by $i_1$.

Spanning conjecture. If $k eleq r eleq 2k-n-2$, then $(R_n/(E+(Q-1)))_r$ is spanned by the expressions in the generating family for which $i_1<(n-1)+(r-k)$; if $k-n<r<k$, the expressions in the stated proposition span $U$; and if $r eleq k-n$, then $U_r=(R_n)_r$.