Binomial basis conjecture for #P closure properties

Let $\varphi$ be a multivariate polynomial closure property of $\#P$, meaning that applying $\varphi$ to polynomially many $\#P$ functions yields a function in the indicated class. A closure property relativizes if the corresponding closure holds for every oracle version $\#P^A$. Binomial basis conjecture. Every polynomial closure property of $\#P$ relativizes. Equivalently, the polynomial closure properties of $\#P$ are exactly the binomial-good polynomials, namely those whose expression over the binomial basis has only nonnegative integer coefficients. The binomial basis theorem proves the analogous classification for $\operatorname{GapP}$ and $\operatorname{GapP}_{\geq 0}$, while the $\#P$ case is conjectured and would classify all polynomial closure properties of $\#P$.