Factorization conjecture for the Hilbert polynomial of ${\cal E}_n^0$

Let ${\cal E}_n^0$ be the quadratic algebra, let $Z_{n,k}$ be the sets of normal monomials defined in the paper, and write $H(A;t)$ for the Hilbert polynomial of a graded object $A$. Factorization property.

$$H({\cal E}_n^0;t)=H(Z_{n,2};t)H(Z_{n,3};t)\cdots H(Z_{n,n};t).$$

The factorization is motivated by the normal-monomial basis calculations carried out through degree six and would describe the full Hilbert polynomial from the factors associated with the sets $Z_{n,k}$. The source gives no resolution.