Nonnegativity conjecture for Hilbert coefficients of quadratic algebras

Let $S_n=k[x_1,\ldots,x_n]$ and let $I$ be a graded ideal such that $S_n/I$ is Artinian and $I$ is generated by quadratic forms. The Hilbert coefficients $e_i(I)$ are defined by the eventual polynomial expression for $l(S_n/I^s)$ in the binomial basis.

Nonnegativity conjecture. If $S_n/I$ is a quadratic algebra, then $e_i(I)\ge0$ for all $i$.

The conjecture proposes a uniform positivity property for Hilbert coefficients in the quadratic Artinian setting; no resolution is supplied in the source.