No-ghost-term conjecture for equal-degree complete intersections

Let $R=k[x_1,\ldots,x_n]$ and let ${\mathfrak c}\subset R$ be a complete intersection generated by forms all of the same degree. Let $A$ be a relatively compressed level Artinian quotient of $R/{\mathfrak c}$ with socle dimension $c$ and socle degree at least $2$. Assume either $n=3$ and $c\geq2$, or $n\geq4$. No-ghost-term conjecture. The minimal free resolution of $A$ has no ghost terms, Koszul or otherwise. This is a stronger proposed conclusion in the equal-degree case and is stated without a resolution in the source.