Non-Koszul ghost-term linkage conjecture for relatively compressed level algebras

Let $R=k[x_1,\ldots,x_n]$ and let ${\mathfrak c}\subset R$ be a general complete intersection with fixed generator degrees. Let $A=R/I$ be a relatively compressed level quotient of $R/{\mathfrak c}$ of socle degree at least $2$ and socle dimension $c\geq1$. Assume either $n=3$ and $c\geq2$, or $n\geq4$. Non-Koszul ghost-term linkage conjecture. If the minimal free resolution of $R/I$ has non-Koszul ghost terms, then $I$ is linked in two steps—first by ${\mathfrak c}$ and then by a predictable complete intersection—to an ideal containing at least two independent linear forms. The conjecture proposes that all non-Koszul ghost terms in the stated range arise through this linkage mechanism; the source gives examples with the asserted property but no proof in general.