The monomial almost-complete-intersection Rees algebra conjecture

Let $I$ be a monomial ideal of $k[x_1,\ldots,x_n]$. Suppose that $I$ is an almost complete intersection of finite colength, meaning that it has finite colength and one more minimal generator than its height. Its Rees algebra is denoted by $\mathbf R[It]$. Monomial Rees algebra conjecture. The Rees algebra

$$\mathbf R[It]$$

is almost Cohen–Macaulay. The statement is motivated by the preceding verified examples, including the ideals $I(n,n,n,1,1,1)$ and the higher-dimensional case discussed in the remark; its general validity for all monomial almost complete intersections of finite colength is not established in the supplied text.