Existence of Tychonoff spaces separating successive diagonal ranks

A rank $n$-diagonal is a diagonal satisfying the rank-$n$ condition described in the surrounding theory. Diagonal-rank separation conjecture. For every natural number $n$ there is a Tychonoff space $X_n$ with a rank $n$-diagonal that is not a rank $n+1$-diagonal. This asks whether each successive diagonal-rank level is genuinely distinct; the supplied text gives no resolution, so the problem remains open.