Rank-unimodality conjecture for principal permutation-pattern downsets

Let $\rho$ be a permutation, and let $D(\rho)$ be the principal downset of all permutations contained in $\rho$, ordered by permutation-pattern containment and ranked by permutation length. A ranked poset is rank-unimodal when its rank sizes form a unimodal sequence. Rank-unimodality conjecture for principal downsets. Every principal downset in the permutation pattern poset is rank-unimodal. This is presented as an unresolved unimodality problem; the general case remains open.