Saks-West conjecture on semiantichains and unichain coverings

Let $P$ and $Q$ be posets. A unichain in $P\times Q$ is a chain of the form $\{p\}\times C'$ or $C\times\{q\}$, where $C$ and $C'$ are chains in $P$ and $Q$, respectively. A semiantichain is a subset $S\subseteq P\times Q$ such that no two distinct elements of $S$ are contained in a unichain.

Saks-West conjecture. In every product $P\times Q$ of two posets, the size of a largest semiantichain equals the size of a smallest unichain covering.

This conjecture generalizes the Greene–Kleitman theorem and its equivalent formulation for products of a chain with a poset. It proposes a min–max relation between semiantichains and unichain coverings for arbitrary products of two posets; the supplied source does not indicate whether it has been resolved.