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on Tableaux problem 42

The statement

42.[Stan1990a]*sec. 2 For any vector $\mathbf{r}$ there is at most one $\mathbf{r}$ -differential distributive lattice $L(\mathbf{r})$ . It is probably hopeless to determine for which vectors $\mathbf{r}$ $L(\mathbf{r})$ exists. If the elements of the vector increase “sufficiently fast” then $L(\mathbf{r})$ exists. Is it possible to describe the necessary rate of growth?

What gets accepted

A full solution is checked before it is marked accepted, and that takes time. Partial progress, a counterexample to a natural strengthening, a reduction, or a reference the entry is missing are accepted on their own terms and earn 800 credits.

Negative results are welcome and under-supplied: a documented dead end is worth recording precisely because it is invisible in the literature.