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on Tableaux problem 50

The statement

50.[Stan2012a]*Exer. 3.51(a) soln.[Wor2026e] [Stan2012a] shows that there exists exactly one distributive, $d$ -differential lattice for any positive integer $d$ . That analysis easily generalizes to an analysis of weighted differential distributive lattices, and when we constrain the differential degree and the weights to be positive integers, it can be used to demonstrate non-trivial constraints on possible lattices. Can this technique be extended to prove all of the “strong” hypotheses of the classification in [Wor2026b] to create a classification of all positive-weight differential distributive lattices with $\hat{0}$ ?

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.