Equiconstitution conjecture for the Toda–Uehara tilting generator

Let $T^*\operatorname{Gr}(2,4)$ be the cotangent bundle of the Grassmannian of $2$-planes in a $4$-dimensional vector space, and let $\mathcal{Z}$ be the tilting generator constructed in the paper. A Toda–Uehara tilting generator means any tilting generator obtained from the Toda–Uehara construction; generators in this class may differ in the multiplicities of their indecomposable summands, while their indecomposable summands are fixed.

Equiconstitution conjecture. The tilting generator $\mathcal{Z}$ is equiconstituted with any Toda–Uehara tilting generator.

The Toda–Uehara construction gives a more implicit, noncanonical class of tilting generators. The authors have not been able to prove or disprove the equivalence of their construction with this class, but they show that the two constructions have a large summand in common.