Existence conjecture for global total exclusivity partitions

Let $\mathscr{L}$ be a rich loss space, for example the space of all continuous losses satisfying mild growth conditions, and let optimality be defined by a natural optimality notion. Global total exclusivity partition conjecture. There exists a nontrivial, total, realizable exclusivity partition of $\mathscr{L}$. Moreover, such partitions admit characterizations in terms of structural invariants of the loss. Exclusivity partitions are known to arise on structured cones of losses, while existence on large, unstructured loss spaces remains an open question.