Shellability conjecture for intervals in the second class of level Eulerian posets

A level Eulerian poset is the poset from Section~; for each interval in this poset, consider its order complex.

Shellability conjecture. The intervals in the level Eulerian poset from Section~ are shellable, and hence their order complexes are homeomorphic to spheres.

This conjecture proposes that the second class of level Eulerian posets has the same spherical topological behavior established for the first class, despite the failure of the method used there to prove shellability.