The elliptic Omnibus Conjecture

A simply-connected topological space $X$ of finite type is rationally elliptic when its rational cohomology and rational homotopy are both finite dimensional. Elliptic Omnibus Conjecture. Every simply-connected topological space of finite type with finite dimensional rational homotopy and finite dimensional even-degree rational cohomology is rationally elliptic. This is a stronger version of the Omnibus Conjecture, and the counterexamples discussed in the paper do not apply because they have infinite dimensional rational homotopy; the source does not state a resolution of this elliptic version.