The algebraic H-conjecture for elliptic Sullivan minimal algebras

Let $(\Lambda V,d)$ be an elliptic Sullivan minimal algebra, so its cohomology and generating graded vector space are finite-dimensional. The algebraic H-conjecture. One has

$$\dim H(\Lambda V,d)\geq \dim V.$$

This is the Sullivan-model formulation of Hilali's conjecture. The paper notes that it has been resolved for several classes, while the general statement remains open.