The manifold g-conjecture for h-prime vectors

Let $\Delta$ be a homology manifold, let $h'_i$ denote its h-prime vector, and let $\beta_{i-1}$ denote its $(i-1)$st Betti number. Manifold g-conjecture. For every $i\ge\lceil d/2\rceil$,

$$h'_i\ge h'_{i+1}+\binom{d-1}{i}\beta_{i-1}.$$

This conjecture is the numerical consequence suggested by the manifold algebraic g-conjecture and would impose lower bounds on the h-prime vector in terms of topology. The source presents it as open.