Finiteness conjecture for Forman–Ricci-positive 5-polytopes

Let $P$ be a polytope, and call it Forman–Ricci-positive when its Forman–Ricci curvature satisfies $\kappa_F(e)>0$ for every edge $e$. Finiteness conjecture for Forman–Ricci-positive 5-polytopes. There are finitely many Forman–Ricci-positive $5$-polytopes.

The statement is a restatement of the conjecture posed after the preceding finiteness theorem for simplicial $5$-polytopes; it is intended to extend finiteness to all $5$-dimensional polytopes. The source gives no resolution status.