The facet lower-bound conjecture for k-neighborly polytopes

Let $P$ be a $d$-dimensional convex polytope, and let $f_i(P)$ denote the number of its $i$-dimensional faces. A polytope is $k$-neighborly if every subset of $k$ vertices is the vertex set of a face; here $k\geq 2$. Facet lower-bound conjecture. The number of facets satisfies

$$f_{d-1}(P)\geq f_0(P).$$

This proposes a lower bound for the facets of neighborly polytopes, complementing known face-number bounds for simplicial polytopes. The source does not provide evidence of resolution, so the conjecture is recorded as open.