Circumscribability conjecture for neighborly polytopes

A polytope is neighborly if every set of at most half the dimension's vertices forms a face, and a polytope is circumscribable if it has a realization whose facets are tangent to a common sphere. The source shows that cyclic polytopes with sufficiently many vertices are not circumscribable. The neighborly-polytope circumscribability conjecture. Neighborly polytopes with sufficiently many vertices are not circumscribable. This extends the observed obstruction for cyclic polytopes to all neighborly polytopes; the claim is presented as an open conjecture.