Möbius uniqueness conjecture for edge-scribable polytopes

Let $d\ge 2$ and let $P$ be an edge-scribable $(d+1)$-polytope. A polytope is Möbius unique if its edge-scribed realizations are equivalent under Möbius transformations. Möbius uniqueness conjecture. Every edge-scribable $(d+1)$-polytope is Möbius unique. The statement extends the known results that every $(d+1)$-simplex is Möbius unique and that every polyhedron is Möbius unique. The source notes that in dimension $4$ it was not known whether there are edge-scribable $4$-polytopes that are not Möbius unique.