Ball conjecture for projective multiaffine real stable polynomial spaces

Let $\mathbb{P}\underline{\mathrm{S}}^d_n$ be the projective space of all multiaffine homogeneous real stable polynomials of degree $d$ in $n$ variables. Ball conjecture. The space $\mathbb{P}\underline{\mathrm{S}}^d_n$ is homeomorphic to a closed Euclidean ball. The supplied text does not state whether this claim is resolved or remains open, and does not provide further context about its status.