Yuzvinsky's uniqueness conjecture for $(4,d)$-multinets

Let a hyperplane arrangement be given, and let a $(4,d)$-multinet be a multinet with four classes and degree $d$. Yuzvinsky's uniqueness conjecture. The only $(4,d)$-multinet on a hyperplane arrangement is the $(4,3)$-net on the Hessian arrangement. Only the $(4,3)$-net on the Hessian arrangement is known, while the asserted uniqueness remains open.