Classification conjecture for Furstenberg systems of non-pretentious multiplicative functions

Let $f:\mathbb{N}\to\{-1,0,+1\}$ be a non-pretentious multiplicative function. Write $1_{f(n)=0}$ for the multiplicative function that equals $1$ when $f(n)=0$ and $0$ otherwise. Classification conjecture. The function $f$ has a unique Furstenberg system, isomorphic to the direct product of the Furstenberg system of the pretentious function $1_{f(n)=0}$ and a Bernoulli system. This conjecture is supported in the paper by showing that it follows from the stated alternative Elliott conjecture; the supplied text gives no resolution status.