Veech's conjecture on the Pinsker-factor criterion for Sarnak's conjecture

Let $(Z,\mathcal{D},\kappa,R)$ be a measure-theoretic dynamical system, let $\Pi(\kappa)$ denote its Pinsker factor, let $\boldsymbol{\mu}$ be the arithmetic function under consideration, let $V_S(\boldsymbol{\mu})$ be the family of Furstenberg systems associated with $\boldsymbol{\mu}$, and let $\pi_0$ denote the corresponding function in each Furstenberg system. Sarnak's conjecture is the assertion that $\boldsymbol{\mu}\perp \mathscr{C}_{\rm ZE}$, where $\mathscr{C}_{\rm ZE}$ is the class of topological systems of zero entropy.

Veech's conjecture. Condition $\pi_0\perp L^2(\Pi(\kappa))$ for each Furstenberg system $\kappa\in V_S(\boldsymbol{\mu})$ is equivalent to Sarnak's conjecture.

Veech's conjecture gives a necessary-and-sufficient Pinsker-factor characterization of Sarnak's conjecture; the supplied text does not state whether it has been resolved.