Möbius orthogonality conjecture for nilsequences

Let $G/\Gamma$ be a $k$-step nilmanifold, let $T_g(x\Gamma)=xg\Gamma$, and let $(F(T_g^n\cdot x))_{n\in\mathbb{N}}$ be a $k$-step nilsequence. The Möbius orthogonality conjecture for nilsequences. For every $A>0$,

$$\mathbb{E}_{n\leqslant N}\mu(n)F(T_g^n\cdot x)\ll_{A,G/\Gamma,F}\log^{-A}N.$$

This is a quantitative form of Möbius disjointness from nilsequences and is proposed as a reduction step in the Hardy–Littlewood method. The supplied text gives no resolution status, so it is recorded as open.