The weak Polynomial inverse conjecture for the $U^3$ norm over $\mathbb{Z}/N\mathbb{Z}$

Let $f:\mathbb{Z}/N\mathbb{Z}\to\mathbb{C}$ be a $K$-approximate quadratic. An elementary $2$-step nilsequence is a sequence $F(g^nx_0)$, where $F:G/\Gamma\to\mathbb{C}$ is Lipschitz, $g\in G$, $x_0\in G/\Gamma$, and $G/\Gamma$ is an elementary $2$-step nilsystem. Weak Polynomial inverse conjecture for the $U^3$ norm over $\mathbb{Z}/N\mathbb{Z}$. The function $f$ $\exp(-K^{o(1)})$-correlates with an elementary $2$-step nilsequence $F(g^nx_0)$, where $F$ is Lipschitz of order at most $\exp(K^{o(1)})$ and the nilsystem has dimension at most $K^{o(1)}$. This is the weak polynomial counterpart of the known inverse theorem for the $U^3$ norm over cyclic groups; the source gives no resolution evidence.