The Polynomial inverse conjecture for the $U^3$ norm over $\mathbb{F}_2^n$

Let $f:\mathbb{F}_2^n\to\mathbb{C}$ be a $K$-approximate quadratic, meaning that $f$ has large $U^3$ norm in the sense used in the paper. A quadratic phase is a function of the form $(-1)^\psi$, where $\psi$ is a quadratic polynomial. Polynomial inverse conjecture for the $U^3$ norm over $\mathbb{F}_2^n$. The function $f$ $K^{-C}$-correlates with a quadratic phase $(-1)^\psi$. This is one of the polynomial inverse conjectures for the $U^3$ Gowers norm; the source gives no resolution evidence.