The Gowers norm additive uncertainty conjecture

Let $N,d$ be positive integers, let $f:\mathbb{Z}_N^d\to\mathbb{C}$ be a signal with support $E$ and Fourier support $\Sigma$, and let $\|\cdot\|_{U^k}$ denote the Gowers $U^k$ norm for $k\geq 2$. Gowers norm additive uncertainty conjecture. One should have

$$1\leq |E|\cdot\|1_\Sigma\|_{U^k}^{2^k/(k+1)}.$$

This extends the additive energy uncertainty principle from the $U^2$ norm to higher Gowers norms. The source presents it as a direction for future research and gives no resolution.