Glazyrin–Karasev–Polyanskii polynomial plank conjecture

Let $P_1,\ldots,P_N\in\mathbb R[x_1,\ldots,x_d]$ be nonzero polynomials, let $B^d\subset\mathbb R^d$ be the unit ball, and let $\delta_1,\ldots,\delta_N>0$ satisfy

$$\sum_{k=1}^N\delta_k\deg P_k\leq 1.$$

Polynomial plank conjecture. There exists a point $p\in B^d$ such that, for every $k=1,\ldots,N$, the distance from $p$ to the zero set of $P_k$ is at least $\delta_k$.

This conjecture extends the one-polynomial polynomial plank theorem to different distances from several zero sets. The paper attributes it to the authors' earlier work and does not state that it has been resolved.