Directed landscape two-dimensional black-noise conjecture

A two-dimensional noise is a probability space $(\Omega,\mathcal F,\mathbb P)$ equipped with sub-$\sigma$-algebras associated with open rectangles in $\mathbb R^2$ and measure-preserving translations satisfying independence for disjoint rectangles, the corresponding generation property, and translation covariance. It is black when its only linear random variable is $0$. For the directed landscape, let $\mathcal F_{(s,t),(x,y)}$ be generated by the random variables $\int_a^b d\mathcal L\circ\pi$ over $s\leq a<b\leq t$ and continuous deterministic paths $\pi:[a,b]\to[x,y]$. Directed landscape two-dimensional black-noise conjecture. The directed landscape is a two-dimensional black noise. If true, this would show that the directed landscape is noise-like in its space variables as well as its time variables; the source attributes the conjecture to Bálint Virág and gives no resolution.