Direction-separated tubes satisfy polynomial Wolff axioms

Let $\mathbb{T}$ be a collection of tubes whose directions are $\delta$-separated, meaning that distinct tube directions are separated by at least $\delta$ in the relevant direction space. Let the polynomial Wolff inequality be denoted by the paper's generalized Wolff inequality, with constants $\{K_E\}$.

Direction-separated polynomial Wolff conjecture. Every set of tubes pointing in $\delta$-separated directions satisfies the polynomial Wolff axioms; more precisely, it satisfies the generalized Wolff inequality with constants $\{K_E\}$ independent of $\delta$.

This conjecture would connect arbitrary direction-separated Kakeya tube collections to the polynomial Wolff estimates proved in the paper; the source states that it is open.